From 097355ac7ae5bf23713015b94c640546e2c3a34d Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 25 Sep 2023 06:47:25 +0200
Subject: [PATCH] update lecture notes

---
 .../_build/.doctrees/chapter1.doctree         |   Bin 563392 -> 392865 bytes
 .../_build/.doctrees/chapter10.doctree        |   Bin 525351 -> 228738 bytes
 .../_build/.doctrees/chapter11.doctree        |   Bin 785342 -> 238470 bytes
 .../_build/.doctrees/chapter12.doctree        |   Bin 230758 -> 136135 bytes
 .../_build/.doctrees/chapter13.doctree        |   Bin 167616 -> 139383 bytes
 .../_build/.doctrees/chapter2.doctree         |   Bin 505419 -> 332770 bytes
 .../_build/.doctrees/chapter3.doctree         |   Bin 1636128 -> 320805 bytes
 .../_build/.doctrees/chapter4.doctree         |   Bin 938484 -> 89117 bytes
 .../_build/.doctrees/chapter5.doctree         |   Bin 543388 -> 146914 bytes
 .../_build/.doctrees/chapter6.doctree         |   Bin 314870 -> 134628 bytes
 .../_build/.doctrees/chapter7.doctree         |   Bin 148292 -> 134101 bytes
 .../_build/.doctrees/chapter8.doctree         |   Bin 213157 -> 131339 bytes
 .../_build/.doctrees/chapter9.doctree         |   Bin 251402 -> 123261 bytes
 .../.doctrees/chapteroptimization.doctree     |   Bin 902886 -> 269499 bytes
 .../_build/.doctrees/clustering.doctree       |   Bin 80340 -> 58209 bytes
 .../_build/.doctrees/environment.pickle       |   Bin 339365 -> 522472 bytes
 .../_build/.doctrees/exercisesweek34.doctree  |   Bin 37724 -> 32065 bytes
 .../_build/.doctrees/exercisesweek35.doctree  |   Bin 35295 -> 30165 bytes
 .../_build/.doctrees/exercisesweek36.doctree  |   Bin 32777 -> 28952 bytes
 .../_build/.doctrees/exercisesweek37.doctree  |   Bin 20815 -> 18752 bytes
 .../_build/.doctrees/exercisesweek38.doctree  |   Bin 16717 -> 15039 bytes
 .../_build/.doctrees/exercisesweek39.doctree  |   Bin 0 -> 7811 bytes
 .../_build/.doctrees/intro.doctree            |   Bin 53009 -> 45827 bytes
 .../_build/.doctrees/linalg.doctree           |   Bin 190200 -> 130991 bytes
 .../_build/.doctrees/project1.doctree         |   Bin 194371 -> 98567 bytes
 .../_build/.doctrees/schedule.doctree         |   Bin 9337 -> 8802 bytes
 .../_build/.doctrees/statistics.doctree       |   Bin 273313 -> 173171 bytes
 .../_build/.doctrees/teachers.doctree         |   Bin 21629 -> 19820 bytes
 .../_build/.doctrees/textbooks.doctree        |   Bin 27172 -> 22957 bytes
 .../_build/.doctrees/week34.doctree           |   Bin 778584 -> 445117 bytes
 .../_build/.doctrees/week35.doctree           |   Bin 918232 -> 395024 bytes
 .../_build/.doctrees/week36.doctree           |   Bin 284049 -> 254619 bytes
 .../_build/.doctrees/week37.doctree           |   Bin 715316 -> 267626 bytes
 .../_build/.doctrees/week38.doctree           |   Bin 1191352 -> 242029 bytes
 .../_build/.doctrees/week39.doctree           |   Bin 0 -> 322542 bytes
 doc/LectureNotes/_build/html/.buildinfo       |     2 +-
 .../html/_sources/exercisesweek39.ipynb       |    59 +
 .../_build/html/_sources/week39.ipynb         |  4874 +++++++
 ...e.4045f2051d55cab465a707391d5b2007.min.css |     1 +
 .../html/_sphinx_design_static/design-tabs.js |    27 +
 .../_sphinx_javascript_frameworks_compat.js   |   134 +
 .../_build/html/_static/basic.css             |    54 +-
 .../_build/html/_static/copybutton.css        |     3 +-
 .../_build/html/_static/copybutton.js         |    44 +-
 .../_build/html/_static/copybutton_funcs.js   |    17 +-
 ...e.4045f2051d55cab465a707391d5b2007.min.css |     1 +
 .../_build/html/_static/design-tabs.js        |    27 +
 .../_build/html/_static/doctools.js           |   452 +-
 .../html/_static/documentation_options.js     |     6 +-
 .../html/_static/images/logo_deepnote.svg     |     1 +
 .../_build/html/_static/jquery-3.6.0.js       | 10881 ++++++++++++++++
 .../_build/html/_static/jquery.js             |     4 +-
 .../_build/html/_static/language_data.js      |   100 +-
 .../locales/ar/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1541 bytes
 .../locales/ar/LC_MESSAGES/booktheme.po       |    75 +
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 .../locales/de/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/el/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1722 bytes
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 .../locales/eo/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/es/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1396 bytes
 .../locales/es/LC_MESSAGES/booktheme.po       |    75 +
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 .../locales/fi/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/fr/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1412 bytes
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 .../locales/ml/LC_MESSAGES/booktheme.po       |    66 +
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 .../locales/nl/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1356 bytes
 .../locales/nl/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/no/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1317 bytes
 .../locales/no/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/pl/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1371 bytes
 .../locales/pl/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/pt/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1364 bytes
 .../locales/pt/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/ro/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1390 bytes
 .../locales/ro/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/ru/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1722 bytes
 .../locales/ru/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/sk/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1393 bytes
 .../locales/sk/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/sl/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1374 bytes
 .../locales/sl/LC_MESSAGES/booktheme.po       |    75 +
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 .../locales/sr/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/sv/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1349 bytes
 .../locales/sv/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/ta/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1928 bytes
 .../locales/ta/LC_MESSAGES/booktheme.po       |    66 +
 .../locales/te/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1806 bytes
 .../locales/te/LC_MESSAGES/booktheme.po       |    66 +
 .../locales/tg/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1628 bytes
 .../locales/tg/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/th/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1766 bytes
 .../locales/th/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/tl/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1273 bytes
 .../locales/tl/LC_MESSAGES/booktheme.po       |    66 +
 .../locales/tr/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1373 bytes
 .../locales/tr/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/uk/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1681 bytes
 .../locales/uk/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/ur/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1462 bytes
 .../locales/ur/LC_MESSAGES/booktheme.po       |    66 +
 .../locales/vi/LC_MESSAGES/booktheme.mo       |   Bin 0 -> 1431 bytes
 .../locales/vi/LC_MESSAGES/booktheme.po       |    75 +
 .../locales/zh_CN/LC_MESSAGES/booktheme.mo    |   Bin 0 -> 1310 bytes
 .../locales/zh_CN/LC_MESSAGES/booktheme.po    |    75 +
 .../locales/zh_TW/LC_MESSAGES/booktheme.mo    |   Bin 0 -> 1341 bytes
 .../locales/zh_TW/LC_MESSAGES/booktheme.po    |    75 +
 ...69c37c29e427902b24a333a5f9fcb2f0b3ac41.css |  2342 ++++
 .../_build/html/_static/pygments.css          |   226 +-
 .../html/_static/sbt-webpack-macros.html      |    11 +
 .../_build/html/_static/scripts/bootstrap.js  |     3 +
 .../_static/scripts/bootstrap.js.LICENSE.txt  |     5 +
 .../html/_static/scripts/bootstrap.js.map     |     1 +
 .../_static/scripts/pydata-sphinx-theme.js    |     2 +
 .../scripts/pydata-sphinx-theme.js.map        |     1 +
 .../html/_static/scripts/sphinx-book-theme.js |     2 +
 .../_static/scripts/sphinx-book-theme.js.map  |     1 +
 .../_build/html/_static/searchtools.js        |   772 +-
 .../_build/html/_static/styles/bootstrap.css  |     6 +
 .../_static/styles/pydata-sphinx-theme.css    |     1 +
 .../html/_static/styles/sphinx-book-theme.css |     8 +
 .../_build/html/_static/styles/theme.css      |     2 +
 .../vendor/fontawesome/6.1.2/LICENSE.txt      |   165 +
 .../vendor/fontawesome/6.1.2/css/all.min.css  |     5 +
 .../vendor/fontawesome/6.1.2/js/all.min.js    |     2 +
 .../6.1.2/js/all.min.js.LICENSE.txt           |     5 +
 .../6.1.2/webfonts/fa-brands-400.ttf          |   Bin 0 -> 181264 bytes
 .../6.1.2/webfonts/fa-brands-400.woff2        |   Bin 0 -> 105112 bytes
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 .../6.1.2/webfonts/fa-regular-400.woff2       |   Bin 0 -> 24028 bytes
 .../6.1.2/webfonts/fa-solid-900.ttf           |   Bin 0 -> 389948 bytes
 .../6.1.2/webfonts/fa-solid-900.woff2         |   Bin 0 -> 154840 bytes
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 .../6.1.2/webfonts/fa-v4compatibility.woff2   |   Bin 0 -> 4776 bytes
 .../_build/html/_static/webpack-macros.html   |    36 +-
 doc/LectureNotes/_build/html/chapter1.html    |  1295 +-
 doc/LectureNotes/_build/html/chapter10.html   |  2137 +--
 doc/LectureNotes/_build/html/chapter11.html   |  1438 +-
 doc/LectureNotes/_build/html/chapter12.html   |  1303 +-
 doc/LectureNotes/_build/html/chapter13.html   |  1216 +-
 doc/LectureNotes/_build/html/chapter2.html    |  1588 +--
 doc/LectureNotes/_build/html/chapter3.html    |  1699 +--
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 doc/LectureNotes/_build/html/chapter6.html    |  1357 +-
 doc/LectureNotes/_build/html/chapter7.html    |  1090 +-
 doc/LectureNotes/_build/html/chapter8.html    |  1331 +-
 doc/LectureNotes/_build/html/chapter9.html    |  1110 +-
 .../_build/html/chapteroptimization.html      |  1403 +-
 doc/LectureNotes/_build/html/clustering.html  |  1046 +-
 .../_build/html/exercisesweek34.html          |   858 +-
 .../_build/html/exercisesweek35.html          |   832 +-
 .../_build/html/exercisesweek36.html          |   880 +-
 .../_build/html/exercisesweek37.html          |   834 +-
 .../_build/html/exercisesweek38.html          |   806 +-
 .../_build/html/exercisesweek39.html          |   556 +
 doc/LectureNotes/_build/html/genindex.html    |   679 +-
 doc/LectureNotes/_build/html/intro.html       |   933 +-
 doc/LectureNotes/_build/html/linalg.html      |  1080 +-
 doc/LectureNotes/_build/html/objects.inv      |   Bin 1052 -> 1081 bytes
 doc/LectureNotes/_build/html/project1.html    |  1098 +-
 doc/LectureNotes/_build/html/schedule.html    |   765 +-
 doc/LectureNotes/_build/html/search.html      |   750 +-
 doc/LectureNotes/_build/html/searchindex.js   |     2 +-
 doc/LectureNotes/_build/html/statistics.html  |  1055 +-
 doc/LectureNotes/_build/html/teachers.html    |   847 +-
 doc/LectureNotes/_build/html/textbooks.html   |   775 +-
 doc/LectureNotes/_build/html/week34.html      |  2937 ++---
 doc/LectureNotes/_build/html/week35.html      |  2832 ++--
 doc/LectureNotes/_build/html/week36.html      |  1678 +--
 doc/LectureNotes/_build/html/week37.html      |  2101 ++-
 doc/LectureNotes/_build/html/week38.html      |  2257 ++--
 doc/LectureNotes/_build/html/week39.html      |  3326 +++++
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 doc/LectureNotes/_toc.yml                     |     2 +
 237 files changed, 50473 insertions(+), 34642 deletions(-)
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diff --git a/doc/LectureNotes/_build/.doctrees/chapter13.doctree b/doc/LectureNotes/_build/.doctrees/chapter13.doctree
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diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index a3107d3e14ffcb4e62a2e581fe018d1c53a12b49..48ef182b194ce55bfa960b6c24ac455822a1e318 100644
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diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek35.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek35.doctree
index 36073236c4de52d8c98b2411430ed1295aa16d8a..94064df54bacf7bc3cf742dce5051905d3d4b569 100644
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diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek36.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek36.doctree
index 25769698c4012e195ca98895c56ae9ef7722f140..5342debe475e2d378348c103a7a14913d82c19c3 100644
GIT binary patch
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delta 7135
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diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek37.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek37.doctree
index ed4f716e487f6294a5b7a93198891bf95d355d8e..bae0c169ca1658cd37210c8cc9730ee1af699173 100644
GIT binary patch
delta 4090
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delta 5121
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diff --git a/doc/LectureNotes/_build/.doctrees/schedule.doctree b/doc/LectureNotes/_build/.doctrees/schedule.doctree
index a3bde73b5aa238a15ccdaae70a374bf8eadd4e79..201f231fe27d7a55fdc5490f5dfbcaca53166cb7 100644
GIT binary patch
delta 2831
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diff --git a/doc/LectureNotes/_build/html/.buildinfo b/doc/LectureNotes/_build/html/.buildinfo
index 45ed82fee..4bf64394a 100644
--- a/doc/LectureNotes/_build/html/.buildinfo
+++ b/doc/LectureNotes/_build/html/.buildinfo
@@ -1,4 +1,4 @@
 # Sphinx build info version 1
 # This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
-config: c810468e5ce15e612839c964bc8fee3e
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diff --git a/doc/LectureNotes/_build/html/_sources/exercisesweek39.ipynb b/doc/LectureNotes/_build/html/_sources/exercisesweek39.ipynb
new file mode 100644
index 000000000..d685e82d8
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_sources/exercisesweek39.ipynb
@@ -0,0 +1,59 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f35930ac",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html exercisesweek39.do.txt  -->\n",
+    "<!-- dom:TITLE: Exercises week 39 -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cb567a0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Exercises week 39\n",
+    "**September 25-29, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday October 1 at midnight**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "934324b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Overarching aims of the exercises this week\n",
+    "\n",
+    "The aim of the exercises this week is to aid you in getting started\n",
+    "with writing the report. This will be discussed during the lab\n",
+    "sessions as well. One of the lab sessions will be recorded.\n",
+    "\n",
+    "A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
+    "\n",
+    "Similarly, an example of an earlier project can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf>\n",
+    "\n",
+    "Your task this week is to\n",
+    "1. Write an abstract for your project\n",
+    "\n",
+    "2. Write an introduction\n",
+    "\n",
+    "3. Include references\n",
+    "\n",
+    "Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report."
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/doc/LectureNotes/_build/html/_sources/week39.ipynb b/doc/LectureNotes/_build/html/_sources/week39.ipynb
new file mode 100644
index 000000000..f8ed9613e
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_sources/week39.ipynb
@@ -0,0 +1,4874 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "97c9bb6c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html week39.do.txt --no_mako -->\n",
+    "<!-- dom:TITLE: Week 39: Optimization and  Gradient Methods -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ade8d870",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Week 39: Optimization and  Gradient Methods\n",
+    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
+    "\n",
+    "Date: **Week 39**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87cd74c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plan for week 39\n",
+    "\n",
+    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "  * Discussions on how to structure your report for the first project\n",
+    "\n",
+    "  * Exercise for week 39 on how to write the abstract and the introduction of the report and how to include references. \n",
+    "\n",
+    "  * Work on project 1, in particular resampling methods like cross-validation and bootstrap. **For more discussions of project 1, chapter 5 of Goodfellow et al is a good read, in particular sections 5.1-5.5 and 5.7-5.11**.\n",
+    "\n",
+    "These sections summarize neatly what we have done till now and point to what is coming with respect to deep learning. \n",
+    "  * A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
+    "\n",
+    "  \n",
+    "\n",
+    "**Material for the lecture on Thursday September 28.**\n",
+    "\n",
+    "  * Repetition of Logistic regression equations and classification problems and discussion of Gradient methods. Examples on how to implement Logistic Regression and discussion of stochastic gradient descent \n",
+    "\n",
+    "  * Stochastic Gradient descent with examples and automatic differentiation\n",
+    "\n",
+    "  * [Video of lecture](https://youtu.be/)\n",
+    "\n",
+    "  * Whiteboard notes TBA at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep28.pdf>\n",
+    "\n",
+    "  * Readings and Videos:\n",
+    "\n",
+    "    * These lecture notes\n",
+    "\n",
+    "    * For a good discussion on gradient methods, we would like to recommend Goodfellow et al section 4.3-4.5 and sections 8.3-8.6. We will come back to the latter chapter in our discussion of Neural networks as well. \n",
+    "\n",
+    "    * [Video on gradient descent](https://www.youtube.com/watch?v=sDv4f4s2SB8)\n",
+    "\n",
+    "    * [Video on stochastic gradient descent](https://www.youtube.com/watch?v=vMh0zPT0tLI)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "529184e5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Optimization, the central part of any Machine Learning algortithm\n",
+    "\n",
+    "The first few slides here are a repetition from last week. \n",
+    "\n",
+    "Almost every problem in machine learning and data science starts with\n",
+    "a dataset $X$, a model $g(\\beta)$, which is a function of the\n",
+    "parameters $\\beta$ and a cost function $C(X, g(\\beta))$ that allows\n",
+    "us to judge how well the model $g(\\beta)$ explains the observations\n",
+    "$X$. The model is fit by finding the values of $\\beta$ that minimize\n",
+    "the cost function. Ideally we would be able to solve for $\\beta$\n",
+    "analytically, however this is not possible in general and we must use\n",
+    "some approximative/numerical method to compute the minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1a65465a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Revisiting our Logistic Regression case\n",
+    "\n",
+    "In our discussion on Logistic Regression we studied the \n",
+    "case of\n",
+    "two classes, with $y_i$ either\n",
+    "$0$ or $1$. Furthermore we assumed also that we have only two\n",
+    "parameters $\\beta$ in our fitting, that is we\n",
+    "defined probabilities"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b67231b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{align*}\n",
+    "p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
+    "p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3f5e03db",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e83141ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The equations to solve\n",
+    "\n",
+    "Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n",
+    "elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n",
+    "$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n",
+    "$p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We rewrote in a more compact form\n",
+    "the first derivative of the cost function as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cef5864b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2f59bbb1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
+    "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3869b3c6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4656e92",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This defines what is called  the Hessian matrix."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b73ae554",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Solving using Newton-Raphson's method\n",
+    "\n",
+    "If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives. \n",
+    "\n",
+    "Our iterative scheme is then given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "70a2df05",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e36f976",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or in matrix form as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c4959c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c553379e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The right-hand side is computed with the old values of $\\beta$. \n",
+    "\n",
+    "If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "145f9699",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Brief reminder on Newton-Raphson's method\n",
+    "\n",
+    "Let us quickly remind ourselves how we derive the above method.\n",
+    "\n",
+    "Perhaps the most celebrated of all one-dimensional root-finding\n",
+    "routines is Newton's method, also called the Newton-Raphson\n",
+    "method. This method  requires the evaluation of both the\n",
+    "function $f$ and its derivative $f'$ at arbitrary points. \n",
+    "If you can only calculate the derivative\n",
+    "numerically and/or your function is not of the smooth type, we\n",
+    "normally discourage the use of this method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a68f686",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The equations\n",
+    "\n",
+    "The Newton-Raphson formula consists geometrically of extending the\n",
+    "tangent line at a current point until it crosses zero, then setting\n",
+    "the next guess to the abscissa of that zero-crossing.  The mathematics\n",
+    "behind this method is rather simple. Employing a Taylor expansion for\n",
+    "$x$ sufficiently close to the solution $s$, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d523ab61",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"eq:taylornr\"></div>\n",
+    "\n",
+    "$$\n",
+    "f(s)=0=f(x)+(s-x)f'(x)+\\frac{(s-x)^2}{2}f''(x) +\\dots.\n",
+    "    \\label{eq:taylornr} \\tag{1}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8205fd3a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "For small enough values of the function and for well-behaved\n",
+    "functions, the terms beyond linear are unimportant, hence we obtain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98d52e46",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(x)+(s-x)f'(x)\\approx 0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "203f65e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "yielding"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd40195b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "s\\approx x-\\frac{f(x)}{f'(x)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e13a7340",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Having in mind an iterative procedure, it is natural to start iterating with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30c258c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84f880c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple geometric interpretation\n",
+    "\n",
+    "The above is Newton-Raphson's method. It has a simple geometric\n",
+    "interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
+    "$(x_n,f(x_n))$ crosses the $x$-axis.  Close to the solution,\n",
+    "Newton-Raphson converges fast to the desired result. However, if we\n",
+    "are far from a root, where the higher-order terms in the series are\n",
+    "important, the Newton-Raphson formula can give grossly inaccurate\n",
+    "results. For instance, the initial guess for the root might be so far\n",
+    "from the true root as to let the search interval include a local\n",
+    "maximum or minimum of the function.  If an iteration places a trial\n",
+    "guess near such a local extremum, so that the first derivative nearly\n",
+    "vanishes, then Newton-Raphson may fail totally"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b237f214",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Extending to more than one variable\n",
+    "\n",
+    "Newton's method can be generalized to systems of several non-linear equations\n",
+    "and variables. Consider the case with two equations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b4ea1db2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
+    "                     f_2(x_1,x_2) &=0,\\end{array}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b2b6606",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which we Taylor expand to obtain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9d217a4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
+    "                     \\partial f_1/\\partial x_1+h_2\n",
+    "                     \\partial f_1/\\partial x_2+\\dots\\\\\n",
+    "                     0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
+    "                     \\partial f_2/\\partial x_1+h_2\n",
+    "                     \\partial f_2/\\partial x_2+\\dots\n",
+    "                       \\end{array}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54f87f7c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2711fc8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
+    "                         \\partial f_1/\\partial x_1  & \\partial f_1/\\partial x_2 \\\\\n",
+    "                          \\partial f_2/\\partial x_1     &\\partial f_2/\\partial x_2\n",
+    "             \\end{array} \\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e0409f1c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "we can rephrase Newton's method as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53651890",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
+    "\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
+    "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e70e7ac",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9336db1d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
+    "   -{\\bf \\boldsymbol{J}}^{-1}\n",
+    "   \\left(\\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\\\ f_2(x_1^{n},x_2^{n}) \\end{array} \\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c2ae028",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We need thus to compute the inverse of the Jacobian matrix and it\n",
+    "is to understand that difficulties  may\n",
+    "arise in case ${\\bf \\boldsymbol{J}}$ is nearly singular.\n",
+    "\n",
+    "It is rather straightforward to extend the above scheme to systems of\n",
+    "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cdf99885",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent\n",
+    "\n",
+    "The basic idea of gradient descent is\n",
+    "that a function $F(\\mathbf{x})$, \n",
+    "$\\mathbf{x} \\equiv (x_1,\\cdots,x_n)$, decreases fastest if one goes from $\\bf {x}$ in the\n",
+    "direction of the negative gradient $-\\nabla F(\\mathbf{x})$.\n",
+    "\n",
+    "It can be shown that if"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11bb1b41",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d957768",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $\\gamma_k > 0$.\n",
+    "\n",
+    "For $\\gamma_k$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq\n",
+    "F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n",
+    "we are always moving towards smaller function values, i.e a minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "455b420a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on Steepest descent\n",
+    "\n",
+    "The previous observation is the basis of the method of steepest\n",
+    "descent, which is also referred to as just gradient descent (GD). One\n",
+    "starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n",
+    "computes new approximations according to"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aacb8b05",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2bb3385b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The parameter $\\gamma_k$ is often referred to as the step length or\n",
+    "the learning rate within the context of Machine Learning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21326ef0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The ideal\n",
+    "\n",
+    "Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n",
+    "minimum of the function $F$. In general we do not know if we are in a\n",
+    "global or local minimum. In the special case when $F$ is a convex\n",
+    "function, all local minima are also global minima, so in this case\n",
+    "gradient descent can converge to the global solution. The advantage of\n",
+    "this scheme is that it is conceptually simple and straightforward to\n",
+    "implement. However the method in this form has some severe\n",
+    "limitations:\n",
+    "\n",
+    "In machine learing we are often faced with non-convex high dimensional\n",
+    "cost functions with many local minima. Since GD is deterministic we\n",
+    "will get stuck in a local minimum, if the method converges, unless we\n",
+    "have a very good intial guess. This also implies that the scheme is\n",
+    "sensitive to the chosen initial condition.\n",
+    "\n",
+    "Note that the gradient is a function of $\\mathbf{x} =\n",
+    "(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a41b3cc6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The sensitiveness of the gradient descent\n",
+    "\n",
+    "The gradient descent method \n",
+    "is sensitive to the choice of learning rate $\\gamma_k$. This is due\n",
+    "to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n",
+    "F(\\mathbf{x}_k)$ for sufficiently small $\\gamma_k$. The problem is to\n",
+    "determine an optimal learning rate. If the learning rate is chosen too\n",
+    "small the method will take a long time to converge and if it is too\n",
+    "large we can experience erratic behavior.\n",
+    "\n",
+    "Many of these shortcomings can be alleviated by introducing\n",
+    "randomness. One such method is that of Stochastic Gradient Descent\n",
+    "(SGD), see below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a01f11a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Convex functions\n",
+    "\n",
+    "Ideally we want our cost/loss function to be convex(concave).\n",
+    "\n",
+    "First we give the definition of a convex set: A set $C$ in\n",
+    "$\\mathbb{R}^n$ is said to be convex if, for all $x$ and $y$ in $C$ and\n",
+    "all $t \\in (0,1)$ , the point $(1 − t)x + ty$ also belongs to\n",
+    "C. Geometrically this means that every point on the line segment\n",
+    "connecting $x$ and $y$ is in $C$ as discussed below.\n",
+    "\n",
+    "The convex subsets of $\\mathbb{R}$ are the intervals of\n",
+    "$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n",
+    "regular polygons (triangles, rectangles, pentagons, etc...)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "076a32fa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Convex function\n",
+    "\n",
+    "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "73adde3c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conditions on convex functions\n",
+    "\n",
+    "In the following we state first and second-order conditions which\n",
+    "ensures convexity of a function $f$. We write $D_f$ to denote the\n",
+    "domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n",
+    "details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](http://stanford.edu/boyd/cvxbook/, 2004).\n",
+    "\n",
+    "**First order condition.**\n",
+    "\n",
+    "Suppose $f$ is differentiable (i.e $\\nabla f(x)$ is well defined for\n",
+    "all $x$ in the domain of $f$). Then $f$ is convex if and only if $D_f$\n",
+    "is a convex set and $$f(y) \\geq f(x) + \\nabla f(x)^T (y-x) $$ holds\n",
+    "for all $x,y \\in D_f$. This condition means that for a convex function\n",
+    "the first order Taylor expansion (right hand side above) at any point\n",
+    "a global under estimator of the function. To convince yourself you can\n",
+    "make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n",
+    "note that it is always below the graph.\n",
+    "\n",
+    "**Second order condition.**\n",
+    "\n",
+    "Assume that $f$ is twice\n",
+    "differentiable, i.e the Hessian matrix exists at each point in\n",
+    "$D_f$. Then $f$ is convex if and only if $D_f$ is a convex set and its\n",
+    "Hessian is positive semi-definite for all $x\\in D_f$. For a\n",
+    "single-variable function this reduces to $f''(x) \\geq 0$. Geometrically this means that $f$ has nonnegative curvature\n",
+    "everywhere.\n",
+    "\n",
+    "This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9f9ab5ff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on convex functions\n",
+    "\n",
+    "The next result is of great importance to us and the reason why we are\n",
+    "going on about convex functions. In machine learning we frequently\n",
+    "have to minimize a loss/cost function in order to find the best\n",
+    "parameters for the model we are considering. \n",
+    "\n",
+    "Ideally we want the\n",
+    "global minimum (for high-dimensional models it is hard to know\n",
+    "if we have local or global minimum). However, if the cost/loss function\n",
+    "is convex the following result provides invaluable information:\n",
+    "\n",
+    "**Any minimum is global for convex functions.**\n",
+    "\n",
+    "Consider the problem of finding $x \\in \\mathbb{R}^n$ such that $f(x)$\n",
+    "is minimal, where $f$ is convex and differentiable. Then, any point\n",
+    "$x^*$ that satisfies $\\nabla f(x^*) = 0$ is a global minimum.\n",
+    "\n",
+    "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b2a482b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Some simple problems\n",
+    "\n",
+    "1. Show that $f(x)=x^2$ is convex for $x \\in \\mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \\in D_f$ and any $\\lambda \\in [0,1]$ $\\lambda f(x)+(1-\\lambda)f(y)-f(\\lambda x + (1-\\lambda) y ) \\geq 0$.\n",
+    "\n",
+    "2. Using the second order condition show that the following functions are convex on the specified domain.\n",
+    "\n",
+    " * $f(x) = e^x$ is convex for $x \\in \\mathbb{R}$.\n",
+    "\n",
+    " * $g(x) = -\\ln(x)$ is convex for $x \\in (0,\\infty)$.\n",
+    "\n",
+    "3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \\in \\mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex.\n",
+    "\n",
+    "4. A norm is any function that satisfy the following properties\n",
+    "\n",
+    " * $f(\\alpha x) = |\\alpha| f(x)$ for all $\\alpha \\in \\mathbb{R}$.\n",
+    "\n",
+    " * $f(x+y) \\leq f(x) + f(y)$\n",
+    "\n",
+    " * $f(x) \\leq 0$ for all $x \\in \\mathbb{R}^n$ with equality if and only if $x = 0$\n",
+    "\n",
+    "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6566ee55",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Standard steepest descent\n",
+    "\n",
+    "Before we proceed, we would like to discuss the approach called the\n",
+    "**standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able\n",
+    "to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).\n",
+    "\n",
+    "[The success of the CG method](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)\n",
+    "for finding solutions of non-linear problems is based on the theory\n",
+    "of conjugate gradients for linear systems of equations. It belongs to\n",
+    "the class of iterative methods for solving problems from linear\n",
+    "algebra of the type"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2e30cc1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5012b398",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In the iterative process we end up with a problem like"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca65d9a9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec9323dd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n",
+    "\n",
+    "When we have found the exact solution, $\\boldsymbol{r}=0$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5caf0f7f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient method\n",
+    "\n",
+    "The residual is zero when we reach the minimum of the quadratic equation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07734ce6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "468dcb52",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n",
+    "symmetric.  This defines also the Hessian and we want it to be  positive definite."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b63a89ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent  method\n",
+    "\n",
+    "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
+    "We can assume without loss of generality that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "56a122a3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_0=0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3256eb29",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or consider the system"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b6bab858",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ff39e96",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "instead."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6678fce9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent  method\n",
+    "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "853eb11f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c229917",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n",
+    "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c8f310a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8a8c317",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and \n",
+    "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "49b64ed0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Final expressions\n",
+    "We can compute the residual iteratively as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "857ee939",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e5611fa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "384d5aa2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0ce677be",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e97f9044",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d7fbeb68",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "293c09b1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "af88e065",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "leading to the iterative scheme"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2757e302",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87aab66b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "a0e20ff7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "import numpy as np\n",
+    "import numpy.linalg as la\n",
+    "\n",
+    "import scipy.optimize as sopt\n",
+    "\n",
+    "import matplotlib.pyplot as pt\n",
+    "from mpl_toolkits.mplot3d import axes3d\n",
+    "\n",
+    "def f(x):\n",
+    "    return x[0]**2 + 3.0*x[1]**2\n",
+    "\n",
+    "def df(x):\n",
+    "    return np.array([2*x[0], 6*x[1]])\n",
+    "\n",
+    "fig = pt.figure()\n",
+    "ax = fig.gca(projection=\"3d\")\n",
+    "\n",
+    "xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n",
+    "fmesh = f(np.array([xmesh, ymesh]))\n",
+    "ax.plot_surface(xmesh, ymesh, fmesh)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c01b471a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "And then as countor plot"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "5b835c85",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "pt.axis(\"equal\")\n",
+    "pt.contour(xmesh, ymesh, fmesh)\n",
+    "guesses = [np.array([2, 2./5])]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d6a3c121",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Find guesses"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "19e1d73c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "x = guesses[-1]\n",
+    "s = -df(x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9f7b2dfc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Run it!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7d8247e6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "def f1d(alpha):\n",
+    "    return f(x + alpha*s)\n",
+    "\n",
+    "alpha_opt = sopt.golden(f1d)\n",
+    "next_guess = x + alpha_opt * s\n",
+    "guesses.append(next_guess)\n",
+    "print(next_guess)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c44006da",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "What happened?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "bb8a0fd8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "pt.axis(\"equal\")\n",
+    "pt.contour(xmesh, ymesh, fmesh, 50)\n",
+    "it_array = np.array(guesses)\n",
+    "pt.plot(it_array.T[0], it_array.T[1], \"x-\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3d3c98f0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that we did only one iteration here. We can easily add more using our previous guesses."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "29e5e792",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "In the CG method we define so-called conjugate directions and two vectors \n",
+    "$\\boldsymbol{s}$ and $\\boldsymbol{t}$\n",
+    "are said to be\n",
+    "conjugate if"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b0e0db3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "401dd643",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The philosophy of the CG method is to perform searches in various conjugate directions\n",
+    "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc29d596",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1b7adb4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Two vectors are conjugate if they are orthogonal with respect to \n",
+    "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18924232",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "An example is given by the eigenvectors of the matrix"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1764ac31",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "379d5862",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is zero unless $i=j$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9587d8bf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n",
+    "$n\\times n$. At each iteration $i+1$ we obtain the conjugate direction of a vector"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c3d0bfb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4079ca1a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n",
+    "Then the $\\boldsymbol{p}_{i}$  form a basis of $R^n$ and we can expand the solution \n",
+    "$  \\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}$ in this basis, namely"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e5b487a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}  = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b623d7f7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "The coefficients are given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8520c560",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "52575016",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Multiplying with $\\boldsymbol{p}_k^T$  from the left gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b8a85bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e53b0f45",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and we can define the coefficients $\\alpha_k$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2238e15f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f00e8864",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method and iterations\n",
+    "\n",
+    "If we choose the conjugate vectors $\\boldsymbol{p}_k$ carefully, \n",
+    "then we may not need all of them to obtain a good approximation to the solution \n",
+    "$\\boldsymbol{x}$. \n",
+    "We want to regard the conjugate gradient method as an iterative method. \n",
+    "This will us to solve systems where $n$ is so large that the direct \n",
+    "method would take too much time.\n",
+    "\n",
+    "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
+    "We can assume without loss of generality that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7a17895d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_0=0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d4bafcb3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or consider the system"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78a7d2c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3192cbf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "instead."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0d99ed55",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9653ede",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78441105",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n",
+    "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "317355d2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9bb15157",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and \n",
+    "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n",
+    "The other vectors in the basis will be conjugate to the gradient, \n",
+    "hence the name conjugate gradient method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ac584971",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "Let  $\\boldsymbol{r}_k$ be the residual at the $k$-th step:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "911f1dfa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d1472568",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n",
+    "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n",
+    "so the gradient descent method would be to move in the direction $\\boldsymbol{r}_k$. \n",
+    "Here, we insist that the directions $\\boldsymbol{p}_k$ are conjugate to each other, \n",
+    "so we take the direction closest to the gradient $\\boldsymbol{r}_k$  \n",
+    "under the conjugacy constraint. \n",
+    "This gives the following expression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c79708e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "535d3e73",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "We can also  compute the residual iteratively as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad718f62",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0a90fa5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "860e9217",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d8a72c8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "746e6fc0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f76c0e69",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9aee35ca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce9ce258",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Revisiting our first homework\n",
+    "\n",
+    "We will use linear regression as a case study for the gradient descent\n",
+    "methods. Linear regression is a great test case for the gradient\n",
+    "descent methods discussed in the lectures since it has several\n",
+    "desirable properties such as:\n",
+    "\n",
+    "1. An analytical solution (recall homework set 1).\n",
+    "\n",
+    "2. The gradient can be computed analytically.\n",
+    "\n",
+    "3. The cost function is convex which guarantees that gradient descent converges for small enough learning rates\n",
+    "\n",
+    "We revisit an example similar to what we had in the first homework set. We had a function  of the type"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "f902a0f2",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "x = 2*np.random.rand(m,1)\n",
+    "y = 4+3*x+np.random.randn(m,1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36d883b2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n",
+    "The linear regression model is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cde21ef1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f2a021d3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "such that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea0a91e4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "854f3ebb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient descent example\n",
+    "\n",
+    "Let $\\mathbf{y} = (y_1,\\cdots,y_n)^T$, $\\mathbf{\\boldsymbol{y}} = (\\boldsymbol{y}_1,\\cdots,\\boldsymbol{y}_n)^T$ and $\\beta = (\\beta_0, \\beta_1)^T$\n",
+    "\n",
+    "It is convenient to write $\\mathbf{\\boldsymbol{y}} = X\\beta$ where $X \\in \\mathbb{R}^{100 \\times 2} $ is the design matrix given by (we keep the intercept here)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd282d2d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "X \\equiv \\begin{bmatrix}\n",
+    "1 & x_1  \\\\\n",
+    "\\vdots & \\vdots  \\\\\n",
+    "1 & x_{100} &  \\\\\n",
+    "\\end{bmatrix}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd562029",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The cost/loss/risk function is given by ("
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25369bc3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a222f3ea",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and we want to find $\\beta$ such that $C(\\beta)$ is minimized."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1d5fb6f1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The derivative of the cost/loss function\n",
+    "\n",
+    "Computing $\\partial C(\\beta) / \\partial \\beta_0$ and $\\partial C(\\beta) / \\partial \\beta_1$ we can show  that the gradient can be written as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eab2df73",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
+    "\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T(X\\beta - \\mathbf{y}),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "daee1165",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $X$ is the design matrix defined above."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f2c6f5cc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Hessian matrix\n",
+    "The Hessian matrix of $C(\\beta)$ is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ecce0d08",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1}  \\\\\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} &  \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T X.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4308e5f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4ee64b17",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple program\n",
+    "\n",
+    "We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57e8db33",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c42e4032",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can use the expression we computed for the gradient and let use a\n",
+    "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n",
+    "when $||\\nabla_\\beta C(\\beta_k) || \\leq \\epsilon = 10^{-8}$. **Note that the code below does not include the latter stop criterion**.\n",
+    "\n",
+    "And finally we can compare our solution for $\\beta$ with the analytic result given by \n",
+    "$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c430cd3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient Descent Example\n",
+    "\n",
+    "Here our simple example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9ac6096f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "# Importing various packages\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from mpl_toolkits.mplot3d import Axes3D\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+    "import sys\n",
+    "\n",
+    "# the number of datapoints\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* X.T @ X\n",
+    "# Get the eigenvalues\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y\n",
+    "print(beta_linreg)\n",
+    "beta = np.random.randn(2,1)\n",
+    "\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradient = (2.0/n)*X.T @ (X @ beta-y)\n",
+    "    beta -= eta*gradient\n",
+    "\n",
+    "print(beta)\n",
+    "xnew = np.array([[0],[2]])\n",
+    "xbnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = xbnew.dot(beta)\n",
+    "ypredict2 = xbnew.dot(beta_linreg)\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Gradient descent example')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "df783e1d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And a corresponding example using **scikit-learn**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "98f08f24",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Importing various packages\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.linear_model import SGDRegressor\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "beta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(beta_linreg)\n",
+    "sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n",
+    "sgdreg.fit(x,y.ravel())\n",
+    "print(sgdreg.intercept_, sgdreg.coef_)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50a5ab0d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient descent and Ridge\n",
+    "\n",
+    "We have also discussed Ridge regression where the loss function contains a regularized term given by the $L_2$ norm of $\\beta$,"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b35293d4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fed491ee",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0b4c94e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_\\beta C_{\\text{ridge}}(\\beta)  = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
+    "\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
+    "\\end{bmatrix} + 2\\lambda\\begin{bmatrix} \\beta_0 \\\\ \\beta_1\\end{bmatrix} = 2 (\\frac{1}{n}X^T(X\\beta - \\mathbf{y})+\\lambda \\beta).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4f02dce",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9f297ff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e1caf44",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Hessian matrix for Ridge Regression\n",
+    "The Hessian matrix of Ridge Regression for our simple example  is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a046daea",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1}  \\\\\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} &  \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T X+2\\lambda\\boldsymbol{I}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "02f05574",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This implies that the Hessian matrix  is positive definite, hence the stationary point is a\n",
+    "minimum.\n",
+    "Note that the Ridge cost function is convex being  a sum of two convex\n",
+    "functions. Therefore, the stationary point is a global\n",
+    "minimum of this function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "45484749",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Program example for gradient descent with Ridge Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "9973cd20",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from mpl_toolkits.mplot3d import Axes3D\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+    "import sys\n",
+    "\n",
+    "# the number of datapoints\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "\n",
+    "#Ridge parameter lambda\n",
+    "lmbda  = 0.001\n",
+    "Id = n*lmbda* np.eye(XT_X.shape[0])\n",
+    "\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X+2*lmbda* np.eye(XT_X.shape[0])\n",
+    "# Get the eigenvalues\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "\n",
+    "beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y\n",
+    "print(beta_linreg)\n",
+    "# Start plain gradient descent\n",
+    "beta = np.random.randn(2,1)\n",
+    "\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ (X @ (beta)-y)+2*lmbda*beta\n",
+    "    beta -= eta*gradients\n",
+    "\n",
+    "print(beta)\n",
+    "ypredict = X @ beta\n",
+    "ypredict2 = X @ beta_linreg\n",
+    "plt.plot(x, ypredict, \"r-\")\n",
+    "plt.plot(x, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Gradient descent example for Ridge')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1836d4ef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using gradient descent methods, limitations\n",
+    "\n",
+    "* **Gradient descent (GD) finds local minima of our function**. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.\n",
+    "\n",
+    "* **GD is sensitive to initial conditions**. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.\n",
+    "\n",
+    "* **Gradients are computationally expensive to calculate for large datasets**. In many cases in statistics and ML, the cost/loss/risk function is a sum of terms, with one term for each data point. For example, in linear regression, $E \\propto \\sum_{i=1}^n (y_i - \\mathbf{w}^T\\cdot\\mathbf{x}_i)^2$; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over *all* $n$ data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called \"mini batches\". This has the added benefit of introducing stochasticity into our algorithm.\n",
+    "\n",
+    "* **GD is very sensitive to choices of learning rates**. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would *adaptively* choose the learning rates to match the landscape.\n",
+    "\n",
+    "* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n",
+    "\n",
+    "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "88975d3d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Improving gradient descent with momentum\n",
+    "\n",
+    "We discuss here some simple examples where we introduce what is called 'memory'about previous steps, or what is normally called momentum gradient descent. The mathematics is explained below in connection with Stochastic gradient descent."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "56f415e0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from numpy import asarray\n",
+    "from numpy import arange\n",
+    "from numpy.random import rand\n",
+    "from numpy.random import seed\n",
+    "from matplotlib import pyplot\n",
+    " \n",
+    "# objective function\n",
+    "def objective(x):\n",
+    "\treturn x**2.0\n",
+    " \n",
+    "# derivative of objective function\n",
+    "def derivative(x):\n",
+    "\treturn x * 2.0\n",
+    " \n",
+    "# gradient descent algorithm\n",
+    "def gradient_descent(objective, derivative, bounds, n_iter, step_size):\n",
+    "\t# track all solutions\n",
+    "\tsolutions, scores = list(), list()\n",
+    "\t# generate an initial point\n",
+    "\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
+    "\t# run the gradient descent\n",
+    "\tfor i in range(n_iter):\n",
+    "\t\t# calculate gradient\n",
+    "\t\tgradient = derivative(solution)\n",
+    "\t\t# take a step\n",
+    "\t\tsolution = solution - step_size * gradient\n",
+    "\t\t# evaluate candidate point\n",
+    "\t\tsolution_eval = objective(solution)\n",
+    "\t\t# store solution\n",
+    "\t\tsolutions.append(solution)\n",
+    "\t\tscores.append(solution_eval)\n",
+    "\t\t# report progress\n",
+    "\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
+    "\treturn [solutions, scores]\n",
+    " \n",
+    "# seed the pseudo random number generator\n",
+    "seed(4)\n",
+    "# define range for input\n",
+    "bounds = asarray([[-1.0, 1.0]])\n",
+    "# define the total iterations\n",
+    "n_iter = 30\n",
+    "# define the step size\n",
+    "step_size = 0.1\n",
+    "# perform the gradient descent search\n",
+    "solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size)\n",
+    "# sample input range uniformly at 0.1 increments\n",
+    "inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
+    "# compute targets\n",
+    "results = objective(inputs)\n",
+    "# create a line plot of input vs result\n",
+    "pyplot.plot(inputs, results)\n",
+    "# plot the solutions found\n",
+    "pyplot.plot(solutions, scores, '.-', color='red')\n",
+    "# show the plot\n",
+    "pyplot.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3343584",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "ff1e3778",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from numpy import asarray\n",
+    "from numpy import arange\n",
+    "from numpy.random import rand\n",
+    "from numpy.random import seed\n",
+    "from matplotlib import pyplot\n",
+    " \n",
+    "# objective function\n",
+    "def objective(x):\n",
+    "\treturn x**2.0\n",
+    " \n",
+    "# derivative of objective function\n",
+    "def derivative(x):\n",
+    "\treturn x * 2.0\n",
+    " \n",
+    "# gradient descent algorithm\n",
+    "def gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum):\n",
+    "\t# track all solutions\n",
+    "\tsolutions, scores = list(), list()\n",
+    "\t# generate an initial point\n",
+    "\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
+    "\t# keep track of the change\n",
+    "\tchange = 0.0\n",
+    "\t# run the gradient descent\n",
+    "\tfor i in range(n_iter):\n",
+    "\t\t# calculate gradient\n",
+    "\t\tgradient = derivative(solution)\n",
+    "\t\t# calculate update\n",
+    "\t\tnew_change = step_size * gradient + momentum * change\n",
+    "\t\t# take a step\n",
+    "\t\tsolution = solution - new_change\n",
+    "\t\t# save the change\n",
+    "\t\tchange = new_change\n",
+    "\t\t# evaluate candidate point\n",
+    "\t\tsolution_eval = objective(solution)\n",
+    "\t\t# store solution\n",
+    "\t\tsolutions.append(solution)\n",
+    "\t\tscores.append(solution_eval)\n",
+    "\t\t# report progress\n",
+    "\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
+    "\treturn [solutions, scores]\n",
+    " \n",
+    "# seed the pseudo random number generator\n",
+    "seed(4)\n",
+    "# define range for input\n",
+    "bounds = asarray([[-1.0, 1.0]])\n",
+    "# define the total iterations\n",
+    "n_iter = 30\n",
+    "# define the step size\n",
+    "step_size = 0.1\n",
+    "# define momentum\n",
+    "momentum = 0.3\n",
+    "# perform the gradient descent search with momentum\n",
+    "solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum)\n",
+    "# sample input range uniformly at 0.1 increments\n",
+    "inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
+    "# compute targets\n",
+    "results = objective(inputs)\n",
+    "# create a line plot of input vs result\n",
+    "pyplot.plot(inputs, results)\n",
+    "# plot the solutions found\n",
+    "pyplot.plot(solutions, scores, '.-', color='red')\n",
+    "# show the plot\n",
+    "pyplot.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1d70995",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Overview video on Stochastic Gradient Descent\n",
+    "\n",
+    "[What is Stochastic Gradient Descent](https://www.youtube.com/watch?v=vMh0zPT0tLI&ab_channel=StatQuestwithJoshStarmer)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "930a5be8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Batches and mini-batches\n",
+    "\n",
+    "In gradient descent we compute the cost function and its gradient for all data points we have.\n",
+    "\n",
+    "In large-scale applications such as the [ILSVRC challenge](https://www.image-net.org/challenges/LSVRC/), the\n",
+    "training data can have on order of millions of examples. Hence, it\n",
+    "seems wasteful to compute the full cost function over the entire\n",
+    "training set in order to perform only a single parameter update. A\n",
+    "very common approach to addressing this challenge is to compute the\n",
+    "gradient over batches of the training data. For example, a typical batch could contain some thousand  examples from\n",
+    "an  entire training set of several millions. This batch is then used to\n",
+    "perform a parameter update."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a7fb7ef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Stochastic Gradient Descent (SGD)\n",
+    "\n",
+    "In stochastic gradient descent, the extreme case is the case where we\n",
+    "have only one batch, that is we include the whole data set.\n",
+    "\n",
+    "This process is called Stochastic Gradient\n",
+    "Descent (SGD) (or also sometimes on-line gradient descent). This is\n",
+    "relatively less common to see because in practice due to vectorized\n",
+    "code optimizations it can be computationally much more efficient to\n",
+    "evaluate the gradient for 100 examples, than the gradient for one\n",
+    "example 100 times. Even though SGD technically refers to using a\n",
+    "single example at a time to evaluate the gradient, you will hear\n",
+    "people use the term SGD even when referring to mini-batch gradient\n",
+    "descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD\n",
+    "for “Batch gradient descent” are rare to see), where it is usually\n",
+    "assumed that mini-batches are used. The size of the mini-batch is a\n",
+    "hyperparameter but it is not very common to cross-validate or bootstrap it. It is\n",
+    "usually based on memory constraints (if any), or set to some value,\n",
+    "e.g. 32, 64 or 128. We use powers of 2 in practice because many\n",
+    "vectorized operation implementations work faster when their inputs are\n",
+    "sized in powers of 2.\n",
+    "\n",
+    "In our notes with  SGD we mean stochastic gradient descent with mini-batches."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbff87b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Stochastic Gradient Descent\n",
+    "\n",
+    "Stochastic gradient descent (SGD) and variants thereof address some of\n",
+    "the shortcomings of the Gradient descent method discussed above.\n",
+    "\n",
+    "The underlying idea of SGD comes from the observation that the cost\n",
+    "function, which we want to minimize, can almost always be written as a\n",
+    "sum over $n$ data points $\\{\\mathbf{x}_i\\}_{i=1}^n$,"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd292df5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b2ffa4e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Computation of gradients\n",
+    "\n",
+    "This in turn means that the gradient can be\n",
+    "computed as a sum over $i$-gradients"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0abe4b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "65c15c60",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Stochasticity/randomness is introduced by only taking the\n",
+    "gradient on a subset of the data called minibatches.  If there are $n$\n",
+    "data points and the size of each minibatch is $M$, there will be $n/M$\n",
+    "minibatches. We denote these minibatches by $B_k$ where\n",
+    "$k=1,\\cdots,n/M$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "460354c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## SGD example\n",
+    "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
+    "and we choose to have $M=5$ minibathces,\n",
+    "then each minibatch contains two data points. In particular we have\n",
+    "$B_1 = (\\mathbf{x}_1,\\mathbf{x}_2), \\cdots, B_5 =\n",
+    "(\\mathbf{x}_9,\\mathbf{x}_{10})$. Note that if you choose $M=1$ you\n",
+    "have only a single batch with all data points and on the other extreme,\n",
+    "you may choose $M=n$ resulting in a minibatch for each datapoint, i.e\n",
+    "$B_k = \\mathbf{x}_k$.\n",
+    "\n",
+    "The idea is now to approximate the gradient by replacing the sum over\n",
+    "all data points with a sum over the data points in one the minibatches\n",
+    "picked at random in each gradient descent step"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2a5dfcd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_{\\beta}\n",
+    "C(\\mathbf{\\beta}) = \\sum_{i=1}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}) \\rightarrow \\sum_{i \\in B_k}^n \\nabla_\\beta\n",
+    "c_i(\\mathbf{x}_i, \\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eeeb0fe8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The gradient step\n",
+    "\n",
+    "Thus a gradient descent step now looks like"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b49c741",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta})\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8ba7b9be",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $k$ is picked at random with equal\n",
+    "probability from $[1,n/M]$. An iteration over the number of\n",
+    "minibathces (n/M) is commonly referred to as an epoch. Thus it is\n",
+    "typical to choose a number of epochs and for each epoch iterate over\n",
+    "the number of minibatches, as exemplified in the code below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50da33c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple example code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "31bd6a24",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "\n",
+    "n = 100 #100 datapoints \n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "n_epochs = 10 #number of epochs\n",
+    "\n",
+    "j = 0\n",
+    "for epoch in range(1,n_epochs+1):\n",
+    "    for i in range(m):\n",
+    "        k = np.random.randint(m) #Pick the k-th minibatch at random\n",
+    "        #Compute the gradient using the data in minibatch Bk\n",
+    "        #Compute new suggestion for \n",
+    "        j += 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0deb8111",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Taking the gradient only on a subset of the data has two important\n",
+    "benefits. First, it introduces randomness which decreases the chance\n",
+    "that our opmization scheme gets stuck in a local minima. Second, if\n",
+    "the size of the minibatches are small relative to the number of\n",
+    "datapoints ($M <  n$), the computation of the gradient is much\n",
+    "cheaper since we sum over the datapoints in the $k-th$ minibatch and not\n",
+    "all $n$ datapoints."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16d54f02",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## When do we stop?\n",
+    "\n",
+    "A natural question is when do we stop the search for a new minimum?\n",
+    "One possibility is to compute the full gradient after a given number\n",
+    "of epochs and check if the norm of the gradient is smaller than some\n",
+    "threshold and stop if true. However, the condition that the gradient\n",
+    "is zero is valid also for local minima, so this would only tell us\n",
+    "that we are close to a local/global minimum. However, we could also\n",
+    "evaluate the cost function at this point, store the result and\n",
+    "continue the search. If the test kicks in at a later stage we can\n",
+    "compare the values of the cost function and keep the $\\beta$ that\n",
+    "gave the lowest value."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b300d06b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Slightly different approach\n",
+    "\n",
+    "Another approach is to let the step length $\\gamma_j$ depend on the\n",
+    "number of epochs in such a way that it becomes very small after a\n",
+    "reasonable time such that we do not move at all. Such approaches are\n",
+    "also called scaling. There are many such ways to [scale the learning\n",
+    "rate](https://towardsdatascience.com/gradient-descent-the-learning-rate-and-the-importance-of-feature-scaling-6c0b416596e1)\n",
+    "and [discussions here](https://www.jmlr.org/papers/volume23/20-1258/20-1258.pdf). See\n",
+    "also\n",
+    "<https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1>\n",
+    "for a discussion of different scaling functions for the learning rate."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bc7778d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Time decay rate\n",
+    "\n",
+    "As an example, let $e = 0,1,2,3,\\cdots$ denote the current epoch and let $t_0, t_1 > 0$ be two fixed numbers. Furthermore, let $t = e \\cdot m + i$ where $m$ is the number of minibatches and $i=0,\\cdots,m-1$. Then the function $$\\gamma_j(t; t_0, t_1) = \\frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length $\\gamma_j (0; t_0, t_1) = t_0/t_1$ which decays in *time* $t$.\n",
+    "\n",
+    "In this way we can fix the number of epochs, compute $\\beta$ and\n",
+    "evaluate the cost function at the end. Repeating the computation will\n",
+    "give a different result since the scheme is random by design. Then we\n",
+    "pick the final $\\beta$ that gives the lowest value of the cost\n",
+    "function."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "a60fe5bd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "\n",
+    "def step_length(t,t0,t1):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "n = 100 #100 datapoints \n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "n_epochs = 500 #number of epochs\n",
+    "t0 = 1.0\n",
+    "t1 = 10\n",
+    "\n",
+    "gamma_j = t0/t1\n",
+    "j = 0\n",
+    "for epoch in range(1,n_epochs+1):\n",
+    "    for i in range(m):\n",
+    "        k = np.random.randint(m) #Pick the k-th minibatch at random\n",
+    "        #Compute the gradient using the data in minibatch Bk\n",
+    "        #Compute new suggestion for beta\n",
+    "        t = epoch*m+i\n",
+    "        gamma_j = step_length(t,t0,t1)\n",
+    "        j += 1\n",
+    "\n",
+    "print(\"gamma_j after %d epochs: %g\" % (n_epochs,gamma_j))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2192721f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Code with a Number of Minibatches which varies\n",
+    "\n",
+    "In the code here we vary the number of mini-batches."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "e404f2c5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Importing various packages\n",
+    "from math import exp, sqrt\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ ((X @ theta)-y)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fffdbb91",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Replace or not\n",
+    "\n",
+    "In the above code, we have use replacement in setting up the\n",
+    "mini-batches. The discussion\n",
+    "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
+    "useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cce7a0e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Momentum based GD\n",
+    "\n",
+    "The stochastic gradient descent (SGD) is almost always used with a\n",
+    "*momentum* or inertia term that serves as a memory of the direction we\n",
+    "are moving in parameter space.  This is typically implemented as\n",
+    "follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3154c365",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a2a9ceca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
+    "\\label{_auto1} \\tag{2}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3374c700",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have introduced a momentum parameter $\\gamma$, with\n",
+    "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
+    "indicate the gradient is to be taken over a different mini-batch at\n",
+    "each step. We call this algorithm gradient descent with momentum\n",
+    "(GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a\n",
+    "running average of recently encountered gradients and\n",
+    "$(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory\n",
+    "used in the averaging procedure. Consistent with this, when\n",
+    "$\\gamma=0$, this just reduces down to ordinary SGD as discussed\n",
+    "earlier. An equivalent way of writing the updates is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "893d86fe",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca2449e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3cbd4adb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on momentum based approaches\n",
+    "\n",
+    "Let us try to get more intuition from these equations. It is helpful\n",
+    "to consider a simple physical analogy with a particle of mass $m$\n",
+    "moving in a viscous medium with drag coefficient $\\mu$ and potential\n",
+    "$E(\\mathbf{w})$. If we denote the particle's position by $\\mathbf{w}$,\n",
+    "then its motion is described by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3f07cbc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "99f2ac0f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can discretize this equation in the usual way to get"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "83336244",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "efd3e708",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Rearranging this equation, we can rewrite this as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c24d65c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "853d885b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Momentum parameter\n",
+    "\n",
+    "Notice that this equation is identical to previous one if we identify\n",
+    "the position of the particle, $\\mathbf{w}$, with the parameters\n",
+    "$\\boldsymbol{\\theta}$. This allows us to identify the momentum\n",
+    "parameter and learning rate with the mass of the particle and the\n",
+    "viscous drag as:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ab54645",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90f1503b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Thus, as the name suggests, the momentum parameter is proportional to\n",
+    "the mass of the particle and effectively provides inertia.\n",
+    "Furthermore, in the large viscosity/small learning rate limit, our\n",
+    "memory time scales as $(1-\\gamma)^{-1} \\approx m/(\\mu \\Delta t)$.\n",
+    "\n",
+    "Why is momentum useful? SGD momentum helps the gradient descent\n",
+    "algorithm gain speed in directions with persistent but small gradients\n",
+    "even in the presence of stochasticity, while suppressing oscillations\n",
+    "in high-curvature directions. This becomes especially important in\n",
+    "situations where the landscape is shallow and flat in some directions\n",
+    "and narrow and steep in others. It has been argued that first-order\n",
+    "methods (with appropriate initial conditions) can perform comparable\n",
+    "to more expensive second order methods, especially in the context of\n",
+    "complex deep learning models.\n",
+    "\n",
+    "These beneficial properties of momentum can sometimes become even more\n",
+    "pronounced by using a slight modification of the classical momentum\n",
+    "algorithm called Nesterov Accelerated Gradient (NAG).\n",
+    "\n",
+    "In the NAG algorithm, rather than calculating the gradient at the\n",
+    "current parameters, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t)$, one\n",
+    "calculates the gradient at the expected value of the parameters given\n",
+    "our current momentum, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma\n",
+    "\\mathbf{v}_{t-1})$. This yields the NAG update rule"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d496d988",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "258ca1e6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto2\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t}.\n",
+    "\\label{_auto2} \\tag{3}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84278058",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "feaee2f4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Second moment of the gradient\n",
+    "\n",
+    "In stochastic gradient descent, with and without momentum, we still\n",
+    "have to specify a schedule for tuning the learning rates $\\eta_t$\n",
+    "as a function of time.  As discussed in the context of Newton's\n",
+    "method, this presents a number of dilemmas. The learning rate is\n",
+    "limited by the steepest direction which can change depending on the\n",
+    "current position in the landscape. To circumvent this problem, ideally\n",
+    "our algorithm would keep track of curvature and take large steps in\n",
+    "shallow, flat directions and small steps in steep, narrow directions.\n",
+    "Second-order methods accomplish this by calculating or approximating\n",
+    "the Hessian and normalizing the learning rate by the\n",
+    "curvature. However, this is very computationally expensive for\n",
+    "extremely large models. Ideally, we would like to be able to\n",
+    "adaptively change the step size to match the landscape without paying\n",
+    "the steep computational price of calculating or approximating\n",
+    "Hessians.\n",
+    "\n",
+    "Recently, a number of methods have been introduced that accomplish\n",
+    "this by tracking not only the gradient, but also the second moment of\n",
+    "the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and\n",
+    "[ADAM](https://arxiv.org/abs/1412.6980)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "218edcf1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMS prop\n",
+    "\n",
+    "In RMS prop, in addition to keeping a running average of the first\n",
+    "moment of the gradient, we also keep track of the second moment\n",
+    "denoted by $\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}_t^2]$. The update rule\n",
+    "for RMS prop is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18dbc91c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto3\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto3} \\tag{4}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0bfcf74a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5fedd6f0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b210b2a4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\beta$ controls the averaging time of the second moment and is\n",
+    "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
+    "typically chosen to be $10^{-3}$, and $\\epsilon\\sim 10^{-8} $ is a\n",
+    "small regularization constant to prevent divergences. Multiplication\n",
+    "and division by vectors is understood as an element-wise operation. It\n",
+    "is clear from this formula that the learning rate is reduced in\n",
+    "directions where the norm of the gradient is consistently large. This\n",
+    "greatly speeds up the convergence by allowing us to use a larger\n",
+    "learning rate for flat directions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34ffacbb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
+    "\n",
+    "A related algorithm is the ADAM optimizer. In\n",
+    "[ADAM](https://arxiv.org/abs/1412.6980), we keep a running average of\n",
+    "both the first and second moment of the gradient and use this\n",
+    "information to adaptively change the learning rate for different\n",
+    "parameters.  The method isefficient when working with large\n",
+    "problems involving lots data and/or parameters.  It is a combination of the\n",
+    "gradient descent with momentum algorithm and the RMSprop algorithm\n",
+    "discussed above.\n",
+    "\n",
+    "In addition to keeping a running average of the first and\n",
+    "second moments of the gradient\n",
+    "(i.e. $\\mathbf{m}_t=\\mathbb{E}[\\mathbf{g}_t]$ and\n",
+    "$\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}^2_t]$, respectively), ADAM\n",
+    "performs an additional bias correction to account for the fact that we\n",
+    "are estimating the first two moments of the gradient using a running\n",
+    "average (denoted by the hats in the update rule below). The update\n",
+    "rule for ADAM is given by (where multiplication and division are once\n",
+    "again understood to be element-wise operations below)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd03375d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto4\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto4} \\tag{5}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0db5d6e0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84c709d9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4e47496",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "164f27df",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "591f4833",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e2127e8a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto5\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\label{_auto5} \\tag{6}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5cef8b84",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
+    "second moment and are typically taken to be $0.9$ and $0.99$\n",
+    "respectively, and $\\eta$ and $\\epsilon$ are identical to RMSprop.\n",
+    "\n",
+    "Like in RMSprop, the effective step size of a parameter depends on the\n",
+    "magnitude of its gradient squared.  To understand this better, let us\n",
+    "rewrite this expression in terms of the variance\n",
+    "$\\boldsymbol{\\sigma}_t^2 = \\boldsymbol{\\mathbf{s}}_t -\n",
+    "(\\boldsymbol{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The\n",
+    "update rule for this parameter is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "505c8905",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca96ddec",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
+    "\n",
+    "The algorithms we have implemented are well described in the text by [Goodfellow, Bengio and Courville, chapter 8](https://www.deeplearningbook.org/contents/optimization.html).\n",
+    "\n",
+    "The codes which implement these algorithms are discussed after our presentation of automatic differentiation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fa011176",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Practical tips\n",
+    "\n",
+    "* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
+    "\n",
+    "* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
+    "\n",
+    "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
+    "\n",
+    "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
+    "\n",
+    "Geron's text, see chapter 11, has several interesting discussions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b91c4543",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Automatic differentiation\n",
+    "\n",
+    "[Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), \n",
+    "also called algorithmic\n",
+    "differentiation or computational differentiation,is a set of\n",
+    "techniques to numerically evaluate the derivative of a function\n",
+    "specified by a computer program. AD exploits the fact that every\n",
+    "computer program, no matter how complicated, executes a sequence of\n",
+    "elementary arithmetic operations (addition, subtraction,\n",
+    "multiplication, division, etc.) and elementary functions (exp, log,\n",
+    "sin, cos, etc.). By applying the chain rule repeatedly to these\n",
+    "operations, derivatives of arbitrary order can be computed\n",
+    "automatically, accurately to working precision, and using at most a\n",
+    "small constant factor more arithmetic operations than the original\n",
+    "program.\n",
+    "\n",
+    "Automatic differentiation is neither:\n",
+    "\n",
+    "* Symbolic differentiation, nor\n",
+    "\n",
+    "* Numerical differentiation (the method of finite differences).\n",
+    "\n",
+    "Symbolic differentiation can lead to inefficient code and faces the\n",
+    "difficulty of converting a computer program into a single expression,\n",
+    "while numerical differentiation can introduce round-off errors in the\n",
+    "discretization process and cancellation\n",
+    "\n",
+    "Python has tools for so-called **automatic differentiation**.\n",
+    "Consider the following example"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f13065e5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22937f5e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which has the following derivative"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e1459fe1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "441a109a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Using **autograd** we have"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "9043abae",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "\n",
+    "# To do elementwise differentiation:\n",
+    "from autograd import elementwise_grad as egrad \n",
+    "\n",
+    "# To plot:\n",
+    "import matplotlib.pyplot as plt \n",
+    "\n",
+    "\n",
+    "def f(x):\n",
+    "    return np.sin(2*np.pi*x + x**2)\n",
+    "\n",
+    "def f_grad_analytic(x):\n",
+    "    return np.cos(2*np.pi*x + x**2)*(2*np.pi + 2*x)\n",
+    "\n",
+    "# Do the comparison:\n",
+    "x = np.linspace(0,1,1000)\n",
+    "\n",
+    "f_grad = egrad(f)\n",
+    "\n",
+    "computed = f_grad(x)\n",
+    "analytic = f_grad_analytic(x)\n",
+    "\n",
+    "plt.title('Derivative computed from Autograd compared with the analytical derivative')\n",
+    "plt.plot(x,computed,label='autograd')\n",
+    "plt.plot(x,analytic,label='analytic')\n",
+    "\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel('y')\n",
+    "plt.legend()\n",
+    "\n",
+    "plt.show()\n",
+    "\n",
+    "print(\"The max absolute difference is: %g\"%(np.max(np.abs(computed - analytic))))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "787d5d78",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using autograd\n",
+    "\n",
+    "Here we\n",
+    "experiment with what kind of functions Autograd is capable\n",
+    "of finding the gradient of. The following Python functions are just\n",
+    "meant to illustrate what Autograd can do, but please feel free to\n",
+    "experiment with other, possibly more complicated, functions as well."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "6a677479",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def f1(x):\n",
+    "    return x**3 + 1\n",
+    "\n",
+    "f1_grad = grad(f1)\n",
+    "\n",
+    "# Remember to send in float as argument to the computed gradient from Autograd!\n",
+    "a = 1.0\n",
+    "\n",
+    "# See the evaluated gradient at a using autograd:\n",
+    "print(\"The gradient of f1 evaluated at a = %g using autograd is: %g\"%(a,f1_grad(a)))\n",
+    "\n",
+    "# Compare with the analytical derivative, that is f1'(x) = 3*x**2 \n",
+    "grad_analytical = 3*a**2\n",
+    "print(\"The gradient of f1 evaluated at a = %g by finding the analytic expression is: %g\"%(a,grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f94a1d32",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Autograd with more complicated functions\n",
+    "\n",
+    "To differentiate with respect to two (or more) arguments of a Python\n",
+    "function, Autograd need to know at which variable the function if\n",
+    "being differentiated with respect to."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "c0eb89fd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f2(x1,x2):\n",
+    "    return 3*x1**3 + x2*(x1 - 5) + 1\n",
+    "\n",
+    "# By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1\n",
+    "f2_grad_x1 = grad(f2,0)\n",
+    "\n",
+    "# ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad\n",
+    "f2_grad_x2 = grad(f2,1)\n",
+    "\n",
+    "x1 = 1.0\n",
+    "x2 = 3.0 \n",
+    "\n",
+    "print(\"Evaluating at x1 = %g, x2 = %g\"%(x1,x2))\n",
+    "print(\"-\"*30)\n",
+    "\n",
+    "# Compare with the analytical derivatives:\n",
+    "\n",
+    "# Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:\n",
+    "f2_grad_x1_analytical = 9*x1**2 + x2\n",
+    "\n",
+    "# Derivative of f2 w.r.t x2 is: x1 - 5:\n",
+    "f2_grad_x2_analytical = x1 - 5\n",
+    "\n",
+    "# See the evaluated derivations:\n",
+    "print(\"The derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
+    "print(\"The analytical derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
+    "\n",
+    "print()\n",
+    "\n",
+    "print(\"The derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))\n",
+    "print(\"The analytical derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "05d7497d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24e3ca02",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More complicated functions using the elements of their arguments directly"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "a616e696",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f3(x): # Assumes x is an array of length 5 or higher\n",
+    "    return 2*x[0] + 3*x[1] + 5*x[2] + 7*x[3] + 11*x[4]**2\n",
+    "\n",
+    "f3_grad = grad(f3)\n",
+    "\n",
+    "x = np.linspace(0,4,5)\n",
+    "\n",
+    "# Print the computed gradient:\n",
+    "print(\"The computed gradient of f3 is: \", f3_grad(x))\n",
+    "\n",
+    "# The analytical gradient is: (2, 3, 5, 7, 22*x[4])\n",
+    "f3_grad_analytical = np.array([2, 3, 5, 7, 22*x[4]])\n",
+    "\n",
+    "# Print the analytical gradient:\n",
+    "print(\"The analytical gradient of f3 is: \", f3_grad_analytical)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f695da56",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that in this case, when sending an array as input argument, the\n",
+    "output from Autograd is another array. This is the true gradient of\n",
+    "the function, as opposed to the function in the previous example. By\n",
+    "using arrays to represent the variables, the output from Autograd\n",
+    "might be easier to work with, as the output is closer to what one\n",
+    "could expect form a gradient-evaluting function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ac073ee",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Functions using mathematical functions from Numpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "efc8906e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f4(x):\n",
+    "    return np.sqrt(1+x**2) + np.exp(x) + np.sin(2*np.pi*x)\n",
+    "\n",
+    "f4_grad = grad(f4)\n",
+    "\n",
+    "x = 2.7\n",
+    "\n",
+    "# Print the computed derivative:\n",
+    "print(\"The computed derivative of f4 at x = %g is: %g\"%(x,f4_grad(x)))\n",
+    "\n",
+    "# The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi\n",
+    "f4_grad_analytical = x/np.sqrt(1 + x**2) + np.exp(x) + np.cos(2*np.pi*x)*2*np.pi\n",
+    "\n",
+    "# Print the analytical gradient:\n",
+    "print(\"The analytical gradient of f4 at x = %g is: %g\"%(x,f4_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c587e8f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More autograd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "6428be1f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f5(x):\n",
+    "    if x >= 0:\n",
+    "        return x**2\n",
+    "    else:\n",
+    "        return -3*x + 1\n",
+    "\n",
+    "f5_grad = grad(f5)\n",
+    "\n",
+    "x = 2.7\n",
+    "\n",
+    "# Print the computed derivative:\n",
+    "print(\"The computed derivative of f5 at x = %g is: %g\"%(x,f5_grad(x)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8e1de777",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And  with loops"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "770ff6aa",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f6_for(x):\n",
+    "    val = 0\n",
+    "    for i in range(10):\n",
+    "        val = val + x**i\n",
+    "    return val\n",
+    "\n",
+    "def f6_while(x):\n",
+    "    val = 0\n",
+    "    i = 0\n",
+    "    while i < 10:\n",
+    "        val = val + x**i\n",
+    "        i = i + 1\n",
+    "    return val\n",
+    "\n",
+    "f6_for_grad = grad(f6_for)\n",
+    "f6_while_grad = grad(f6_while)\n",
+    "\n",
+    "x = 0.5\n",
+    "\n",
+    "# Print the computed derivaties of f6_for and f6_while\n",
+    "print(\"The computed derivative of f6_for at x = %g is: %g\"%(x,f6_for_grad(x)))\n",
+    "print(\"The computed derivative of f6_while at x = %g is: %g\"%(x,f6_while_grad(x)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "b924cc5d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "# Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9\n",
+    "# The analytical derivative is: sum(i*x**(i-1)) \n",
+    "f6_grad_analytical = 0\n",
+    "for i in range(10):\n",
+    "    f6_grad_analytical += i*x**(i-1)\n",
+    "\n",
+    "print(\"The analytical derivative of f6 at x = %g is: %g\"%(x,f6_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f0b0e1e9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using recursion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "1585ab28",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def f7(n): # Assume that n is an integer\n",
+    "    if n == 1 or n == 0:\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return n*f7(n-1)\n",
+    "\n",
+    "f7_grad = grad(f7)\n",
+    "\n",
+    "n = 2.0\n",
+    "\n",
+    "print(\"The computed derivative of f7 at n = %d is: %g\"%(n,f7_grad(n)))\n",
+    "\n",
+    "# The function f7 is an implementation of the factorial of n.\n",
+    "# By using the product rule, one can find that the derivative is:\n",
+    "\n",
+    "f7_grad_analytical = 0\n",
+    "for i in range(int(n)-1):\n",
+    "    tmp = 1\n",
+    "    for k in range(int(n)-1):\n",
+    "        if k != i:\n",
+    "            tmp *= (n - k)\n",
+    "    f7_grad_analytical += tmp\n",
+    "\n",
+    "print(\"The analytical derivative of f7 at n = %d is: %g\"%(n,f7_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2718df1a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8fa5235",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Unsupported functions\n",
+    "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n",
+    "\n",
+    "Assigning a value to the variable being differentiated with respect to"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "196a52d6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f8(x): # Assume x is an array\n",
+    "    x[2] = 3\n",
+    "    return x*2\n",
+    "\n",
+    "f8_grad = grad(f8)\n",
+    "\n",
+    "x = 8.4\n",
+    "\n",
+    "print(\"The derivative of f8 is:\",f8_grad(x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9127a2c5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b12ed61",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The syntax a.dot(b) when finding the dot product"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "8ced55c8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f9(a): # Assume a is an array with 2 elements\n",
+    "    b = np.array([1.0,2.0])\n",
+    "    return a.dot(b)\n",
+    "\n",
+    "f9_grad = grad(f9)\n",
+    "\n",
+    "x = np.array([1.0,0.0])\n",
+    "\n",
+    "print(\"The derivative of f9 is:\",f9_grad(x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "92ebdc2b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Here we are told that the 'dot' function does not belong to Autograd's\n",
+    "version of a Numpy array.  To overcome this, an alternative syntax\n",
+    "which also computed the dot product can be used:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "276f763e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f9_alternative(x): # Assume a is an array with 2 elements\n",
+    "    b = np.array([1.0,2.0])\n",
+    "    return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2\n",
+    "\n",
+    "f9_alternative_grad = grad(f9_alternative)\n",
+    "\n",
+    "x = np.array([3.0,0.0])\n",
+    "\n",
+    "print(\"The gradient of f9 is:\",f9_alternative_grad(x))\n",
+    "\n",
+    "# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively\n",
+    "# w.r.t x is (b_1, b_2)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7841ad0b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Recommended to avoid\n",
+    "The documentation recommends to avoid inplace operations such as"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "10107989",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "a += b\n",
+    "a -= b\n",
+    "a*= b\n",
+    "a /=b"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c1139c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Autograd with OLS\n",
+    "\n",
+    "We conclude the part on optmization by showing how we can make codes\n",
+    "for linear regression and logistic regression using **autograd**. The\n",
+    "first example shows results with ordinary leats squares."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "3022af88",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "04d09021",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "71bf4b6d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x#+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 30\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "# Now improve with momentum gradient descent\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "for iter in range(Niterations):\n",
+    "    # calculate gradient\n",
+    "    gradients = training_gradient(theta)\n",
+    "    # calculate update\n",
+    "    new_change = eta*gradients+delta_momentum*change\n",
+    "    # take a step\n",
+    "    theta -= new_change\n",
+    "    # save the change\n",
+    "    change = new_change\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd wth momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad417bba",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## But noen of these can compete with Newton's method"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "c394bcef",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Newton's method\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(beta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "# Note that here the Hessian does not depend on the parameters beta\n",
+    "invH = np.linalg.pinv(H)\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta = np.random.randn(2,1)\n",
+    "Niterations = 5\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(beta)\n",
+    "    beta -= invH @ gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"beta from own Newton code\")\n",
+    "print(beta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e4cf4b5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Including Stochastic Gradient Descent with Autograd\n",
+    "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "47411bcf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8e30af2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "dd594924",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        # calculate update\n",
+    "        new_change = eta*gradients+delta_momentum*change\n",
+    "        # take a step\n",
+    "        theta -= new_change\n",
+    "        # save the change\n",
+    "        change = new_change\n",
+    "print(\"theta from own sdg with momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75c4c29d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Similar (second order function now) problem but now with AdaGrad"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "4dd14fc5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        Giter += gradients*gradients\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "        theta -= update\n",
+    "print(\"theta from own AdaGrad\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be4ce0cd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Running this code we note an almost perfect agreement with the results from matrix inversion."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b739495",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "ae87789c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameter rho\n",
+    "rho = 0.99\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "\t# Accumulated gradient\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
+    "\t# Taking the diagonal only and inverting\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "\t# Hadamard product\n",
+    "        theta -= update\n",
+    "print(\"theta from own RMSprop\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76c8872b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "e99dbaa4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980\n",
+    "beta1 = 0.9\n",
+    "beta2 = 0.999\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-7\n",
+    "iter = 0\n",
+    "for epoch in range(n_epochs):\n",
+    "    first_moment = 0.0\n",
+    "    second_moment = 0.0\n",
+    "    iter += 1\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        # Computing moments first\n",
+    "        first_moment = beta1*first_moment + (1-beta1)*gradients\n",
+    "        second_moment = beta2*second_moment+(1-beta2)*gradients*gradients\n",
+    "        first_term = first_moment/(1.0-beta1**iter)\n",
+    "        second_term = second_moment/(1.0-beta2**iter)\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        update = eta*first_term/(np.sqrt(second_term)+delta)\n",
+    "        theta -= update\n",
+    "print(\"theta from own ADAM\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "596df570",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And Logistic Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "6693f042",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def sigmoid(x):\n",
+    "    return 0.5 * (np.tanh(x / 2.) + 1)\n",
+    "\n",
+    "def logistic_predictions(weights, inputs):\n",
+    "    # Outputs probability of a label being true according to logistic model.\n",
+    "    return sigmoid(np.dot(inputs, weights))\n",
+    "\n",
+    "def training_loss(weights):\n",
+    "    # Training loss is the negative log-likelihood of the training labels.\n",
+    "    preds = logistic_predictions(weights, inputs)\n",
+    "    label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n",
+    "    return -np.sum(np.log(label_probabilities))\n",
+    "\n",
+    "# Build a toy dataset.\n",
+    "inputs = np.array([[0.52, 1.12,  0.77],\n",
+    "                   [0.88, -1.08, 0.15],\n",
+    "                   [0.52, 0.06, -1.30],\n",
+    "                   [0.74, -2.49, 1.39]])\n",
+    "targets = np.array([True, True, False, True])\n",
+    "\n",
+    "# Define a function that returns gradients of training loss using Autograd.\n",
+    "training_gradient_fun = grad(training_loss)\n",
+    "\n",
+    "# Optimize weights using gradient descent.\n",
+    "weights = np.array([0.0, 0.0, 0.0])\n",
+    "print(\"Initial loss:\", training_loss(weights))\n",
+    "for i in range(100):\n",
+    "    weights -= training_gradient_fun(weights) * 0.01\n",
+    "\n",
+    "print(\"Trained loss:\", training_loss(weights))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a40ed853",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
+    "brought together for high-performance numerical computing and machine learning research.\n",
+    "It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.\n",
+    "\n",
+    "Here's a simple example on how you can use **JAX** to compute the derivate of the logistic function."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "02f88360",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import jax.numpy as jnp\n",
+    "from jax import grad, jit, vmap\n",
+    "\n",
+    "def sum_logistic(x):\n",
+    "  return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))\n",
+    "\n",
+    "x_small = jnp.arange(3.)\n",
+    "derivative_fn = grad(sum_logistic)\n",
+    "print(derivative_fn(x_small))"
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
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diff --git a/doc/LectureNotes/_build/html/_sphinx_design_static/design-tabs.js b/doc/LectureNotes/_build/html/_sphinx_design_static/design-tabs.js
new file mode 100644
index 000000000..36b38cf0d
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_sphinx_design_static/design-tabs.js
@@ -0,0 +1,27 @@
+var sd_labels_by_text = {};
+
+function ready() {
+  const li = document.getElementsByClassName("sd-tab-label");
+  for (const label of li) {
+    syncId = label.getAttribute("data-sync-id");
+    if (syncId) {
+      label.onclick = onLabelClick;
+      if (!sd_labels_by_text[syncId]) {
+        sd_labels_by_text[syncId] = [];
+      }
+      sd_labels_by_text[syncId].push(label);
+    }
+  }
+}
+
+function onLabelClick() {
+  // Activate other inputs with the same sync id.
+  syncId = this.getAttribute("data-sync-id");
+  for (label of sd_labels_by_text[syncId]) {
+    if (label === this) continue;
+    label.previousElementSibling.checked = true;
+  }
+  window.localStorage.setItem("sphinx-design-last-tab", syncId);
+}
+
+document.addEventListener("DOMContentLoaded", ready, false);
diff --git a/doc/LectureNotes/_build/html/_static/_sphinx_javascript_frameworks_compat.js b/doc/LectureNotes/_build/html/_static/_sphinx_javascript_frameworks_compat.js
new file mode 100644
index 000000000..8549469dc
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/_sphinx_javascript_frameworks_compat.js
@@ -0,0 +1,134 @@
+/*
+ * _sphinx_javascript_frameworks_compat.js
+ * ~~~~~~~~~~
+ *
+ * Compatability shim for jQuery and underscores.js.
+ *
+ * WILL BE REMOVED IN Sphinx 6.0
+ * xref RemovedInSphinx60Warning
+ *
+ */
+
+/**
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+ */
+$u = _.noConflict();
+
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+    if (!x) {
+        return x
+    }
+    return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+    if (typeof s === 'undefined')
+        s = document.location.search;
+    var parts = s.substr(s.indexOf('?') + 1).split('&');
+    var result = {};
+    for (var i = 0; i < parts.length; i++) {
+        var tmp = parts[i].split('=', 2);
+        var key = jQuery.urldecode(tmp[0]);
+        var value = jQuery.urldecode(tmp[1]);
+        if (key in result)
+            result[key].push(value);
+        else
+            result[key] = [value];
+    }
+    return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+    function highlight(node, addItems) {
+        if (node.nodeType === 3) {
+            var val = node.nodeValue;
+            var pos = val.toLowerCase().indexOf(text);
+            if (pos >= 0 &&
+                !jQuery(node.parentNode).hasClass(className) &&
+                !jQuery(node.parentNode).hasClass("nohighlight")) {
+                var span;
+                var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+                if (isInSVG) {
+                    span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+                } else {
+                    span = document.createElement("span");
+                    span.className = className;
+                }
+                span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+                node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+                    document.createTextNode(val.substr(pos + text.length)),
+                    node.nextSibling));
+                node.nodeValue = val.substr(0, pos);
+                if (isInSVG) {
+                    var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+                    var bbox = node.parentElement.getBBox();
+                    rect.x.baseVal.value = bbox.x;
+                    rect.y.baseVal.value = bbox.y;
+                    rect.width.baseVal.value = bbox.width;
+                    rect.height.baseVal.value = bbox.height;
+                    rect.setAttribute('class', className);
+                    addItems.push({
+                        "parent": node.parentNode,
+                        "target": rect});
+                }
+            }
+        }
+        else if (!jQuery(node).is("button, select, textarea")) {
+            jQuery.each(node.childNodes, function() {
+                highlight(this, addItems);
+            });
+        }
+    }
+    var addItems = [];
+    var result = this.each(function() {
+        highlight(this, addItems);
+    });
+    for (var i = 0; i < addItems.length; ++i) {
+        jQuery(addItems[i].parent).before(addItems[i].target);
+    }
+    return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+    jQuery.uaMatch = function(ua) {
+        ua = ua.toLowerCase();
+
+        var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+            /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+            /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+            /(msie) ([\w.]+)/.exec(ua) ||
+            ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+            [];
+
+        return {
+            browser: match[ 1 ] || "",
+            version: match[ 2 ] || "0"
+        };
+    };
+    jQuery.browser = {};
+    jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
diff --git a/doc/LectureNotes/_build/html/_static/basic.css b/doc/LectureNotes/_build/html/_static/basic.css
index d54be8067..9e364ed34 100644
--- a/doc/LectureNotes/_build/html/_static/basic.css
+++ b/doc/LectureNotes/_build/html/_static/basic.css
@@ -222,7 +222,7 @@ table.modindextable td {
 /* -- general body styles --------------------------------------------------- */
 
 div.body {
-    min-width: 450px;
+    min-width: 360px;
     max-width: 800px;
 }
 
@@ -237,16 +237,6 @@ a.headerlink {
     visibility: hidden;
 }
 
-a.brackets:before,
-span.brackets > a:before{
-    content: "[";
-}
-
-a.brackets:after,
-span.brackets > a:after {
-    content: "]";
-}
-
 h1:hover > a.headerlink,
 h2:hover > a.headerlink,
 h3:hover > a.headerlink,
@@ -334,12 +324,16 @@ aside.sidebar {
 p.sidebar-title {
     font-weight: bold;
 }
+nav.contents,
+aside.topic,
 
 div.admonition, div.topic, blockquote {
     clear: left;
 }
 
 /* -- topics ---------------------------------------------------------------- */
+nav.contents,
+aside.topic,
 
 div.topic {
     border: 1px solid #ccc;
@@ -379,6 +373,9 @@ div.body p.centered {
 
 div.sidebar > :last-child,
 aside.sidebar > :last-child,
+nav.contents > :last-child,
+aside.topic > :last-child,
+
 div.topic > :last-child,
 div.admonition > :last-child {
     margin-bottom: 0;
@@ -386,6 +383,9 @@ div.admonition > :last-child {
 
 div.sidebar::after,
 aside.sidebar::after,
+nav.contents::after,
+aside.topic::after,
+
 div.topic::after,
 div.admonition::after,
 blockquote::after {
@@ -428,10 +428,6 @@ table.docutils td, table.docutils th {
     border-bottom: 1px solid #aaa;
 }
 
-table.footnote td, table.footnote th {
-    border: 0 !important;
-}
-
 th {
     text-align: left;
     padding-right: 5px;
@@ -615,6 +611,7 @@ ul.simple p {
     margin-bottom: 0;
 }
 
+/* Docutils 0.17 and older (footnotes & citations) */
 dl.footnote > dt,
 dl.citation > dt {
     float: left;
@@ -632,6 +629,33 @@ dl.citation > dd:after {
     clear: both;
 }
 
+/* Docutils 0.18+ (footnotes & citations) */
+aside.footnote > span,
+div.citation > span {
+    float: left;
+}
+aside.footnote > span:last-of-type,
+div.citation > span:last-of-type {
+  padding-right: 0.5em;
+}
+aside.footnote > p {
+  margin-left: 2em;
+}
+div.citation > p {
+  margin-left: 4em;
+}
+aside.footnote > p:last-of-type,
+div.citation > p:last-of-type {
+    margin-bottom: 0em;
+}
+aside.footnote > p:last-of-type:after,
+div.citation > p:last-of-type:after {
+    content: "";
+    clear: both;
+}
+
+/* Footnotes & citations ends */
+
 dl.field-list {
     display: grid;
     grid-template-columns: fit-content(30%) auto;
diff --git a/doc/LectureNotes/_build/html/_static/copybutton.css b/doc/LectureNotes/_build/html/_static/copybutton.css
index 40eafe5fc..f1916ec7d 100644
--- a/doc/LectureNotes/_build/html/_static/copybutton.css
+++ b/doc/LectureNotes/_build/html/_static/copybutton.css
@@ -35,7 +35,8 @@ div.highlight  {
     position: relative;
 }
 
-.highlight:hover button.copybtn {
+/* Show the copybutton */
+.highlight:hover button.copybtn, button.copybtn.success {
 	opacity: 1;
 }
 
diff --git a/doc/LectureNotes/_build/html/_static/copybutton.js b/doc/LectureNotes/_build/html/_static/copybutton.js
index 40ac33108..2ea7ff3e2 100644
--- a/doc/LectureNotes/_build/html/_static/copybutton.js
+++ b/doc/LectureNotes/_build/html/_static/copybutton.js
@@ -20,7 +20,7 @@ const messages = {
   },
   'fr' : {
     'copy': 'Copier',
-    'copy_to_clipboard': 'Copié dans le presse-papier',
+    'copy_to_clipboard': 'Copier dans le presse-papier',
     'copy_success': 'Copié !',
     'copy_failure': 'Échec de la copie',
   },
@@ -102,18 +102,25 @@ const clearSelection = () => {
   }
 }
 
-// Changes tooltip text for two seconds, then changes it back
+// Changes tooltip text for a moment, then changes it back
+// We want the timeout of our `success` class to be a bit shorter than the
+// tooltip and icon change, so that we can hide the icon before changing back.
+var timeoutIcon = 2000;
+var timeoutSuccessClass = 1500;
+
 const temporarilyChangeTooltip = (el, oldText, newText) => {
   el.setAttribute('data-tooltip', newText)
   el.classList.add('success')
-  setTimeout(() => el.setAttribute('data-tooltip', oldText), 2000)
-  setTimeout(() => el.classList.remove('success'), 2000)
+  // Remove success a little bit sooner than we change the tooltip
+  // So that we can use CSS to hide the copybutton first
+  setTimeout(() => el.classList.remove('success'), timeoutSuccessClass)
+  setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon)
 }
 
 // Changes the copy button icon for two seconds, then changes it back
 const temporarilyChangeIcon = (el) => {
   el.innerHTML = iconCheck;
-  setTimeout(() => {el.innerHTML = iconCopy}, 2000)
+  setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon)
 }
 
 const addCopyButtonToCodeCells = () => {
@@ -125,7 +132,8 @@ const addCopyButtonToCodeCells = () => {
   }
 
   // Add copybuttons to all of our code cells
-  const codeCells = document.querySelectorAll('div.highlight pre')
+  const COPYBUTTON_SELECTOR = 'div.highlight pre';
+  const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR)
   codeCells.forEach((codeCell, index) => {
     const id = codeCellId(index)
     codeCell.setAttribute('id', id)
@@ -141,10 +149,25 @@ function escapeRegExp(string) {
     return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
 }
 
+/**
+ * Removes excluded text from a Node.
+ *
+ * @param {Node} target Node to filter.
+ * @param {string} exclude CSS selector of nodes to exclude.
+ * @returns {DOMString} Text from `target` with text removed.
+ */
+function filterText(target, exclude) {
+    const clone = target.cloneNode(true);  // clone as to not modify the live DOM
+    if (exclude) {
+        // remove excluded nodes
+        clone.querySelectorAll(exclude).forEach(node => node.remove());
+    }
+    return clone.innerText;
+}
+
 // Callback when a copy button is clicked. Will be passed the node that was clicked
 // should then grab the text and replace pieces of text that shouldn't be used in output
 function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
-
     var regexp;
     var match;
 
@@ -199,7 +222,12 @@ function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onl
 
 var copyTargetText = (trigger) => {
   var target = document.querySelector(trigger.attributes['data-clipboard-target'].value);
-  return formatCopyText(target.innerText, '', false, true, true, true, '', '')
+
+  // get filtered text
+  let exclude = '.linenos';
+
+  let text = filterText(target, exclude);
+  return formatCopyText(text, '', false, true, true, true, '', '')
 }
 
   // Initialize with a callback so we can modify the text before copy
diff --git a/doc/LectureNotes/_build/html/_static/copybutton_funcs.js b/doc/LectureNotes/_build/html/_static/copybutton_funcs.js
index b9168c556..dbe1aaad7 100644
--- a/doc/LectureNotes/_build/html/_static/copybutton_funcs.js
+++ b/doc/LectureNotes/_build/html/_static/copybutton_funcs.js
@@ -2,10 +2,25 @@ function escapeRegExp(string) {
     return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
 }
 
+/**
+ * Removes excluded text from a Node.
+ *
+ * @param {Node} target Node to filter.
+ * @param {string} exclude CSS selector of nodes to exclude.
+ * @returns {DOMString} Text from `target` with text removed.
+ */
+export function filterText(target, exclude) {
+    const clone = target.cloneNode(true);  // clone as to not modify the live DOM
+    if (exclude) {
+        // remove excluded nodes
+        clone.querySelectorAll(exclude).forEach(node => node.remove());
+    }
+    return clone.innerText;
+}
+
 // Callback when a copy button is clicked. Will be passed the node that was clicked
 // should then grab the text and replace pieces of text that shouldn't be used in output
 export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
-
     var regexp;
     var match;
 
diff --git a/doc/LectureNotes/_build/html/_static/design-style.4045f2051d55cab465a707391d5b2007.min.css b/doc/LectureNotes/_build/html/_static/design-style.4045f2051d55cab465a707391d5b2007.min.css
new file mode 100644
index 000000000..3225661c2
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/design-style.4045f2051d55cab465a707391d5b2007.min.css
@@ -0,0 +1 @@
+.sd-bg-primary{background-color:var(--sd-color-primary) !important}.sd-bg-text-primary{color:var(--sd-color-primary-text) !important}button.sd-bg-primary:focus,button.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) !important}a.sd-bg-primary:focus,a.sd-bg-primary:hover{background-color:var(--sd-color-primary-highlight) !important}.sd-bg-secondary{background-color:var(--sd-color-secondary) !important}.sd-bg-text-secondary{color:var(--sd-color-secondary-text) !important}button.sd-bg-secondary:focus,button.sd-bg-secondary:hover{background-color:var(--sd-color-secondary-highlight) !important}a.sd-bg-secondary:focus,a.sd-bg-secondary:hover{background-color:var(--sd-color-secondary-highlight) !important}.sd-bg-success{background-color:var(--sd-color-success) !important}.sd-bg-text-success{color:var(--sd-color-success-text) !important}button.sd-bg-success:focus,button.sd-bg-success:hover{background-color:var(--sd-color-success-highlight) !important}a.sd-bg-success:focus,a.sd-bg-success:hover{background-color:var(--sd-color-success-highlight) !important}.sd-bg-info{background-color:var(--sd-color-info) !important}.sd-bg-text-info{color:var(--sd-color-info-text) !important}button.sd-bg-info:focus,button.sd-bg-info:hover{background-color:var(--sd-color-info-highlight) !important}a.sd-bg-info:focus,a.sd-bg-info:hover{background-color:var(--sd-color-info-highlight) !important}.sd-bg-warning{background-color:var(--sd-color-warning) !important}.sd-bg-text-warning{color:var(--sd-color-warning-text) !important}button.sd-bg-warning:focus,button.sd-bg-warning:hover{background-color:var(--sd-color-warning-highlight) !important}a.sd-bg-warning:focus,a.sd-bg-warning:hover{background-color:var(--sd-color-warning-highlight) !important}.sd-bg-danger{background-color:var(--sd-color-danger) !important}.sd-bg-text-danger{color:var(--sd-color-danger-text) !important}button.sd-bg-danger:focus,button.sd-bg-danger:hover{background-color:var(--sd-color-danger-highlight) !important}a.sd-bg-danger:focus,a.sd-bg-danger:hover{background-color:var(--sd-color-danger-highlight) !important}.sd-bg-light{background-color:var(--sd-color-light) !important}.sd-bg-text-light{color:var(--sd-color-light-text) !important}button.sd-bg-light:focus,button.sd-bg-light:hover{background-color:var(--sd-color-light-highlight) !important}a.sd-bg-light:focus,a.sd-bg-light:hover{background-color:var(--sd-color-light-highlight) !important}.sd-bg-muted{background-color:var(--sd-color-muted) !important}.sd-bg-text-muted{color:var(--sd-color-muted-text) !important}button.sd-bg-muted:focus,button.sd-bg-muted:hover{background-color:var(--sd-color-muted-highlight) !important}a.sd-bg-muted:focus,a.sd-bg-muted:hover{background-color:var(--sd-color-muted-highlight) !important}.sd-bg-dark{background-color:var(--sd-color-dark) !important}.sd-bg-text-dark{color:var(--sd-color-dark-text) !important}button.sd-bg-dark:focus,button.sd-bg-dark:hover{background-color:var(--sd-color-dark-highlight) !important}a.sd-bg-dark:focus,a.sd-bg-dark:hover{background-color:var(--sd-color-dark-highlight) !important}.sd-bg-black{background-color:var(--sd-color-black) !important}.sd-bg-text-black{color:var(--sd-color-black-text) !important}button.sd-bg-black:focus,button.sd-bg-black:hover{background-color:var(--sd-color-black-highlight) !important}a.sd-bg-black:focus,a.sd-bg-black:hover{background-color:var(--sd-color-black-highlight) !important}.sd-bg-white{background-color:var(--sd-color-white) !important}.sd-bg-text-white{color:var(--sd-color-white-text) !important}button.sd-bg-white:focus,button.sd-bg-white:hover{background-color:var(--sd-color-white-highlight) !important}a.sd-bg-white:focus,a.sd-bg-white:hover{background-color:var(--sd-color-white-highlight) !important}.sd-text-primary,.sd-text-primary>p{color:var(--sd-color-primary) !important}a.sd-text-primary:focus,a.sd-text-primary:hover{color:var(--sd-color-primary-highlight) !important}.sd-text-secondary,.sd-text-secondary>p{color:var(--sd-color-secondary) !important}a.sd-text-secondary:focus,a.sd-text-secondary:hover{color:var(--sd-color-secondary-highlight) !important}.sd-text-success,.sd-text-success>p{color:var(--sd-color-success) !important}a.sd-text-success:focus,a.sd-text-success:hover{color:var(--sd-color-success-highlight) !important}.sd-text-info,.sd-text-info>p{color:var(--sd-color-info) !important}a.sd-text-info:focus,a.sd-text-info:hover{color:var(--sd-color-info-highlight) !important}.sd-text-warning,.sd-text-warning>p{color:var(--sd-color-warning) !important}a.sd-text-warning:focus,a.sd-text-warning:hover{color:var(--sd-color-warning-highlight) !important}.sd-text-danger,.sd-text-danger>p{color:var(--sd-color-danger) !important}a.sd-text-danger:focus,a.sd-text-danger:hover{color:var(--sd-color-danger-highlight) !important}.sd-text-light,.sd-text-light>p{color:var(--sd-color-light) !important}a.sd-text-light:focus,a.sd-text-light:hover{color:var(--sd-color-light-highlight) !important}.sd-text-muted,.sd-text-muted>p{color:var(--sd-color-muted) !important}a.sd-text-muted:focus,a.sd-text-muted:hover{color:var(--sd-color-muted-highlight) !important}.sd-text-dark,.sd-text-dark>p{color:var(--sd-color-dark) !important}a.sd-text-dark:focus,a.sd-text-dark:hover{color:var(--sd-color-dark-highlight) !important}.sd-text-black,.sd-text-black>p{color:var(--sd-color-black) !important}a.sd-text-black:focus,a.sd-text-black:hover{color:var(--sd-color-black-highlight) !important}.sd-text-white,.sd-text-white>p{color:var(--sd-color-white) !important}a.sd-text-white:focus,a.sd-text-white:hover{color:var(--sd-color-white-highlight) !important}.sd-outline-primary{border-color:var(--sd-color-primary) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-primary:focus,a.sd-outline-primary:hover{border-color:var(--sd-color-primary-highlight) !important}.sd-outline-secondary{border-color:var(--sd-color-secondary) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-secondary:focus,a.sd-outline-secondary:hover{border-color:var(--sd-color-secondary-highlight) !important}.sd-outline-success{border-color:var(--sd-color-success) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-success:focus,a.sd-outline-success:hover{border-color:var(--sd-color-success-highlight) !important}.sd-outline-info{border-color:var(--sd-color-info) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-info:focus,a.sd-outline-info:hover{border-color:var(--sd-color-info-highlight) !important}.sd-outline-warning{border-color:var(--sd-color-warning) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-warning:focus,a.sd-outline-warning:hover{border-color:var(--sd-color-warning-highlight) !important}.sd-outline-danger{border-color:var(--sd-color-danger) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-danger:focus,a.sd-outline-danger:hover{border-color:var(--sd-color-danger-highlight) !important}.sd-outline-light{border-color:var(--sd-color-light) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-light:focus,a.sd-outline-light:hover{border-color:var(--sd-color-light-highlight) !important}.sd-outline-muted{border-color:var(--sd-color-muted) !important;border-style:solid !important;border-width:1px !important}a.sd-outline-muted:focus,a.sd-outline-muted:hover{border-color:var(--sd-color-muted-highlight) !important}.sd-outline-dark{border-color:var(--sd-color-dark) !important;border-style:solid !important;border-width:1px 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0;position:relative}.sd-tab-set>input{opacity:0;position:absolute}.sd-tab-set>input:checked+label{border-color:var(--sd-color-tabs-underline-active);color:var(--sd-color-tabs-label-active)}.sd-tab-set>input:checked+label+.sd-tab-content{display:block}.sd-tab-set>input:not(:checked)+label:hover{color:var(--sd-color-tabs-label-hover);border-color:var(--sd-color-tabs-underline-hover)}.sd-tab-set>input:focus+label{outline-style:auto}.sd-tab-set>input:not(.focus-visible)+label{outline:none;-webkit-tap-highlight-color:transparent}.sd-tab-set>label{border-bottom:.125rem solid transparent;margin-bottom:0;color:var(--sd-color-tabs-label-inactive);border-color:var(--sd-color-tabs-underline-inactive);cursor:pointer;font-size:var(--sd-fontsize-tabs-label);font-weight:700;padding:1em 1.25em .5em;transition:color 250ms;width:auto;z-index:1}html .sd-tab-set>label:hover{color:var(--sd-color-tabs-label-active)}.sd-col>.sd-tab-set{width:100%}.sd-tab-content{box-shadow:0 -0.0625rem var(--sd-color-tabs-overline),0 .0625rem var(--sd-color-tabs-underline);display:none;order:99;padding-bottom:.75rem;padding-top:.75rem;width:100%}.sd-tab-content>:first-child{margin-top:0 !important}.sd-tab-content>:last-child{margin-bottom:0 !important}.sd-tab-content>.sd-tab-set{margin:0}.sd-sphinx-override,.sd-sphinx-override *{-moz-box-sizing:border-box;-webkit-box-sizing:border-box;box-sizing:border-box}.sd-sphinx-override p{margin-top:0}:root{--sd-color-primary: #007bff;--sd-color-secondary: #6c757d;--sd-color-success: #28a745;--sd-color-info: #17a2b8;--sd-color-warning: #f0b37e;--sd-color-danger: #dc3545;--sd-color-light: #f8f9fa;--sd-color-muted: #6c757d;--sd-color-dark: #212529;--sd-color-black: black;--sd-color-white: white;--sd-color-primary-highlight: #0069d9;--sd-color-secondary-highlight: #5c636a;--sd-color-success-highlight: #228e3b;--sd-color-info-highlight: #148a9c;--sd-color-warning-highlight: #cc986b;--sd-color-danger-highlight: #bb2d3b;--sd-color-light-highlight: #d3d4d5;--sd-color-muted-highlight: #5c636a;--sd-color-dark-highlight: #1c1f23;--sd-color-black-highlight: black;--sd-color-white-highlight: #d9d9d9;--sd-color-primary-text: #fff;--sd-color-secondary-text: #fff;--sd-color-success-text: #fff;--sd-color-info-text: #fff;--sd-color-warning-text: #212529;--sd-color-danger-text: #fff;--sd-color-light-text: #212529;--sd-color-muted-text: #fff;--sd-color-dark-text: #fff;--sd-color-black-text: #fff;--sd-color-white-text: #212529;--sd-color-shadow: rgba(0, 0, 0, 0.15);--sd-color-card-border: rgba(0, 0, 0, 0.125);--sd-color-card-border-hover: hsla(231, 99%, 66%, 1);--sd-color-card-background: transparent;--sd-color-card-text: inherit;--sd-color-card-header: transparent;--sd-color-card-footer: transparent;--sd-color-tabs-label-active: hsla(231, 99%, 66%, 1);--sd-color-tabs-label-hover: hsla(231, 99%, 66%, 1);--sd-color-tabs-label-inactive: hsl(0, 0%, 66%);--sd-color-tabs-underline-active: hsla(231, 99%, 66%, 1);--sd-color-tabs-underline-hover: rgba(178, 206, 245, 0.62);--sd-color-tabs-underline-inactive: transparent;--sd-color-tabs-overline: rgb(222, 222, 222);--sd-color-tabs-underline: rgb(222, 222, 222);--sd-fontsize-tabs-label: 1rem}
diff --git a/doc/LectureNotes/_build/html/_static/design-tabs.js b/doc/LectureNotes/_build/html/_static/design-tabs.js
new file mode 100644
index 000000000..36b38cf0d
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/design-tabs.js
@@ -0,0 +1,27 @@
+var sd_labels_by_text = {};
+
+function ready() {
+  const li = document.getElementsByClassName("sd-tab-label");
+  for (const label of li) {
+    syncId = label.getAttribute("data-sync-id");
+    if (syncId) {
+      label.onclick = onLabelClick;
+      if (!sd_labels_by_text[syncId]) {
+        sd_labels_by_text[syncId] = [];
+      }
+      sd_labels_by_text[syncId].push(label);
+    }
+  }
+}
+
+function onLabelClick() {
+  // Activate other inputs with the same sync id.
+  syncId = this.getAttribute("data-sync-id");
+  for (label of sd_labels_by_text[syncId]) {
+    if (label === this) continue;
+    label.previousElementSibling.checked = true;
+  }
+  window.localStorage.setItem("sphinx-design-last-tab", syncId);
+}
+
+document.addEventListener("DOMContentLoaded", ready, false);
diff --git a/doc/LectureNotes/_build/html/_static/doctools.js b/doc/LectureNotes/_build/html/_static/doctools.js
index e509e4834..c3db08d1c 100644
--- a/doc/LectureNotes/_build/html/_static/doctools.js
+++ b/doc/LectureNotes/_build/html/_static/doctools.js
@@ -2,325 +2,263 @@
  * doctools.js
  * ~~~~~~~~~~~
  *
- * Sphinx JavaScript utilities for all documentation.
+ * Base JavaScript utilities for all Sphinx HTML documentation.
  *
  * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS.
  * :license: BSD, see LICENSE for details.
  *
  */
+"use strict";
 
-/**
- * select a different prefix for underscore
- */
-$u = _.noConflict();
-
-/**
- * make the code below compatible with browsers without
- * an installed firebug like debugger
-if (!window.console || !console.firebug) {
-  var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
-    "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
-    "profile", "profileEnd"];
-  window.console = {};
-  for (var i = 0; i < names.length; ++i)
-    window.console[names[i]] = function() {};
-}
- */
-
-/**
- * small helper function to urldecode strings
- *
- * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
- */
-jQuery.urldecode = function(x) {
-  if (!x) {
-    return x
+const _ready = (callback) => {
+  if (document.readyState !== "loading") {
+    callback();
+  } else {
+    document.addEventListener("DOMContentLoaded", callback);
   }
-  return decodeURIComponent(x.replace(/\+/g, ' '));
 };
 
 /**
- * small helper function to urlencode strings
- */
-jQuery.urlencode = encodeURIComponent;
-
-/**
- * This function returns the parsed url parameters of the
- * current request. Multiple values per key are supported,
- * it will always return arrays of strings for the value parts.
- */
-jQuery.getQueryParameters = function(s) {
-  if (typeof s === 'undefined')
-    s = document.location.search;
-  var parts = s.substr(s.indexOf('?') + 1).split('&');
-  var result = {};
-  for (var i = 0; i < parts.length; i++) {
-    var tmp = parts[i].split('=', 2);
-    var key = jQuery.urldecode(tmp[0]);
-    var value = jQuery.urldecode(tmp[1]);
-    if (key in result)
-      result[key].push(value);
-    else
-      result[key] = [value];
-  }
-  return result;
-};
-
-/**
- * highlight a given string on a jquery object by wrapping it in
+ * highlight a given string on a node by wrapping it in
  * span elements with the given class name.
  */
-jQuery.fn.highlightText = function(text, className) {
-  function highlight(node, addItems) {
-    if (node.nodeType === 3) {
-      var val = node.nodeValue;
-      var pos = val.toLowerCase().indexOf(text);
-      if (pos >= 0 &&
-          !jQuery(node.parentNode).hasClass(className) &&
-          !jQuery(node.parentNode).hasClass("nohighlight")) {
-        var span;
-        var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
-        if (isInSVG) {
-          span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
-        } else {
-          span = document.createElement("span");
-          span.className = className;
-        }
-        span.appendChild(document.createTextNode(val.substr(pos, text.length)));
-        node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+const _highlight = (node, addItems, text, className) => {
+  if (node.nodeType === Node.TEXT_NODE) {
+    const val = node.nodeValue;
+    const parent = node.parentNode;
+    const pos = val.toLowerCase().indexOf(text);
+    if (
+      pos >= 0 &&
+      !parent.classList.contains(className) &&
+      !parent.classList.contains("nohighlight")
+    ) {
+      let span;
+
+      const closestNode = parent.closest("body, svg, foreignObject");
+      const isInSVG = closestNode && closestNode.matches("svg");
+      if (isInSVG) {
+        span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+      } else {
+        span = document.createElement("span");
+        span.classList.add(className);
+      }
+
+      span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+      parent.insertBefore(
+        span,
+        parent.insertBefore(
           document.createTextNode(val.substr(pos + text.length)),
-          node.nextSibling));
-        node.nodeValue = val.substr(0, pos);
-        if (isInSVG) {
-          var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
-          var bbox = node.parentElement.getBBox();
-          rect.x.baseVal.value = bbox.x;
-          rect.y.baseVal.value = bbox.y;
-          rect.width.baseVal.value = bbox.width;
-          rect.height.baseVal.value = bbox.height;
-          rect.setAttribute('class', className);
-          addItems.push({
-              "parent": node.parentNode,
-              "target": rect});
-        }
+          node.nextSibling
+        )
+      );
+      node.nodeValue = val.substr(0, pos);
+
+      if (isInSVG) {
+        const rect = document.createElementNS(
+          "http://www.w3.org/2000/svg",
+          "rect"
+        );
+        const bbox = parent.getBBox();
+        rect.x.baseVal.value = bbox.x;
+        rect.y.baseVal.value = bbox.y;
+        rect.width.baseVal.value = bbox.width;
+        rect.height.baseVal.value = bbox.height;
+        rect.setAttribute("class", className);
+        addItems.push({ parent: parent, target: rect });
       }
     }
-    else if (!jQuery(node).is("button, select, textarea")) {
-      jQuery.each(node.childNodes, function() {
-        highlight(this, addItems);
-      });
-    }
+  } else if (node.matches && !node.matches("button, select, textarea")) {
+    node.childNodes.forEach((el) => _highlight(el, addItems, text, className));
   }
-  var addItems = [];
-  var result = this.each(function() {
-    highlight(this, addItems);
-  });
-  for (var i = 0; i < addItems.length; ++i) {
-    jQuery(addItems[i].parent).before(addItems[i].target);
-  }
-  return result;
 };
-
-/*
- * backward compatibility for jQuery.browser
- * This will be supported until firefox bug is fixed.
- */
-if (!jQuery.browser) {
-  jQuery.uaMatch = function(ua) {
-    ua = ua.toLowerCase();
-
-    var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
-      /(webkit)[ \/]([\w.]+)/.exec(ua) ||
-      /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
-      /(msie) ([\w.]+)/.exec(ua) ||
-      ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
-      [];
-
-    return {
-      browser: match[ 1 ] || "",
-      version: match[ 2 ] || "0"
-    };
-  };
-  jQuery.browser = {};
-  jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
-}
+const _highlightText = (thisNode, text, className) => {
+  let addItems = [];
+  _highlight(thisNode, addItems, text, className);
+  addItems.forEach((obj) =>
+    obj.parent.insertAdjacentElement("beforebegin", obj.target)
+  );
+};
 
 /**
  * Small JavaScript module for the documentation.
  */
-var Documentation = {
-
-  init : function() {
-    this.fixFirefoxAnchorBug();
-    this.highlightSearchWords();
-    this.initIndexTable();
-    if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
-      this.initOnKeyListeners();
-    }
+const Documentation = {
+  init: () => {
+    Documentation.highlightSearchWords();
+    Documentation.initDomainIndexTable();
+    Documentation.initOnKeyListeners();
   },
 
   /**
    * i18n support
    */
-  TRANSLATIONS : {},
-  PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
-  LOCALE : 'unknown',
+  TRANSLATIONS: {},
+  PLURAL_EXPR: (n) => (n === 1 ? 0 : 1),
+  LOCALE: "unknown",
 
   // gettext and ngettext don't access this so that the functions
   // can safely bound to a different name (_ = Documentation.gettext)
-  gettext : function(string) {
-    var translated = Documentation.TRANSLATIONS[string];
-    if (typeof translated === 'undefined')
-      return string;
-    return (typeof translated === 'string') ? translated : translated[0];
+  gettext: (string) => {
+    const translated = Documentation.TRANSLATIONS[string];
+    switch (typeof translated) {
+      case "undefined":
+        return string; // no translation
+      case "string":
+        return translated; // translation exists
+      default:
+        return translated[0]; // (singular, plural) translation tuple exists
+    }
   },
 
-  ngettext : function(singular, plural, n) {
-    var translated = Documentation.TRANSLATIONS[singular];
-    if (typeof translated === 'undefined')
-      return (n == 1) ? singular : plural;
-    return translated[Documentation.PLURALEXPR(n)];
+  ngettext: (singular, plural, n) => {
+    const translated = Documentation.TRANSLATIONS[singular];
+    if (typeof translated !== "undefined")
+      return translated[Documentation.PLURAL_EXPR(n)];
+    return n === 1 ? singular : plural;
   },
 
-  addTranslations : function(catalog) {
-    for (var key in catalog.messages)
-      this.TRANSLATIONS[key] = catalog.messages[key];
-    this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
-    this.LOCALE = catalog.locale;
-  },
-
-  /**
-   * add context elements like header anchor links
-   */
-  addContextElements : function() {
-    $('div[id] > :header:first').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this headline')).
-      appendTo(this);
-    });
-    $('dt[id]').each(function() {
-      $('<a class="headerlink">\u00B6</a>').
-      attr('href', '#' + this.id).
-      attr('title', _('Permalink to this definition')).
-      appendTo(this);
-    });
-  },
-
-  /**
-   * workaround a firefox stupidity
-   * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
-   */
-  fixFirefoxAnchorBug : function() {
-    if (document.location.hash && $.browser.mozilla)
-      window.setTimeout(function() {
-        document.location.href += '';
-      }, 10);
+  addTranslations: (catalog) => {
+    Object.assign(Documentation.TRANSLATIONS, catalog.messages);
+    Documentation.PLURAL_EXPR = new Function(
+      "n",
+      `return (${catalog.plural_expr})`
+    );
+    Documentation.LOCALE = catalog.locale;
   },
 
   /**
    * highlight the search words provided in the url in the text
    */
-  highlightSearchWords : function() {
-    var params = $.getQueryParameters();
-    var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
-    if (terms.length) {
-      var body = $('div.body');
-      if (!body.length) {
-        body = $('body');
-      }
-      window.setTimeout(function() {
-        $.each(terms, function() {
-          body.highlightText(this.toLowerCase(), 'highlighted');
-        });
-      }, 10);
-      $('<p class="highlight-link"><a href="javascript:Documentation.' +
-        'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
-          .appendTo($('#searchbox'));
-    }
-  },
+  highlightSearchWords: () => {
+    const highlight =
+      new URLSearchParams(window.location.search).get("highlight") || "";
+    const terms = highlight.toLowerCase().split(/\s+/).filter(x => x);
+    if (terms.length === 0) return; // nothing to do
 
-  /**
-   * init the domain index toggle buttons
-   */
-  initIndexTable : function() {
-    var togglers = $('img.toggler').click(function() {
-      var src = $(this).attr('src');
-      var idnum = $(this).attr('id').substr(7);
-      $('tr.cg-' + idnum).toggle();
-      if (src.substr(-9) === 'minus.png')
-        $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
-      else
-        $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
-    }).css('display', '');
-    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
-        togglers.click();
-    }
+    // There should never be more than one element matching "div.body"
+    const divBody = document.querySelectorAll("div.body");
+    const body = divBody.length ? divBody[0] : document.querySelector("body");
+    window.setTimeout(() => {
+      terms.forEach((term) => _highlightText(body, term, "highlighted"));
+    }, 10);
+
+    const searchBox = document.getElementById("searchbox");
+    if (searchBox === null) return;
+    searchBox.appendChild(
+      document
+        .createRange()
+        .createContextualFragment(
+          '<p class="highlight-link">' +
+            '<a href="javascript:Documentation.hideSearchWords()">' +
+            Documentation.gettext("Hide Search Matches") +
+            "</a></p>"
+        )
+    );
   },
 
   /**
    * helper function to hide the search marks again
    */
-  hideSearchWords : function() {
-    $('#searchbox .highlight-link').fadeOut(300);
-    $('span.highlighted').removeClass('highlighted');
-    var url = new URL(window.location);
-    url.searchParams.delete('highlight');
-    window.history.replaceState({}, '', url);
+  hideSearchWords: () => {
+    document
+      .querySelectorAll("#searchbox .highlight-link")
+      .forEach((el) => el.remove());
+    document
+      .querySelectorAll("span.highlighted")
+      .forEach((el) => el.classList.remove("highlighted"));
+    const url = new URL(window.location);
+    url.searchParams.delete("highlight");
+    window.history.replaceState({}, "", url);
   },
 
   /**
-   * make the url absolute
+   * helper function to focus on search bar
    */
-  makeURL : function(relativeURL) {
-    return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
+  focusSearchBar: () => {
+    document.querySelectorAll("input[name=q]")[0]?.focus();
   },
 
   /**
-   * get the current relative url
+   * Initialise the domain index toggle buttons
    */
-  getCurrentURL : function() {
-    var path = document.location.pathname;
-    var parts = path.split(/\//);
-    $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
-      if (this === '..')
-        parts.pop();
-    });
-    var url = parts.join('/');
-    return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
+  initDomainIndexTable: () => {
+    const toggler = (el) => {
+      const idNumber = el.id.substr(7);
+      const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`);
+      if (el.src.substr(-9) === "minus.png") {
+        el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`;
+        toggledRows.forEach((el) => (el.style.display = "none"));
+      } else {
+        el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`;
+        toggledRows.forEach((el) => (el.style.display = ""));
+      }
+    };
+
+    const togglerElements = document.querySelectorAll("img.toggler");
+    togglerElements.forEach((el) =>
+      el.addEventListener("click", (event) => toggler(event.currentTarget))
+    );
+    togglerElements.forEach((el) => (el.style.display = ""));
+    if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler);
   },
 
-  initOnKeyListeners: function() {
-    $(document).keydown(function(event) {
-      var activeElementType = document.activeElement.tagName;
-      // don't navigate when in search box, textarea, dropdown or button
-      if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
-          && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey
-          && !event.shiftKey) {
-        switch (event.keyCode) {
-          case 37: // left
-            var prevHref = $('link[rel="prev"]').prop('href');
-            if (prevHref) {
-              window.location.href = prevHref;
-              return false;
+  initOnKeyListeners: () => {
+    // only install a listener if it is really needed
+    if (
+      !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS &&
+      !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS
+    )
+      return;
+
+    const blacklistedElements = new Set([
+      "TEXTAREA",
+      "INPUT",
+      "SELECT",
+      "BUTTON",
+    ]);
+    document.addEventListener("keydown", (event) => {
+      if (blacklistedElements.has(document.activeElement.tagName)) return; // bail for input elements
+      if (event.altKey || event.ctrlKey || event.metaKey) return; // bail with special keys
+
+      if (!event.shiftKey) {
+        switch (event.key) {
+          case "ArrowLeft":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const prevLink = document.querySelector('link[rel="prev"]');
+            if (prevLink && prevLink.href) {
+              window.location.href = prevLink.href;
+              event.preventDefault();
             }
             break;
-          case 39: // right
-            var nextHref = $('link[rel="next"]').prop('href');
-            if (nextHref) {
-              window.location.href = nextHref;
-              return false;
+          case "ArrowRight":
+            if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break;
+
+            const nextLink = document.querySelector('link[rel="next"]');
+            if (nextLink && nextLink.href) {
+              window.location.href = nextLink.href;
+              event.preventDefault();
             }
             break;
+          case "Escape":
+            if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+            Documentation.hideSearchWords();
+            event.preventDefault();
         }
       }
+
+      // some keyboard layouts may need Shift to get /
+      switch (event.key) {
+        case "/":
+          if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break;
+          Documentation.focusSearchBar();
+          event.preventDefault();
+      }
     });
-  }
+  },
 };
 
 // quick alias for translations
-_ = Documentation.gettext;
+const _ = Documentation.gettext;
 
-$(document).ready(function() {
-  Documentation.init();
-});
+_ready(Documentation.init);
diff --git a/doc/LectureNotes/_build/html/_static/documentation_options.js b/doc/LectureNotes/_build/html/_static/documentation_options.js
index 93b7c24d6..30637825d 100644
--- a/doc/LectureNotes/_build/html/_static/documentation_options.js
+++ b/doc/LectureNotes/_build/html/_static/documentation_options.js
@@ -1,12 +1,14 @@
 var DOCUMENTATION_OPTIONS = {
     URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
     VERSION: '',
-    LANGUAGE: 'None',
+    LANGUAGE: 'en',
     COLLAPSE_INDEX: false,
     BUILDER: 'html',
     FILE_SUFFIX: '.html',
     LINK_SUFFIX: '.html',
     HAS_SOURCE: true,
     SOURCELINK_SUFFIX: '',
-    NAVIGATION_WITH_KEYS: true
+    NAVIGATION_WITH_KEYS: true,
+    SHOW_SEARCH_SUMMARY: true,
+    ENABLE_SEARCH_SHORTCUTS: false,
 };
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/_static/images/logo_deepnote.svg b/doc/LectureNotes/_build/html/_static/images/logo_deepnote.svg
new file mode 100644
index 000000000..fa77ebfc2
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/images/logo_deepnote.svg
@@ -0,0 +1 @@
+<svg viewBox="0 0 128 128" fill="none" xmlns="http://www.w3.org/2000/svg"><path fill-rule="evenodd" clip-rule="evenodd" d="M0 128h52.512l29.539-11.077-11.077-43.487-34.051 3.693L0 128Z" fill="#0076D4"/><path fill-rule="evenodd" clip-rule="evenodd" d="M52.513 128s16.6-8.759 19.673-24.277c3.072-15.517-12.091-26.594-35.263-26.594 0-.41 20.343-28.718 20.343-28.718l49.4 1.435L95.71 107.7l-20.452 15.978L52.513 128Z" fill="#002868"/><path fill-rule="evenodd" clip-rule="evenodd" d="M0 60.718 41.025.001s1.006.01 3.282 0c16.082-.068 81.23 3.12 81.23 60.368 0 65.352-73.025 67.631-73.025 67.631s30.495-5.839 30.495-34.816c0-28.978-27.541-32.466-45.264-32.466H0Z" fill="#00A9FF"/></svg>
diff --git a/doc/LectureNotes/_build/html/_static/jquery-3.6.0.js b/doc/LectureNotes/_build/html/_static/jquery-3.6.0.js
new file mode 100644
index 000000000..fc6c299b7
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/jquery-3.6.0.js
@@ -0,0 +1,10881 @@
+/*!
+ * jQuery JavaScript Library v3.6.0
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright OpenJS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2021-03-02T17:08Z
+ */
+( function( global, factory ) {
+
+	"use strict";
+
+	if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+		// For CommonJS and CommonJS-like environments where a proper `window`
+		// is present, execute the factory and get jQuery.
+		// For environments that do not have a `window` with a `document`
+		// (such as Node.js), expose a factory as module.exports.
+		// This accentuates the need for the creation of a real `window`.
+		// e.g. var jQuery = require("jquery")(window);
+		// See ticket #14549 for more info.
+		module.exports = global.document ?
+			factory( global, true ) :
+			function( w ) {
+				if ( !w.document ) {
+					throw new Error( "jQuery requires a window with a document" );
+				}
+				return factory( w );
+			};
+	} else {
+		factory( global );
+	}
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+	return arr.flat.call( array );
+} : function( array ) {
+	return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+		// Support: Chrome <=57, Firefox <=52
+		// In some browsers, typeof returns "function" for HTML <object> elements
+		// (i.e., `typeof document.createElement( "object" ) === "function"`).
+		// We don't want to classify *any* DOM node as a function.
+		// Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5
+		// Plus for old WebKit, typeof returns "function" for HTML collections
+		// (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756)
+		return typeof obj === "function" && typeof obj.nodeType !== "number" &&
+			typeof obj.item !== "function";
+	};
+
+
+var isWindow = function isWindow( obj ) {
+		return obj != null && obj === obj.window;
+	};
+
+
+var document = window.document;
+
+
+
+	var preservedScriptAttributes = {
+		type: true,
+		src: true,
+		nonce: true,
+		noModule: true
+	};
+
+	function DOMEval( code, node, doc ) {
+		doc = doc || document;
+
+		var i, val,
+			script = doc.createElement( "script" );
+
+		script.text = code;
+		if ( node ) {
+			for ( i in preservedScriptAttributes ) {
+
+				// Support: Firefox 64+, Edge 18+
+				// Some browsers don't support the "nonce" property on scripts.
+				// On the other hand, just using `getAttribute` is not enough as
+				// the `nonce` attribute is reset to an empty string whenever it
+				// becomes browsing-context connected.
+				// See https://github.com/whatwg/html/issues/2369
+				// See https://html.spec.whatwg.org/#nonce-attributes
+				// The `node.getAttribute` check was added for the sake of
+				// `jQuery.globalEval` so that it can fake a nonce-containing node
+				// via an object.
+				val = node[ i ] || node.getAttribute && node.getAttribute( i );
+				if ( val ) {
+					script.setAttribute( i, val );
+				}
+			}
+		}
+		doc.head.appendChild( script ).parentNode.removeChild( script );
+	}
+
+
+function toType( obj ) {
+	if ( obj == null ) {
+		return obj + "";
+	}
+
+	// Support: Android <=2.3 only (functionish RegExp)
+	return typeof obj === "object" || typeof obj === "function" ?
+		class2type[ toString.call( obj ) ] || "object" :
+		typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+	version = "3.6.0",
+
+	// Define a local copy of jQuery
+	jQuery = function( selector, context ) {
+
+		// The jQuery object is actually just the init constructor 'enhanced'
+		// Need init if jQuery is called (just allow error to be thrown if not included)
+		return new jQuery.fn.init( selector, context );
+	};
+
+jQuery.fn = jQuery.prototype = {
+
+	// The current version of jQuery being used
+	jquery: version,
+
+	constructor: jQuery,
+
+	// The default length of a jQuery object is 0
+	length: 0,
+
+	toArray: function() {
+		return slice.call( this );
+	},
+
+	// Get the Nth element in the matched element set OR
+	// Get the whole matched element set as a clean array
+	get: function( num ) {
+
+		// Return all the elements in a clean array
+		if ( num == null ) {
+			return slice.call( this );
+		}
+
+		// Return just the one element from the set
+		return num < 0 ? this[ num + this.length ] : this[ num ];
+	},
+
+	// Take an array of elements and push it onto the stack
+	// (returning the new matched element set)
+	pushStack: function( elems ) {
+
+		// Build a new jQuery matched element set
+		var ret = jQuery.merge( this.constructor(), elems );
+
+		// Add the old object onto the stack (as a reference)
+		ret.prevObject = this;
+
+		// Return the newly-formed element set
+		return ret;
+	},
+
+	// Execute a callback for every element in the matched set.
+	each: function( callback ) {
+		return jQuery.each( this, callback );
+	},
+
+	map: function( callback ) {
+		return this.pushStack( jQuery.map( this, function( elem, i ) {
+			return callback.call( elem, i, elem );
+		} ) );
+	},
+
+	slice: function() {
+		return this.pushStack( slice.apply( this, arguments ) );
+	},
+
+	first: function() {
+		return this.eq( 0 );
+	},
+
+	last: function() {
+		return this.eq( -1 );
+	},
+
+	even: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return ( i + 1 ) % 2;
+		} ) );
+	},
+
+	odd: function() {
+		return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+			return i % 2;
+		} ) );
+	},
+
+	eq: function( i ) {
+		var len = this.length,
+			j = +i + ( i < 0 ? len : 0 );
+		return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+	},
+
+	end: function() {
+		return this.prevObject || this.constructor();
+	},
+
+	// For internal use only.
+	// Behaves like an Array's method, not like a jQuery method.
+	push: push,
+	sort: arr.sort,
+	splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+	var options, name, src, copy, copyIsArray, clone,
+		target = arguments[ 0 ] || {},
+		i = 1,
+		length = arguments.length,
+		deep = false;
+
+	// Handle a deep copy situation
+	if ( typeof target === "boolean" ) {
+		deep = target;
+
+		// Skip the boolean and the target
+		target = arguments[ i ] || {};
+		i++;
+	}
+
+	// Handle case when target is a string or something (possible in deep copy)
+	if ( typeof target !== "object" && !isFunction( target ) ) {
+		target = {};
+	}
+
+	// Extend jQuery itself if only one argument is passed
+	if ( i === length ) {
+		target = this;
+		i--;
+	}
+
+	for ( ; i < length; i++ ) {
+
+		// Only deal with non-null/undefined values
+		if ( ( options = arguments[ i ] ) != null ) {
+
+			// Extend the base object
+			for ( name in options ) {
+				copy = options[ name ];
+
+				// Prevent Object.prototype pollution
+				// Prevent never-ending loop
+				if ( name === "__proto__" || target === copy ) {
+					continue;
+				}
+
+				// Recurse if we're merging plain objects or arrays
+				if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+					( copyIsArray = Array.isArray( copy ) ) ) ) {
+					src = target[ name ];
+
+					// Ensure proper type for the source value
+					if ( copyIsArray && !Array.isArray( src ) ) {
+						clone = [];
+					} else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+						clone = {};
+					} else {
+						clone = src;
+					}
+					copyIsArray = false;
+
+					// Never move original objects, clone them
+					target[ name ] = jQuery.extend( deep, clone, copy );
+
+				// Don't bring in undefined values
+				} else if ( copy !== undefined ) {
+					target[ name ] = copy;
+				}
+			}
+		}
+	}
+
+	// Return the modified object
+	return target;
+};
+
+jQuery.extend( {
+
+	// Unique for each copy of jQuery on the page
+	expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+	// Assume jQuery is ready without the ready module
+	isReady: true,
+
+	error: function( msg ) {
+		throw new Error( msg );
+	},
+
+	noop: function() {},
+
+	isPlainObject: function( obj ) {
+		var proto, Ctor;
+
+		// Detect obvious negatives
+		// Use toString instead of jQuery.type to catch host objects
+		if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+			return false;
+		}
+
+		proto = getProto( obj );
+
+		// Objects with no prototype (e.g., `Object.create( null )`) are plain
+		if ( !proto ) {
+			return true;
+		}
+
+		// Objects with prototype are plain iff they were constructed by a global Object function
+		Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+		return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+	},
+
+	isEmptyObject: function( obj ) {
+		var name;
+
+		for ( name in obj ) {
+			return false;
+		}
+		return true;
+	},
+
+	// Evaluates a script in a provided context; falls back to the global one
+	// if not specified.
+	globalEval: function( code, options, doc ) {
+		DOMEval( code, { nonce: options && options.nonce }, doc );
+	},
+
+	each: function( obj, callback ) {
+		var length, i = 0;
+
+		if ( isArrayLike( obj ) ) {
+			length = obj.length;
+			for ( ; i < length; i++ ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		} else {
+			for ( i in obj ) {
+				if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+					break;
+				}
+			}
+		}
+
+		return obj;
+	},
+
+	// results is for internal usage only
+	makeArray: function( arr, results ) {
+		var ret = results || [];
+
+		if ( arr != null ) {
+			if ( isArrayLike( Object( arr ) ) ) {
+				jQuery.merge( ret,
+					typeof arr === "string" ?
+						[ arr ] : arr
+				);
+			} else {
+				push.call( ret, arr );
+			}
+		}
+
+		return ret;
+	},
+
+	inArray: function( elem, arr, i ) {
+		return arr == null ? -1 : indexOf.call( arr, elem, i );
+	},
+
+	// Support: Android <=4.0 only, PhantomJS 1 only
+	// push.apply(_, arraylike) throws on ancient WebKit
+	merge: function( first, second ) {
+		var len = +second.length,
+			j = 0,
+			i = first.length;
+
+		for ( ; j < len; j++ ) {
+			first[ i++ ] = second[ j ];
+		}
+
+		first.length = i;
+
+		return first;
+	},
+
+	grep: function( elems, callback, invert ) {
+		var callbackInverse,
+			matches = [],
+			i = 0,
+			length = elems.length,
+			callbackExpect = !invert;
+
+		// Go through the array, only saving the items
+		// that pass the validator function
+		for ( ; i < length; i++ ) {
+			callbackInverse = !callback( elems[ i ], i );
+			if ( callbackInverse !== callbackExpect ) {
+				matches.push( elems[ i ] );
+			}
+		}
+
+		return matches;
+	},
+
+	// arg is for internal usage only
+	map: function( elems, callback, arg ) {
+		var length, value,
+			i = 0,
+			ret = [];
+
+		// Go through the array, translating each of the items to their new values
+		if ( isArrayLike( elems ) ) {
+			length = elems.length;
+			for ( ; i < length; i++ ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+
+		// Go through every key on the object,
+		} else {
+			for ( i in elems ) {
+				value = callback( elems[ i ], i, arg );
+
+				if ( value != null ) {
+					ret.push( value );
+				}
+			}
+		}
+
+		// Flatten any nested arrays
+		return flat( ret );
+	},
+
+	// A global GUID counter for objects
+	guid: 1,
+
+	// jQuery.support is not used in Core but other projects attach their
+	// properties to it so it needs to exist.
+	support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+	jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+	function( _i, name ) {
+		class2type[ "[object " + name + "]" ] = name.toLowerCase();
+	} );
+
+function isArrayLike( obj ) {
+
+	// Support: real iOS 8.2 only (not reproducible in simulator)
+	// `in` check used to prevent JIT error (gh-2145)
+	// hasOwn isn't used here due to false negatives
+	// regarding Nodelist length in IE
+	var length = !!obj && "length" in obj && obj.length,
+		type = toType( obj );
+
+	if ( isFunction( obj ) || isWindow( obj ) ) {
+		return false;
+	}
+
+	return type === "array" || length === 0 ||
+		typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.6
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2021-02-16
+ */
+( function( window ) {
+var i,
+	support,
+	Expr,
+	getText,
+	isXML,
+	tokenize,
+	compile,
+	select,
+	outermostContext,
+	sortInput,
+	hasDuplicate,
+
+	// Local document vars
+	setDocument,
+	document,
+	docElem,
+	documentIsHTML,
+	rbuggyQSA,
+	rbuggyMatches,
+	matches,
+	contains,
+
+	// Instance-specific data
+	expando = "sizzle" + 1 * new Date(),
+	preferredDoc = window.document,
+	dirruns = 0,
+	done = 0,
+	classCache = createCache(),
+	tokenCache = createCache(),
+	compilerCache = createCache(),
+	nonnativeSelectorCache = createCache(),
+	sortOrder = function( a, b ) {
+		if ( a === b ) {
+			hasDuplicate = true;
+		}
+		return 0;
+	},
+
+	// Instance methods
+	hasOwn = ( {} ).hasOwnProperty,
+	arr = [],
+	pop = arr.pop,
+	pushNative = arr.push,
+	push = arr.push,
+	slice = arr.slice,
+
+	// Use a stripped-down indexOf as it's faster than native
+	// https://jsperf.com/thor-indexof-vs-for/5
+	indexOf = function( list, elem ) {
+		var i = 0,
+			len = list.length;
+		for ( ; i < len; i++ ) {
+			if ( list[ i ] === elem ) {
+				return i;
+			}
+		}
+		return -1;
+	},
+
+	booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+		"ismap|loop|multiple|open|readonly|required|scoped",
+
+	// Regular expressions
+
+	// http://www.w3.org/TR/css3-selectors/#whitespace
+	whitespace = "[\\x20\\t\\r\\n\\f]",
+
+	// https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+	identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+		"?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+	// Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+	attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+		// Operator (capture 2)
+		"*([*^$|!~]?=)" + whitespace +
+
+		// "Attribute values must be CSS identifiers [capture 5]
+		// or strings [capture 3 or capture 4]"
+		"*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+		whitespace + "*\\]",
+
+	pseudos = ":(" + identifier + ")(?:\\((" +
+
+		// To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+		// 1. quoted (capture 3; capture 4 or capture 5)
+		"('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+		// 2. simple (capture 6)
+		"((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+		// 3. anything else (capture 2)
+		".*" +
+		")\\)|)",
+
+	// Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+	rwhitespace = new RegExp( whitespace + "+", "g" ),
+	rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+		whitespace + "+$", "g" ),
+
+	rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+	rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+		"*" ),
+	rdescend = new RegExp( whitespace + "|>" ),
+
+	rpseudo = new RegExp( pseudos ),
+	ridentifier = new RegExp( "^" + identifier + "$" ),
+
+	matchExpr = {
+		"ID": new RegExp( "^#(" + identifier + ")" ),
+		"CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+		"TAG": new RegExp( "^(" + identifier + "|[*])" ),
+		"ATTR": new RegExp( "^" + attributes ),
+		"PSEUDO": new RegExp( "^" + pseudos ),
+		"CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+			whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+			whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+		"bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+		// For use in libraries implementing .is()
+		// We use this for POS matching in `select`
+		"needsContext": new RegExp( "^" + whitespace +
+			"*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+			"*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+	},
+
+	rhtml = /HTML$/i,
+	rinputs = /^(?:input|select|textarea|button)$/i,
+	rheader = /^h\d$/i,
+
+	rnative = /^[^{]+\{\s*\[native \w/,
+
+	// Easily-parseable/retrievable ID or TAG or CLASS selectors
+	rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+	rsibling = /[+~]/,
+
+	// CSS escapes
+	// http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+	runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+	funescape = function( escape, nonHex ) {
+		var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+		return nonHex ?
+
+			// Strip the backslash prefix from a non-hex escape sequence
+			nonHex :
+
+			// Replace a hexadecimal escape sequence with the encoded Unicode code point
+			// Support: IE <=11+
+			// For values outside the Basic Multilingual Plane (BMP), manually construct a
+			// surrogate pair
+			high < 0 ?
+				String.fromCharCode( high + 0x10000 ) :
+				String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+	},
+
+	// CSS string/identifier serialization
+	// https://drafts.csswg.org/cssom/#common-serializing-idioms
+	rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+	fcssescape = function( ch, asCodePoint ) {
+		if ( asCodePoint ) {
+
+			// U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+			if ( ch === "\0" ) {
+				return "\uFFFD";
+			}
+
+			// Control characters and (dependent upon position) numbers get escaped as code points
+			return ch.slice( 0, -1 ) + "\\" +
+				ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+		}
+
+		// Other potentially-special ASCII characters get backslash-escaped
+		return "\\" + ch;
+	},
+
+	// Used for iframes
+	// See setDocument()
+	// Removing the function wrapper causes a "Permission Denied"
+	// error in IE
+	unloadHandler = function() {
+		setDocument();
+	},
+
+	inDisabledFieldset = addCombinator(
+		function( elem ) {
+			return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+		},
+		{ dir: "parentNode", next: "legend" }
+	);
+
+// Optimize for push.apply( _, NodeList )
+try {
+	push.apply(
+		( arr = slice.call( preferredDoc.childNodes ) ),
+		preferredDoc.childNodes
+	);
+
+	// Support: Android<4.0
+	// Detect silently failing push.apply
+	// eslint-disable-next-line no-unused-expressions
+	arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+	push = { apply: arr.length ?
+
+		// Leverage slice if possible
+		function( target, els ) {
+			pushNative.apply( target, slice.call( els ) );
+		} :
+
+		// Support: IE<9
+		// Otherwise append directly
+		function( target, els ) {
+			var j = target.length,
+				i = 0;
+
+			// Can't trust NodeList.length
+			while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+			target.length = j - 1;
+		}
+	};
+}
+
+function Sizzle( selector, context, results, seed ) {
+	var m, i, elem, nid, match, groups, newSelector,
+		newContext = context && context.ownerDocument,
+
+		// nodeType defaults to 9, since context defaults to document
+		nodeType = context ? context.nodeType : 9;
+
+	results = results || [];
+
+	// Return early from calls with invalid selector or context
+	if ( typeof selector !== "string" || !selector ||
+		nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+		return results;
+	}
+
+	// Try to shortcut find operations (as opposed to filters) in HTML documents
+	if ( !seed ) {
+		setDocument( context );
+		context = context || document;
+
+		if ( documentIsHTML ) {
+
+			// If the selector is sufficiently simple, try using a "get*By*" DOM method
+			// (excepting DocumentFragment context, where the methods don't exist)
+			if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+				// ID selector
+				if ( ( m = match[ 1 ] ) ) {
+
+					// Document context
+					if ( nodeType === 9 ) {
+						if ( ( elem = context.getElementById( m ) ) ) {
+
+							// Support: IE, Opera, Webkit
+							// TODO: identify versions
+							// getElementById can match elements by name instead of ID
+							if ( elem.id === m ) {
+								results.push( elem );
+								return results;
+							}
+						} else {
+							return results;
+						}
+
+					// Element context
+					} else {
+
+						// Support: IE, Opera, Webkit
+						// TODO: identify versions
+						// getElementById can match elements by name instead of ID
+						if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+							contains( context, elem ) &&
+							elem.id === m ) {
+
+							results.push( elem );
+							return results;
+						}
+					}
+
+				// Type selector
+				} else if ( match[ 2 ] ) {
+					push.apply( results, context.getElementsByTagName( selector ) );
+					return results;
+
+				// Class selector
+				} else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+					context.getElementsByClassName ) {
+
+					push.apply( results, context.getElementsByClassName( m ) );
+					return results;
+				}
+			}
+
+			// Take advantage of querySelectorAll
+			if ( support.qsa &&
+				!nonnativeSelectorCache[ selector + " " ] &&
+				( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+				// Support: IE 8 only
+				// Exclude object elements
+				( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+				newSelector = selector;
+				newContext = context;
+
+				// qSA considers elements outside a scoping root when evaluating child or
+				// descendant combinators, which is not what we want.
+				// In such cases, we work around the behavior by prefixing every selector in the
+				// list with an ID selector referencing the scope context.
+				// The technique has to be used as well when a leading combinator is used
+				// as such selectors are not recognized by querySelectorAll.
+				// Thanks to Andrew Dupont for this technique.
+				if ( nodeType === 1 &&
+					( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+					// Expand context for sibling selectors
+					newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+						context;
+
+					// We can use :scope instead of the ID hack if the browser
+					// supports it & if we're not changing the context.
+					if ( newContext !== context || !support.scope ) {
+
+						// Capture the context ID, setting it first if necessary
+						if ( ( nid = context.getAttribute( "id" ) ) ) {
+							nid = nid.replace( rcssescape, fcssescape );
+						} else {
+							context.setAttribute( "id", ( nid = expando ) );
+						}
+					}
+
+					// Prefix every selector in the list
+					groups = tokenize( selector );
+					i = groups.length;
+					while ( i-- ) {
+						groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+							toSelector( groups[ i ] );
+					}
+					newSelector = groups.join( "," );
+				}
+
+				try {
+					push.apply( results,
+						newContext.querySelectorAll( newSelector )
+					);
+					return results;
+				} catch ( qsaError ) {
+					nonnativeSelectorCache( selector, true );
+				} finally {
+					if ( nid === expando ) {
+						context.removeAttribute( "id" );
+					}
+				}
+			}
+		}
+	}
+
+	// All others
+	return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ *	property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ *	deleting the oldest entry
+ */
+function createCache() {
+	var keys = [];
+
+	function cache( key, value ) {
+
+		// Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+		if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+			// Only keep the most recent entries
+			delete cache[ keys.shift() ];
+		}
+		return ( cache[ key + " " ] = value );
+	}
+	return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+	fn[ expando ] = true;
+	return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+	var el = document.createElement( "fieldset" );
+
+	try {
+		return !!fn( el );
+	} catch ( e ) {
+		return false;
+	} finally {
+
+		// Remove from its parent by default
+		if ( el.parentNode ) {
+			el.parentNode.removeChild( el );
+		}
+
+		// release memory in IE
+		el = null;
+	}
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+	var arr = attrs.split( "|" ),
+		i = arr.length;
+
+	while ( i-- ) {
+		Expr.attrHandle[ arr[ i ] ] = handler;
+	}
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+	var cur = b && a,
+		diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+			a.sourceIndex - b.sourceIndex;
+
+	// Use IE sourceIndex if available on both nodes
+	if ( diff ) {
+		return diff;
+	}
+
+	// Check if b follows a
+	if ( cur ) {
+		while ( ( cur = cur.nextSibling ) ) {
+			if ( cur === b ) {
+				return -1;
+			}
+		}
+	}
+
+	return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return name === "input" && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+	return function( elem ) {
+		var name = elem.nodeName.toLowerCase();
+		return ( name === "input" || name === "button" ) && elem.type === type;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+	// Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+	return function( elem ) {
+
+		// Only certain elements can match :enabled or :disabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+		// https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+		if ( "form" in elem ) {
+
+			// Check for inherited disabledness on relevant non-disabled elements:
+			// * listed form-associated elements in a disabled fieldset
+			//   https://html.spec.whatwg.org/multipage/forms.html#category-listed
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+			// * option elements in a disabled optgroup
+			//   https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+			// All such elements have a "form" property.
+			if ( elem.parentNode && elem.disabled === false ) {
+
+				// Option elements defer to a parent optgroup if present
+				if ( "label" in elem ) {
+					if ( "label" in elem.parentNode ) {
+						return elem.parentNode.disabled === disabled;
+					} else {
+						return elem.disabled === disabled;
+					}
+				}
+
+				// Support: IE 6 - 11
+				// Use the isDisabled shortcut property to check for disabled fieldset ancestors
+				return elem.isDisabled === disabled ||
+
+					// Where there is no isDisabled, check manually
+					/* jshint -W018 */
+					elem.isDisabled !== !disabled &&
+					inDisabledFieldset( elem ) === disabled;
+			}
+
+			return elem.disabled === disabled;
+
+		// Try to winnow out elements that can't be disabled before trusting the disabled property.
+		// Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+		// even exist on them, let alone have a boolean value.
+		} else if ( "label" in elem ) {
+			return elem.disabled === disabled;
+		}
+
+		// Remaining elements are neither :enabled nor :disabled
+		return false;
+	};
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+	return markFunction( function( argument ) {
+		argument = +argument;
+		return markFunction( function( seed, matches ) {
+			var j,
+				matchIndexes = fn( [], seed.length, argument ),
+				i = matchIndexes.length;
+
+			// Match elements found at the specified indexes
+			while ( i-- ) {
+				if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+					seed[ j ] = !( matches[ j ] = seed[ j ] );
+				}
+			}
+		} );
+	} );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+	return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+	var namespace = elem && elem.namespaceURI,
+		docElem = elem && ( elem.ownerDocument || elem ).documentElement;
+
+	// Support: IE <=8
+	// Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+	// https://bugs.jquery.com/ticket/4833
+	return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+	var hasCompare, subWindow,
+		doc = node ? node.ownerDocument || node : preferredDoc;
+
+	// Return early if doc is invalid or already selected
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+		return document;
+	}
+
+	// Update global variables
+	document = doc;
+	docElem = document.documentElement;
+	documentIsHTML = !isXML( document );
+
+	// Support: IE 9 - 11+, Edge 12 - 18+
+	// Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( preferredDoc != document &&
+		( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+		// Support: IE 11, Edge
+		if ( subWindow.addEventListener ) {
+			subWindow.addEventListener( "unload", unloadHandler, false );
+
+		// Support: IE 9 - 10 only
+		} else if ( subWindow.attachEvent ) {
+			subWindow.attachEvent( "onunload", unloadHandler );
+		}
+	}
+
+	// Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+	// Safari 4 - 5 only, Opera <=11.6 - 12.x only
+	// IE/Edge & older browsers don't support the :scope pseudo-class.
+	// Support: Safari 6.0 only
+	// Safari 6.0 supports :scope but it's an alias of :root there.
+	support.scope = assert( function( el ) {
+		docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+		return typeof el.querySelectorAll !== "undefined" &&
+			!el.querySelectorAll( ":scope fieldset div" ).length;
+	} );
+
+	/* Attributes
+	---------------------------------------------------------------------- */
+
+	// Support: IE<8
+	// Verify that getAttribute really returns attributes and not properties
+	// (excepting IE8 booleans)
+	support.attributes = assert( function( el ) {
+		el.className = "i";
+		return !el.getAttribute( "className" );
+	} );
+
+	/* getElement(s)By*
+	---------------------------------------------------------------------- */
+
+	// Check if getElementsByTagName("*") returns only elements
+	support.getElementsByTagName = assert( function( el ) {
+		el.appendChild( document.createComment( "" ) );
+		return !el.getElementsByTagName( "*" ).length;
+	} );
+
+	// Support: IE<9
+	support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+	// Support: IE<10
+	// Check if getElementById returns elements by name
+	// The broken getElementById methods don't pick up programmatically-set names,
+	// so use a roundabout getElementsByName test
+	support.getById = assert( function( el ) {
+		docElem.appendChild( el ).id = expando;
+		return !document.getElementsByName || !document.getElementsByName( expando ).length;
+	} );
+
+	// ID filter and find
+	if ( support.getById ) {
+		Expr.filter[ "ID" ] = function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				return elem.getAttribute( "id" ) === attrId;
+			};
+		};
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var elem = context.getElementById( id );
+				return elem ? [ elem ] : [];
+			}
+		};
+	} else {
+		Expr.filter[ "ID" ] =  function( id ) {
+			var attrId = id.replace( runescape, funescape );
+			return function( elem ) {
+				var node = typeof elem.getAttributeNode !== "undefined" &&
+					elem.getAttributeNode( "id" );
+				return node && node.value === attrId;
+			};
+		};
+
+		// Support: IE 6 - 7 only
+		// getElementById is not reliable as a find shortcut
+		Expr.find[ "ID" ] = function( id, context ) {
+			if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+				var node, i, elems,
+					elem = context.getElementById( id );
+
+				if ( elem ) {
+
+					// Verify the id attribute
+					node = elem.getAttributeNode( "id" );
+					if ( node && node.value === id ) {
+						return [ elem ];
+					}
+
+					// Fall back on getElementsByName
+					elems = context.getElementsByName( id );
+					i = 0;
+					while ( ( elem = elems[ i++ ] ) ) {
+						node = elem.getAttributeNode( "id" );
+						if ( node && node.value === id ) {
+							return [ elem ];
+						}
+					}
+				}
+
+				return [];
+			}
+		};
+	}
+
+	// Tag
+	Expr.find[ "TAG" ] = support.getElementsByTagName ?
+		function( tag, context ) {
+			if ( typeof context.getElementsByTagName !== "undefined" ) {
+				return context.getElementsByTagName( tag );
+
+			// DocumentFragment nodes don't have gEBTN
+			} else if ( support.qsa ) {
+				return context.querySelectorAll( tag );
+			}
+		} :
+
+		function( tag, context ) {
+			var elem,
+				tmp = [],
+				i = 0,
+
+				// By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+				results = context.getElementsByTagName( tag );
+
+			// Filter out possible comments
+			if ( tag === "*" ) {
+				while ( ( elem = results[ i++ ] ) ) {
+					if ( elem.nodeType === 1 ) {
+						tmp.push( elem );
+					}
+				}
+
+				return tmp;
+			}
+			return results;
+		};
+
+	// Class
+	Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+		if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+			return context.getElementsByClassName( className );
+		}
+	};
+
+	/* QSA/matchesSelector
+	---------------------------------------------------------------------- */
+
+	// QSA and matchesSelector support
+
+	// matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+	rbuggyMatches = [];
+
+	// qSa(:focus) reports false when true (Chrome 21)
+	// We allow this because of a bug in IE8/9 that throws an error
+	// whenever `document.activeElement` is accessed on an iframe
+	// So, we allow :focus to pass through QSA all the time to avoid the IE error
+	// See https://bugs.jquery.com/ticket/13378
+	rbuggyQSA = [];
+
+	if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+		// Build QSA regex
+		// Regex strategy adopted from Diego Perini
+		assert( function( el ) {
+
+			var input;
+
+			// Select is set to empty string on purpose
+			// This is to test IE's treatment of not explicitly
+			// setting a boolean content attribute,
+			// since its presence should be enough
+			// https://bugs.jquery.com/ticket/12359
+			docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
+				"<select id='" + expando + "-\r\\' msallowcapture=''>" +
+				"<option selected=''></option></select>";
+
+			// Support: IE8, Opera 11-12.16
+			// Nothing should be selected when empty strings follow ^= or $= or *=
+			// The test attribute must be unknown in Opera but "safe" for WinRT
+			// https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+			if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+				rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+			}
+
+			// Support: IE8
+			// Boolean attributes and "value" are not treated correctly
+			if ( !el.querySelectorAll( "[selected]" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+			}
+
+			// Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+			if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+				rbuggyQSA.push( "~=" );
+			}
+
+			// Support: IE 11+, Edge 15 - 18+
+			// IE 11/Edge don't find elements on a `[name='']` query in some cases.
+			// Adding a temporary attribute to the document before the selection works
+			// around the issue.
+			// Interestingly, IE 10 & older don't seem to have the issue.
+			input = document.createElement( "input" );
+			input.setAttribute( "name", "" );
+			el.appendChild( input );
+			if ( !el.querySelectorAll( "[name='']" ).length ) {
+				rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+					whitespace + "*(?:''|\"\")" );
+			}
+
+			// Webkit/Opera - :checked should return selected option elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			// IE8 throws error here and will not see later tests
+			if ( !el.querySelectorAll( ":checked" ).length ) {
+				rbuggyQSA.push( ":checked" );
+			}
+
+			// Support: Safari 8+, iOS 8+
+			// https://bugs.webkit.org/show_bug.cgi?id=136851
+			// In-page `selector#id sibling-combinator selector` fails
+			if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+				rbuggyQSA.push( ".#.+[+~]" );
+			}
+
+			// Support: Firefox <=3.6 - 5 only
+			// Old Firefox doesn't throw on a badly-escaped identifier.
+			el.querySelectorAll( "\\\f" );
+			rbuggyQSA.push( "[\\r\\n\\f]" );
+		} );
+
+		assert( function( el ) {
+			el.innerHTML = "<a href='' disabled='disabled'></a>" +
+				"<select disabled='disabled'><option/></select>";
+
+			// Support: Windows 8 Native Apps
+			// The type and name attributes are restricted during .innerHTML assignment
+			var input = document.createElement( "input" );
+			input.setAttribute( "type", "hidden" );
+			el.appendChild( input ).setAttribute( "name", "D" );
+
+			// Support: IE8
+			// Enforce case-sensitivity of name attribute
+			if ( el.querySelectorAll( "[name=d]" ).length ) {
+				rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+			}
+
+			// FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+			// IE8 throws error here and will not see later tests
+			if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: IE9-11+
+			// IE's :disabled selector does not pick up the children of disabled fieldsets
+			docElem.appendChild( el ).disabled = true;
+			if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+				rbuggyQSA.push( ":enabled", ":disabled" );
+			}
+
+			// Support: Opera 10 - 11 only
+			// Opera 10-11 does not throw on post-comma invalid pseudos
+			el.querySelectorAll( "*,:x" );
+			rbuggyQSA.push( ",.*:" );
+		} );
+	}
+
+	if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+		docElem.webkitMatchesSelector ||
+		docElem.mozMatchesSelector ||
+		docElem.oMatchesSelector ||
+		docElem.msMatchesSelector ) ) ) ) {
+
+		assert( function( el ) {
+
+			// Check to see if it's possible to do matchesSelector
+			// on a disconnected node (IE 9)
+			support.disconnectedMatch = matches.call( el, "*" );
+
+			// This should fail with an exception
+			// Gecko does not error, returns false instead
+			matches.call( el, "[s!='']:x" );
+			rbuggyMatches.push( "!=", pseudos );
+		} );
+	}
+
+	rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+	rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+	/* Contains
+	---------------------------------------------------------------------- */
+	hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+	// Element contains another
+	// Purposefully self-exclusive
+	// As in, an element does not contain itself
+	contains = hasCompare || rnative.test( docElem.contains ) ?
+		function( a, b ) {
+			var adown = a.nodeType === 9 ? a.documentElement : a,
+				bup = b && b.parentNode;
+			return a === bup || !!( bup && bup.nodeType === 1 && (
+				adown.contains ?
+					adown.contains( bup ) :
+					a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+			) );
+		} :
+		function( a, b ) {
+			if ( b ) {
+				while ( ( b = b.parentNode ) ) {
+					if ( b === a ) {
+						return true;
+					}
+				}
+			}
+			return false;
+		};
+
+	/* Sorting
+	---------------------------------------------------------------------- */
+
+	// Document order sorting
+	sortOrder = hasCompare ?
+	function( a, b ) {
+
+		// Flag for duplicate removal
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		// Sort on method existence if only one input has compareDocumentPosition
+		var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+		if ( compare ) {
+			return compare;
+		}
+
+		// Calculate position if both inputs belong to the same document
+		// Support: IE 11+, Edge 17 - 18+
+		// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+		// two documents; shallow comparisons work.
+		// eslint-disable-next-line eqeqeq
+		compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+			a.compareDocumentPosition( b ) :
+
+			// Otherwise we know they are disconnected
+			1;
+
+		// Disconnected nodes
+		if ( compare & 1 ||
+			( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+			// Choose the first element that is related to our preferred document
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( a == document || a.ownerDocument == preferredDoc &&
+				contains( preferredDoc, a ) ) {
+				return -1;
+			}
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			// eslint-disable-next-line eqeqeq
+			if ( b == document || b.ownerDocument == preferredDoc &&
+				contains( preferredDoc, b ) ) {
+				return 1;
+			}
+
+			// Maintain original order
+			return sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+		}
+
+		return compare & 4 ? -1 : 1;
+	} :
+	function( a, b ) {
+
+		// Exit early if the nodes are identical
+		if ( a === b ) {
+			hasDuplicate = true;
+			return 0;
+		}
+
+		var cur,
+			i = 0,
+			aup = a.parentNode,
+			bup = b.parentNode,
+			ap = [ a ],
+			bp = [ b ];
+
+		// Parentless nodes are either documents or disconnected
+		if ( !aup || !bup ) {
+
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			return a == document ? -1 :
+				b == document ? 1 :
+				/* eslint-enable eqeqeq */
+				aup ? -1 :
+				bup ? 1 :
+				sortInput ?
+				( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+				0;
+
+		// If the nodes are siblings, we can do a quick check
+		} else if ( aup === bup ) {
+			return siblingCheck( a, b );
+		}
+
+		// Otherwise we need full lists of their ancestors for comparison
+		cur = a;
+		while ( ( cur = cur.parentNode ) ) {
+			ap.unshift( cur );
+		}
+		cur = b;
+		while ( ( cur = cur.parentNode ) ) {
+			bp.unshift( cur );
+		}
+
+		// Walk down the tree looking for a discrepancy
+		while ( ap[ i ] === bp[ i ] ) {
+			i++;
+		}
+
+		return i ?
+
+			// Do a sibling check if the nodes have a common ancestor
+			siblingCheck( ap[ i ], bp[ i ] ) :
+
+			// Otherwise nodes in our document sort first
+			// Support: IE 11+, Edge 17 - 18+
+			// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+			// two documents; shallow comparisons work.
+			/* eslint-disable eqeqeq */
+			ap[ i ] == preferredDoc ? -1 :
+			bp[ i ] == preferredDoc ? 1 :
+			/* eslint-enable eqeqeq */
+			0;
+	};
+
+	return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+	return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+	setDocument( elem );
+
+	if ( support.matchesSelector && documentIsHTML &&
+		!nonnativeSelectorCache[ expr + " " ] &&
+		( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+		( !rbuggyQSA     || !rbuggyQSA.test( expr ) ) ) {
+
+		try {
+			var ret = matches.call( elem, expr );
+
+			// IE 9's matchesSelector returns false on disconnected nodes
+			if ( ret || support.disconnectedMatch ||
+
+				// As well, disconnected nodes are said to be in a document
+				// fragment in IE 9
+				elem.document && elem.document.nodeType !== 11 ) {
+				return ret;
+			}
+		} catch ( e ) {
+			nonnativeSelectorCache( expr, true );
+		}
+	}
+
+	return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( context.ownerDocument || context ) != document ) {
+		setDocument( context );
+	}
+	return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+	// Set document vars if needed
+	// Support: IE 11+, Edge 17 - 18+
+	// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+	// two documents; shallow comparisons work.
+	// eslint-disable-next-line eqeqeq
+	if ( ( elem.ownerDocument || elem ) != document ) {
+		setDocument( elem );
+	}
+
+	var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+		// Don't get fooled by Object.prototype properties (jQuery #13807)
+		val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+			fn( elem, name, !documentIsHTML ) :
+			undefined;
+
+	return val !== undefined ?
+		val :
+		support.attributes || !documentIsHTML ?
+			elem.getAttribute( name ) :
+			( val = elem.getAttributeNode( name ) ) && val.specified ?
+				val.value :
+				null;
+};
+
+Sizzle.escape = function( sel ) {
+	return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+	throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+	var elem,
+		duplicates = [],
+		j = 0,
+		i = 0;
+
+	// Unless we *know* we can detect duplicates, assume their presence
+	hasDuplicate = !support.detectDuplicates;
+	sortInput = !support.sortStable && results.slice( 0 );
+	results.sort( sortOrder );
+
+	if ( hasDuplicate ) {
+		while ( ( elem = results[ i++ ] ) ) {
+			if ( elem === results[ i ] ) {
+				j = duplicates.push( i );
+			}
+		}
+		while ( j-- ) {
+			results.splice( duplicates[ j ], 1 );
+		}
+	}
+
+	// Clear input after sorting to release objects
+	// See https://github.com/jquery/sizzle/pull/225
+	sortInput = null;
+
+	return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+	var node,
+		ret = "",
+		i = 0,
+		nodeType = elem.nodeType;
+
+	if ( !nodeType ) {
+
+		// If no nodeType, this is expected to be an array
+		while ( ( node = elem[ i++ ] ) ) {
+
+			// Do not traverse comment nodes
+			ret += getText( node );
+		}
+	} else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+		// Use textContent for elements
+		// innerText usage removed for consistency of new lines (jQuery #11153)
+		if ( typeof elem.textContent === "string" ) {
+			return elem.textContent;
+		} else {
+
+			// Traverse its children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				ret += getText( elem );
+			}
+		}
+	} else if ( nodeType === 3 || nodeType === 4 ) {
+		return elem.nodeValue;
+	}
+
+	// Do not include comment or processing instruction nodes
+
+	return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+	// Can be adjusted by the user
+	cacheLength: 50,
+
+	createPseudo: markFunction,
+
+	match: matchExpr,
+
+	attrHandle: {},
+
+	find: {},
+
+	relative: {
+		">": { dir: "parentNode", first: true },
+		" ": { dir: "parentNode" },
+		"+": { dir: "previousSibling", first: true },
+		"~": { dir: "previousSibling" }
+	},
+
+	preFilter: {
+		"ATTR": function( match ) {
+			match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+			// Move the given value to match[3] whether quoted or unquoted
+			match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+				match[ 5 ] || "" ).replace( runescape, funescape );
+
+			if ( match[ 2 ] === "~=" ) {
+				match[ 3 ] = " " + match[ 3 ] + " ";
+			}
+
+			return match.slice( 0, 4 );
+		},
+
+		"CHILD": function( match ) {
+
+			/* matches from matchExpr["CHILD"]
+				1 type (only|nth|...)
+				2 what (child|of-type)
+				3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+				4 xn-component of xn+y argument ([+-]?\d*n|)
+				5 sign of xn-component
+				6 x of xn-component
+				7 sign of y-component
+				8 y of y-component
+			*/
+			match[ 1 ] = match[ 1 ].toLowerCase();
+
+			if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+				// nth-* requires argument
+				if ( !match[ 3 ] ) {
+					Sizzle.error( match[ 0 ] );
+				}
+
+				// numeric x and y parameters for Expr.filter.CHILD
+				// remember that false/true cast respectively to 0/1
+				match[ 4 ] = +( match[ 4 ] ?
+					match[ 5 ] + ( match[ 6 ] || 1 ) :
+					2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+				match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+				// other types prohibit arguments
+			} else if ( match[ 3 ] ) {
+				Sizzle.error( match[ 0 ] );
+			}
+
+			return match;
+		},
+
+		"PSEUDO": function( match ) {
+			var excess,
+				unquoted = !match[ 6 ] && match[ 2 ];
+
+			if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+				return null;
+			}
+
+			// Accept quoted arguments as-is
+			if ( match[ 3 ] ) {
+				match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+			// Strip excess characters from unquoted arguments
+			} else if ( unquoted && rpseudo.test( unquoted ) &&
+
+				// Get excess from tokenize (recursively)
+				( excess = tokenize( unquoted, true ) ) &&
+
+				// advance to the next closing parenthesis
+				( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+				// excess is a negative index
+				match[ 0 ] = match[ 0 ].slice( 0, excess );
+				match[ 2 ] = unquoted.slice( 0, excess );
+			}
+
+			// Return only captures needed by the pseudo filter method (type and argument)
+			return match.slice( 0, 3 );
+		}
+	},
+
+	filter: {
+
+		"TAG": function( nodeNameSelector ) {
+			var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+			return nodeNameSelector === "*" ?
+				function() {
+					return true;
+				} :
+				function( elem ) {
+					return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+				};
+		},
+
+		"CLASS": function( className ) {
+			var pattern = classCache[ className + " " ];
+
+			return pattern ||
+				( pattern = new RegExp( "(^|" + whitespace +
+					")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+						className, function( elem ) {
+							return pattern.test(
+								typeof elem.className === "string" && elem.className ||
+								typeof elem.getAttribute !== "undefined" &&
+									elem.getAttribute( "class" ) ||
+								""
+							);
+				} );
+		},
+
+		"ATTR": function( name, operator, check ) {
+			return function( elem ) {
+				var result = Sizzle.attr( elem, name );
+
+				if ( result == null ) {
+					return operator === "!=";
+				}
+				if ( !operator ) {
+					return true;
+				}
+
+				result += "";
+
+				/* eslint-disable max-len */
+
+				return operator === "=" ? result === check :
+					operator === "!=" ? result !== check :
+					operator === "^=" ? check && result.indexOf( check ) === 0 :
+					operator === "*=" ? check && result.indexOf( check ) > -1 :
+					operator === "$=" ? check && result.slice( -check.length ) === check :
+					operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+					operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+					false;
+				/* eslint-enable max-len */
+
+			};
+		},
+
+		"CHILD": function( type, what, _argument, first, last ) {
+			var simple = type.slice( 0, 3 ) !== "nth",
+				forward = type.slice( -4 ) !== "last",
+				ofType = what === "of-type";
+
+			return first === 1 && last === 0 ?
+
+				// Shortcut for :nth-*(n)
+				function( elem ) {
+					return !!elem.parentNode;
+				} :
+
+				function( elem, _context, xml ) {
+					var cache, uniqueCache, outerCache, node, nodeIndex, start,
+						dir = simple !== forward ? "nextSibling" : "previousSibling",
+						parent = elem.parentNode,
+						name = ofType && elem.nodeName.toLowerCase(),
+						useCache = !xml && !ofType,
+						diff = false;
+
+					if ( parent ) {
+
+						// :(first|last|only)-(child|of-type)
+						if ( simple ) {
+							while ( dir ) {
+								node = elem;
+								while ( ( node = node[ dir ] ) ) {
+									if ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) {
+
+										return false;
+									}
+								}
+
+								// Reverse direction for :only-* (if we haven't yet done so)
+								start = dir = type === "only" && !start && "nextSibling";
+							}
+							return true;
+						}
+
+						start = [ forward ? parent.firstChild : parent.lastChild ];
+
+						// non-xml :nth-child(...) stores cache data on `parent`
+						if ( forward && useCache ) {
+
+							// Seek `elem` from a previously-cached index
+
+							// ...in a gzip-friendly way
+							node = parent;
+							outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+							// Support: IE <9 only
+							// Defend against cloned attroperties (jQuery gh-1709)
+							uniqueCache = outerCache[ node.uniqueID ] ||
+								( outerCache[ node.uniqueID ] = {} );
+
+							cache = uniqueCache[ type ] || [];
+							nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+							diff = nodeIndex && cache[ 2 ];
+							node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+							while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+								// Fallback to seeking `elem` from the start
+								( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+								// When found, cache indexes on `parent` and break
+								if ( node.nodeType === 1 && ++diff && node === elem ) {
+									uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+									break;
+								}
+							}
+
+						} else {
+
+							// Use previously-cached element index if available
+							if ( useCache ) {
+
+								// ...in a gzip-friendly way
+								node = elem;
+								outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+								// Support: IE <9 only
+								// Defend against cloned attroperties (jQuery gh-1709)
+								uniqueCache = outerCache[ node.uniqueID ] ||
+									( outerCache[ node.uniqueID ] = {} );
+
+								cache = uniqueCache[ type ] || [];
+								nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+								diff = nodeIndex;
+							}
+
+							// xml :nth-child(...)
+							// or :nth-last-child(...) or :nth(-last)?-of-type(...)
+							if ( diff === false ) {
+
+								// Use the same loop as above to seek `elem` from the start
+								while ( ( node = ++nodeIndex && node && node[ dir ] ||
+									( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+									if ( ( ofType ?
+										node.nodeName.toLowerCase() === name :
+										node.nodeType === 1 ) &&
+										++diff ) {
+
+										// Cache the index of each encountered element
+										if ( useCache ) {
+											outerCache = node[ expando ] ||
+												( node[ expando ] = {} );
+
+											// Support: IE <9 only
+											// Defend against cloned attroperties (jQuery gh-1709)
+											uniqueCache = outerCache[ node.uniqueID ] ||
+												( outerCache[ node.uniqueID ] = {} );
+
+											uniqueCache[ type ] = [ dirruns, diff ];
+										}
+
+										if ( node === elem ) {
+											break;
+										}
+									}
+								}
+							}
+						}
+
+						// Incorporate the offset, then check against cycle size
+						diff -= last;
+						return diff === first || ( diff % first === 0 && diff / first >= 0 );
+					}
+				};
+		},
+
+		"PSEUDO": function( pseudo, argument ) {
+
+			// pseudo-class names are case-insensitive
+			// http://www.w3.org/TR/selectors/#pseudo-classes
+			// Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+			// Remember that setFilters inherits from pseudos
+			var args,
+				fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+					Sizzle.error( "unsupported pseudo: " + pseudo );
+
+			// The user may use createPseudo to indicate that
+			// arguments are needed to create the filter function
+			// just as Sizzle does
+			if ( fn[ expando ] ) {
+				return fn( argument );
+			}
+
+			// But maintain support for old signatures
+			if ( fn.length > 1 ) {
+				args = [ pseudo, pseudo, "", argument ];
+				return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+					markFunction( function( seed, matches ) {
+						var idx,
+							matched = fn( seed, argument ),
+							i = matched.length;
+						while ( i-- ) {
+							idx = indexOf( seed, matched[ i ] );
+							seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+						}
+					} ) :
+					function( elem ) {
+						return fn( elem, 0, args );
+					};
+			}
+
+			return fn;
+		}
+	},
+
+	pseudos: {
+
+		// Potentially complex pseudos
+		"not": markFunction( function( selector ) {
+
+			// Trim the selector passed to compile
+			// to avoid treating leading and trailing
+			// spaces as combinators
+			var input = [],
+				results = [],
+				matcher = compile( selector.replace( rtrim, "$1" ) );
+
+			return matcher[ expando ] ?
+				markFunction( function( seed, matches, _context, xml ) {
+					var elem,
+						unmatched = matcher( seed, null, xml, [] ),
+						i = seed.length;
+
+					// Match elements unmatched by `matcher`
+					while ( i-- ) {
+						if ( ( elem = unmatched[ i ] ) ) {
+							seed[ i ] = !( matches[ i ] = elem );
+						}
+					}
+				} ) :
+				function( elem, _context, xml ) {
+					input[ 0 ] = elem;
+					matcher( input, null, xml, results );
+
+					// Don't keep the element (issue #299)
+					input[ 0 ] = null;
+					return !results.pop();
+				};
+		} ),
+
+		"has": markFunction( function( selector ) {
+			return function( elem ) {
+				return Sizzle( selector, elem ).length > 0;
+			};
+		} ),
+
+		"contains": markFunction( function( text ) {
+			text = text.replace( runescape, funescape );
+			return function( elem ) {
+				return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+			};
+		} ),
+
+		// "Whether an element is represented by a :lang() selector
+		// is based solely on the element's language value
+		// being equal to the identifier C,
+		// or beginning with the identifier C immediately followed by "-".
+		// The matching of C against the element's language value is performed case-insensitively.
+		// The identifier C does not have to be a valid language name."
+		// http://www.w3.org/TR/selectors/#lang-pseudo
+		"lang": markFunction( function( lang ) {
+
+			// lang value must be a valid identifier
+			if ( !ridentifier.test( lang || "" ) ) {
+				Sizzle.error( "unsupported lang: " + lang );
+			}
+			lang = lang.replace( runescape, funescape ).toLowerCase();
+			return function( elem ) {
+				var elemLang;
+				do {
+					if ( ( elemLang = documentIsHTML ?
+						elem.lang :
+						elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+						elemLang = elemLang.toLowerCase();
+						return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+					}
+				} while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+				return false;
+			};
+		} ),
+
+		// Miscellaneous
+		"target": function( elem ) {
+			var hash = window.location && window.location.hash;
+			return hash && hash.slice( 1 ) === elem.id;
+		},
+
+		"root": function( elem ) {
+			return elem === docElem;
+		},
+
+		"focus": function( elem ) {
+			return elem === document.activeElement &&
+				( !document.hasFocus || document.hasFocus() ) &&
+				!!( elem.type || elem.href || ~elem.tabIndex );
+		},
+
+		// Boolean properties
+		"enabled": createDisabledPseudo( false ),
+		"disabled": createDisabledPseudo( true ),
+
+		"checked": function( elem ) {
+
+			// In CSS3, :checked should return both checked and selected elements
+			// http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+			var nodeName = elem.nodeName.toLowerCase();
+			return ( nodeName === "input" && !!elem.checked ) ||
+				( nodeName === "option" && !!elem.selected );
+		},
+
+		"selected": function( elem ) {
+
+			// Accessing this property makes selected-by-default
+			// options in Safari work properly
+			if ( elem.parentNode ) {
+				// eslint-disable-next-line no-unused-expressions
+				elem.parentNode.selectedIndex;
+			}
+
+			return elem.selected === true;
+		},
+
+		// Contents
+		"empty": function( elem ) {
+
+			// http://www.w3.org/TR/selectors/#empty-pseudo
+			// :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+			//   but not by others (comment: 8; processing instruction: 7; etc.)
+			// nodeType < 6 works because attributes (2) do not appear as children
+			for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+				if ( elem.nodeType < 6 ) {
+					return false;
+				}
+			}
+			return true;
+		},
+
+		"parent": function( elem ) {
+			return !Expr.pseudos[ "empty" ]( elem );
+		},
+
+		// Element/input types
+		"header": function( elem ) {
+			return rheader.test( elem.nodeName );
+		},
+
+		"input": function( elem ) {
+			return rinputs.test( elem.nodeName );
+		},
+
+		"button": function( elem ) {
+			var name = elem.nodeName.toLowerCase();
+			return name === "input" && elem.type === "button" || name === "button";
+		},
+
+		"text": function( elem ) {
+			var attr;
+			return elem.nodeName.toLowerCase() === "input" &&
+				elem.type === "text" &&
+
+				// Support: IE<8
+				// New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+				( ( attr = elem.getAttribute( "type" ) ) == null ||
+					attr.toLowerCase() === "text" );
+		},
+
+		// Position-in-collection
+		"first": createPositionalPseudo( function() {
+			return [ 0 ];
+		} ),
+
+		"last": createPositionalPseudo( function( _matchIndexes, length ) {
+			return [ length - 1 ];
+		} ),
+
+		"eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+			return [ argument < 0 ? argument + length : argument ];
+		} ),
+
+		"even": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 0;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"odd": createPositionalPseudo( function( matchIndexes, length ) {
+			var i = 1;
+			for ( ; i < length; i += 2 ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ?
+				argument + length :
+				argument > length ?
+					length :
+					argument;
+			for ( ; --i >= 0; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} ),
+
+		"gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+			var i = argument < 0 ? argument + length : argument;
+			for ( ; ++i < length; ) {
+				matchIndexes.push( i );
+			}
+			return matchIndexes;
+		} )
+	}
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+	Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+	Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+	var matched, match, tokens, type,
+		soFar, groups, preFilters,
+		cached = tokenCache[ selector + " " ];
+
+	if ( cached ) {
+		return parseOnly ? 0 : cached.slice( 0 );
+	}
+
+	soFar = selector;
+	groups = [];
+	preFilters = Expr.preFilter;
+
+	while ( soFar ) {
+
+		// Comma and first run
+		if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+			if ( match ) {
+
+				// Don't consume trailing commas as valid
+				soFar = soFar.slice( match[ 0 ].length ) || soFar;
+			}
+			groups.push( ( tokens = [] ) );
+		}
+
+		matched = false;
+
+		// Combinators
+		if ( ( match = rcombinators.exec( soFar ) ) ) {
+			matched = match.shift();
+			tokens.push( {
+				value: matched,
+
+				// Cast descendant combinators to space
+				type: match[ 0 ].replace( rtrim, " " )
+			} );
+			soFar = soFar.slice( matched.length );
+		}
+
+		// Filters
+		for ( type in Expr.filter ) {
+			if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+				( match = preFilters[ type ]( match ) ) ) ) {
+				matched = match.shift();
+				tokens.push( {
+					value: matched,
+					type: type,
+					matches: match
+				} );
+				soFar = soFar.slice( matched.length );
+			}
+		}
+
+		if ( !matched ) {
+			break;
+		}
+	}
+
+	// Return the length of the invalid excess
+	// if we're just parsing
+	// Otherwise, throw an error or return tokens
+	return parseOnly ?
+		soFar.length :
+		soFar ?
+			Sizzle.error( selector ) :
+
+			// Cache the tokens
+			tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+	var i = 0,
+		len = tokens.length,
+		selector = "";
+	for ( ; i < len; i++ ) {
+		selector += tokens[ i ].value;
+	}
+	return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+	var dir = combinator.dir,
+		skip = combinator.next,
+		key = skip || dir,
+		checkNonElements = base && key === "parentNode",
+		doneName = done++;
+
+	return combinator.first ?
+
+		// Check against closest ancestor/preceding element
+		function( elem, context, xml ) {
+			while ( ( elem = elem[ dir ] ) ) {
+				if ( elem.nodeType === 1 || checkNonElements ) {
+					return matcher( elem, context, xml );
+				}
+			}
+			return false;
+		} :
+
+		// Check against all ancestor/preceding elements
+		function( elem, context, xml ) {
+			var oldCache, uniqueCache, outerCache,
+				newCache = [ dirruns, doneName ];
+
+			// We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+			if ( xml ) {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						if ( matcher( elem, context, xml ) ) {
+							return true;
+						}
+					}
+				}
+			} else {
+				while ( ( elem = elem[ dir ] ) ) {
+					if ( elem.nodeType === 1 || checkNonElements ) {
+						outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+						// Support: IE <9 only
+						// Defend against cloned attroperties (jQuery gh-1709)
+						uniqueCache = outerCache[ elem.uniqueID ] ||
+							( outerCache[ elem.uniqueID ] = {} );
+
+						if ( skip && skip === elem.nodeName.toLowerCase() ) {
+							elem = elem[ dir ] || elem;
+						} else if ( ( oldCache = uniqueCache[ key ] ) &&
+							oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+							// Assign to newCache so results back-propagate to previous elements
+							return ( newCache[ 2 ] = oldCache[ 2 ] );
+						} else {
+
+							// Reuse newcache so results back-propagate to previous elements
+							uniqueCache[ key ] = newCache;
+
+							// A match means we're done; a fail means we have to keep checking
+							if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+								return true;
+							}
+						}
+					}
+				}
+			}
+			return false;
+		};
+}
+
+function elementMatcher( matchers ) {
+	return matchers.length > 1 ?
+		function( elem, context, xml ) {
+			var i = matchers.length;
+			while ( i-- ) {
+				if ( !matchers[ i ]( elem, context, xml ) ) {
+					return false;
+				}
+			}
+			return true;
+		} :
+		matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+	var i = 0,
+		len = contexts.length;
+	for ( ; i < len; i++ ) {
+		Sizzle( selector, contexts[ i ], results );
+	}
+	return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+	var elem,
+		newUnmatched = [],
+		i = 0,
+		len = unmatched.length,
+		mapped = map != null;
+
+	for ( ; i < len; i++ ) {
+		if ( ( elem = unmatched[ i ] ) ) {
+			if ( !filter || filter( elem, context, xml ) ) {
+				newUnmatched.push( elem );
+				if ( mapped ) {
+					map.push( i );
+				}
+			}
+		}
+	}
+
+	return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+	if ( postFilter && !postFilter[ expando ] ) {
+		postFilter = setMatcher( postFilter );
+	}
+	if ( postFinder && !postFinder[ expando ] ) {
+		postFinder = setMatcher( postFinder, postSelector );
+	}
+	return markFunction( function( seed, results, context, xml ) {
+		var temp, i, elem,
+			preMap = [],
+			postMap = [],
+			preexisting = results.length,
+
+			// Get initial elements from seed or context
+			elems = seed || multipleContexts(
+				selector || "*",
+				context.nodeType ? [ context ] : context,
+				[]
+			),
+
+			// Prefilter to get matcher input, preserving a map for seed-results synchronization
+			matcherIn = preFilter && ( seed || !selector ) ?
+				condense( elems, preMap, preFilter, context, xml ) :
+				elems,
+
+			matcherOut = matcher ?
+
+				// If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+				postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+					// ...intermediate processing is necessary
+					[] :
+
+					// ...otherwise use results directly
+					results :
+				matcherIn;
+
+		// Find primary matches
+		if ( matcher ) {
+			matcher( matcherIn, matcherOut, context, xml );
+		}
+
+		// Apply postFilter
+		if ( postFilter ) {
+			temp = condense( matcherOut, postMap );
+			postFilter( temp, [], context, xml );
+
+			// Un-match failing elements by moving them back to matcherIn
+			i = temp.length;
+			while ( i-- ) {
+				if ( ( elem = temp[ i ] ) ) {
+					matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+				}
+			}
+		}
+
+		if ( seed ) {
+			if ( postFinder || preFilter ) {
+				if ( postFinder ) {
+
+					// Get the final matcherOut by condensing this intermediate into postFinder contexts
+					temp = [];
+					i = matcherOut.length;
+					while ( i-- ) {
+						if ( ( elem = matcherOut[ i ] ) ) {
+
+							// Restore matcherIn since elem is not yet a final match
+							temp.push( ( matcherIn[ i ] = elem ) );
+						}
+					}
+					postFinder( null, ( matcherOut = [] ), temp, xml );
+				}
+
+				// Move matched elements from seed to results to keep them synchronized
+				i = matcherOut.length;
+				while ( i-- ) {
+					if ( ( elem = matcherOut[ i ] ) &&
+						( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+						seed[ temp ] = !( results[ temp ] = elem );
+					}
+				}
+			}
+
+		// Add elements to results, through postFinder if defined
+		} else {
+			matcherOut = condense(
+				matcherOut === results ?
+					matcherOut.splice( preexisting, matcherOut.length ) :
+					matcherOut
+			);
+			if ( postFinder ) {
+				postFinder( null, results, matcherOut, xml );
+			} else {
+				push.apply( results, matcherOut );
+			}
+		}
+	} );
+}
+
+function matcherFromTokens( tokens ) {
+	var checkContext, matcher, j,
+		len = tokens.length,
+		leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+		implicitRelative = leadingRelative || Expr.relative[ " " ],
+		i = leadingRelative ? 1 : 0,
+
+		// The foundational matcher ensures that elements are reachable from top-level context(s)
+		matchContext = addCombinator( function( elem ) {
+			return elem === checkContext;
+		}, implicitRelative, true ),
+		matchAnyContext = addCombinator( function( elem ) {
+			return indexOf( checkContext, elem ) > -1;
+		}, implicitRelative, true ),
+		matchers = [ function( elem, context, xml ) {
+			var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+				( checkContext = context ).nodeType ?
+					matchContext( elem, context, xml ) :
+					matchAnyContext( elem, context, xml ) );
+
+			// Avoid hanging onto element (issue #299)
+			checkContext = null;
+			return ret;
+		} ];
+
+	for ( ; i < len; i++ ) {
+		if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+			matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+		} else {
+			matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+			// Return special upon seeing a positional matcher
+			if ( matcher[ expando ] ) {
+
+				// Find the next relative operator (if any) for proper handling
+				j = ++i;
+				for ( ; j < len; j++ ) {
+					if ( Expr.relative[ tokens[ j ].type ] ) {
+						break;
+					}
+				}
+				return setMatcher(
+					i > 1 && elementMatcher( matchers ),
+					i > 1 && toSelector(
+
+					// If the preceding token was a descendant combinator, insert an implicit any-element `*`
+					tokens
+						.slice( 0, i - 1 )
+						.concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+					).replace( rtrim, "$1" ),
+					matcher,
+					i < j && matcherFromTokens( tokens.slice( i, j ) ),
+					j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+					j < len && toSelector( tokens )
+				);
+			}
+			matchers.push( matcher );
+		}
+	}
+
+	return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+	var bySet = setMatchers.length > 0,
+		byElement = elementMatchers.length > 0,
+		superMatcher = function( seed, context, xml, results, outermost ) {
+			var elem, j, matcher,
+				matchedCount = 0,
+				i = "0",
+				unmatched = seed && [],
+				setMatched = [],
+				contextBackup = outermostContext,
+
+				// We must always have either seed elements or outermost context
+				elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+				// Use integer dirruns iff this is the outermost matcher
+				dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+				len = elems.length;
+
+			if ( outermost ) {
+
+				// Support: IE 11+, Edge 17 - 18+
+				// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+				// two documents; shallow comparisons work.
+				// eslint-disable-next-line eqeqeq
+				outermostContext = context == document || context || outermost;
+			}
+
+			// Add elements passing elementMatchers directly to results
+			// Support: IE<9, Safari
+			// Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
+			for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+				if ( byElement && elem ) {
+					j = 0;
+
+					// Support: IE 11+, Edge 17 - 18+
+					// IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+					// two documents; shallow comparisons work.
+					// eslint-disable-next-line eqeqeq
+					if ( !context && elem.ownerDocument != document ) {
+						setDocument( elem );
+						xml = !documentIsHTML;
+					}
+					while ( ( matcher = elementMatchers[ j++ ] ) ) {
+						if ( matcher( elem, context || document, xml ) ) {
+							results.push( elem );
+							break;
+						}
+					}
+					if ( outermost ) {
+						dirruns = dirrunsUnique;
+					}
+				}
+
+				// Track unmatched elements for set filters
+				if ( bySet ) {
+
+					// They will have gone through all possible matchers
+					if ( ( elem = !matcher && elem ) ) {
+						matchedCount--;
+					}
+
+					// Lengthen the array for every element, matched or not
+					if ( seed ) {
+						unmatched.push( elem );
+					}
+				}
+			}
+
+			// `i` is now the count of elements visited above, and adding it to `matchedCount`
+			// makes the latter nonnegative.
+			matchedCount += i;
+
+			// Apply set filters to unmatched elements
+			// NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+			// equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+			// no element matchers and no seed.
+			// Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+			// case, which will result in a "00" `matchedCount` that differs from `i` but is also
+			// numerically zero.
+			if ( bySet && i !== matchedCount ) {
+				j = 0;
+				while ( ( matcher = setMatchers[ j++ ] ) ) {
+					matcher( unmatched, setMatched, context, xml );
+				}
+
+				if ( seed ) {
+
+					// Reintegrate element matches to eliminate the need for sorting
+					if ( matchedCount > 0 ) {
+						while ( i-- ) {
+							if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+								setMatched[ i ] = pop.call( results );
+							}
+						}
+					}
+
+					// Discard index placeholder values to get only actual matches
+					setMatched = condense( setMatched );
+				}
+
+				// Add matches to results
+				push.apply( results, setMatched );
+
+				// Seedless set matches succeeding multiple successful matchers stipulate sorting
+				if ( outermost && !seed && setMatched.length > 0 &&
+					( matchedCount + setMatchers.length ) > 1 ) {
+
+					Sizzle.uniqueSort( results );
+				}
+			}
+
+			// Override manipulation of globals by nested matchers
+			if ( outermost ) {
+				dirruns = dirrunsUnique;
+				outermostContext = contextBackup;
+			}
+
+			return unmatched;
+		};
+
+	return bySet ?
+		markFunction( superMatcher ) :
+		superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+	var i,
+		setMatchers = [],
+		elementMatchers = [],
+		cached = compilerCache[ selector + " " ];
+
+	if ( !cached ) {
+
+		// Generate a function of recursive functions that can be used to check each element
+		if ( !match ) {
+			match = tokenize( selector );
+		}
+		i = match.length;
+		while ( i-- ) {
+			cached = matcherFromTokens( match[ i ] );
+			if ( cached[ expando ] ) {
+				setMatchers.push( cached );
+			} else {
+				elementMatchers.push( cached );
+			}
+		}
+
+		// Cache the compiled function
+		cached = compilerCache(
+			selector,
+			matcherFromGroupMatchers( elementMatchers, setMatchers )
+		);
+
+		// Save selector and tokenization
+		cached.selector = selector;
+	}
+	return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ *  selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ *  selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+	var i, tokens, token, type, find,
+		compiled = typeof selector === "function" && selector,
+		match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+	results = results || [];
+
+	// Try to minimize operations if there is only one selector in the list and no seed
+	// (the latter of which guarantees us context)
+	if ( match.length === 1 ) {
+
+		// Reduce context if the leading compound selector is an ID
+		tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+		if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+			context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+			context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+				.replace( runescape, funescape ), context ) || [] )[ 0 ];
+			if ( !context ) {
+				return results;
+
+			// Precompiled matchers will still verify ancestry, so step up a level
+			} else if ( compiled ) {
+				context = context.parentNode;
+			}
+
+			selector = selector.slice( tokens.shift().value.length );
+		}
+
+		// Fetch a seed set for right-to-left matching
+		i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+		while ( i-- ) {
+			token = tokens[ i ];
+
+			// Abort if we hit a combinator
+			if ( Expr.relative[ ( type = token.type ) ] ) {
+				break;
+			}
+			if ( ( find = Expr.find[ type ] ) ) {
+
+				// Search, expanding context for leading sibling combinators
+				if ( ( seed = find(
+					token.matches[ 0 ].replace( runescape, funescape ),
+					rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+						context
+				) ) ) {
+
+					// If seed is empty or no tokens remain, we can return early
+					tokens.splice( i, 1 );
+					selector = seed.length && toSelector( tokens );
+					if ( !selector ) {
+						push.apply( results, seed );
+						return results;
+					}
+
+					break;
+				}
+			}
+		}
+	}
+
+	// Compile and execute a filtering function if one is not provided
+	// Provide `match` to avoid retokenization if we modified the selector above
+	( compiled || compile( selector, match ) )(
+		seed,
+		context,
+		!documentIsHTML,
+		results,
+		!context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+	);
+	return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+	// Should return 1, but returns 4 (following)
+	return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+	el.innerHTML = "<a href='#'></a>";
+	return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+	addHandle( "type|href|height|width", function( elem, name, isXML ) {
+		if ( !isXML ) {
+			return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+		}
+	} );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+	el.innerHTML = "<input/>";
+	el.firstChild.setAttribute( "value", "" );
+	return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+	addHandle( "value", function( elem, _name, isXML ) {
+		if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+			return elem.defaultValue;
+		}
+	} );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+	return el.getAttribute( "disabled" ) == null;
+} ) ) {
+	addHandle( booleans, function( elem, name, isXML ) {
+		var val;
+		if ( !isXML ) {
+			return elem[ name ] === true ? name.toLowerCase() :
+				( val = elem.getAttributeNode( name ) ) && val.specified ?
+					val.value :
+					null;
+		}
+	} );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+	var matched = [],
+		truncate = until !== undefined;
+
+	while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+		if ( elem.nodeType === 1 ) {
+			if ( truncate && jQuery( elem ).is( until ) ) {
+				break;
+			}
+			matched.push( elem );
+		}
+	}
+	return matched;
+};
+
+
+var siblings = function( n, elem ) {
+	var matched = [];
+
+	for ( ; n; n = n.nextSibling ) {
+		if ( n.nodeType === 1 && n !== elem ) {
+			matched.push( n );
+		}
+	}
+
+	return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+	return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+}
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+	if ( isFunction( qualifier ) ) {
+		return jQuery.grep( elements, function( elem, i ) {
+			return !!qualifier.call( elem, i, elem ) !== not;
+		} );
+	}
+
+	// Single element
+	if ( qualifier.nodeType ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( elem === qualifier ) !== not;
+		} );
+	}
+
+	// Arraylike of elements (jQuery, arguments, Array)
+	if ( typeof qualifier !== "string" ) {
+		return jQuery.grep( elements, function( elem ) {
+			return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+		} );
+	}
+
+	// Filtered directly for both simple and complex selectors
+	return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+	var elem = elems[ 0 ];
+
+	if ( not ) {
+		expr = ":not(" + expr + ")";
+	}
+
+	if ( elems.length === 1 && elem.nodeType === 1 ) {
+		return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+	}
+
+	return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+		return elem.nodeType === 1;
+	} ) );
+};
+
+jQuery.fn.extend( {
+	find: function( selector ) {
+		var i, ret,
+			len = this.length,
+			self = this;
+
+		if ( typeof selector !== "string" ) {
+			return this.pushStack( jQuery( selector ).filter( function() {
+				for ( i = 0; i < len; i++ ) {
+					if ( jQuery.contains( self[ i ], this ) ) {
+						return true;
+					}
+				}
+			} ) );
+		}
+
+		ret = this.pushStack( [] );
+
+		for ( i = 0; i < len; i++ ) {
+			jQuery.find( selector, self[ i ], ret );
+		}
+
+		return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+	},
+	filter: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], false ) );
+	},
+	not: function( selector ) {
+		return this.pushStack( winnow( this, selector || [], true ) );
+	},
+	is: function( selector ) {
+		return !!winnow(
+			this,
+
+			// If this is a positional/relative selector, check membership in the returned set
+			// so $("p:first").is("p:last") won't return true for a doc with two "p".
+			typeof selector === "string" && rneedsContext.test( selector ) ?
+				jQuery( selector ) :
+				selector || [],
+			false
+		).length;
+	}
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+	// A simple way to check for HTML strings
+	// Prioritize #id over <tag> to avoid XSS via location.hash (#9521)
+	// Strict HTML recognition (#11290: must start with <)
+	// Shortcut simple #id case for speed
+	rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+	init = jQuery.fn.init = function( selector, context, root ) {
+		var match, elem;
+
+		// HANDLE: $(""), $(null), $(undefined), $(false)
+		if ( !selector ) {
+			return this;
+		}
+
+		// Method init() accepts an alternate rootjQuery
+		// so migrate can support jQuery.sub (gh-2101)
+		root = root || rootjQuery;
+
+		// Handle HTML strings
+		if ( typeof selector === "string" ) {
+			if ( selector[ 0 ] === "<" &&
+				selector[ selector.length - 1 ] === ">" &&
+				selector.length >= 3 ) {
+
+				// Assume that strings that start and end with <> are HTML and skip the regex check
+				match = [ null, selector, null ];
+
+			} else {
+				match = rquickExpr.exec( selector );
+			}
+
+			// Match html or make sure no context is specified for #id
+			if ( match && ( match[ 1 ] || !context ) ) {
+
+				// HANDLE: $(html) -> $(array)
+				if ( match[ 1 ] ) {
+					context = context instanceof jQuery ? context[ 0 ] : context;
+
+					// Option to run scripts is true for back-compat
+					// Intentionally let the error be thrown if parseHTML is not present
+					jQuery.merge( this, jQuery.parseHTML(
+						match[ 1 ],
+						context && context.nodeType ? context.ownerDocument || context : document,
+						true
+					) );
+
+					// HANDLE: $(html, props)
+					if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+						for ( match in context ) {
+
+							// Properties of context are called as methods if possible
+							if ( isFunction( this[ match ] ) ) {
+								this[ match ]( context[ match ] );
+
+							// ...and otherwise set as attributes
+							} else {
+								this.attr( match, context[ match ] );
+							}
+						}
+					}
+
+					return this;
+
+				// HANDLE: $(#id)
+				} else {
+					elem = document.getElementById( match[ 2 ] );
+
+					if ( elem ) {
+
+						// Inject the element directly into the jQuery object
+						this[ 0 ] = elem;
+						this.length = 1;
+					}
+					return this;
+				}
+
+			// HANDLE: $(expr, $(...))
+			} else if ( !context || context.jquery ) {
+				return ( context || root ).find( selector );
+
+			// HANDLE: $(expr, context)
+			// (which is just equivalent to: $(context).find(expr)
+			} else {
+				return this.constructor( context ).find( selector );
+			}
+
+		// HANDLE: $(DOMElement)
+		} else if ( selector.nodeType ) {
+			this[ 0 ] = selector;
+			this.length = 1;
+			return this;
+
+		// HANDLE: $(function)
+		// Shortcut for document ready
+		} else if ( isFunction( selector ) ) {
+			return root.ready !== undefined ?
+				root.ready( selector ) :
+
+				// Execute immediately if ready is not present
+				selector( jQuery );
+		}
+
+		return jQuery.makeArray( selector, this );
+	};
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+	// Methods guaranteed to produce a unique set when starting from a unique set
+	guaranteedUnique = {
+		children: true,
+		contents: true,
+		next: true,
+		prev: true
+	};
+
+jQuery.fn.extend( {
+	has: function( target ) {
+		var targets = jQuery( target, this ),
+			l = targets.length;
+
+		return this.filter( function() {
+			var i = 0;
+			for ( ; i < l; i++ ) {
+				if ( jQuery.contains( this, targets[ i ] ) ) {
+					return true;
+				}
+			}
+		} );
+	},
+
+	closest: function( selectors, context ) {
+		var cur,
+			i = 0,
+			l = this.length,
+			matched = [],
+			targets = typeof selectors !== "string" && jQuery( selectors );
+
+		// Positional selectors never match, since there's no _selection_ context
+		if ( !rneedsContext.test( selectors ) ) {
+			for ( ; i < l; i++ ) {
+				for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+					// Always skip document fragments
+					if ( cur.nodeType < 11 && ( targets ?
+						targets.index( cur ) > -1 :
+
+						// Don't pass non-elements to Sizzle
+						cur.nodeType === 1 &&
+							jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+						matched.push( cur );
+						break;
+					}
+				}
+			}
+		}
+
+		return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+	},
+
+	// Determine the position of an element within the set
+	index: function( elem ) {
+
+		// No argument, return index in parent
+		if ( !elem ) {
+			return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+		}
+
+		// Index in selector
+		if ( typeof elem === "string" ) {
+			return indexOf.call( jQuery( elem ), this[ 0 ] );
+		}
+
+		// Locate the position of the desired element
+		return indexOf.call( this,
+
+			// If it receives a jQuery object, the first element is used
+			elem.jquery ? elem[ 0 ] : elem
+		);
+	},
+
+	add: function( selector, context ) {
+		return this.pushStack(
+			jQuery.uniqueSort(
+				jQuery.merge( this.get(), jQuery( selector, context ) )
+			)
+		);
+	},
+
+	addBack: function( selector ) {
+		return this.add( selector == null ?
+			this.prevObject : this.prevObject.filter( selector )
+		);
+	}
+} );
+
+function sibling( cur, dir ) {
+	while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+	return cur;
+}
+
+jQuery.each( {
+	parent: function( elem ) {
+		var parent = elem.parentNode;
+		return parent && parent.nodeType !== 11 ? parent : null;
+	},
+	parents: function( elem ) {
+		return dir( elem, "parentNode" );
+	},
+	parentsUntil: function( elem, _i, until ) {
+		return dir( elem, "parentNode", until );
+	},
+	next: function( elem ) {
+		return sibling( elem, "nextSibling" );
+	},
+	prev: function( elem ) {
+		return sibling( elem, "previousSibling" );
+	},
+	nextAll: function( elem ) {
+		return dir( elem, "nextSibling" );
+	},
+	prevAll: function( elem ) {
+		return dir( elem, "previousSibling" );
+	},
+	nextUntil: function( elem, _i, until ) {
+		return dir( elem, "nextSibling", until );
+	},
+	prevUntil: function( elem, _i, until ) {
+		return dir( elem, "previousSibling", until );
+	},
+	siblings: function( elem ) {
+		return siblings( ( elem.parentNode || {} ).firstChild, elem );
+	},
+	children: function( elem ) {
+		return siblings( elem.firstChild );
+	},
+	contents: function( elem ) {
+		if ( elem.contentDocument != null &&
+
+			// Support: IE 11+
+			// <object> elements with no `data` attribute has an object
+			// `contentDocument` with a `null` prototype.
+			getProto( elem.contentDocument ) ) {
+
+			return elem.contentDocument;
+		}
+
+		// Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+		// Treat the template element as a regular one in browsers that
+		// don't support it.
+		if ( nodeName( elem, "template" ) ) {
+			elem = elem.content || elem;
+		}
+
+		return jQuery.merge( [], elem.childNodes );
+	}
+}, function( name, fn ) {
+	jQuery.fn[ name ] = function( until, selector ) {
+		var matched = jQuery.map( this, fn, until );
+
+		if ( name.slice( -5 ) !== "Until" ) {
+			selector = until;
+		}
+
+		if ( selector && typeof selector === "string" ) {
+			matched = jQuery.filter( selector, matched );
+		}
+
+		if ( this.length > 1 ) {
+
+			// Remove duplicates
+			if ( !guaranteedUnique[ name ] ) {
+				jQuery.uniqueSort( matched );
+			}
+
+			// Reverse order for parents* and prev-derivatives
+			if ( rparentsprev.test( name ) ) {
+				matched.reverse();
+			}
+		}
+
+		return this.pushStack( matched );
+	};
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+	var object = {};
+	jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+		object[ flag ] = true;
+	} );
+	return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ *	options: an optional list of space-separated options that will change how
+ *			the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ *	once:			will ensure the callback list can only be fired once (like a Deferred)
+ *
+ *	memory:			will keep track of previous values and will call any callback added
+ *					after the list has been fired right away with the latest "memorized"
+ *					values (like a Deferred)
+ *
+ *	unique:			will ensure a callback can only be added once (no duplicate in the list)
+ *
+ *	stopOnFalse:	interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+	// Convert options from String-formatted to Object-formatted if needed
+	// (we check in cache first)
+	options = typeof options === "string" ?
+		createOptions( options ) :
+		jQuery.extend( {}, options );
+
+	var // Flag to know if list is currently firing
+		firing,
+
+		// Last fire value for non-forgettable lists
+		memory,
+
+		// Flag to know if list was already fired
+		fired,
+
+		// Flag to prevent firing
+		locked,
+
+		// Actual callback list
+		list = [],
+
+		// Queue of execution data for repeatable lists
+		queue = [],
+
+		// Index of currently firing callback (modified by add/remove as needed)
+		firingIndex = -1,
+
+		// Fire callbacks
+		fire = function() {
+
+			// Enforce single-firing
+			locked = locked || options.once;
+
+			// Execute callbacks for all pending executions,
+			// respecting firingIndex overrides and runtime changes
+			fired = firing = true;
+			for ( ; queue.length; firingIndex = -1 ) {
+				memory = queue.shift();
+				while ( ++firingIndex < list.length ) {
+
+					// Run callback and check for early termination
+					if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+						options.stopOnFalse ) {
+
+						// Jump to end and forget the data so .add doesn't re-fire
+						firingIndex = list.length;
+						memory = false;
+					}
+				}
+			}
+
+			// Forget the data if we're done with it
+			if ( !options.memory ) {
+				memory = false;
+			}
+
+			firing = false;
+
+			// Clean up if we're done firing for good
+			if ( locked ) {
+
+				// Keep an empty list if we have data for future add calls
+				if ( memory ) {
+					list = [];
+
+				// Otherwise, this object is spent
+				} else {
+					list = "";
+				}
+			}
+		},
+
+		// Actual Callbacks object
+		self = {
+
+			// Add a callback or a collection of callbacks to the list
+			add: function() {
+				if ( list ) {
+
+					// If we have memory from a past run, we should fire after adding
+					if ( memory && !firing ) {
+						firingIndex = list.length - 1;
+						queue.push( memory );
+					}
+
+					( function add( args ) {
+						jQuery.each( args, function( _, arg ) {
+							if ( isFunction( arg ) ) {
+								if ( !options.unique || !self.has( arg ) ) {
+									list.push( arg );
+								}
+							} else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+								// Inspect recursively
+								add( arg );
+							}
+						} );
+					} )( arguments );
+
+					if ( memory && !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Remove a callback from the list
+			remove: function() {
+				jQuery.each( arguments, function( _, arg ) {
+					var index;
+					while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+						list.splice( index, 1 );
+
+						// Handle firing indexes
+						if ( index <= firingIndex ) {
+							firingIndex--;
+						}
+					}
+				} );
+				return this;
+			},
+
+			// Check if a given callback is in the list.
+			// If no argument is given, return whether or not list has callbacks attached.
+			has: function( fn ) {
+				return fn ?
+					jQuery.inArray( fn, list ) > -1 :
+					list.length > 0;
+			},
+
+			// Remove all callbacks from the list
+			empty: function() {
+				if ( list ) {
+					list = [];
+				}
+				return this;
+			},
+
+			// Disable .fire and .add
+			// Abort any current/pending executions
+			// Clear all callbacks and values
+			disable: function() {
+				locked = queue = [];
+				list = memory = "";
+				return this;
+			},
+			disabled: function() {
+				return !list;
+			},
+
+			// Disable .fire
+			// Also disable .add unless we have memory (since it would have no effect)
+			// Abort any pending executions
+			lock: function() {
+				locked = queue = [];
+				if ( !memory && !firing ) {
+					list = memory = "";
+				}
+				return this;
+			},
+			locked: function() {
+				return !!locked;
+			},
+
+			// Call all callbacks with the given context and arguments
+			fireWith: function( context, args ) {
+				if ( !locked ) {
+					args = args || [];
+					args = [ context, args.slice ? args.slice() : args ];
+					queue.push( args );
+					if ( !firing ) {
+						fire();
+					}
+				}
+				return this;
+			},
+
+			// Call all the callbacks with the given arguments
+			fire: function() {
+				self.fireWith( this, arguments );
+				return this;
+			},
+
+			// To know if the callbacks have already been called at least once
+			fired: function() {
+				return !!fired;
+			}
+		};
+
+	return self;
+};
+
+
+function Identity( v ) {
+	return v;
+}
+function Thrower( ex ) {
+	throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+	var method;
+
+	try {
+
+		// Check for promise aspect first to privilege synchronous behavior
+		if ( value && isFunction( ( method = value.promise ) ) ) {
+			method.call( value ).done( resolve ).fail( reject );
+
+		// Other thenables
+		} else if ( value && isFunction( ( method = value.then ) ) ) {
+			method.call( value, resolve, reject );
+
+		// Other non-thenables
+		} else {
+
+			// Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+			// * false: [ value ].slice( 0 ) => resolve( value )
+			// * true: [ value ].slice( 1 ) => resolve()
+			resolve.apply( undefined, [ value ].slice( noValue ) );
+		}
+
+	// For Promises/A+, convert exceptions into rejections
+	// Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+	// Deferred#then to conditionally suppress rejection.
+	} catch ( value ) {
+
+		// Support: Android 4.0 only
+		// Strict mode functions invoked without .call/.apply get global-object context
+		reject.apply( undefined, [ value ] );
+	}
+}
+
+jQuery.extend( {
+
+	Deferred: function( func ) {
+		var tuples = [
+
+				// action, add listener, callbacks,
+				// ... .then handlers, argument index, [final state]
+				[ "notify", "progress", jQuery.Callbacks( "memory" ),
+					jQuery.Callbacks( "memory" ), 2 ],
+				[ "resolve", "done", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+				[ "reject", "fail", jQuery.Callbacks( "once memory" ),
+					jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+			],
+			state = "pending",
+			promise = {
+				state: function() {
+					return state;
+				},
+				always: function() {
+					deferred.done( arguments ).fail( arguments );
+					return this;
+				},
+				"catch": function( fn ) {
+					return promise.then( null, fn );
+				},
+
+				// Keep pipe for back-compat
+				pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+					var fns = arguments;
+
+					return jQuery.Deferred( function( newDefer ) {
+						jQuery.each( tuples, function( _i, tuple ) {
+
+							// Map tuples (progress, done, fail) to arguments (done, fail, progress)
+							var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+							// deferred.progress(function() { bind to newDefer or newDefer.notify })
+							// deferred.done(function() { bind to newDefer or newDefer.resolve })
+							// deferred.fail(function() { bind to newDefer or newDefer.reject })
+							deferred[ tuple[ 1 ] ]( function() {
+								var returned = fn && fn.apply( this, arguments );
+								if ( returned && isFunction( returned.promise ) ) {
+									returned.promise()
+										.progress( newDefer.notify )
+										.done( newDefer.resolve )
+										.fail( newDefer.reject );
+								} else {
+									newDefer[ tuple[ 0 ] + "With" ](
+										this,
+										fn ? [ returned ] : arguments
+									);
+								}
+							} );
+						} );
+						fns = null;
+					} ).promise();
+				},
+				then: function( onFulfilled, onRejected, onProgress ) {
+					var maxDepth = 0;
+					function resolve( depth, deferred, handler, special ) {
+						return function() {
+							var that = this,
+								args = arguments,
+								mightThrow = function() {
+									var returned, then;
+
+									// Support: Promises/A+ section 2.3.3.3.3
+									// https://promisesaplus.com/#point-59
+									// Ignore double-resolution attempts
+									if ( depth < maxDepth ) {
+										return;
+									}
+
+									returned = handler.apply( that, args );
+
+									// Support: Promises/A+ section 2.3.1
+									// https://promisesaplus.com/#point-48
+									if ( returned === deferred.promise() ) {
+										throw new TypeError( "Thenable self-resolution" );
+									}
+
+									// Support: Promises/A+ sections 2.3.3.1, 3.5
+									// https://promisesaplus.com/#point-54
+									// https://promisesaplus.com/#point-75
+									// Retrieve `then` only once
+									then = returned &&
+
+										// Support: Promises/A+ section 2.3.4
+										// https://promisesaplus.com/#point-64
+										// Only check objects and functions for thenability
+										( typeof returned === "object" ||
+											typeof returned === "function" ) &&
+										returned.then;
+
+									// Handle a returned thenable
+									if ( isFunction( then ) ) {
+
+										// Special processors (notify) just wait for resolution
+										if ( special ) {
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special )
+											);
+
+										// Normal processors (resolve) also hook into progress
+										} else {
+
+											// ...and disregard older resolution values
+											maxDepth++;
+
+											then.call(
+												returned,
+												resolve( maxDepth, deferred, Identity, special ),
+												resolve( maxDepth, deferred, Thrower, special ),
+												resolve( maxDepth, deferred, Identity,
+													deferred.notifyWith )
+											);
+										}
+
+									// Handle all other returned values
+									} else {
+
+										// Only substitute handlers pass on context
+										// and multiple values (non-spec behavior)
+										if ( handler !== Identity ) {
+											that = undefined;
+											args = [ returned ];
+										}
+
+										// Process the value(s)
+										// Default process is resolve
+										( special || deferred.resolveWith )( that, args );
+									}
+								},
+
+								// Only normal processors (resolve) catch and reject exceptions
+								process = special ?
+									mightThrow :
+									function() {
+										try {
+											mightThrow();
+										} catch ( e ) {
+
+											if ( jQuery.Deferred.exceptionHook ) {
+												jQuery.Deferred.exceptionHook( e,
+													process.stackTrace );
+											}
+
+											// Support: Promises/A+ section 2.3.3.3.4.1
+											// https://promisesaplus.com/#point-61
+											// Ignore post-resolution exceptions
+											if ( depth + 1 >= maxDepth ) {
+
+												// Only substitute handlers pass on context
+												// and multiple values (non-spec behavior)
+												if ( handler !== Thrower ) {
+													that = undefined;
+													args = [ e ];
+												}
+
+												deferred.rejectWith( that, args );
+											}
+										}
+									};
+
+							// Support: Promises/A+ section 2.3.3.3.1
+							// https://promisesaplus.com/#point-57
+							// Re-resolve promises immediately to dodge false rejection from
+							// subsequent errors
+							if ( depth ) {
+								process();
+							} else {
+
+								// Call an optional hook to record the stack, in case of exception
+								// since it's otherwise lost when execution goes async
+								if ( jQuery.Deferred.getStackHook ) {
+									process.stackTrace = jQuery.Deferred.getStackHook();
+								}
+								window.setTimeout( process );
+							}
+						};
+					}
+
+					return jQuery.Deferred( function( newDefer ) {
+
+						// progress_handlers.add( ... )
+						tuples[ 0 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onProgress ) ?
+									onProgress :
+									Identity,
+								newDefer.notifyWith
+							)
+						);
+
+						// fulfilled_handlers.add( ... )
+						tuples[ 1 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onFulfilled ) ?
+									onFulfilled :
+									Identity
+							)
+						);
+
+						// rejected_handlers.add( ... )
+						tuples[ 2 ][ 3 ].add(
+							resolve(
+								0,
+								newDefer,
+								isFunction( onRejected ) ?
+									onRejected :
+									Thrower
+							)
+						);
+					} ).promise();
+				},
+
+				// Get a promise for this deferred
+				// If obj is provided, the promise aspect is added to the object
+				promise: function( obj ) {
+					return obj != null ? jQuery.extend( obj, promise ) : promise;
+				}
+			},
+			deferred = {};
+
+		// Add list-specific methods
+		jQuery.each( tuples, function( i, tuple ) {
+			var list = tuple[ 2 ],
+				stateString = tuple[ 5 ];
+
+			// promise.progress = list.add
+			// promise.done = list.add
+			// promise.fail = list.add
+			promise[ tuple[ 1 ] ] = list.add;
+
+			// Handle state
+			if ( stateString ) {
+				list.add(
+					function() {
+
+						// state = "resolved" (i.e., fulfilled)
+						// state = "rejected"
+						state = stateString;
+					},
+
+					// rejected_callbacks.disable
+					// fulfilled_callbacks.disable
+					tuples[ 3 - i ][ 2 ].disable,
+
+					// rejected_handlers.disable
+					// fulfilled_handlers.disable
+					tuples[ 3 - i ][ 3 ].disable,
+
+					// progress_callbacks.lock
+					tuples[ 0 ][ 2 ].lock,
+
+					// progress_handlers.lock
+					tuples[ 0 ][ 3 ].lock
+				);
+			}
+
+			// progress_handlers.fire
+			// fulfilled_handlers.fire
+			// rejected_handlers.fire
+			list.add( tuple[ 3 ].fire );
+
+			// deferred.notify = function() { deferred.notifyWith(...) }
+			// deferred.resolve = function() { deferred.resolveWith(...) }
+			// deferred.reject = function() { deferred.rejectWith(...) }
+			deferred[ tuple[ 0 ] ] = function() {
+				deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+				return this;
+			};
+
+			// deferred.notifyWith = list.fireWith
+			// deferred.resolveWith = list.fireWith
+			// deferred.rejectWith = list.fireWith
+			deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+		} );
+
+		// Make the deferred a promise
+		promise.promise( deferred );
+
+		// Call given func if any
+		if ( func ) {
+			func.call( deferred, deferred );
+		}
+
+		// All done!
+		return deferred;
+	},
+
+	// Deferred helper
+	when: function( singleValue ) {
+		var
+
+			// count of uncompleted subordinates
+			remaining = arguments.length,
+
+			// count of unprocessed arguments
+			i = remaining,
+
+			// subordinate fulfillment data
+			resolveContexts = Array( i ),
+			resolveValues = slice.call( arguments ),
+
+			// the primary Deferred
+			primary = jQuery.Deferred(),
+
+			// subordinate callback factory
+			updateFunc = function( i ) {
+				return function( value ) {
+					resolveContexts[ i ] = this;
+					resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+					if ( !( --remaining ) ) {
+						primary.resolveWith( resolveContexts, resolveValues );
+					}
+				};
+			};
+
+		// Single- and empty arguments are adopted like Promise.resolve
+		if ( remaining <= 1 ) {
+			adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject,
+				!remaining );
+
+			// Use .then() to unwrap secondary thenables (cf. gh-3000)
+			if ( primary.state() === "pending" ||
+				isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+				return primary.then();
+			}
+		}
+
+		// Multiple arguments are aggregated like Promise.all array elements
+		while ( i-- ) {
+			adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject );
+		}
+
+		return primary.promise();
+	}
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+	// Support: IE 8 - 9 only
+	// Console exists when dev tools are open, which can happen at any time
+	if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+		window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+	}
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+	window.setTimeout( function() {
+		throw error;
+	} );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+	readyList
+		.then( fn )
+
+		// Wrap jQuery.readyException in a function so that the lookup
+		// happens at the time of error handling instead of callback
+		// registration.
+		.catch( function( error ) {
+			jQuery.readyException( error );
+		} );
+
+	return this;
+};
+
+jQuery.extend( {
+
+	// Is the DOM ready to be used? Set to true once it occurs.
+	isReady: false,
+
+	// A counter to track how many items to wait for before
+	// the ready event fires. See #6781
+	readyWait: 1,
+
+	// Handle when the DOM is ready
+	ready: function( wait ) {
+
+		// Abort if there are pending holds or we're already ready
+		if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+			return;
+		}
+
+		// Remember that the DOM is ready
+		jQuery.isReady = true;
+
+		// If a normal DOM Ready event fired, decrement, and wait if need be
+		if ( wait !== true && --jQuery.readyWait > 0 ) {
+			return;
+		}
+
+		// If there are functions bound, to execute
+		readyList.resolveWith( document, [ jQuery ] );
+	}
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+	document.removeEventListener( "DOMContentLoaded", completed );
+	window.removeEventListener( "load", completed );
+	jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+	( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+	// Handle it asynchronously to allow scripts the opportunity to delay ready
+	window.setTimeout( jQuery.ready );
+
+} else {
+
+	// Use the handy event callback
+	document.addEventListener( "DOMContentLoaded", completed );
+
+	// A fallback to window.onload, that will always work
+	window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+	var i = 0,
+		len = elems.length,
+		bulk = key == null;
+
+	// Sets many values
+	if ( toType( key ) === "object" ) {
+		chainable = true;
+		for ( i in key ) {
+			access( elems, fn, i, key[ i ], true, emptyGet, raw );
+		}
+
+	// Sets one value
+	} else if ( value !== undefined ) {
+		chainable = true;
+
+		if ( !isFunction( value ) ) {
+			raw = true;
+		}
+
+		if ( bulk ) {
+
+			// Bulk operations run against the entire set
+			if ( raw ) {
+				fn.call( elems, value );
+				fn = null;
+
+			// ...except when executing function values
+			} else {
+				bulk = fn;
+				fn = function( elem, _key, value ) {
+					return bulk.call( jQuery( elem ), value );
+				};
+			}
+		}
+
+		if ( fn ) {
+			for ( ; i < len; i++ ) {
+				fn(
+					elems[ i ], key, raw ?
+						value :
+						value.call( elems[ i ], i, fn( elems[ i ], key ) )
+				);
+			}
+		}
+	}
+
+	if ( chainable ) {
+		return elems;
+	}
+
+	// Gets
+	if ( bulk ) {
+		return fn.call( elems );
+	}
+
+	return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+	rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+	return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+	return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+	// Accepts only:
+	//  - Node
+	//    - Node.ELEMENT_NODE
+	//    - Node.DOCUMENT_NODE
+	//  - Object
+	//    - Any
+	return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+	this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+	cache: function( owner ) {
+
+		// Check if the owner object already has a cache
+		var value = owner[ this.expando ];
+
+		// If not, create one
+		if ( !value ) {
+			value = {};
+
+			// We can accept data for non-element nodes in modern browsers,
+			// but we should not, see #8335.
+			// Always return an empty object.
+			if ( acceptData( owner ) ) {
+
+				// If it is a node unlikely to be stringify-ed or looped over
+				// use plain assignment
+				if ( owner.nodeType ) {
+					owner[ this.expando ] = value;
+
+				// Otherwise secure it in a non-enumerable property
+				// configurable must be true to allow the property to be
+				// deleted when data is removed
+				} else {
+					Object.defineProperty( owner, this.expando, {
+						value: value,
+						configurable: true
+					} );
+				}
+			}
+		}
+
+		return value;
+	},
+	set: function( owner, data, value ) {
+		var prop,
+			cache = this.cache( owner );
+
+		// Handle: [ owner, key, value ] args
+		// Always use camelCase key (gh-2257)
+		if ( typeof data === "string" ) {
+			cache[ camelCase( data ) ] = value;
+
+		// Handle: [ owner, { properties } ] args
+		} else {
+
+			// Copy the properties one-by-one to the cache object
+			for ( prop in data ) {
+				cache[ camelCase( prop ) ] = data[ prop ];
+			}
+		}
+		return cache;
+	},
+	get: function( owner, key ) {
+		return key === undefined ?
+			this.cache( owner ) :
+
+			// Always use camelCase key (gh-2257)
+			owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+	},
+	access: function( owner, key, value ) {
+
+		// In cases where either:
+		//
+		//   1. No key was specified
+		//   2. A string key was specified, but no value provided
+		//
+		// Take the "read" path and allow the get method to determine
+		// which value to return, respectively either:
+		//
+		//   1. The entire cache object
+		//   2. The data stored at the key
+		//
+		if ( key === undefined ||
+				( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+			return this.get( owner, key );
+		}
+
+		// When the key is not a string, or both a key and value
+		// are specified, set or extend (existing objects) with either:
+		//
+		//   1. An object of properties
+		//   2. A key and value
+		//
+		this.set( owner, key, value );
+
+		// Since the "set" path can have two possible entry points
+		// return the expected data based on which path was taken[*]
+		return value !== undefined ? value : key;
+	},
+	remove: function( owner, key ) {
+		var i,
+			cache = owner[ this.expando ];
+
+		if ( cache === undefined ) {
+			return;
+		}
+
+		if ( key !== undefined ) {
+
+			// Support array or space separated string of keys
+			if ( Array.isArray( key ) ) {
+
+				// If key is an array of keys...
+				// We always set camelCase keys, so remove that.
+				key = key.map( camelCase );
+			} else {
+				key = camelCase( key );
+
+				// If a key with the spaces exists, use it.
+				// Otherwise, create an array by matching non-whitespace
+				key = key in cache ?
+					[ key ] :
+					( key.match( rnothtmlwhite ) || [] );
+			}
+
+			i = key.length;
+
+			while ( i-- ) {
+				delete cache[ key[ i ] ];
+			}
+		}
+
+		// Remove the expando if there's no more data
+		if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+			// Support: Chrome <=35 - 45
+			// Webkit & Blink performance suffers when deleting properties
+			// from DOM nodes, so set to undefined instead
+			// https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+			if ( owner.nodeType ) {
+				owner[ this.expando ] = undefined;
+			} else {
+				delete owner[ this.expando ];
+			}
+		}
+	},
+	hasData: function( owner ) {
+		var cache = owner[ this.expando ];
+		return cache !== undefined && !jQuery.isEmptyObject( cache );
+	}
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+//	Implementation Summary
+//
+//	1. Enforce API surface and semantic compatibility with 1.9.x branch
+//	2. Improve the module's maintainability by reducing the storage
+//		paths to a single mechanism.
+//	3. Use the same single mechanism to support "private" and "user" data.
+//	4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+//	5. Avoid exposing implementation details on user objects (eg. expando properties)
+//	6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+	rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+	if ( data === "true" ) {
+		return true;
+	}
+
+	if ( data === "false" ) {
+		return false;
+	}
+
+	if ( data === "null" ) {
+		return null;
+	}
+
+	// Only convert to a number if it doesn't change the string
+	if ( data === +data + "" ) {
+		return +data;
+	}
+
+	if ( rbrace.test( data ) ) {
+		return JSON.parse( data );
+	}
+
+	return data;
+}
+
+function dataAttr( elem, key, data ) {
+	var name;
+
+	// If nothing was found internally, try to fetch any
+	// data from the HTML5 data-* attribute
+	if ( data === undefined && elem.nodeType === 1 ) {
+		name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+		data = elem.getAttribute( name );
+
+		if ( typeof data === "string" ) {
+			try {
+				data = getData( data );
+			} catch ( e ) {}
+
+			// Make sure we set the data so it isn't changed later
+			dataUser.set( elem, key, data );
+		} else {
+			data = undefined;
+		}
+	}
+	return data;
+}
+
+jQuery.extend( {
+	hasData: function( elem ) {
+		return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+	},
+
+	data: function( elem, name, data ) {
+		return dataUser.access( elem, name, data );
+	},
+
+	removeData: function( elem, name ) {
+		dataUser.remove( elem, name );
+	},
+
+	// TODO: Now that all calls to _data and _removeData have been replaced
+	// with direct calls to dataPriv methods, these can be deprecated.
+	_data: function( elem, name, data ) {
+		return dataPriv.access( elem, name, data );
+	},
+
+	_removeData: function( elem, name ) {
+		dataPriv.remove( elem, name );
+	}
+} );
+
+jQuery.fn.extend( {
+	data: function( key, value ) {
+		var i, name, data,
+			elem = this[ 0 ],
+			attrs = elem && elem.attributes;
+
+		// Gets all values
+		if ( key === undefined ) {
+			if ( this.length ) {
+				data = dataUser.get( elem );
+
+				if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+					i = attrs.length;
+					while ( i-- ) {
+
+						// Support: IE 11 only
+						// The attrs elements can be null (#14894)
+						if ( attrs[ i ] ) {
+							name = attrs[ i ].name;
+							if ( name.indexOf( "data-" ) === 0 ) {
+								name = camelCase( name.slice( 5 ) );
+								dataAttr( elem, name, data[ name ] );
+							}
+						}
+					}
+					dataPriv.set( elem, "hasDataAttrs", true );
+				}
+			}
+
+			return data;
+		}
+
+		// Sets multiple values
+		if ( typeof key === "object" ) {
+			return this.each( function() {
+				dataUser.set( this, key );
+			} );
+		}
+
+		return access( this, function( value ) {
+			var data;
+
+			// The calling jQuery object (element matches) is not empty
+			// (and therefore has an element appears at this[ 0 ]) and the
+			// `value` parameter was not undefined. An empty jQuery object
+			// will result in `undefined` for elem = this[ 0 ] which will
+			// throw an exception if an attempt to read a data cache is made.
+			if ( elem && value === undefined ) {
+
+				// Attempt to get data from the cache
+				// The key will always be camelCased in Data
+				data = dataUser.get( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// Attempt to "discover" the data in
+				// HTML5 custom data-* attrs
+				data = dataAttr( elem, key );
+				if ( data !== undefined ) {
+					return data;
+				}
+
+				// We tried really hard, but the data doesn't exist.
+				return;
+			}
+
+			// Set the data...
+			this.each( function() {
+
+				// We always store the camelCased key
+				dataUser.set( this, key, value );
+			} );
+		}, null, value, arguments.length > 1, null, true );
+	},
+
+	removeData: function( key ) {
+		return this.each( function() {
+			dataUser.remove( this, key );
+		} );
+	}
+} );
+
+
+jQuery.extend( {
+	queue: function( elem, type, data ) {
+		var queue;
+
+		if ( elem ) {
+			type = ( type || "fx" ) + "queue";
+			queue = dataPriv.get( elem, type );
+
+			// Speed up dequeue by getting out quickly if this is just a lookup
+			if ( data ) {
+				if ( !queue || Array.isArray( data ) ) {
+					queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+				} else {
+					queue.push( data );
+				}
+			}
+			return queue || [];
+		}
+	},
+
+	dequeue: function( elem, type ) {
+		type = type || "fx";
+
+		var queue = jQuery.queue( elem, type ),
+			startLength = queue.length,
+			fn = queue.shift(),
+			hooks = jQuery._queueHooks( elem, type ),
+			next = function() {
+				jQuery.dequeue( elem, type );
+			};
+
+		// If the fx queue is dequeued, always remove the progress sentinel
+		if ( fn === "inprogress" ) {
+			fn = queue.shift();
+			startLength--;
+		}
+
+		if ( fn ) {
+
+			// Add a progress sentinel to prevent the fx queue from being
+			// automatically dequeued
+			if ( type === "fx" ) {
+				queue.unshift( "inprogress" );
+			}
+
+			// Clear up the last queue stop function
+			delete hooks.stop;
+			fn.call( elem, next, hooks );
+		}
+
+		if ( !startLength && hooks ) {
+			hooks.empty.fire();
+		}
+	},
+
+	// Not public - generate a queueHooks object, or return the current one
+	_queueHooks: function( elem, type ) {
+		var key = type + "queueHooks";
+		return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+			empty: jQuery.Callbacks( "once memory" ).add( function() {
+				dataPriv.remove( elem, [ type + "queue", key ] );
+			} )
+		} );
+	}
+} );
+
+jQuery.fn.extend( {
+	queue: function( type, data ) {
+		var setter = 2;
+
+		if ( typeof type !== "string" ) {
+			data = type;
+			type = "fx";
+			setter--;
+		}
+
+		if ( arguments.length < setter ) {
+			return jQuery.queue( this[ 0 ], type );
+		}
+
+		return data === undefined ?
+			this :
+			this.each( function() {
+				var queue = jQuery.queue( this, type, data );
+
+				// Ensure a hooks for this queue
+				jQuery._queueHooks( this, type );
+
+				if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+					jQuery.dequeue( this, type );
+				}
+			} );
+	},
+	dequeue: function( type ) {
+		return this.each( function() {
+			jQuery.dequeue( this, type );
+		} );
+	},
+	clearQueue: function( type ) {
+		return this.queue( type || "fx", [] );
+	},
+
+	// Get a promise resolved when queues of a certain type
+	// are emptied (fx is the type by default)
+	promise: function( type, obj ) {
+		var tmp,
+			count = 1,
+			defer = jQuery.Deferred(),
+			elements = this,
+			i = this.length,
+			resolve = function() {
+				if ( !( --count ) ) {
+					defer.resolveWith( elements, [ elements ] );
+				}
+			};
+
+		if ( typeof type !== "string" ) {
+			obj = type;
+			type = undefined;
+		}
+		type = type || "fx";
+
+		while ( i-- ) {
+			tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+			if ( tmp && tmp.empty ) {
+				count++;
+				tmp.empty.add( resolve );
+			}
+		}
+		resolve();
+		return defer.promise( obj );
+	}
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+	var isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem );
+		},
+		composed = { composed: true };
+
+	// Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+	// Check attachment across shadow DOM boundaries when possible (gh-3504)
+	// Support: iOS 10.0-10.2 only
+	// Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+	// leading to errors. We need to check for `getRootNode`.
+	if ( documentElement.getRootNode ) {
+		isAttached = function( elem ) {
+			return jQuery.contains( elem.ownerDocument, elem ) ||
+				elem.getRootNode( composed ) === elem.ownerDocument;
+		};
+	}
+var isHiddenWithinTree = function( elem, el ) {
+
+		// isHiddenWithinTree might be called from jQuery#filter function;
+		// in that case, element will be second argument
+		elem = el || elem;
+
+		// Inline style trumps all
+		return elem.style.display === "none" ||
+			elem.style.display === "" &&
+
+			// Otherwise, check computed style
+			// Support: Firefox <=43 - 45
+			// Disconnected elements can have computed display: none, so first confirm that elem is
+			// in the document.
+			isAttached( elem ) &&
+
+			jQuery.css( elem, "display" ) === "none";
+	};
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+	var adjusted, scale,
+		maxIterations = 20,
+		currentValue = tween ?
+			function() {
+				return tween.cur();
+			} :
+			function() {
+				return jQuery.css( elem, prop, "" );
+			},
+		initial = currentValue(),
+		unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+		// Starting value computation is required for potential unit mismatches
+		initialInUnit = elem.nodeType &&
+			( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+			rcssNum.exec( jQuery.css( elem, prop ) );
+
+	if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+		// Support: Firefox <=54
+		// Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+		initial = initial / 2;
+
+		// Trust units reported by jQuery.css
+		unit = unit || initialInUnit[ 3 ];
+
+		// Iteratively approximate from a nonzero starting point
+		initialInUnit = +initial || 1;
+
+		while ( maxIterations-- ) {
+
+			// Evaluate and update our best guess (doubling guesses that zero out).
+			// Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+			jQuery.style( elem, prop, initialInUnit + unit );
+			if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+				maxIterations = 0;
+			}
+			initialInUnit = initialInUnit / scale;
+
+		}
+
+		initialInUnit = initialInUnit * 2;
+		jQuery.style( elem, prop, initialInUnit + unit );
+
+		// Make sure we update the tween properties later on
+		valueParts = valueParts || [];
+	}
+
+	if ( valueParts ) {
+		initialInUnit = +initialInUnit || +initial || 0;
+
+		// Apply relative offset (+=/-=) if specified
+		adjusted = valueParts[ 1 ] ?
+			initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+			+valueParts[ 2 ];
+		if ( tween ) {
+			tween.unit = unit;
+			tween.start = initialInUnit;
+			tween.end = adjusted;
+		}
+	}
+	return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+	var temp,
+		doc = elem.ownerDocument,
+		nodeName = elem.nodeName,
+		display = defaultDisplayMap[ nodeName ];
+
+	if ( display ) {
+		return display;
+	}
+
+	temp = doc.body.appendChild( doc.createElement( nodeName ) );
+	display = jQuery.css( temp, "display" );
+
+	temp.parentNode.removeChild( temp );
+
+	if ( display === "none" ) {
+		display = "block";
+	}
+	defaultDisplayMap[ nodeName ] = display;
+
+	return display;
+}
+
+function showHide( elements, show ) {
+	var display, elem,
+		values = [],
+		index = 0,
+		length = elements.length;
+
+	// Determine new display value for elements that need to change
+	for ( ; index < length; index++ ) {
+		elem = elements[ index ];
+		if ( !elem.style ) {
+			continue;
+		}
+
+		display = elem.style.display;
+		if ( show ) {
+
+			// Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+			// check is required in this first loop unless we have a nonempty display value (either
+			// inline or about-to-be-restored)
+			if ( display === "none" ) {
+				values[ index ] = dataPriv.get( elem, "display" ) || null;
+				if ( !values[ index ] ) {
+					elem.style.display = "";
+				}
+			}
+			if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+				values[ index ] = getDefaultDisplay( elem );
+			}
+		} else {
+			if ( display !== "none" ) {
+				values[ index ] = "none";
+
+				// Remember what we're overwriting
+				dataPriv.set( elem, "display", display );
+			}
+		}
+	}
+
+	// Set the display of the elements in a second loop to avoid constant reflow
+	for ( index = 0; index < length; index++ ) {
+		if ( values[ index ] != null ) {
+			elements[ index ].style.display = values[ index ];
+		}
+	}
+
+	return elements;
+}
+
+jQuery.fn.extend( {
+	show: function() {
+		return showHide( this, true );
+	},
+	hide: function() {
+		return showHide( this );
+	},
+	toggle: function( state ) {
+		if ( typeof state === "boolean" ) {
+			return state ? this.show() : this.hide();
+		}
+
+		return this.each( function() {
+			if ( isHiddenWithinTree( this ) ) {
+				jQuery( this ).show();
+			} else {
+				jQuery( this ).hide();
+			}
+		} );
+	}
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+	var fragment = document.createDocumentFragment(),
+		div = fragment.appendChild( document.createElement( "div" ) ),
+		input = document.createElement( "input" );
+
+	// Support: Android 4.0 - 4.3 only
+	// Check state lost if the name is set (#11217)
+	// Support: Windows Web Apps (WWA)
+	// `name` and `type` must use .setAttribute for WWA (#14901)
+	input.setAttribute( "type", "radio" );
+	input.setAttribute( "checked", "checked" );
+	input.setAttribute( "name", "t" );
+
+	div.appendChild( input );
+
+	// Support: Android <=4.1 only
+	// Older WebKit doesn't clone checked state correctly in fragments
+	support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+	// Support: IE <=11 only
+	// Make sure textarea (and checkbox) defaultValue is properly cloned
+	div.innerHTML = "<textarea>x</textarea>";
+	support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+	// Support: IE <=9 only
+	// IE <=9 replaces <option> tags with their contents when inserted outside of
+	// the select element.
+	div.innerHTML = "<option></option>";
+	support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+	// XHTML parsers do not magically insert elements in the
+	// same way that tag soup parsers do. So we cannot shorten
+	// this by omitting <tbody> or other required elements.
+	thead: [ 1, "<table>", "</table>" ],
+	col: [ 2, "<table><colgroup>", "</colgroup></table>" ],
+	tr: [ 2, "<table><tbody>", "</tbody></table>" ],
+	td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ],
+
+	_default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+	wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
+
+function getAll( context, tag ) {
+
+	// Support: IE <=9 - 11 only
+	// Use typeof to avoid zero-argument method invocation on host objects (#15151)
+	var ret;
+
+	if ( typeof context.getElementsByTagName !== "undefined" ) {
+		ret = context.getElementsByTagName( tag || "*" );
+
+	} else if ( typeof context.querySelectorAll !== "undefined" ) {
+		ret = context.querySelectorAll( tag || "*" );
+
+	} else {
+		ret = [];
+	}
+
+	if ( tag === undefined || tag && nodeName( context, tag ) ) {
+		return jQuery.merge( [ context ], ret );
+	}
+
+	return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+	var i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		dataPriv.set(
+			elems[ i ],
+			"globalEval",
+			!refElements || dataPriv.get( refElements[ i ], "globalEval" )
+		);
+	}
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+	var elem, tmp, tag, wrap, attached, j,
+		fragment = context.createDocumentFragment(),
+		nodes = [],
+		i = 0,
+		l = elems.length;
+
+	for ( ; i < l; i++ ) {
+		elem = elems[ i ];
+
+		if ( elem || elem === 0 ) {
+
+			// Add nodes directly
+			if ( toType( elem ) === "object" ) {
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+			// Convert non-html into a text node
+			} else if ( !rhtml.test( elem ) ) {
+				nodes.push( context.createTextNode( elem ) );
+
+			// Convert html into DOM nodes
+			} else {
+				tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+				// Deserialize a standard representation
+				tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+				wrap = wrapMap[ tag ] || wrapMap._default;
+				tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+				// Descend through wrappers to the right content
+				j = wrap[ 0 ];
+				while ( j-- ) {
+					tmp = tmp.lastChild;
+				}
+
+				// Support: Android <=4.0 only, PhantomJS 1 only
+				// push.apply(_, arraylike) throws on ancient WebKit
+				jQuery.merge( nodes, tmp.childNodes );
+
+				// Remember the top-level container
+				tmp = fragment.firstChild;
+
+				// Ensure the created nodes are orphaned (#12392)
+				tmp.textContent = "";
+			}
+		}
+	}
+
+	// Remove wrapper from fragment
+	fragment.textContent = "";
+
+	i = 0;
+	while ( ( elem = nodes[ i++ ] ) ) {
+
+		// Skip elements already in the context collection (trac-4087)
+		if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+			if ( ignored ) {
+				ignored.push( elem );
+			}
+			continue;
+		}
+
+		attached = isAttached( elem );
+
+		// Append to fragment
+		tmp = getAll( fragment.appendChild( elem ), "script" );
+
+		// Preserve script evaluation history
+		if ( attached ) {
+			setGlobalEval( tmp );
+		}
+
+		// Capture executables
+		if ( scripts ) {
+			j = 0;
+			while ( ( elem = tmp[ j++ ] ) ) {
+				if ( rscriptType.test( elem.type || "" ) ) {
+					scripts.push( elem );
+				}
+			}
+		}
+	}
+
+	return fragment;
+}
+
+
+var rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+	return true;
+}
+
+function returnFalse() {
+	return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+	return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+	try {
+		return document.activeElement;
+	} catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+	var origFn, type;
+
+	// Types can be a map of types/handlers
+	if ( typeof types === "object" ) {
+
+		// ( types-Object, selector, data )
+		if ( typeof selector !== "string" ) {
+
+			// ( types-Object, data )
+			data = data || selector;
+			selector = undefined;
+		}
+		for ( type in types ) {
+			on( elem, type, selector, data, types[ type ], one );
+		}
+		return elem;
+	}
+
+	if ( data == null && fn == null ) {
+
+		// ( types, fn )
+		fn = selector;
+		data = selector = undefined;
+	} else if ( fn == null ) {
+		if ( typeof selector === "string" ) {
+
+			// ( types, selector, fn )
+			fn = data;
+			data = undefined;
+		} else {
+
+			// ( types, data, fn )
+			fn = data;
+			data = selector;
+			selector = undefined;
+		}
+	}
+	if ( fn === false ) {
+		fn = returnFalse;
+	} else if ( !fn ) {
+		return elem;
+	}
+
+	if ( one === 1 ) {
+		origFn = fn;
+		fn = function( event ) {
+
+			// Can use an empty set, since event contains the info
+			jQuery().off( event );
+			return origFn.apply( this, arguments );
+		};
+
+		// Use same guid so caller can remove using origFn
+		fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+	}
+	return elem.each( function() {
+		jQuery.event.add( this, types, fn, data, selector );
+	} );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+	global: {},
+
+	add: function( elem, types, handler, data, selector ) {
+
+		var handleObjIn, eventHandle, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.get( elem );
+
+		// Only attach events to objects that accept data
+		if ( !acceptData( elem ) ) {
+			return;
+		}
+
+		// Caller can pass in an object of custom data in lieu of the handler
+		if ( handler.handler ) {
+			handleObjIn = handler;
+			handler = handleObjIn.handler;
+			selector = handleObjIn.selector;
+		}
+
+		// Ensure that invalid selectors throw exceptions at attach time
+		// Evaluate against documentElement in case elem is a non-element node (e.g., document)
+		if ( selector ) {
+			jQuery.find.matchesSelector( documentElement, selector );
+		}
+
+		// Make sure that the handler has a unique ID, used to find/remove it later
+		if ( !handler.guid ) {
+			handler.guid = jQuery.guid++;
+		}
+
+		// Init the element's event structure and main handler, if this is the first
+		if ( !( events = elemData.events ) ) {
+			events = elemData.events = Object.create( null );
+		}
+		if ( !( eventHandle = elemData.handle ) ) {
+			eventHandle = elemData.handle = function( e ) {
+
+				// Discard the second event of a jQuery.event.trigger() and
+				// when an event is called after a page has unloaded
+				return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+					jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+			};
+		}
+
+		// Handle multiple events separated by a space
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// There *must* be a type, no attaching namespace-only handlers
+			if ( !type ) {
+				continue;
+			}
+
+			// If event changes its type, use the special event handlers for the changed type
+			special = jQuery.event.special[ type ] || {};
+
+			// If selector defined, determine special event api type, otherwise given type
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+
+			// Update special based on newly reset type
+			special = jQuery.event.special[ type ] || {};
+
+			// handleObj is passed to all event handlers
+			handleObj = jQuery.extend( {
+				type: type,
+				origType: origType,
+				data: data,
+				handler: handler,
+				guid: handler.guid,
+				selector: selector,
+				needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+				namespace: namespaces.join( "." )
+			}, handleObjIn );
+
+			// Init the event handler queue if we're the first
+			if ( !( handlers = events[ type ] ) ) {
+				handlers = events[ type ] = [];
+				handlers.delegateCount = 0;
+
+				// Only use addEventListener if the special events handler returns false
+				if ( !special.setup ||
+					special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+					if ( elem.addEventListener ) {
+						elem.addEventListener( type, eventHandle );
+					}
+				}
+			}
+
+			if ( special.add ) {
+				special.add.call( elem, handleObj );
+
+				if ( !handleObj.handler.guid ) {
+					handleObj.handler.guid = handler.guid;
+				}
+			}
+
+			// Add to the element's handler list, delegates in front
+			if ( selector ) {
+				handlers.splice( handlers.delegateCount++, 0, handleObj );
+			} else {
+				handlers.push( handleObj );
+			}
+
+			// Keep track of which events have ever been used, for event optimization
+			jQuery.event.global[ type ] = true;
+		}
+
+	},
+
+	// Detach an event or set of events from an element
+	remove: function( elem, types, handler, selector, mappedTypes ) {
+
+		var j, origCount, tmp,
+			events, t, handleObj,
+			special, handlers, type, namespaces, origType,
+			elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+		if ( !elemData || !( events = elemData.events ) ) {
+			return;
+		}
+
+		// Once for each type.namespace in types; type may be omitted
+		types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+		t = types.length;
+		while ( t-- ) {
+			tmp = rtypenamespace.exec( types[ t ] ) || [];
+			type = origType = tmp[ 1 ];
+			namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+			// Unbind all events (on this namespace, if provided) for the element
+			if ( !type ) {
+				for ( type in events ) {
+					jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+				}
+				continue;
+			}
+
+			special = jQuery.event.special[ type ] || {};
+			type = ( selector ? special.delegateType : special.bindType ) || type;
+			handlers = events[ type ] || [];
+			tmp = tmp[ 2 ] &&
+				new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+			// Remove matching events
+			origCount = j = handlers.length;
+			while ( j-- ) {
+				handleObj = handlers[ j ];
+
+				if ( ( mappedTypes || origType === handleObj.origType ) &&
+					( !handler || handler.guid === handleObj.guid ) &&
+					( !tmp || tmp.test( handleObj.namespace ) ) &&
+					( !selector || selector === handleObj.selector ||
+						selector === "**" && handleObj.selector ) ) {
+					handlers.splice( j, 1 );
+
+					if ( handleObj.selector ) {
+						handlers.delegateCount--;
+					}
+					if ( special.remove ) {
+						special.remove.call( elem, handleObj );
+					}
+				}
+			}
+
+			// Remove generic event handler if we removed something and no more handlers exist
+			// (avoids potential for endless recursion during removal of special event handlers)
+			if ( origCount && !handlers.length ) {
+				if ( !special.teardown ||
+					special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+					jQuery.removeEvent( elem, type, elemData.handle );
+				}
+
+				delete events[ type ];
+			}
+		}
+
+		// Remove data and the expando if it's no longer used
+		if ( jQuery.isEmptyObject( events ) ) {
+			dataPriv.remove( elem, "handle events" );
+		}
+	},
+
+	dispatch: function( nativeEvent ) {
+
+		var i, j, ret, matched, handleObj, handlerQueue,
+			args = new Array( arguments.length ),
+
+			// Make a writable jQuery.Event from the native event object
+			event = jQuery.event.fix( nativeEvent ),
+
+			handlers = (
+				dataPriv.get( this, "events" ) || Object.create( null )
+			)[ event.type ] || [],
+			special = jQuery.event.special[ event.type ] || {};
+
+		// Use the fix-ed jQuery.Event rather than the (read-only) native event
+		args[ 0 ] = event;
+
+		for ( i = 1; i < arguments.length; i++ ) {
+			args[ i ] = arguments[ i ];
+		}
+
+		event.delegateTarget = this;
+
+		// Call the preDispatch hook for the mapped type, and let it bail if desired
+		if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+			return;
+		}
+
+		// Determine handlers
+		handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+		// Run delegates first; they may want to stop propagation beneath us
+		i = 0;
+		while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+			event.currentTarget = matched.elem;
+
+			j = 0;
+			while ( ( handleObj = matched.handlers[ j++ ] ) &&
+				!event.isImmediatePropagationStopped() ) {
+
+				// If the event is namespaced, then each handler is only invoked if it is
+				// specially universal or its namespaces are a superset of the event's.
+				if ( !event.rnamespace || handleObj.namespace === false ||
+					event.rnamespace.test( handleObj.namespace ) ) {
+
+					event.handleObj = handleObj;
+					event.data = handleObj.data;
+
+					ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+						handleObj.handler ).apply( matched.elem, args );
+
+					if ( ret !== undefined ) {
+						if ( ( event.result = ret ) === false ) {
+							event.preventDefault();
+							event.stopPropagation();
+						}
+					}
+				}
+			}
+		}
+
+		// Call the postDispatch hook for the mapped type
+		if ( special.postDispatch ) {
+			special.postDispatch.call( this, event );
+		}
+
+		return event.result;
+	},
+
+	handlers: function( event, handlers ) {
+		var i, handleObj, sel, matchedHandlers, matchedSelectors,
+			handlerQueue = [],
+			delegateCount = handlers.delegateCount,
+			cur = event.target;
+
+		// Find delegate handlers
+		if ( delegateCount &&
+
+			// Support: IE <=9
+			// Black-hole SVG <use> instance trees (trac-13180)
+			cur.nodeType &&
+
+			// Support: Firefox <=42
+			// Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+			// https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+			// Support: IE 11 only
+			// ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+			!( event.type === "click" && event.button >= 1 ) ) {
+
+			for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+				// Don't check non-elements (#13208)
+				// Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+				if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+					matchedHandlers = [];
+					matchedSelectors = {};
+					for ( i = 0; i < delegateCount; i++ ) {
+						handleObj = handlers[ i ];
+
+						// Don't conflict with Object.prototype properties (#13203)
+						sel = handleObj.selector + " ";
+
+						if ( matchedSelectors[ sel ] === undefined ) {
+							matchedSelectors[ sel ] = handleObj.needsContext ?
+								jQuery( sel, this ).index( cur ) > -1 :
+								jQuery.find( sel, this, null, [ cur ] ).length;
+						}
+						if ( matchedSelectors[ sel ] ) {
+							matchedHandlers.push( handleObj );
+						}
+					}
+					if ( matchedHandlers.length ) {
+						handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+					}
+				}
+			}
+		}
+
+		// Add the remaining (directly-bound) handlers
+		cur = this;
+		if ( delegateCount < handlers.length ) {
+			handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+		}
+
+		return handlerQueue;
+	},
+
+	addProp: function( name, hook ) {
+		Object.defineProperty( jQuery.Event.prototype, name, {
+			enumerable: true,
+			configurable: true,
+
+			get: isFunction( hook ) ?
+				function() {
+					if ( this.originalEvent ) {
+						return hook( this.originalEvent );
+					}
+				} :
+				function() {
+					if ( this.originalEvent ) {
+						return this.originalEvent[ name ];
+					}
+				},
+
+			set: function( value ) {
+				Object.defineProperty( this, name, {
+					enumerable: true,
+					configurable: true,
+					writable: true,
+					value: value
+				} );
+			}
+		} );
+	},
+
+	fix: function( originalEvent ) {
+		return originalEvent[ jQuery.expando ] ?
+			originalEvent :
+			new jQuery.Event( originalEvent );
+	},
+
+	special: {
+		load: {
+
+			// Prevent triggered image.load events from bubbling to window.load
+			noBubble: true
+		},
+		click: {
+
+			// Utilize native event to ensure correct state for checkable inputs
+			setup: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Claim the first handler
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					// dataPriv.set( el, "click", ... )
+					leverageNative( el, "click", returnTrue );
+				}
+
+				// Return false to allow normal processing in the caller
+				return false;
+			},
+			trigger: function( data ) {
+
+				// For mutual compressibility with _default, replace `this` access with a local var.
+				// `|| data` is dead code meant only to preserve the variable through minification.
+				var el = this || data;
+
+				// Force setup before triggering a click
+				if ( rcheckableType.test( el.type ) &&
+					el.click && nodeName( el, "input" ) ) {
+
+					leverageNative( el, "click" );
+				}
+
+				// Return non-false to allow normal event-path propagation
+				return true;
+			},
+
+			// For cross-browser consistency, suppress native .click() on links
+			// Also prevent it if we're currently inside a leveraged native-event stack
+			_default: function( event ) {
+				var target = event.target;
+				return rcheckableType.test( target.type ) &&
+					target.click && nodeName( target, "input" ) &&
+					dataPriv.get( target, "click" ) ||
+					nodeName( target, "a" );
+			}
+		},
+
+		beforeunload: {
+			postDispatch: function( event ) {
+
+				// Support: Firefox 20+
+				// Firefox doesn't alert if the returnValue field is not set.
+				if ( event.result !== undefined && event.originalEvent ) {
+					event.originalEvent.returnValue = event.result;
+				}
+			}
+		}
+	}
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+	// Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+	if ( !expectSync ) {
+		if ( dataPriv.get( el, type ) === undefined ) {
+			jQuery.event.add( el, type, returnTrue );
+		}
+		return;
+	}
+
+	// Register the controller as a special universal handler for all event namespaces
+	dataPriv.set( el, type, false );
+	jQuery.event.add( el, type, {
+		namespace: false,
+		handler: function( event ) {
+			var notAsync, result,
+				saved = dataPriv.get( this, type );
+
+			if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+				// Interrupt processing of the outer synthetic .trigger()ed event
+				// Saved data should be false in such cases, but might be a leftover capture object
+				// from an async native handler (gh-4350)
+				if ( !saved.length ) {
+
+					// Store arguments for use when handling the inner native event
+					// There will always be at least one argument (an event object), so this array
+					// will not be confused with a leftover capture object.
+					saved = slice.call( arguments );
+					dataPriv.set( this, type, saved );
+
+					// Trigger the native event and capture its result
+					// Support: IE <=9 - 11+
+					// focus() and blur() are asynchronous
+					notAsync = expectSync( this, type );
+					this[ type ]();
+					result = dataPriv.get( this, type );
+					if ( saved !== result || notAsync ) {
+						dataPriv.set( this, type, false );
+					} else {
+						result = {};
+					}
+					if ( saved !== result ) {
+
+						// Cancel the outer synthetic event
+						event.stopImmediatePropagation();
+						event.preventDefault();
+
+						// Support: Chrome 86+
+						// In Chrome, if an element having a focusout handler is blurred by
+						// clicking outside of it, it invokes the handler synchronously. If
+						// that handler calls `.remove()` on the element, the data is cleared,
+						// leaving `result` undefined. We need to guard against this.
+						return result && result.value;
+					}
+
+				// If this is an inner synthetic event for an event with a bubbling surrogate
+				// (focus or blur), assume that the surrogate already propagated from triggering the
+				// native event and prevent that from happening again here.
+				// This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+				// bubbling surrogate propagates *after* the non-bubbling base), but that seems
+				// less bad than duplication.
+				} else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+					event.stopPropagation();
+				}
+
+			// If this is a native event triggered above, everything is now in order
+			// Fire an inner synthetic event with the original arguments
+			} else if ( saved.length ) {
+
+				// ...and capture the result
+				dataPriv.set( this, type, {
+					value: jQuery.event.trigger(
+
+						// Support: IE <=9 - 11+
+						// Extend with the prototype to reset the above stopImmediatePropagation()
+						jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+						saved.slice( 1 ),
+						this
+					)
+				} );
+
+				// Abort handling of the native event
+				event.stopImmediatePropagation();
+			}
+		}
+	} );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+	// This "if" is needed for plain objects
+	if ( elem.removeEventListener ) {
+		elem.removeEventListener( type, handle );
+	}
+};
+
+jQuery.Event = function( src, props ) {
+
+	// Allow instantiation without the 'new' keyword
+	if ( !( this instanceof jQuery.Event ) ) {
+		return new jQuery.Event( src, props );
+	}
+
+	// Event object
+	if ( src && src.type ) {
+		this.originalEvent = src;
+		this.type = src.type;
+
+		// Events bubbling up the document may have been marked as prevented
+		// by a handler lower down the tree; reflect the correct value.
+		this.isDefaultPrevented = src.defaultPrevented ||
+				src.defaultPrevented === undefined &&
+
+				// Support: Android <=2.3 only
+				src.returnValue === false ?
+			returnTrue :
+			returnFalse;
+
+		// Create target properties
+		// Support: Safari <=6 - 7 only
+		// Target should not be a text node (#504, #13143)
+		this.target = ( src.target && src.target.nodeType === 3 ) ?
+			src.target.parentNode :
+			src.target;
+
+		this.currentTarget = src.currentTarget;
+		this.relatedTarget = src.relatedTarget;
+
+	// Event type
+	} else {
+		this.type = src;
+	}
+
+	// Put explicitly provided properties onto the event object
+	if ( props ) {
+		jQuery.extend( this, props );
+	}
+
+	// Create a timestamp if incoming event doesn't have one
+	this.timeStamp = src && src.timeStamp || Date.now();
+
+	// Mark it as fixed
+	this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+	constructor: jQuery.Event,
+	isDefaultPrevented: returnFalse,
+	isPropagationStopped: returnFalse,
+	isImmediatePropagationStopped: returnFalse,
+	isSimulated: false,
+
+	preventDefault: function() {
+		var e = this.originalEvent;
+
+		this.isDefaultPrevented = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.preventDefault();
+		}
+	},
+	stopPropagation: function() {
+		var e = this.originalEvent;
+
+		this.isPropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopPropagation();
+		}
+	},
+	stopImmediatePropagation: function() {
+		var e = this.originalEvent;
+
+		this.isImmediatePropagationStopped = returnTrue;
+
+		if ( e && !this.isSimulated ) {
+			e.stopImmediatePropagation();
+		}
+
+		this.stopPropagation();
+	}
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+	altKey: true,
+	bubbles: true,
+	cancelable: true,
+	changedTouches: true,
+	ctrlKey: true,
+	detail: true,
+	eventPhase: true,
+	metaKey: true,
+	pageX: true,
+	pageY: true,
+	shiftKey: true,
+	view: true,
+	"char": true,
+	code: true,
+	charCode: true,
+	key: true,
+	keyCode: true,
+	button: true,
+	buttons: true,
+	clientX: true,
+	clientY: true,
+	offsetX: true,
+	offsetY: true,
+	pointerId: true,
+	pointerType: true,
+	screenX: true,
+	screenY: true,
+	targetTouches: true,
+	toElement: true,
+	touches: true,
+	which: true
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+	jQuery.event.special[ type ] = {
+
+		// Utilize native event if possible so blur/focus sequence is correct
+		setup: function() {
+
+			// Claim the first handler
+			// dataPriv.set( this, "focus", ... )
+			// dataPriv.set( this, "blur", ... )
+			leverageNative( this, type, expectSync );
+
+			// Return false to allow normal processing in the caller
+			return false;
+		},
+		trigger: function() {
+
+			// Force setup before trigger
+			leverageNative( this, type );
+
+			// Return non-false to allow normal event-path propagation
+			return true;
+		},
+
+		// Suppress native focus or blur as it's already being fired
+		// in leverageNative.
+		_default: function() {
+			return true;
+		},
+
+		delegateType: delegateType
+	};
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+	mouseenter: "mouseover",
+	mouseleave: "mouseout",
+	pointerenter: "pointerover",
+	pointerleave: "pointerout"
+}, function( orig, fix ) {
+	jQuery.event.special[ orig ] = {
+		delegateType: fix,
+		bindType: fix,
+
+		handle: function( event ) {
+			var ret,
+				target = this,
+				related = event.relatedTarget,
+				handleObj = event.handleObj;
+
+			// For mouseenter/leave call the handler if related is outside the target.
+			// NB: No relatedTarget if the mouse left/entered the browser window
+			if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+				event.type = handleObj.origType;
+				ret = handleObj.handler.apply( this, arguments );
+				event.type = fix;
+			}
+			return ret;
+		}
+	};
+} );
+
+jQuery.fn.extend( {
+
+	on: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn );
+	},
+	one: function( types, selector, data, fn ) {
+		return on( this, types, selector, data, fn, 1 );
+	},
+	off: function( types, selector, fn ) {
+		var handleObj, type;
+		if ( types && types.preventDefault && types.handleObj ) {
+
+			// ( event )  dispatched jQuery.Event
+			handleObj = types.handleObj;
+			jQuery( types.delegateTarget ).off(
+				handleObj.namespace ?
+					handleObj.origType + "." + handleObj.namespace :
+					handleObj.origType,
+				handleObj.selector,
+				handleObj.handler
+			);
+			return this;
+		}
+		if ( typeof types === "object" ) {
+
+			// ( types-object [, selector] )
+			for ( type in types ) {
+				this.off( type, selector, types[ type ] );
+			}
+			return this;
+		}
+		if ( selector === false || typeof selector === "function" ) {
+
+			// ( types [, fn] )
+			fn = selector;
+			selector = undefined;
+		}
+		if ( fn === false ) {
+			fn = returnFalse;
+		}
+		return this.each( function() {
+			jQuery.event.remove( this, types, fn, selector );
+		} );
+	}
+} );
+
+
+var
+
+	// Support: IE <=10 - 11, Edge 12 - 13 only
+	// In IE/Edge using regex groups here causes severe slowdowns.
+	// See https://connect.microsoft.com/IE/feedback/details/1736512/
+	rnoInnerhtml = /<script|<style|<link/i,
+
+	// checked="checked" or checked
+	rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i,
+	rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+	if ( nodeName( elem, "table" ) &&
+		nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+		return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+	}
+
+	return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+	elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+	return elem;
+}
+function restoreScript( elem ) {
+	if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+		elem.type = elem.type.slice( 5 );
+	} else {
+		elem.removeAttribute( "type" );
+	}
+
+	return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+	var i, l, type, pdataOld, udataOld, udataCur, events;
+
+	if ( dest.nodeType !== 1 ) {
+		return;
+	}
+
+	// 1. Copy private data: events, handlers, etc.
+	if ( dataPriv.hasData( src ) ) {
+		pdataOld = dataPriv.get( src );
+		events = pdataOld.events;
+
+		if ( events ) {
+			dataPriv.remove( dest, "handle events" );
+
+			for ( type in events ) {
+				for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+					jQuery.event.add( dest, type, events[ type ][ i ] );
+				}
+			}
+		}
+	}
+
+	// 2. Copy user data
+	if ( dataUser.hasData( src ) ) {
+		udataOld = dataUser.access( src );
+		udataCur = jQuery.extend( {}, udataOld );
+
+		dataUser.set( dest, udataCur );
+	}
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+	var nodeName = dest.nodeName.toLowerCase();
+
+	// Fails to persist the checked state of a cloned checkbox or radio button.
+	if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+		dest.checked = src.checked;
+
+	// Fails to return the selected option to the default selected state when cloning options
+	} else if ( nodeName === "input" || nodeName === "textarea" ) {
+		dest.defaultValue = src.defaultValue;
+	}
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+	// Flatten any nested arrays
+	args = flat( args );
+
+	var fragment, first, scripts, hasScripts, node, doc,
+		i = 0,
+		l = collection.length,
+		iNoClone = l - 1,
+		value = args[ 0 ],
+		valueIsFunction = isFunction( value );
+
+	// We can't cloneNode fragments that contain checked, in WebKit
+	if ( valueIsFunction ||
+			( l > 1 && typeof value === "string" &&
+				!support.checkClone && rchecked.test( value ) ) ) {
+		return collection.each( function( index ) {
+			var self = collection.eq( index );
+			if ( valueIsFunction ) {
+				args[ 0 ] = value.call( this, index, self.html() );
+			}
+			domManip( self, args, callback, ignored );
+		} );
+	}
+
+	if ( l ) {
+		fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+		first = fragment.firstChild;
+
+		if ( fragment.childNodes.length === 1 ) {
+			fragment = first;
+		}
+
+		// Require either new content or an interest in ignored elements to invoke the callback
+		if ( first || ignored ) {
+			scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+			hasScripts = scripts.length;
+
+			// Use the original fragment for the last item
+			// instead of the first because it can end up
+			// being emptied incorrectly in certain situations (#8070).
+			for ( ; i < l; i++ ) {
+				node = fragment;
+
+				if ( i !== iNoClone ) {
+					node = jQuery.clone( node, true, true );
+
+					// Keep references to cloned scripts for later restoration
+					if ( hasScripts ) {
+
+						// Support: Android <=4.0 only, PhantomJS 1 only
+						// push.apply(_, arraylike) throws on ancient WebKit
+						jQuery.merge( scripts, getAll( node, "script" ) );
+					}
+				}
+
+				callback.call( collection[ i ], node, i );
+			}
+
+			if ( hasScripts ) {
+				doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+				// Reenable scripts
+				jQuery.map( scripts, restoreScript );
+
+				// Evaluate executable scripts on first document insertion
+				for ( i = 0; i < hasScripts; i++ ) {
+					node = scripts[ i ];
+					if ( rscriptType.test( node.type || "" ) &&
+						!dataPriv.access( node, "globalEval" ) &&
+						jQuery.contains( doc, node ) ) {
+
+						if ( node.src && ( node.type || "" ).toLowerCase()  !== "module" ) {
+
+							// Optional AJAX dependency, but won't run scripts if not present
+							if ( jQuery._evalUrl && !node.noModule ) {
+								jQuery._evalUrl( node.src, {
+									nonce: node.nonce || node.getAttribute( "nonce" )
+								}, doc );
+							}
+						} else {
+							DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return collection;
+}
+
+function remove( elem, selector, keepData ) {
+	var node,
+		nodes = selector ? jQuery.filter( selector, elem ) : elem,
+		i = 0;
+
+	for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+		if ( !keepData && node.nodeType === 1 ) {
+			jQuery.cleanData( getAll( node ) );
+		}
+
+		if ( node.parentNode ) {
+			if ( keepData && isAttached( node ) ) {
+				setGlobalEval( getAll( node, "script" ) );
+			}
+			node.parentNode.removeChild( node );
+		}
+	}
+
+	return elem;
+}
+
+jQuery.extend( {
+	htmlPrefilter: function( html ) {
+		return html;
+	},
+
+	clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+		var i, l, srcElements, destElements,
+			clone = elem.cloneNode( true ),
+			inPage = isAttached( elem );
+
+		// Fix IE cloning issues
+		if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+				!jQuery.isXMLDoc( elem ) ) {
+
+			// We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+			destElements = getAll( clone );
+			srcElements = getAll( elem );
+
+			for ( i = 0, l = srcElements.length; i < l; i++ ) {
+				fixInput( srcElements[ i ], destElements[ i ] );
+			}
+		}
+
+		// Copy the events from the original to the clone
+		if ( dataAndEvents ) {
+			if ( deepDataAndEvents ) {
+				srcElements = srcElements || getAll( elem );
+				destElements = destElements || getAll( clone );
+
+				for ( i = 0, l = srcElements.length; i < l; i++ ) {
+					cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+				}
+			} else {
+				cloneCopyEvent( elem, clone );
+			}
+		}
+
+		// Preserve script evaluation history
+		destElements = getAll( clone, "script" );
+		if ( destElements.length > 0 ) {
+			setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+		}
+
+		// Return the cloned set
+		return clone;
+	},
+
+	cleanData: function( elems ) {
+		var data, elem, type,
+			special = jQuery.event.special,
+			i = 0;
+
+		for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+			if ( acceptData( elem ) ) {
+				if ( ( data = elem[ dataPriv.expando ] ) ) {
+					if ( data.events ) {
+						for ( type in data.events ) {
+							if ( special[ type ] ) {
+								jQuery.event.remove( elem, type );
+
+							// This is a shortcut to avoid jQuery.event.remove's overhead
+							} else {
+								jQuery.removeEvent( elem, type, data.handle );
+							}
+						}
+					}
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataPriv.expando ] = undefined;
+				}
+				if ( elem[ dataUser.expando ] ) {
+
+					// Support: Chrome <=35 - 45+
+					// Assign undefined instead of using delete, see Data#remove
+					elem[ dataUser.expando ] = undefined;
+				}
+			}
+		}
+	}
+} );
+
+jQuery.fn.extend( {
+	detach: function( selector ) {
+		return remove( this, selector, true );
+	},
+
+	remove: function( selector ) {
+		return remove( this, selector );
+	},
+
+	text: function( value ) {
+		return access( this, function( value ) {
+			return value === undefined ?
+				jQuery.text( this ) :
+				this.empty().each( function() {
+					if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+						this.textContent = value;
+					}
+				} );
+		}, null, value, arguments.length );
+	},
+
+	append: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.appendChild( elem );
+			}
+		} );
+	},
+
+	prepend: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+				var target = manipulationTarget( this, elem );
+				target.insertBefore( elem, target.firstChild );
+			}
+		} );
+	},
+
+	before: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this );
+			}
+		} );
+	},
+
+	after: function() {
+		return domManip( this, arguments, function( elem ) {
+			if ( this.parentNode ) {
+				this.parentNode.insertBefore( elem, this.nextSibling );
+			}
+		} );
+	},
+
+	empty: function() {
+		var elem,
+			i = 0;
+
+		for ( ; ( elem = this[ i ] ) != null; i++ ) {
+			if ( elem.nodeType === 1 ) {
+
+				// Prevent memory leaks
+				jQuery.cleanData( getAll( elem, false ) );
+
+				// Remove any remaining nodes
+				elem.textContent = "";
+			}
+		}
+
+		return this;
+	},
+
+	clone: function( dataAndEvents, deepDataAndEvents ) {
+		dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+		deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+		return this.map( function() {
+			return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+		} );
+	},
+
+	html: function( value ) {
+		return access( this, function( value ) {
+			var elem = this[ 0 ] || {},
+				i = 0,
+				l = this.length;
+
+			if ( value === undefined && elem.nodeType === 1 ) {
+				return elem.innerHTML;
+			}
+
+			// See if we can take a shortcut and just use innerHTML
+			if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+				!wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+				value = jQuery.htmlPrefilter( value );
+
+				try {
+					for ( ; i < l; i++ ) {
+						elem = this[ i ] || {};
+
+						// Remove element nodes and prevent memory leaks
+						if ( elem.nodeType === 1 ) {
+							jQuery.cleanData( getAll( elem, false ) );
+							elem.innerHTML = value;
+						}
+					}
+
+					elem = 0;
+
+				// If using innerHTML throws an exception, use the fallback method
+				} catch ( e ) {}
+			}
+
+			if ( elem ) {
+				this.empty().append( value );
+			}
+		}, null, value, arguments.length );
+	},
+
+	replaceWith: function() {
+		var ignored = [];
+
+		// Make the changes, replacing each non-ignored context element with the new content
+		return domManip( this, arguments, function( elem ) {
+			var parent = this.parentNode;
+
+			if ( jQuery.inArray( this, ignored ) < 0 ) {
+				jQuery.cleanData( getAll( this ) );
+				if ( parent ) {
+					parent.replaceChild( elem, this );
+				}
+			}
+
+		// Force callback invocation
+		}, ignored );
+	}
+} );
+
+jQuery.each( {
+	appendTo: "append",
+	prependTo: "prepend",
+	insertBefore: "before",
+	insertAfter: "after",
+	replaceAll: "replaceWith"
+}, function( name, original ) {
+	jQuery.fn[ name ] = function( selector ) {
+		var elems,
+			ret = [],
+			insert = jQuery( selector ),
+			last = insert.length - 1,
+			i = 0;
+
+		for ( ; i <= last; i++ ) {
+			elems = i === last ? this : this.clone( true );
+			jQuery( insert[ i ] )[ original ]( elems );
+
+			// Support: Android <=4.0 only, PhantomJS 1 only
+			// .get() because push.apply(_, arraylike) throws on ancient WebKit
+			push.apply( ret, elems.get() );
+		}
+
+		return this.pushStack( ret );
+	};
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+		// Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+		// IE throws on elements created in popups
+		// FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+		var view = elem.ownerDocument.defaultView;
+
+		if ( !view || !view.opener ) {
+			view = window;
+		}
+
+		return view.getComputedStyle( elem );
+	};
+
+var swap = function( elem, options, callback ) {
+	var ret, name,
+		old = {};
+
+	// Remember the old values, and insert the new ones
+	for ( name in options ) {
+		old[ name ] = elem.style[ name ];
+		elem.style[ name ] = options[ name ];
+	}
+
+	ret = callback.call( elem );
+
+	// Revert the old values
+	for ( name in options ) {
+		elem.style[ name ] = old[ name ];
+	}
+
+	return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+	// Executing both pixelPosition & boxSizingReliable tests require only one layout
+	// so they're executed at the same time to save the second computation.
+	function computeStyleTests() {
+
+		// This is a singleton, we need to execute it only once
+		if ( !div ) {
+			return;
+		}
+
+		container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+			"margin-top:1px;padding:0;border:0";
+		div.style.cssText =
+			"position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+			"margin:auto;border:1px;padding:1px;" +
+			"width:60%;top:1%";
+		documentElement.appendChild( container ).appendChild( div );
+
+		var divStyle = window.getComputedStyle( div );
+		pixelPositionVal = divStyle.top !== "1%";
+
+		// Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+		reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+		// Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+		// Some styles come back with percentage values, even though they shouldn't
+		div.style.right = "60%";
+		pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+		// Support: IE 9 - 11 only
+		// Detect misreporting of content dimensions for box-sizing:border-box elements
+		boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+		// Support: IE 9 only
+		// Detect overflow:scroll screwiness (gh-3699)
+		// Support: Chrome <=64
+		// Don't get tricked when zoom affects offsetWidth (gh-4029)
+		div.style.position = "absolute";
+		scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+		documentElement.removeChild( container );
+
+		// Nullify the div so it wouldn't be stored in the memory and
+		// it will also be a sign that checks already performed
+		div = null;
+	}
+
+	function roundPixelMeasures( measure ) {
+		return Math.round( parseFloat( measure ) );
+	}
+
+	var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+		reliableTrDimensionsVal, reliableMarginLeftVal,
+		container = document.createElement( "div" ),
+		div = document.createElement( "div" );
+
+	// Finish early in limited (non-browser) environments
+	if ( !div.style ) {
+		return;
+	}
+
+	// Support: IE <=9 - 11 only
+	// Style of cloned element affects source element cloned (#8908)
+	div.style.backgroundClip = "content-box";
+	div.cloneNode( true ).style.backgroundClip = "";
+	support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+	jQuery.extend( support, {
+		boxSizingReliable: function() {
+			computeStyleTests();
+			return boxSizingReliableVal;
+		},
+		pixelBoxStyles: function() {
+			computeStyleTests();
+			return pixelBoxStylesVal;
+		},
+		pixelPosition: function() {
+			computeStyleTests();
+			return pixelPositionVal;
+		},
+		reliableMarginLeft: function() {
+			computeStyleTests();
+			return reliableMarginLeftVal;
+		},
+		scrollboxSize: function() {
+			computeStyleTests();
+			return scrollboxSizeVal;
+		},
+
+		// Support: IE 9 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Behavior in IE 9 is more subtle than in newer versions & it passes
+		// some versions of this test; make sure not to make it pass there!
+		//
+		// Support: Firefox 70+
+		// Only Firefox includes border widths
+		// in computed dimensions. (gh-4529)
+		reliableTrDimensions: function() {
+			var table, tr, trChild, trStyle;
+			if ( reliableTrDimensionsVal == null ) {
+				table = document.createElement( "table" );
+				tr = document.createElement( "tr" );
+				trChild = document.createElement( "div" );
+
+				table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate";
+				tr.style.cssText = "border:1px solid";
+
+				// Support: Chrome 86+
+				// Height set through cssText does not get applied.
+				// Computed height then comes back as 0.
+				tr.style.height = "1px";
+				trChild.style.height = "9px";
+
+				// Support: Android 8 Chrome 86+
+				// In our bodyBackground.html iframe,
+				// display for all div elements is set to "inline",
+				// which causes a problem only in Android 8 Chrome 86.
+				// Ensuring the div is display: block
+				// gets around this issue.
+				trChild.style.display = "block";
+
+				documentElement
+					.appendChild( table )
+					.appendChild( tr )
+					.appendChild( trChild );
+
+				trStyle = window.getComputedStyle( tr );
+				reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) +
+					parseInt( trStyle.borderTopWidth, 10 ) +
+					parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight;
+
+				documentElement.removeChild( table );
+			}
+			return reliableTrDimensionsVal;
+		}
+	} );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+	var width, minWidth, maxWidth, ret,
+
+		// Support: Firefox 51+
+		// Retrieving style before computed somehow
+		// fixes an issue with getting wrong values
+		// on detached elements
+		style = elem.style;
+
+	computed = computed || getStyles( elem );
+
+	// getPropertyValue is needed for:
+	//   .css('filter') (IE 9 only, #12537)
+	//   .css('--customProperty) (#3144)
+	if ( computed ) {
+		ret = computed.getPropertyValue( name ) || computed[ name ];
+
+		if ( ret === "" && !isAttached( elem ) ) {
+			ret = jQuery.style( elem, name );
+		}
+
+		// A tribute to the "awesome hack by Dean Edwards"
+		// Android Browser returns percentage for some values,
+		// but width seems to be reliably pixels.
+		// This is against the CSSOM draft spec:
+		// https://drafts.csswg.org/cssom/#resolved-values
+		if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+			// Remember the original values
+			width = style.width;
+			minWidth = style.minWidth;
+			maxWidth = style.maxWidth;
+
+			// Put in the new values to get a computed value out
+			style.minWidth = style.maxWidth = style.width = ret;
+			ret = computed.width;
+
+			// Revert the changed values
+			style.width = width;
+			style.minWidth = minWidth;
+			style.maxWidth = maxWidth;
+		}
+	}
+
+	return ret !== undefined ?
+
+		// Support: IE <=9 - 11 only
+		// IE returns zIndex value as an integer.
+		ret + "" :
+		ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+	// Define the hook, we'll check on the first run if it's really needed.
+	return {
+		get: function() {
+			if ( conditionFn() ) {
+
+				// Hook not needed (or it's not possible to use it due
+				// to missing dependency), remove it.
+				delete this.get;
+				return;
+			}
+
+			// Hook needed; redefine it so that the support test is not executed again.
+			return ( this.get = hookFn ).apply( this, arguments );
+		}
+	};
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+	emptyStyle = document.createElement( "div" ).style,
+	vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+	// Check for vendor prefixed names
+	var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+		i = cssPrefixes.length;
+
+	while ( i-- ) {
+		name = cssPrefixes[ i ] + capName;
+		if ( name in emptyStyle ) {
+			return name;
+		}
+	}
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+	var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+	if ( final ) {
+		return final;
+	}
+	if ( name in emptyStyle ) {
+		return name;
+	}
+	return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+	// Swappable if display is none or starts with table
+	// except "table", "table-cell", or "table-caption"
+	// See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+	rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+	rcustomProp = /^--/,
+	cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+	cssNormalTransform = {
+		letterSpacing: "0",
+		fontWeight: "400"
+	};
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+	// Any relative (+/-) values have already been
+	// normalized at this point
+	var matches = rcssNum.exec( value );
+	return matches ?
+
+		// Guard against undefined "subtract", e.g., when used as in cssHooks
+		Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+		value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+	var i = dimension === "width" ? 1 : 0,
+		extra = 0,
+		delta = 0;
+
+	// Adjustment may not be necessary
+	if ( box === ( isBorderBox ? "border" : "content" ) ) {
+		return 0;
+	}
+
+	for ( ; i < 4; i += 2 ) {
+
+		// Both box models exclude margin
+		if ( box === "margin" ) {
+			delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+		}
+
+		// If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+		if ( !isBorderBox ) {
+
+			// Add padding
+			delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+			// For "border" or "margin", add border
+			if ( box !== "padding" ) {
+				delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+			// But still keep track of it otherwise
+			} else {
+				extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+
+		// If we get here with a border-box (content + padding + border), we're seeking "content" or
+		// "padding" or "margin"
+		} else {
+
+			// For "content", subtract padding
+			if ( box === "content" ) {
+				delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+			}
+
+			// For "content" or "padding", subtract border
+			if ( box !== "margin" ) {
+				delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+			}
+		}
+	}
+
+	// Account for positive content-box scroll gutter when requested by providing computedVal
+	if ( !isBorderBox && computedVal >= 0 ) {
+
+		// offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+		// Assuming integer scroll gutter, subtract the rest and round down
+		delta += Math.max( 0, Math.ceil(
+			elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+			computedVal -
+			delta -
+			extra -
+			0.5
+
+		// If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+		// Use an explicit zero to avoid NaN (gh-3964)
+		) ) || 0;
+	}
+
+	return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+	// Start with computed style
+	var styles = getStyles( elem ),
+
+		// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+		// Fake content-box until we know it's needed to know the true value.
+		boxSizingNeeded = !support.boxSizingReliable() || extra,
+		isBorderBox = boxSizingNeeded &&
+			jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+		valueIsBorderBox = isBorderBox,
+
+		val = curCSS( elem, dimension, styles ),
+		offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+	// Support: Firefox <=54
+	// Return a confounding non-pixel value or feign ignorance, as appropriate.
+	if ( rnumnonpx.test( val ) ) {
+		if ( !extra ) {
+			return val;
+		}
+		val = "auto";
+	}
+
+
+	// Support: IE 9 - 11 only
+	// Use offsetWidth/offsetHeight for when box sizing is unreliable.
+	// In those cases, the computed value can be trusted to be border-box.
+	if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+		// Support: IE 10 - 11+, Edge 15 - 18+
+		// IE/Edge misreport `getComputedStyle` of table rows with width/height
+		// set in CSS while `offset*` properties report correct values.
+		// Interestingly, in some cases IE 9 doesn't suffer from this issue.
+		!support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+		// Fall back to offsetWidth/offsetHeight when value is "auto"
+		// This happens for inline elements with no explicit setting (gh-3571)
+		val === "auto" ||
+
+		// Support: Android <=4.1 - 4.3 only
+		// Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+		!parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+		// Make sure the element is visible & connected
+		elem.getClientRects().length ) {
+
+		isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+		// Where available, offsetWidth/offsetHeight approximate border box dimensions.
+		// Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+		// retrieved value as a content box dimension.
+		valueIsBorderBox = offsetProp in elem;
+		if ( valueIsBorderBox ) {
+			val = elem[ offsetProp ];
+		}
+	}
+
+	// Normalize "" and auto
+	val = parseFloat( val ) || 0;
+
+	// Adjust for the element's box model
+	return ( val +
+		boxModelAdjustment(
+			elem,
+			dimension,
+			extra || ( isBorderBox ? "border" : "content" ),
+			valueIsBorderBox,
+			styles,
+
+			// Provide the current computed size to request scroll gutter calculation (gh-3589)
+			val
+		)
+	) + "px";
+}
+
+jQuery.extend( {
+
+	// Add in style property hooks for overriding the default
+	// behavior of getting and setting a style property
+	cssHooks: {
+		opacity: {
+			get: function( elem, computed ) {
+				if ( computed ) {
+
+					// We should always get a number back from opacity
+					var ret = curCSS( elem, "opacity" );
+					return ret === "" ? "1" : ret;
+				}
+			}
+		}
+	},
+
+	// Don't automatically add "px" to these possibly-unitless properties
+	cssNumber: {
+		"animationIterationCount": true,
+		"columnCount": true,
+		"fillOpacity": true,
+		"flexGrow": true,
+		"flexShrink": true,
+		"fontWeight": true,
+		"gridArea": true,
+		"gridColumn": true,
+		"gridColumnEnd": true,
+		"gridColumnStart": true,
+		"gridRow": true,
+		"gridRowEnd": true,
+		"gridRowStart": true,
+		"lineHeight": true,
+		"opacity": true,
+		"order": true,
+		"orphans": true,
+		"widows": true,
+		"zIndex": true,
+		"zoom": true
+	},
+
+	// Add in properties whose names you wish to fix before
+	// setting or getting the value
+	cssProps: {},
+
+	// Get and set the style property on a DOM Node
+	style: function( elem, name, value, extra ) {
+
+		// Don't set styles on text and comment nodes
+		if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+			return;
+		}
+
+		// Make sure that we're working with the right name
+		var ret, type, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name ),
+			style = elem.style;
+
+		// Make sure that we're working with the right name. We don't
+		// want to query the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Gets hook for the prefixed version, then unprefixed version
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// Check if we're setting a value
+		if ( value !== undefined ) {
+			type = typeof value;
+
+			// Convert "+=" or "-=" to relative numbers (#7345)
+			if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+				value = adjustCSS( elem, name, ret );
+
+				// Fixes bug #9237
+				type = "number";
+			}
+
+			// Make sure that null and NaN values aren't set (#7116)
+			if ( value == null || value !== value ) {
+				return;
+			}
+
+			// If a number was passed in, add the unit (except for certain CSS properties)
+			// The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+			// "px" to a few hardcoded values.
+			if ( type === "number" && !isCustomProp ) {
+				value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+			}
+
+			// background-* props affect original clone's values
+			if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+				style[ name ] = "inherit";
+			}
+
+			// If a hook was provided, use that value, otherwise just set the specified value
+			if ( !hooks || !( "set" in hooks ) ||
+				( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+				if ( isCustomProp ) {
+					style.setProperty( name, value );
+				} else {
+					style[ name ] = value;
+				}
+			}
+
+		} else {
+
+			// If a hook was provided get the non-computed value from there
+			if ( hooks && "get" in hooks &&
+				( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+				return ret;
+			}
+
+			// Otherwise just get the value from the style object
+			return style[ name ];
+		}
+	},
+
+	css: function( elem, name, extra, styles ) {
+		var val, num, hooks,
+			origName = camelCase( name ),
+			isCustomProp = rcustomProp.test( name );
+
+		// Make sure that we're working with the right name. We don't
+		// want to modify the value if it is a CSS custom property
+		// since they are user-defined.
+		if ( !isCustomProp ) {
+			name = finalPropName( origName );
+		}
+
+		// Try prefixed name followed by the unprefixed name
+		hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+		// If a hook was provided get the computed value from there
+		if ( hooks && "get" in hooks ) {
+			val = hooks.get( elem, true, extra );
+		}
+
+		// Otherwise, if a way to get the computed value exists, use that
+		if ( val === undefined ) {
+			val = curCSS( elem, name, styles );
+		}
+
+		// Convert "normal" to computed value
+		if ( val === "normal" && name in cssNormalTransform ) {
+			val = cssNormalTransform[ name ];
+		}
+
+		// Make numeric if forced or a qualifier was provided and val looks numeric
+		if ( extra === "" || extra ) {
+			num = parseFloat( val );
+			return extra === true || isFinite( num ) ? num || 0 : val;
+		}
+
+		return val;
+	}
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+	jQuery.cssHooks[ dimension ] = {
+		get: function( elem, computed, extra ) {
+			if ( computed ) {
+
+				// Certain elements can have dimension info if we invisibly show them
+				// but it must have a current display style that would benefit
+				return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+					// Support: Safari 8+
+					// Table columns in Safari have non-zero offsetWidth & zero
+					// getBoundingClientRect().width unless display is changed.
+					// Support: IE <=11 only
+					// Running getBoundingClientRect on a disconnected node
+					// in IE throws an error.
+					( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+					swap( elem, cssShow, function() {
+						return getWidthOrHeight( elem, dimension, extra );
+					} ) :
+					getWidthOrHeight( elem, dimension, extra );
+			}
+		},
+
+		set: function( elem, value, extra ) {
+			var matches,
+				styles = getStyles( elem ),
+
+				// Only read styles.position if the test has a chance to fail
+				// to avoid forcing a reflow.
+				scrollboxSizeBuggy = !support.scrollboxSize() &&
+					styles.position === "absolute",
+
+				// To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+				boxSizingNeeded = scrollboxSizeBuggy || extra,
+				isBorderBox = boxSizingNeeded &&
+					jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+				subtract = extra ?
+					boxModelAdjustment(
+						elem,
+						dimension,
+						extra,
+						isBorderBox,
+						styles
+					) :
+					0;
+
+			// Account for unreliable border-box dimensions by comparing offset* to computed and
+			// faking a content-box to get border and padding (gh-3699)
+			if ( isBorderBox && scrollboxSizeBuggy ) {
+				subtract -= Math.ceil(
+					elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+					parseFloat( styles[ dimension ] ) -
+					boxModelAdjustment( elem, dimension, "border", false, styles ) -
+					0.5
+				);
+			}
+
+			// Convert to pixels if value adjustment is needed
+			if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+				( matches[ 3 ] || "px" ) !== "px" ) {
+
+				elem.style[ dimension ] = value;
+				value = jQuery.css( elem, dimension );
+			}
+
+			return setPositiveNumber( elem, value, subtract );
+		}
+	};
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+	function( elem, computed ) {
+		if ( computed ) {
+			return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+				elem.getBoundingClientRect().left -
+					swap( elem, { marginLeft: 0 }, function() {
+						return elem.getBoundingClientRect().left;
+					} )
+			) + "px";
+		}
+	}
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+	margin: "",
+	padding: "",
+	border: "Width"
+}, function( prefix, suffix ) {
+	jQuery.cssHooks[ prefix + suffix ] = {
+		expand: function( value ) {
+			var i = 0,
+				expanded = {},
+
+				// Assumes a single number if not a string
+				parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+			for ( ; i < 4; i++ ) {
+				expanded[ prefix + cssExpand[ i ] + suffix ] =
+					parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+			}
+
+			return expanded;
+		}
+	};
+
+	if ( prefix !== "margin" ) {
+		jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+	}
+} );
+
+jQuery.fn.extend( {
+	css: function( name, value ) {
+		return access( this, function( elem, name, value ) {
+			var styles, len,
+				map = {},
+				i = 0;
+
+			if ( Array.isArray( name ) ) {
+				styles = getStyles( elem );
+				len = name.length;
+
+				for ( ; i < len; i++ ) {
+					map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+				}
+
+				return map;
+			}
+
+			return value !== undefined ?
+				jQuery.style( elem, name, value ) :
+				jQuery.css( elem, name );
+		}, name, value, arguments.length > 1 );
+	}
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+	return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+	constructor: Tween,
+	init: function( elem, options, prop, end, easing, unit ) {
+		this.elem = elem;
+		this.prop = prop;
+		this.easing = easing || jQuery.easing._default;
+		this.options = options;
+		this.start = this.now = this.cur();
+		this.end = end;
+		this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+	},
+	cur: function() {
+		var hooks = Tween.propHooks[ this.prop ];
+
+		return hooks && hooks.get ?
+			hooks.get( this ) :
+			Tween.propHooks._default.get( this );
+	},
+	run: function( percent ) {
+		var eased,
+			hooks = Tween.propHooks[ this.prop ];
+
+		if ( this.options.duration ) {
+			this.pos = eased = jQuery.easing[ this.easing ](
+				percent, this.options.duration * percent, 0, 1, this.options.duration
+			);
+		} else {
+			this.pos = eased = percent;
+		}
+		this.now = ( this.end - this.start ) * eased + this.start;
+
+		if ( this.options.step ) {
+			this.options.step.call( this.elem, this.now, this );
+		}
+
+		if ( hooks && hooks.set ) {
+			hooks.set( this );
+		} else {
+			Tween.propHooks._default.set( this );
+		}
+		return this;
+	}
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+	_default: {
+		get: function( tween ) {
+			var result;
+
+			// Use a property on the element directly when it is not a DOM element,
+			// or when there is no matching style property that exists.
+			if ( tween.elem.nodeType !== 1 ||
+				tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+				return tween.elem[ tween.prop ];
+			}
+
+			// Passing an empty string as a 3rd parameter to .css will automatically
+			// attempt a parseFloat and fallback to a string if the parse fails.
+			// Simple values such as "10px" are parsed to Float;
+			// complex values such as "rotate(1rad)" are returned as-is.
+			result = jQuery.css( tween.elem, tween.prop, "" );
+
+			// Empty strings, null, undefined and "auto" are converted to 0.
+			return !result || result === "auto" ? 0 : result;
+		},
+		set: function( tween ) {
+
+			// Use step hook for back compat.
+			// Use cssHook if its there.
+			// Use .style if available and use plain properties where available.
+			if ( jQuery.fx.step[ tween.prop ] ) {
+				jQuery.fx.step[ tween.prop ]( tween );
+			} else if ( tween.elem.nodeType === 1 && (
+				jQuery.cssHooks[ tween.prop ] ||
+					tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+				jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+			} else {
+				tween.elem[ tween.prop ] = tween.now;
+			}
+		}
+	}
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+	set: function( tween ) {
+		if ( tween.elem.nodeType && tween.elem.parentNode ) {
+			tween.elem[ tween.prop ] = tween.now;
+		}
+	}
+};
+
+jQuery.easing = {
+	linear: function( p ) {
+		return p;
+	},
+	swing: function( p ) {
+		return 0.5 - Math.cos( p * Math.PI ) / 2;
+	},
+	_default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+	fxNow, inProgress,
+	rfxtypes = /^(?:toggle|show|hide)$/,
+	rrun = /queueHooks$/;
+
+function schedule() {
+	if ( inProgress ) {
+		if ( document.hidden === false && window.requestAnimationFrame ) {
+			window.requestAnimationFrame( schedule );
+		} else {
+			window.setTimeout( schedule, jQuery.fx.interval );
+		}
+
+		jQuery.fx.tick();
+	}
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+	window.setTimeout( function() {
+		fxNow = undefined;
+	} );
+	return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+	var which,
+		i = 0,
+		attrs = { height: type };
+
+	// If we include width, step value is 1 to do all cssExpand values,
+	// otherwise step value is 2 to skip over Left and Right
+	includeWidth = includeWidth ? 1 : 0;
+	for ( ; i < 4; i += 2 - includeWidth ) {
+		which = cssExpand[ i ];
+		attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+	}
+
+	if ( includeWidth ) {
+		attrs.opacity = attrs.width = type;
+	}
+
+	return attrs;
+}
+
+function createTween( value, prop, animation ) {
+	var tween,
+		collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+		index = 0,
+		length = collection.length;
+	for ( ; index < length; index++ ) {
+		if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+			// We're done with this property
+			return tween;
+		}
+	}
+}
+
+function defaultPrefilter( elem, props, opts ) {
+	var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+		isBox = "width" in props || "height" in props,
+		anim = this,
+		orig = {},
+		style = elem.style,
+		hidden = elem.nodeType && isHiddenWithinTree( elem ),
+		dataShow = dataPriv.get( elem, "fxshow" );
+
+	// Queue-skipping animations hijack the fx hooks
+	if ( !opts.queue ) {
+		hooks = jQuery._queueHooks( elem, "fx" );
+		if ( hooks.unqueued == null ) {
+			hooks.unqueued = 0;
+			oldfire = hooks.empty.fire;
+			hooks.empty.fire = function() {
+				if ( !hooks.unqueued ) {
+					oldfire();
+				}
+			};
+		}
+		hooks.unqueued++;
+
+		anim.always( function() {
+
+			// Ensure the complete handler is called before this completes
+			anim.always( function() {
+				hooks.unqueued--;
+				if ( !jQuery.queue( elem, "fx" ).length ) {
+					hooks.empty.fire();
+				}
+			} );
+		} );
+	}
+
+	// Detect show/hide animations
+	for ( prop in props ) {
+		value = props[ prop ];
+		if ( rfxtypes.test( value ) ) {
+			delete props[ prop ];
+			toggle = toggle || value === "toggle";
+			if ( value === ( hidden ? "hide" : "show" ) ) {
+
+				// Pretend to be hidden if this is a "show" and
+				// there is still data from a stopped show/hide
+				if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+					hidden = true;
+
+				// Ignore all other no-op show/hide data
+				} else {
+					continue;
+				}
+			}
+			orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+		}
+	}
+
+	// Bail out if this is a no-op like .hide().hide()
+	propTween = !jQuery.isEmptyObject( props );
+	if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+		return;
+	}
+
+	// Restrict "overflow" and "display" styles during box animations
+	if ( isBox && elem.nodeType === 1 ) {
+
+		// Support: IE <=9 - 11, Edge 12 - 15
+		// Record all 3 overflow attributes because IE does not infer the shorthand
+		// from identically-valued overflowX and overflowY and Edge just mirrors
+		// the overflowX value there.
+		opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+		// Identify a display type, preferring old show/hide data over the CSS cascade
+		restoreDisplay = dataShow && dataShow.display;
+		if ( restoreDisplay == null ) {
+			restoreDisplay = dataPriv.get( elem, "display" );
+		}
+		display = jQuery.css( elem, "display" );
+		if ( display === "none" ) {
+			if ( restoreDisplay ) {
+				display = restoreDisplay;
+			} else {
+
+				// Get nonempty value(s) by temporarily forcing visibility
+				showHide( [ elem ], true );
+				restoreDisplay = elem.style.display || restoreDisplay;
+				display = jQuery.css( elem, "display" );
+				showHide( [ elem ] );
+			}
+		}
+
+		// Animate inline elements as inline-block
+		if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+			if ( jQuery.css( elem, "float" ) === "none" ) {
+
+				// Restore the original display value at the end of pure show/hide animations
+				if ( !propTween ) {
+					anim.done( function() {
+						style.display = restoreDisplay;
+					} );
+					if ( restoreDisplay == null ) {
+						display = style.display;
+						restoreDisplay = display === "none" ? "" : display;
+					}
+				}
+				style.display = "inline-block";
+			}
+		}
+	}
+
+	if ( opts.overflow ) {
+		style.overflow = "hidden";
+		anim.always( function() {
+			style.overflow = opts.overflow[ 0 ];
+			style.overflowX = opts.overflow[ 1 ];
+			style.overflowY = opts.overflow[ 2 ];
+		} );
+	}
+
+	// Implement show/hide animations
+	propTween = false;
+	for ( prop in orig ) {
+
+		// General show/hide setup for this element animation
+		if ( !propTween ) {
+			if ( dataShow ) {
+				if ( "hidden" in dataShow ) {
+					hidden = dataShow.hidden;
+				}
+			} else {
+				dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+			}
+
+			// Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+			if ( toggle ) {
+				dataShow.hidden = !hidden;
+			}
+
+			// Show elements before animating them
+			if ( hidden ) {
+				showHide( [ elem ], true );
+			}
+
+			/* eslint-disable no-loop-func */
+
+			anim.done( function() {
+
+				/* eslint-enable no-loop-func */
+
+				// The final step of a "hide" animation is actually hiding the element
+				if ( !hidden ) {
+					showHide( [ elem ] );
+				}
+				dataPriv.remove( elem, "fxshow" );
+				for ( prop in orig ) {
+					jQuery.style( elem, prop, orig[ prop ] );
+				}
+			} );
+		}
+
+		// Per-property setup
+		propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+		if ( !( prop in dataShow ) ) {
+			dataShow[ prop ] = propTween.start;
+			if ( hidden ) {
+				propTween.end = propTween.start;
+				propTween.start = 0;
+			}
+		}
+	}
+}
+
+function propFilter( props, specialEasing ) {
+	var index, name, easing, value, hooks;
+
+	// camelCase, specialEasing and expand cssHook pass
+	for ( index in props ) {
+		name = camelCase( index );
+		easing = specialEasing[ name ];
+		value = props[ index ];
+		if ( Array.isArray( value ) ) {
+			easing = value[ 1 ];
+			value = props[ index ] = value[ 0 ];
+		}
+
+		if ( index !== name ) {
+			props[ name ] = value;
+			delete props[ index ];
+		}
+
+		hooks = jQuery.cssHooks[ name ];
+		if ( hooks && "expand" in hooks ) {
+			value = hooks.expand( value );
+			delete props[ name ];
+
+			// Not quite $.extend, this won't overwrite existing keys.
+			// Reusing 'index' because we have the correct "name"
+			for ( index in value ) {
+				if ( !( index in props ) ) {
+					props[ index ] = value[ index ];
+					specialEasing[ index ] = easing;
+				}
+			}
+		} else {
+			specialEasing[ name ] = easing;
+		}
+	}
+}
+
+function Animation( elem, properties, options ) {
+	var result,
+		stopped,
+		index = 0,
+		length = Animation.prefilters.length,
+		deferred = jQuery.Deferred().always( function() {
+
+			// Don't match elem in the :animated selector
+			delete tick.elem;
+		} ),
+		tick = function() {
+			if ( stopped ) {
+				return false;
+			}
+			var currentTime = fxNow || createFxNow(),
+				remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+				// Support: Android 2.3 only
+				// Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+				temp = remaining / animation.duration || 0,
+				percent = 1 - temp,
+				index = 0,
+				length = animation.tweens.length;
+
+			for ( ; index < length; index++ ) {
+				animation.tweens[ index ].run( percent );
+			}
+
+			deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+			// If there's more to do, yield
+			if ( percent < 1 && length ) {
+				return remaining;
+			}
+
+			// If this was an empty animation, synthesize a final progress notification
+			if ( !length ) {
+				deferred.notifyWith( elem, [ animation, 1, 0 ] );
+			}
+
+			// Resolve the animation and report its conclusion
+			deferred.resolveWith( elem, [ animation ] );
+			return false;
+		},
+		animation = deferred.promise( {
+			elem: elem,
+			props: jQuery.extend( {}, properties ),
+			opts: jQuery.extend( true, {
+				specialEasing: {},
+				easing: jQuery.easing._default
+			}, options ),
+			originalProperties: properties,
+			originalOptions: options,
+			startTime: fxNow || createFxNow(),
+			duration: options.duration,
+			tweens: [],
+			createTween: function( prop, end ) {
+				var tween = jQuery.Tween( elem, animation.opts, prop, end,
+					animation.opts.specialEasing[ prop ] || animation.opts.easing );
+				animation.tweens.push( tween );
+				return tween;
+			},
+			stop: function( gotoEnd ) {
+				var index = 0,
+
+					// If we are going to the end, we want to run all the tweens
+					// otherwise we skip this part
+					length = gotoEnd ? animation.tweens.length : 0;
+				if ( stopped ) {
+					return this;
+				}
+				stopped = true;
+				for ( ; index < length; index++ ) {
+					animation.tweens[ index ].run( 1 );
+				}
+
+				// Resolve when we played the last frame; otherwise, reject
+				if ( gotoEnd ) {
+					deferred.notifyWith( elem, [ animation, 1, 0 ] );
+					deferred.resolveWith( elem, [ animation, gotoEnd ] );
+				} else {
+					deferred.rejectWith( elem, [ animation, gotoEnd ] );
+				}
+				return this;
+			}
+		} ),
+		props = animation.props;
+
+	propFilter( props, animation.opts.specialEasing );
+
+	for ( ; index < length; index++ ) {
+		result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+		if ( result ) {
+			if ( isFunction( result.stop ) ) {
+				jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+					result.stop.bind( result );
+			}
+			return result;
+		}
+	}
+
+	jQuery.map( props, createTween, animation );
+
+	if ( isFunction( animation.opts.start ) ) {
+		animation.opts.start.call( elem, animation );
+	}
+
+	// Attach callbacks from options
+	animation
+		.progress( animation.opts.progress )
+		.done( animation.opts.done, animation.opts.complete )
+		.fail( animation.opts.fail )
+		.always( animation.opts.always );
+
+	jQuery.fx.timer(
+		jQuery.extend( tick, {
+			elem: elem,
+			anim: animation,
+			queue: animation.opts.queue
+		} )
+	);
+
+	return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+	tweeners: {
+		"*": [ function( prop, value ) {
+			var tween = this.createTween( prop, value );
+			adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+			return tween;
+		} ]
+	},
+
+	tweener: function( props, callback ) {
+		if ( isFunction( props ) ) {
+			callback = props;
+			props = [ "*" ];
+		} else {
+			props = props.match( rnothtmlwhite );
+		}
+
+		var prop,
+			index = 0,
+			length = props.length;
+
+		for ( ; index < length; index++ ) {
+			prop = props[ index ];
+			Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+			Animation.tweeners[ prop ].unshift( callback );
+		}
+	},
+
+	prefilters: [ defaultPrefilter ],
+
+	prefilter: function( callback, prepend ) {
+		if ( prepend ) {
+			Animation.prefilters.unshift( callback );
+		} else {
+			Animation.prefilters.push( callback );
+		}
+	}
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+	var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+		complete: fn || !fn && easing ||
+			isFunction( speed ) && speed,
+		duration: speed,
+		easing: fn && easing || easing && !isFunction( easing ) && easing
+	};
+
+	// Go to the end state if fx are off
+	if ( jQuery.fx.off ) {
+		opt.duration = 0;
+
+	} else {
+		if ( typeof opt.duration !== "number" ) {
+			if ( opt.duration in jQuery.fx.speeds ) {
+				opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+			} else {
+				opt.duration = jQuery.fx.speeds._default;
+			}
+		}
+	}
+
+	// Normalize opt.queue - true/undefined/null -> "fx"
+	if ( opt.queue == null || opt.queue === true ) {
+		opt.queue = "fx";
+	}
+
+	// Queueing
+	opt.old = opt.complete;
+
+	opt.complete = function() {
+		if ( isFunction( opt.old ) ) {
+			opt.old.call( this );
+		}
+
+		if ( opt.queue ) {
+			jQuery.dequeue( this, opt.queue );
+		}
+	};
+
+	return opt;
+};
+
+jQuery.fn.extend( {
+	fadeTo: function( speed, to, easing, callback ) {
+
+		// Show any hidden elements after setting opacity to 0
+		return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+			// Animate to the value specified
+			.end().animate( { opacity: to }, speed, easing, callback );
+	},
+	animate: function( prop, speed, easing, callback ) {
+		var empty = jQuery.isEmptyObject( prop ),
+			optall = jQuery.speed( speed, easing, callback ),
+			doAnimation = function() {
+
+				// Operate on a copy of prop so per-property easing won't be lost
+				var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+				// Empty animations, or finishing resolves immediately
+				if ( empty || dataPriv.get( this, "finish" ) ) {
+					anim.stop( true );
+				}
+			};
+
+		doAnimation.finish = doAnimation;
+
+		return empty || optall.queue === false ?
+			this.each( doAnimation ) :
+			this.queue( optall.queue, doAnimation );
+	},
+	stop: function( type, clearQueue, gotoEnd ) {
+		var stopQueue = function( hooks ) {
+			var stop = hooks.stop;
+			delete hooks.stop;
+			stop( gotoEnd );
+		};
+
+		if ( typeof type !== "string" ) {
+			gotoEnd = clearQueue;
+			clearQueue = type;
+			type = undefined;
+		}
+		if ( clearQueue ) {
+			this.queue( type || "fx", [] );
+		}
+
+		return this.each( function() {
+			var dequeue = true,
+				index = type != null && type + "queueHooks",
+				timers = jQuery.timers,
+				data = dataPriv.get( this );
+
+			if ( index ) {
+				if ( data[ index ] && data[ index ].stop ) {
+					stopQueue( data[ index ] );
+				}
+			} else {
+				for ( index in data ) {
+					if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+						stopQueue( data[ index ] );
+					}
+				}
+			}
+
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this &&
+					( type == null || timers[ index ].queue === type ) ) {
+
+					timers[ index ].anim.stop( gotoEnd );
+					dequeue = false;
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Start the next in the queue if the last step wasn't forced.
+			// Timers currently will call their complete callbacks, which
+			// will dequeue but only if they were gotoEnd.
+			if ( dequeue || !gotoEnd ) {
+				jQuery.dequeue( this, type );
+			}
+		} );
+	},
+	finish: function( type ) {
+		if ( type !== false ) {
+			type = type || "fx";
+		}
+		return this.each( function() {
+			var index,
+				data = dataPriv.get( this ),
+				queue = data[ type + "queue" ],
+				hooks = data[ type + "queueHooks" ],
+				timers = jQuery.timers,
+				length = queue ? queue.length : 0;
+
+			// Enable finishing flag on private data
+			data.finish = true;
+
+			// Empty the queue first
+			jQuery.queue( this, type, [] );
+
+			if ( hooks && hooks.stop ) {
+				hooks.stop.call( this, true );
+			}
+
+			// Look for any active animations, and finish them
+			for ( index = timers.length; index--; ) {
+				if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+					timers[ index ].anim.stop( true );
+					timers.splice( index, 1 );
+				}
+			}
+
+			// Look for any animations in the old queue and finish them
+			for ( index = 0; index < length; index++ ) {
+				if ( queue[ index ] && queue[ index ].finish ) {
+					queue[ index ].finish.call( this );
+				}
+			}
+
+			// Turn off finishing flag
+			delete data.finish;
+		} );
+	}
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+	var cssFn = jQuery.fn[ name ];
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return speed == null || typeof speed === "boolean" ?
+			cssFn.apply( this, arguments ) :
+			this.animate( genFx( name, true ), speed, easing, callback );
+	};
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+	slideDown: genFx( "show" ),
+	slideUp: genFx( "hide" ),
+	slideToggle: genFx( "toggle" ),
+	fadeIn: { opacity: "show" },
+	fadeOut: { opacity: "hide" },
+	fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+	jQuery.fn[ name ] = function( speed, easing, callback ) {
+		return this.animate( props, speed, easing, callback );
+	};
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+	var timer,
+		i = 0,
+		timers = jQuery.timers;
+
+	fxNow = Date.now();
+
+	for ( ; i < timers.length; i++ ) {
+		timer = timers[ i ];
+
+		// Run the timer and safely remove it when done (allowing for external removal)
+		if ( !timer() && timers[ i ] === timer ) {
+			timers.splice( i--, 1 );
+		}
+	}
+
+	if ( !timers.length ) {
+		jQuery.fx.stop();
+	}
+	fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+	jQuery.timers.push( timer );
+	jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+	if ( inProgress ) {
+		return;
+	}
+
+	inProgress = true;
+	schedule();
+};
+
+jQuery.fx.stop = function() {
+	inProgress = null;
+};
+
+jQuery.fx.speeds = {
+	slow: 600,
+	fast: 200,
+
+	// Default speed
+	_default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+	time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+	type = type || "fx";
+
+	return this.queue( type, function( next, hooks ) {
+		var timeout = window.setTimeout( next, time );
+		hooks.stop = function() {
+			window.clearTimeout( timeout );
+		};
+	} );
+};
+
+
+( function() {
+	var input = document.createElement( "input" ),
+		select = document.createElement( "select" ),
+		opt = select.appendChild( document.createElement( "option" ) );
+
+	input.type = "checkbox";
+
+	// Support: Android <=4.3 only
+	// Default value for a checkbox should be "on"
+	support.checkOn = input.value !== "";
+
+	// Support: IE <=11 only
+	// Must access selectedIndex to make default options select
+	support.optSelected = opt.selected;
+
+	// Support: IE <=11 only
+	// An input loses its value after becoming a radio
+	input = document.createElement( "input" );
+	input.value = "t";
+	input.type = "radio";
+	support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+	attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+	attr: function( name, value ) {
+		return access( this, jQuery.attr, name, value, arguments.length > 1 );
+	},
+
+	removeAttr: function( name ) {
+		return this.each( function() {
+			jQuery.removeAttr( this, name );
+		} );
+	}
+} );
+
+jQuery.extend( {
+	attr: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set attributes on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		// Fallback to prop when attributes are not supported
+		if ( typeof elem.getAttribute === "undefined" ) {
+			return jQuery.prop( elem, name, value );
+		}
+
+		// Attribute hooks are determined by the lowercase version
+		// Grab necessary hook if one is defined
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+			hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+				( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+		}
+
+		if ( value !== undefined ) {
+			if ( value === null ) {
+				jQuery.removeAttr( elem, name );
+				return;
+			}
+
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			elem.setAttribute( name, value + "" );
+			return value;
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		ret = jQuery.find.attr( elem, name );
+
+		// Non-existent attributes return null, we normalize to undefined
+		return ret == null ? undefined : ret;
+	},
+
+	attrHooks: {
+		type: {
+			set: function( elem, value ) {
+				if ( !support.radioValue && value === "radio" &&
+					nodeName( elem, "input" ) ) {
+					var val = elem.value;
+					elem.setAttribute( "type", value );
+					if ( val ) {
+						elem.value = val;
+					}
+					return value;
+				}
+			}
+		}
+	},
+
+	removeAttr: function( elem, value ) {
+		var name,
+			i = 0,
+
+			// Attribute names can contain non-HTML whitespace characters
+			// https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+			attrNames = value && value.match( rnothtmlwhite );
+
+		if ( attrNames && elem.nodeType === 1 ) {
+			while ( ( name = attrNames[ i++ ] ) ) {
+				elem.removeAttribute( name );
+			}
+		}
+	}
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+	set: function( elem, value, name ) {
+		if ( value === false ) {
+
+			// Remove boolean attributes when set to false
+			jQuery.removeAttr( elem, name );
+		} else {
+			elem.setAttribute( name, name );
+		}
+		return name;
+	}
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+	var getter = attrHandle[ name ] || jQuery.find.attr;
+
+	attrHandle[ name ] = function( elem, name, isXML ) {
+		var ret, handle,
+			lowercaseName = name.toLowerCase();
+
+		if ( !isXML ) {
+
+			// Avoid an infinite loop by temporarily removing this function from the getter
+			handle = attrHandle[ lowercaseName ];
+			attrHandle[ lowercaseName ] = ret;
+			ret = getter( elem, name, isXML ) != null ?
+				lowercaseName :
+				null;
+			attrHandle[ lowercaseName ] = handle;
+		}
+		return ret;
+	};
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+	rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+	prop: function( name, value ) {
+		return access( this, jQuery.prop, name, value, arguments.length > 1 );
+	},
+
+	removeProp: function( name ) {
+		return this.each( function() {
+			delete this[ jQuery.propFix[ name ] || name ];
+		} );
+	}
+} );
+
+jQuery.extend( {
+	prop: function( elem, name, value ) {
+		var ret, hooks,
+			nType = elem.nodeType;
+
+		// Don't get/set properties on text, comment and attribute nodes
+		if ( nType === 3 || nType === 8 || nType === 2 ) {
+			return;
+		}
+
+		if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+			// Fix name and attach hooks
+			name = jQuery.propFix[ name ] || name;
+			hooks = jQuery.propHooks[ name ];
+		}
+
+		if ( value !== undefined ) {
+			if ( hooks && "set" in hooks &&
+				( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+				return ret;
+			}
+
+			return ( elem[ name ] = value );
+		}
+
+		if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+			return ret;
+		}
+
+		return elem[ name ];
+	},
+
+	propHooks: {
+		tabIndex: {
+			get: function( elem ) {
+
+				// Support: IE <=9 - 11 only
+				// elem.tabIndex doesn't always return the
+				// correct value when it hasn't been explicitly set
+				// https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+				// Use proper attribute retrieval(#12072)
+				var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+				if ( tabindex ) {
+					return parseInt( tabindex, 10 );
+				}
+
+				if (
+					rfocusable.test( elem.nodeName ) ||
+					rclickable.test( elem.nodeName ) &&
+					elem.href
+				) {
+					return 0;
+				}
+
+				return -1;
+			}
+		}
+	},
+
+	propFix: {
+		"for": "htmlFor",
+		"class": "className"
+	}
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+	jQuery.propHooks.selected = {
+		get: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent && parent.parentNode ) {
+				parent.parentNode.selectedIndex;
+			}
+			return null;
+		},
+		set: function( elem ) {
+
+			/* eslint no-unused-expressions: "off" */
+
+			var parent = elem.parentNode;
+			if ( parent ) {
+				parent.selectedIndex;
+
+				if ( parent.parentNode ) {
+					parent.parentNode.selectedIndex;
+				}
+			}
+		}
+	};
+}
+
+jQuery.each( [
+	"tabIndex",
+	"readOnly",
+	"maxLength",
+	"cellSpacing",
+	"cellPadding",
+	"rowSpan",
+	"colSpan",
+	"useMap",
+	"frameBorder",
+	"contentEditable"
+], function() {
+	jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+	// Strip and collapse whitespace according to HTML spec
+	// https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+	function stripAndCollapse( value ) {
+		var tokens = value.match( rnothtmlwhite ) || [];
+		return tokens.join( " " );
+	}
+
+
+function getClass( elem ) {
+	return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+	if ( Array.isArray( value ) ) {
+		return value;
+	}
+	if ( typeof value === "string" ) {
+		return value.match( rnothtmlwhite ) || [];
+	}
+	return [];
+}
+
+jQuery.fn.extend( {
+	addClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+						if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+							cur += clazz + " ";
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	removeClass: function( value ) {
+		var classes, elem, cur, curValue, clazz, j, finalValue,
+			i = 0;
+
+		if ( isFunction( value ) ) {
+			return this.each( function( j ) {
+				jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+			} );
+		}
+
+		if ( !arguments.length ) {
+			return this.attr( "class", "" );
+		}
+
+		classes = classesToArray( value );
+
+		if ( classes.length ) {
+			while ( ( elem = this[ i++ ] ) ) {
+				curValue = getClass( elem );
+
+				// This expression is here for better compressibility (see addClass)
+				cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+				if ( cur ) {
+					j = 0;
+					while ( ( clazz = classes[ j++ ] ) ) {
+
+						// Remove *all* instances
+						while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+							cur = cur.replace( " " + clazz + " ", " " );
+						}
+					}
+
+					// Only assign if different to avoid unneeded rendering.
+					finalValue = stripAndCollapse( cur );
+					if ( curValue !== finalValue ) {
+						elem.setAttribute( "class", finalValue );
+					}
+				}
+			}
+		}
+
+		return this;
+	},
+
+	toggleClass: function( value, stateVal ) {
+		var type = typeof value,
+			isValidValue = type === "string" || Array.isArray( value );
+
+		if ( typeof stateVal === "boolean" && isValidValue ) {
+			return stateVal ? this.addClass( value ) : this.removeClass( value );
+		}
+
+		if ( isFunction( value ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).toggleClass(
+					value.call( this, i, getClass( this ), stateVal ),
+					stateVal
+				);
+			} );
+		}
+
+		return this.each( function() {
+			var className, i, self, classNames;
+
+			if ( isValidValue ) {
+
+				// Toggle individual class names
+				i = 0;
+				self = jQuery( this );
+				classNames = classesToArray( value );
+
+				while ( ( className = classNames[ i++ ] ) ) {
+
+					// Check each className given, space separated list
+					if ( self.hasClass( className ) ) {
+						self.removeClass( className );
+					} else {
+						self.addClass( className );
+					}
+				}
+
+			// Toggle whole class name
+			} else if ( value === undefined || type === "boolean" ) {
+				className = getClass( this );
+				if ( className ) {
+
+					// Store className if set
+					dataPriv.set( this, "__className__", className );
+				}
+
+				// If the element has a class name or if we're passed `false`,
+				// then remove the whole classname (if there was one, the above saved it).
+				// Otherwise bring back whatever was previously saved (if anything),
+				// falling back to the empty string if nothing was stored.
+				if ( this.setAttribute ) {
+					this.setAttribute( "class",
+						className || value === false ?
+							"" :
+							dataPriv.get( this, "__className__" ) || ""
+					);
+				}
+			}
+		} );
+	},
+
+	hasClass: function( selector ) {
+		var className, elem,
+			i = 0;
+
+		className = " " + selector + " ";
+		while ( ( elem = this[ i++ ] ) ) {
+			if ( elem.nodeType === 1 &&
+				( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+				return true;
+			}
+		}
+
+		return false;
+	}
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+	val: function( value ) {
+		var hooks, ret, valueIsFunction,
+			elem = this[ 0 ];
+
+		if ( !arguments.length ) {
+			if ( elem ) {
+				hooks = jQuery.valHooks[ elem.type ] ||
+					jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+				if ( hooks &&
+					"get" in hooks &&
+					( ret = hooks.get( elem, "value" ) ) !== undefined
+				) {
+					return ret;
+				}
+
+				ret = elem.value;
+
+				// Handle most common string cases
+				if ( typeof ret === "string" ) {
+					return ret.replace( rreturn, "" );
+				}
+
+				// Handle cases where value is null/undef or number
+				return ret == null ? "" : ret;
+			}
+
+			return;
+		}
+
+		valueIsFunction = isFunction( value );
+
+		return this.each( function( i ) {
+			var val;
+
+			if ( this.nodeType !== 1 ) {
+				return;
+			}
+
+			if ( valueIsFunction ) {
+				val = value.call( this, i, jQuery( this ).val() );
+			} else {
+				val = value;
+			}
+
+			// Treat null/undefined as ""; convert numbers to string
+			if ( val == null ) {
+				val = "";
+
+			} else if ( typeof val === "number" ) {
+				val += "";
+
+			} else if ( Array.isArray( val ) ) {
+				val = jQuery.map( val, function( value ) {
+					return value == null ? "" : value + "";
+				} );
+			}
+
+			hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+			// If set returns undefined, fall back to normal setting
+			if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+				this.value = val;
+			}
+		} );
+	}
+} );
+
+jQuery.extend( {
+	valHooks: {
+		option: {
+			get: function( elem ) {
+
+				var val = jQuery.find.attr( elem, "value" );
+				return val != null ?
+					val :
+
+					// Support: IE <=10 - 11 only
+					// option.text throws exceptions (#14686, #14858)
+					// Strip and collapse whitespace
+					// https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+					stripAndCollapse( jQuery.text( elem ) );
+			}
+		},
+		select: {
+			get: function( elem ) {
+				var value, option, i,
+					options = elem.options,
+					index = elem.selectedIndex,
+					one = elem.type === "select-one",
+					values = one ? null : [],
+					max = one ? index + 1 : options.length;
+
+				if ( index < 0 ) {
+					i = max;
+
+				} else {
+					i = one ? index : 0;
+				}
+
+				// Loop through all the selected options
+				for ( ; i < max; i++ ) {
+					option = options[ i ];
+
+					// Support: IE <=9 only
+					// IE8-9 doesn't update selected after form reset (#2551)
+					if ( ( option.selected || i === index ) &&
+
+							// Don't return options that are disabled or in a disabled optgroup
+							!option.disabled &&
+							( !option.parentNode.disabled ||
+								!nodeName( option.parentNode, "optgroup" ) ) ) {
+
+						// Get the specific value for the option
+						value = jQuery( option ).val();
+
+						// We don't need an array for one selects
+						if ( one ) {
+							return value;
+						}
+
+						// Multi-Selects return an array
+						values.push( value );
+					}
+				}
+
+				return values;
+			},
+
+			set: function( elem, value ) {
+				var optionSet, option,
+					options = elem.options,
+					values = jQuery.makeArray( value ),
+					i = options.length;
+
+				while ( i-- ) {
+					option = options[ i ];
+
+					/* eslint-disable no-cond-assign */
+
+					if ( option.selected =
+						jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+					) {
+						optionSet = true;
+					}
+
+					/* eslint-enable no-cond-assign */
+				}
+
+				// Force browsers to behave consistently when non-matching value is set
+				if ( !optionSet ) {
+					elem.selectedIndex = -1;
+				}
+				return values;
+			}
+		}
+	}
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+	jQuery.valHooks[ this ] = {
+		set: function( elem, value ) {
+			if ( Array.isArray( value ) ) {
+				return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+			}
+		}
+	};
+	if ( !support.checkOn ) {
+		jQuery.valHooks[ this ].get = function( elem ) {
+			return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+		};
+	}
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+	stopPropagationCallback = function( e ) {
+		e.stopPropagation();
+	};
+
+jQuery.extend( jQuery.event, {
+
+	trigger: function( event, data, elem, onlyHandlers ) {
+
+		var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+			eventPath = [ elem || document ],
+			type = hasOwn.call( event, "type" ) ? event.type : event,
+			namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+		cur = lastElement = tmp = elem = elem || document;
+
+		// Don't do events on text and comment nodes
+		if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+			return;
+		}
+
+		// focus/blur morphs to focusin/out; ensure we're not firing them right now
+		if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+			return;
+		}
+
+		if ( type.indexOf( "." ) > -1 ) {
+
+			// Namespaced trigger; create a regexp to match event type in handle()
+			namespaces = type.split( "." );
+			type = namespaces.shift();
+			namespaces.sort();
+		}
+		ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+		// Caller can pass in a jQuery.Event object, Object, or just an event type string
+		event = event[ jQuery.expando ] ?
+			event :
+			new jQuery.Event( type, typeof event === "object" && event );
+
+		// Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+		event.isTrigger = onlyHandlers ? 2 : 3;
+		event.namespace = namespaces.join( "." );
+		event.rnamespace = event.namespace ?
+			new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+			null;
+
+		// Clean up the event in case it is being reused
+		event.result = undefined;
+		if ( !event.target ) {
+			event.target = elem;
+		}
+
+		// Clone any incoming data and prepend the event, creating the handler arg list
+		data = data == null ?
+			[ event ] :
+			jQuery.makeArray( data, [ event ] );
+
+		// Allow special events to draw outside the lines
+		special = jQuery.event.special[ type ] || {};
+		if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+			return;
+		}
+
+		// Determine event propagation path in advance, per W3C events spec (#9951)
+		// Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+		if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+			bubbleType = special.delegateType || type;
+			if ( !rfocusMorph.test( bubbleType + type ) ) {
+				cur = cur.parentNode;
+			}
+			for ( ; cur; cur = cur.parentNode ) {
+				eventPath.push( cur );
+				tmp = cur;
+			}
+
+			// Only add window if we got to document (e.g., not plain obj or detached DOM)
+			if ( tmp === ( elem.ownerDocument || document ) ) {
+				eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+			}
+		}
+
+		// Fire handlers on the event path
+		i = 0;
+		while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+			lastElement = cur;
+			event.type = i > 1 ?
+				bubbleType :
+				special.bindType || type;
+
+			// jQuery handler
+			handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] &&
+				dataPriv.get( cur, "handle" );
+			if ( handle ) {
+				handle.apply( cur, data );
+			}
+
+			// Native handler
+			handle = ontype && cur[ ontype ];
+			if ( handle && handle.apply && acceptData( cur ) ) {
+				event.result = handle.apply( cur, data );
+				if ( event.result === false ) {
+					event.preventDefault();
+				}
+			}
+		}
+		event.type = type;
+
+		// If nobody prevented the default action, do it now
+		if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+			if ( ( !special._default ||
+				special._default.apply( eventPath.pop(), data ) === false ) &&
+				acceptData( elem ) ) {
+
+				// Call a native DOM method on the target with the same name as the event.
+				// Don't do default actions on window, that's where global variables be (#6170)
+				if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+					// Don't re-trigger an onFOO event when we call its FOO() method
+					tmp = elem[ ontype ];
+
+					if ( tmp ) {
+						elem[ ontype ] = null;
+					}
+
+					// Prevent re-triggering of the same event, since we already bubbled it above
+					jQuery.event.triggered = type;
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.addEventListener( type, stopPropagationCallback );
+					}
+
+					elem[ type ]();
+
+					if ( event.isPropagationStopped() ) {
+						lastElement.removeEventListener( type, stopPropagationCallback );
+					}
+
+					jQuery.event.triggered = undefined;
+
+					if ( tmp ) {
+						elem[ ontype ] = tmp;
+					}
+				}
+			}
+		}
+
+		return event.result;
+	},
+
+	// Piggyback on a donor event to simulate a different one
+	// Used only for `focus(in | out)` events
+	simulate: function( type, elem, event ) {
+		var e = jQuery.extend(
+			new jQuery.Event(),
+			event,
+			{
+				type: type,
+				isSimulated: true
+			}
+		);
+
+		jQuery.event.trigger( e, null, elem );
+	}
+
+} );
+
+jQuery.fn.extend( {
+
+	trigger: function( type, data ) {
+		return this.each( function() {
+			jQuery.event.trigger( type, data, this );
+		} );
+	},
+	triggerHandler: function( type, data ) {
+		var elem = this[ 0 ];
+		if ( elem ) {
+			return jQuery.event.trigger( type, data, elem, true );
+		}
+	}
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+	jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+		// Attach a single capturing handler on the document while someone wants focusin/focusout
+		var handler = function( event ) {
+			jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+		};
+
+		jQuery.event.special[ fix ] = {
+			setup: function() {
+
+				// Handle: regular nodes (via `this.ownerDocument`), window
+				// (via `this.document`) & document (via `this`).
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix );
+
+				if ( !attaches ) {
+					doc.addEventListener( orig, handler, true );
+				}
+				dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+			},
+			teardown: function() {
+				var doc = this.ownerDocument || this.document || this,
+					attaches = dataPriv.access( doc, fix ) - 1;
+
+				if ( !attaches ) {
+					doc.removeEventListener( orig, handler, true );
+					dataPriv.remove( doc, fix );
+
+				} else {
+					dataPriv.access( doc, fix, attaches );
+				}
+			}
+		};
+	} );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+	var xml, parserErrorElem;
+	if ( !data || typeof data !== "string" ) {
+		return null;
+	}
+
+	// Support: IE 9 - 11 only
+	// IE throws on parseFromString with invalid input.
+	try {
+		xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+	} catch ( e ) {}
+
+	parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ];
+	if ( !xml || parserErrorElem ) {
+		jQuery.error( "Invalid XML: " + (
+			parserErrorElem ?
+				jQuery.map( parserErrorElem.childNodes, function( el ) {
+					return el.textContent;
+				} ).join( "\n" ) :
+				data
+		) );
+	}
+	return xml;
+};
+
+
+var
+	rbracket = /\[\]$/,
+	rCRLF = /\r?\n/g,
+	rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+	rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+	var name;
+
+	if ( Array.isArray( obj ) ) {
+
+		// Serialize array item.
+		jQuery.each( obj, function( i, v ) {
+			if ( traditional || rbracket.test( prefix ) ) {
+
+				// Treat each array item as a scalar.
+				add( prefix, v );
+
+			} else {
+
+				// Item is non-scalar (array or object), encode its numeric index.
+				buildParams(
+					prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+					v,
+					traditional,
+					add
+				);
+			}
+		} );
+
+	} else if ( !traditional && toType( obj ) === "object" ) {
+
+		// Serialize object item.
+		for ( name in obj ) {
+			buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+		}
+
+	} else {
+
+		// Serialize scalar item.
+		add( prefix, obj );
+	}
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+	var prefix,
+		s = [],
+		add = function( key, valueOrFunction ) {
+
+			// If value is a function, invoke it and use its return value
+			var value = isFunction( valueOrFunction ) ?
+				valueOrFunction() :
+				valueOrFunction;
+
+			s[ s.length ] = encodeURIComponent( key ) + "=" +
+				encodeURIComponent( value == null ? "" : value );
+		};
+
+	if ( a == null ) {
+		return "";
+	}
+
+	// If an array was passed in, assume that it is an array of form elements.
+	if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+		// Serialize the form elements
+		jQuery.each( a, function() {
+			add( this.name, this.value );
+		} );
+
+	} else {
+
+		// If traditional, encode the "old" way (the way 1.3.2 or older
+		// did it), otherwise encode params recursively.
+		for ( prefix in a ) {
+			buildParams( prefix, a[ prefix ], traditional, add );
+		}
+	}
+
+	// Return the resulting serialization
+	return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+	serialize: function() {
+		return jQuery.param( this.serializeArray() );
+	},
+	serializeArray: function() {
+		return this.map( function() {
+
+			// Can add propHook for "elements" to filter or add form elements
+			var elements = jQuery.prop( this, "elements" );
+			return elements ? jQuery.makeArray( elements ) : this;
+		} ).filter( function() {
+			var type = this.type;
+
+			// Use .is( ":disabled" ) so that fieldset[disabled] works
+			return this.name && !jQuery( this ).is( ":disabled" ) &&
+				rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+				( this.checked || !rcheckableType.test( type ) );
+		} ).map( function( _i, elem ) {
+			var val = jQuery( this ).val();
+
+			if ( val == null ) {
+				return null;
+			}
+
+			if ( Array.isArray( val ) ) {
+				return jQuery.map( val, function( val ) {
+					return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+				} );
+			}
+
+			return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+		} ).get();
+	}
+} );
+
+
+var
+	r20 = /%20/g,
+	rhash = /#.*$/,
+	rantiCache = /([?&])_=[^&]*/,
+	rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+	// #7653, #8125, #8152: local protocol detection
+	rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+	rnoContent = /^(?:GET|HEAD)$/,
+	rprotocol = /^\/\//,
+
+	/* Prefilters
+	 * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+	 * 2) These are called:
+	 *    - BEFORE asking for a transport
+	 *    - AFTER param serialization (s.data is a string if s.processData is true)
+	 * 3) key is the dataType
+	 * 4) the catchall symbol "*" can be used
+	 * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+	 */
+	prefilters = {},
+
+	/* Transports bindings
+	 * 1) key is the dataType
+	 * 2) the catchall symbol "*" can be used
+	 * 3) selection will start with transport dataType and THEN go to "*" if needed
+	 */
+	transports = {},
+
+	// Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+	allTypes = "*/".concat( "*" ),
+
+	// Anchor tag for parsing the document origin
+	originAnchor = document.createElement( "a" );
+
+originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+	// dataTypeExpression is optional and defaults to "*"
+	return function( dataTypeExpression, func ) {
+
+		if ( typeof dataTypeExpression !== "string" ) {
+			func = dataTypeExpression;
+			dataTypeExpression = "*";
+		}
+
+		var dataType,
+			i = 0,
+			dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+		if ( isFunction( func ) ) {
+
+			// For each dataType in the dataTypeExpression
+			while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+				// Prepend if requested
+				if ( dataType[ 0 ] === "+" ) {
+					dataType = dataType.slice( 1 ) || "*";
+					( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+				// Otherwise append
+				} else {
+					( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+				}
+			}
+		}
+	};
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+	var inspected = {},
+		seekingTransport = ( structure === transports );
+
+	function inspect( dataType ) {
+		var selected;
+		inspected[ dataType ] = true;
+		jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+			var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+			if ( typeof dataTypeOrTransport === "string" &&
+				!seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+				options.dataTypes.unshift( dataTypeOrTransport );
+				inspect( dataTypeOrTransport );
+				return false;
+			} else if ( seekingTransport ) {
+				return !( selected = dataTypeOrTransport );
+			}
+		} );
+		return selected;
+	}
+
+	return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+	var key, deep,
+		flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+	for ( key in src ) {
+		if ( src[ key ] !== undefined ) {
+			( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+		}
+	}
+	if ( deep ) {
+		jQuery.extend( true, target, deep );
+	}
+
+	return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+	var ct, type, finalDataType, firstDataType,
+		contents = s.contents,
+		dataTypes = s.dataTypes;
+
+	// Remove auto dataType and get content-type in the process
+	while ( dataTypes[ 0 ] === "*" ) {
+		dataTypes.shift();
+		if ( ct === undefined ) {
+			ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+		}
+	}
+
+	// Check if we're dealing with a known content-type
+	if ( ct ) {
+		for ( type in contents ) {
+			if ( contents[ type ] && contents[ type ].test( ct ) ) {
+				dataTypes.unshift( type );
+				break;
+			}
+		}
+	}
+
+	// Check to see if we have a response for the expected dataType
+	if ( dataTypes[ 0 ] in responses ) {
+		finalDataType = dataTypes[ 0 ];
+	} else {
+
+		// Try convertible dataTypes
+		for ( type in responses ) {
+			if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+				finalDataType = type;
+				break;
+			}
+			if ( !firstDataType ) {
+				firstDataType = type;
+			}
+		}
+
+		// Or just use first one
+		finalDataType = finalDataType || firstDataType;
+	}
+
+	// If we found a dataType
+	// We add the dataType to the list if needed
+	// and return the corresponding response
+	if ( finalDataType ) {
+		if ( finalDataType !== dataTypes[ 0 ] ) {
+			dataTypes.unshift( finalDataType );
+		}
+		return responses[ finalDataType ];
+	}
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+	var conv2, current, conv, tmp, prev,
+		converters = {},
+
+		// Work with a copy of dataTypes in case we need to modify it for conversion
+		dataTypes = s.dataTypes.slice();
+
+	// Create converters map with lowercased keys
+	if ( dataTypes[ 1 ] ) {
+		for ( conv in s.converters ) {
+			converters[ conv.toLowerCase() ] = s.converters[ conv ];
+		}
+	}
+
+	current = dataTypes.shift();
+
+	// Convert to each sequential dataType
+	while ( current ) {
+
+		if ( s.responseFields[ current ] ) {
+			jqXHR[ s.responseFields[ current ] ] = response;
+		}
+
+		// Apply the dataFilter if provided
+		if ( !prev && isSuccess && s.dataFilter ) {
+			response = s.dataFilter( response, s.dataType );
+		}
+
+		prev = current;
+		current = dataTypes.shift();
+
+		if ( current ) {
+
+			// There's only work to do if current dataType is non-auto
+			if ( current === "*" ) {
+
+				current = prev;
+
+			// Convert response if prev dataType is non-auto and differs from current
+			} else if ( prev !== "*" && prev !== current ) {
+
+				// Seek a direct converter
+				conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+				// If none found, seek a pair
+				if ( !conv ) {
+					for ( conv2 in converters ) {
+
+						// If conv2 outputs current
+						tmp = conv2.split( " " );
+						if ( tmp[ 1 ] === current ) {
+
+							// If prev can be converted to accepted input
+							conv = converters[ prev + " " + tmp[ 0 ] ] ||
+								converters[ "* " + tmp[ 0 ] ];
+							if ( conv ) {
+
+								// Condense equivalence converters
+								if ( conv === true ) {
+									conv = converters[ conv2 ];
+
+								// Otherwise, insert the intermediate dataType
+								} else if ( converters[ conv2 ] !== true ) {
+									current = tmp[ 0 ];
+									dataTypes.unshift( tmp[ 1 ] );
+								}
+								break;
+							}
+						}
+					}
+				}
+
+				// Apply converter (if not an equivalence)
+				if ( conv !== true ) {
+
+					// Unless errors are allowed to bubble, catch and return them
+					if ( conv && s.throws ) {
+						response = conv( response );
+					} else {
+						try {
+							response = conv( response );
+						} catch ( e ) {
+							return {
+								state: "parsererror",
+								error: conv ? e : "No conversion from " + prev + " to " + current
+							};
+						}
+					}
+				}
+			}
+		}
+	}
+
+	return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+	// Counter for holding the number of active queries
+	active: 0,
+
+	// Last-Modified header cache for next request
+	lastModified: {},
+	etag: {},
+
+	ajaxSettings: {
+		url: location.href,
+		type: "GET",
+		isLocal: rlocalProtocol.test( location.protocol ),
+		global: true,
+		processData: true,
+		async: true,
+		contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+		/*
+		timeout: 0,
+		data: null,
+		dataType: null,
+		username: null,
+		password: null,
+		cache: null,
+		throws: false,
+		traditional: false,
+		headers: {},
+		*/
+
+		accepts: {
+			"*": allTypes,
+			text: "text/plain",
+			html: "text/html",
+			xml: "application/xml, text/xml",
+			json: "application/json, text/javascript"
+		},
+
+		contents: {
+			xml: /\bxml\b/,
+			html: /\bhtml/,
+			json: /\bjson\b/
+		},
+
+		responseFields: {
+			xml: "responseXML",
+			text: "responseText",
+			json: "responseJSON"
+		},
+
+		// Data converters
+		// Keys separate source (or catchall "*") and destination types with a single space
+		converters: {
+
+			// Convert anything to text
+			"* text": String,
+
+			// Text to html (true = no transformation)
+			"text html": true,
+
+			// Evaluate text as a json expression
+			"text json": JSON.parse,
+
+			// Parse text as xml
+			"text xml": jQuery.parseXML
+		},
+
+		// For options that shouldn't be deep extended:
+		// you can add your own custom options here if
+		// and when you create one that shouldn't be
+		// deep extended (see ajaxExtend)
+		flatOptions: {
+			url: true,
+			context: true
+		}
+	},
+
+	// Creates a full fledged settings object into target
+	// with both ajaxSettings and settings fields.
+	// If target is omitted, writes into ajaxSettings.
+	ajaxSetup: function( target, settings ) {
+		return settings ?
+
+			// Building a settings object
+			ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+			// Extending ajaxSettings
+			ajaxExtend( jQuery.ajaxSettings, target );
+	},
+
+	ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+	ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+	// Main method
+	ajax: function( url, options ) {
+
+		// If url is an object, simulate pre-1.5 signature
+		if ( typeof url === "object" ) {
+			options = url;
+			url = undefined;
+		}
+
+		// Force options to be an object
+		options = options || {};
+
+		var transport,
+
+			// URL without anti-cache param
+			cacheURL,
+
+			// Response headers
+			responseHeadersString,
+			responseHeaders,
+
+			// timeout handle
+			timeoutTimer,
+
+			// Url cleanup var
+			urlAnchor,
+
+			// Request state (becomes false upon send and true upon completion)
+			completed,
+
+			// To know if global events are to be dispatched
+			fireGlobals,
+
+			// Loop variable
+			i,
+
+			// uncached part of the url
+			uncached,
+
+			// Create the final options object
+			s = jQuery.ajaxSetup( {}, options ),
+
+			// Callbacks context
+			callbackContext = s.context || s,
+
+			// Context for global events is callbackContext if it is a DOM node or jQuery collection
+			globalEventContext = s.context &&
+				( callbackContext.nodeType || callbackContext.jquery ) ?
+				jQuery( callbackContext ) :
+				jQuery.event,
+
+			// Deferreds
+			deferred = jQuery.Deferred(),
+			completeDeferred = jQuery.Callbacks( "once memory" ),
+
+			// Status-dependent callbacks
+			statusCode = s.statusCode || {},
+
+			// Headers (they are sent all at once)
+			requestHeaders = {},
+			requestHeadersNames = {},
+
+			// Default abort message
+			strAbort = "canceled",
+
+			// Fake xhr
+			jqXHR = {
+				readyState: 0,
+
+				// Builds headers hashtable if needed
+				getResponseHeader: function( key ) {
+					var match;
+					if ( completed ) {
+						if ( !responseHeaders ) {
+							responseHeaders = {};
+							while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+								responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+									( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+										.concat( match[ 2 ] );
+							}
+						}
+						match = responseHeaders[ key.toLowerCase() + " " ];
+					}
+					return match == null ? null : match.join( ", " );
+				},
+
+				// Raw string
+				getAllResponseHeaders: function() {
+					return completed ? responseHeadersString : null;
+				},
+
+				// Caches the header
+				setRequestHeader: function( name, value ) {
+					if ( completed == null ) {
+						name = requestHeadersNames[ name.toLowerCase() ] =
+							requestHeadersNames[ name.toLowerCase() ] || name;
+						requestHeaders[ name ] = value;
+					}
+					return this;
+				},
+
+				// Overrides response content-type header
+				overrideMimeType: function( type ) {
+					if ( completed == null ) {
+						s.mimeType = type;
+					}
+					return this;
+				},
+
+				// Status-dependent callbacks
+				statusCode: function( map ) {
+					var code;
+					if ( map ) {
+						if ( completed ) {
+
+							// Execute the appropriate callbacks
+							jqXHR.always( map[ jqXHR.status ] );
+						} else {
+
+							// Lazy-add the new callbacks in a way that preserves old ones
+							for ( code in map ) {
+								statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+							}
+						}
+					}
+					return this;
+				},
+
+				// Cancel the request
+				abort: function( statusText ) {
+					var finalText = statusText || strAbort;
+					if ( transport ) {
+						transport.abort( finalText );
+					}
+					done( 0, finalText );
+					return this;
+				}
+			};
+
+		// Attach deferreds
+		deferred.promise( jqXHR );
+
+		// Add protocol if not provided (prefilters might expect it)
+		// Handle falsy url in the settings object (#10093: consistency with old signature)
+		// We also use the url parameter if available
+		s.url = ( ( url || s.url || location.href ) + "" )
+			.replace( rprotocol, location.protocol + "//" );
+
+		// Alias method option to type as per ticket #12004
+		s.type = options.method || options.type || s.method || s.type;
+
+		// Extract dataTypes list
+		s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+		// A cross-domain request is in order when the origin doesn't match the current origin.
+		if ( s.crossDomain == null ) {
+			urlAnchor = document.createElement( "a" );
+
+			// Support: IE <=8 - 11, Edge 12 - 15
+			// IE throws exception on accessing the href property if url is malformed,
+			// e.g. http://example.com:80x/
+			try {
+				urlAnchor.href = s.url;
+
+				// Support: IE <=8 - 11 only
+				// Anchor's host property isn't correctly set when s.url is relative
+				urlAnchor.href = urlAnchor.href;
+				s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+					urlAnchor.protocol + "//" + urlAnchor.host;
+			} catch ( e ) {
+
+				// If there is an error parsing the URL, assume it is crossDomain,
+				// it can be rejected by the transport if it is invalid
+				s.crossDomain = true;
+			}
+		}
+
+		// Convert data if not already a string
+		if ( s.data && s.processData && typeof s.data !== "string" ) {
+			s.data = jQuery.param( s.data, s.traditional );
+		}
+
+		// Apply prefilters
+		inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+		// If request was aborted inside a prefilter, stop there
+		if ( completed ) {
+			return jqXHR;
+		}
+
+		// We can fire global events as of now if asked to
+		// Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+		fireGlobals = jQuery.event && s.global;
+
+		// Watch for a new set of requests
+		if ( fireGlobals && jQuery.active++ === 0 ) {
+			jQuery.event.trigger( "ajaxStart" );
+		}
+
+		// Uppercase the type
+		s.type = s.type.toUpperCase();
+
+		// Determine if request has content
+		s.hasContent = !rnoContent.test( s.type );
+
+		// Save the URL in case we're toying with the If-Modified-Since
+		// and/or If-None-Match header later on
+		// Remove hash to simplify url manipulation
+		cacheURL = s.url.replace( rhash, "" );
+
+		// More options handling for requests with no content
+		if ( !s.hasContent ) {
+
+			// Remember the hash so we can put it back
+			uncached = s.url.slice( cacheURL.length );
+
+			// If data is available and should be processed, append data to url
+			if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+				cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+				// #9682: remove data so that it's not used in an eventual retry
+				delete s.data;
+			}
+
+			// Add or update anti-cache param if needed
+			if ( s.cache === false ) {
+				cacheURL = cacheURL.replace( rantiCache, "$1" );
+				uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+					uncached;
+			}
+
+			// Put hash and anti-cache on the URL that will be requested (gh-1732)
+			s.url = cacheURL + uncached;
+
+		// Change '%20' to '+' if this is encoded form body content (gh-2658)
+		} else if ( s.data && s.processData &&
+			( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+			s.data = s.data.replace( r20, "+" );
+		}
+
+		// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+		if ( s.ifModified ) {
+			if ( jQuery.lastModified[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+			}
+			if ( jQuery.etag[ cacheURL ] ) {
+				jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+			}
+		}
+
+		// Set the correct header, if data is being sent
+		if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+			jqXHR.setRequestHeader( "Content-Type", s.contentType );
+		}
+
+		// Set the Accepts header for the server, depending on the dataType
+		jqXHR.setRequestHeader(
+			"Accept",
+			s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+				s.accepts[ s.dataTypes[ 0 ] ] +
+					( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+				s.accepts[ "*" ]
+		);
+
+		// Check for headers option
+		for ( i in s.headers ) {
+			jqXHR.setRequestHeader( i, s.headers[ i ] );
+		}
+
+		// Allow custom headers/mimetypes and early abort
+		if ( s.beforeSend &&
+			( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+			// Abort if not done already and return
+			return jqXHR.abort();
+		}
+
+		// Aborting is no longer a cancellation
+		strAbort = "abort";
+
+		// Install callbacks on deferreds
+		completeDeferred.add( s.complete );
+		jqXHR.done( s.success );
+		jqXHR.fail( s.error );
+
+		// Get transport
+		transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+		// If no transport, we auto-abort
+		if ( !transport ) {
+			done( -1, "No Transport" );
+		} else {
+			jqXHR.readyState = 1;
+
+			// Send global event
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+			}
+
+			// If request was aborted inside ajaxSend, stop there
+			if ( completed ) {
+				return jqXHR;
+			}
+
+			// Timeout
+			if ( s.async && s.timeout > 0 ) {
+				timeoutTimer = window.setTimeout( function() {
+					jqXHR.abort( "timeout" );
+				}, s.timeout );
+			}
+
+			try {
+				completed = false;
+				transport.send( requestHeaders, done );
+			} catch ( e ) {
+
+				// Rethrow post-completion exceptions
+				if ( completed ) {
+					throw e;
+				}
+
+				// Propagate others as results
+				done( -1, e );
+			}
+		}
+
+		// Callback for when everything is done
+		function done( status, nativeStatusText, responses, headers ) {
+			var isSuccess, success, error, response, modified,
+				statusText = nativeStatusText;
+
+			// Ignore repeat invocations
+			if ( completed ) {
+				return;
+			}
+
+			completed = true;
+
+			// Clear timeout if it exists
+			if ( timeoutTimer ) {
+				window.clearTimeout( timeoutTimer );
+			}
+
+			// Dereference transport for early garbage collection
+			// (no matter how long the jqXHR object will be used)
+			transport = undefined;
+
+			// Cache response headers
+			responseHeadersString = headers || "";
+
+			// Set readyState
+			jqXHR.readyState = status > 0 ? 4 : 0;
+
+			// Determine if successful
+			isSuccess = status >= 200 && status < 300 || status === 304;
+
+			// Get response data
+			if ( responses ) {
+				response = ajaxHandleResponses( s, jqXHR, responses );
+			}
+
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
+				s.converters[ "text script" ] = function() {};
+			}
+
+			// Convert no matter what (that way responseXXX fields are always set)
+			response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+			// If successful, handle type chaining
+			if ( isSuccess ) {
+
+				// Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+				if ( s.ifModified ) {
+					modified = jqXHR.getResponseHeader( "Last-Modified" );
+					if ( modified ) {
+						jQuery.lastModified[ cacheURL ] = modified;
+					}
+					modified = jqXHR.getResponseHeader( "etag" );
+					if ( modified ) {
+						jQuery.etag[ cacheURL ] = modified;
+					}
+				}
+
+				// if no content
+				if ( status === 204 || s.type === "HEAD" ) {
+					statusText = "nocontent";
+
+				// if not modified
+				} else if ( status === 304 ) {
+					statusText = "notmodified";
+
+				// If we have data, let's convert it
+				} else {
+					statusText = response.state;
+					success = response.data;
+					error = response.error;
+					isSuccess = !error;
+				}
+			} else {
+
+				// Extract error from statusText and normalize for non-aborts
+				error = statusText;
+				if ( status || !statusText ) {
+					statusText = "error";
+					if ( status < 0 ) {
+						status = 0;
+					}
+				}
+			}
+
+			// Set data for the fake xhr object
+			jqXHR.status = status;
+			jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+			// Success/Error
+			if ( isSuccess ) {
+				deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+			} else {
+				deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+			}
+
+			// Status-dependent callbacks
+			jqXHR.statusCode( statusCode );
+			statusCode = undefined;
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+					[ jqXHR, s, isSuccess ? success : error ] );
+			}
+
+			// Complete
+			completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+			if ( fireGlobals ) {
+				globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+				// Handle the global AJAX counter
+				if ( !( --jQuery.active ) ) {
+					jQuery.event.trigger( "ajaxStop" );
+				}
+			}
+		}
+
+		return jqXHR;
+	},
+
+	getJSON: function( url, data, callback ) {
+		return jQuery.get( url, data, callback, "json" );
+	},
+
+	getScript: function( url, callback ) {
+		return jQuery.get( url, undefined, callback, "script" );
+	}
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+	jQuery[ method ] = function( url, data, callback, type ) {
+
+		// Shift arguments if data argument was omitted
+		if ( isFunction( data ) ) {
+			type = type || callback;
+			callback = data;
+			data = undefined;
+		}
+
+		// The url can be an options object (which then must have .url)
+		return jQuery.ajax( jQuery.extend( {
+			url: url,
+			type: method,
+			dataType: type,
+			data: data,
+			success: callback
+		}, jQuery.isPlainObject( url ) && url ) );
+	};
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+	var i;
+	for ( i in s.headers ) {
+		if ( i.toLowerCase() === "content-type" ) {
+			s.contentType = s.headers[ i ] || "";
+		}
+	}
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+	return jQuery.ajax( {
+		url: url,
+
+		// Make this explicit, since user can override this through ajaxSetup (#11264)
+		type: "GET",
+		dataType: "script",
+		cache: true,
+		async: false,
+		global: false,
+
+		// Only evaluate the response if it is successful (gh-4126)
+		// dataFilter is not invoked for failure responses, so using it instead
+		// of the default converter is kludgy but it works.
+		converters: {
+			"text script": function() {}
+		},
+		dataFilter: function( response ) {
+			jQuery.globalEval( response, options, doc );
+		}
+	} );
+};
+
+
+jQuery.fn.extend( {
+	wrapAll: function( html ) {
+		var wrap;
+
+		if ( this[ 0 ] ) {
+			if ( isFunction( html ) ) {
+				html = html.call( this[ 0 ] );
+			}
+
+			// The elements to wrap the target around
+			wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+			if ( this[ 0 ].parentNode ) {
+				wrap.insertBefore( this[ 0 ] );
+			}
+
+			wrap.map( function() {
+				var elem = this;
+
+				while ( elem.firstElementChild ) {
+					elem = elem.firstElementChild;
+				}
+
+				return elem;
+			} ).append( this );
+		}
+
+		return this;
+	},
+
+	wrapInner: function( html ) {
+		if ( isFunction( html ) ) {
+			return this.each( function( i ) {
+				jQuery( this ).wrapInner( html.call( this, i ) );
+			} );
+		}
+
+		return this.each( function() {
+			var self = jQuery( this ),
+				contents = self.contents();
+
+			if ( contents.length ) {
+				contents.wrapAll( html );
+
+			} else {
+				self.append( html );
+			}
+		} );
+	},
+
+	wrap: function( html ) {
+		var htmlIsFunction = isFunction( html );
+
+		return this.each( function( i ) {
+			jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+		} );
+	},
+
+	unwrap: function( selector ) {
+		this.parent( selector ).not( "body" ).each( function() {
+			jQuery( this ).replaceWith( this.childNodes );
+		} );
+		return this;
+	}
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+	return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+	return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+	try {
+		return new window.XMLHttpRequest();
+	} catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+		// File protocol always yields status code 0, assume 200
+		0: 200,
+
+		// Support: IE <=9 only
+		// #1450: sometimes IE returns 1223 when it should be 204
+		1223: 204
+	},
+	xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+	var callback, errorCallback;
+
+	// Cross domain only allowed if supported through XMLHttpRequest
+	if ( support.cors || xhrSupported && !options.crossDomain ) {
+		return {
+			send: function( headers, complete ) {
+				var i,
+					xhr = options.xhr();
+
+				xhr.open(
+					options.type,
+					options.url,
+					options.async,
+					options.username,
+					options.password
+				);
+
+				// Apply custom fields if provided
+				if ( options.xhrFields ) {
+					for ( i in options.xhrFields ) {
+						xhr[ i ] = options.xhrFields[ i ];
+					}
+				}
+
+				// Override mime type if needed
+				if ( options.mimeType && xhr.overrideMimeType ) {
+					xhr.overrideMimeType( options.mimeType );
+				}
+
+				// X-Requested-With header
+				// For cross-domain requests, seeing as conditions for a preflight are
+				// akin to a jigsaw puzzle, we simply never set it to be sure.
+				// (it can always be set on a per-request basis or even using ajaxSetup)
+				// For same-domain requests, won't change header if already provided.
+				if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+					headers[ "X-Requested-With" ] = "XMLHttpRequest";
+				}
+
+				// Set headers
+				for ( i in headers ) {
+					xhr.setRequestHeader( i, headers[ i ] );
+				}
+
+				// Callback
+				callback = function( type ) {
+					return function() {
+						if ( callback ) {
+							callback = errorCallback = xhr.onload =
+								xhr.onerror = xhr.onabort = xhr.ontimeout =
+									xhr.onreadystatechange = null;
+
+							if ( type === "abort" ) {
+								xhr.abort();
+							} else if ( type === "error" ) {
+
+								// Support: IE <=9 only
+								// On a manual native abort, IE9 throws
+								// errors on any property access that is not readyState
+								if ( typeof xhr.status !== "number" ) {
+									complete( 0, "error" );
+								} else {
+									complete(
+
+										// File: protocol always yields status 0; see #8605, #14207
+										xhr.status,
+										xhr.statusText
+									);
+								}
+							} else {
+								complete(
+									xhrSuccessStatus[ xhr.status ] || xhr.status,
+									xhr.statusText,
+
+									// Support: IE <=9 only
+									// IE9 has no XHR2 but throws on binary (trac-11426)
+									// For XHR2 non-text, let the caller handle it (gh-2498)
+									( xhr.responseType || "text" ) !== "text"  ||
+									typeof xhr.responseText !== "string" ?
+										{ binary: xhr.response } :
+										{ text: xhr.responseText },
+									xhr.getAllResponseHeaders()
+								);
+							}
+						}
+					};
+				};
+
+				// Listen to events
+				xhr.onload = callback();
+				errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+				// Support: IE 9 only
+				// Use onreadystatechange to replace onabort
+				// to handle uncaught aborts
+				if ( xhr.onabort !== undefined ) {
+					xhr.onabort = errorCallback;
+				} else {
+					xhr.onreadystatechange = function() {
+
+						// Check readyState before timeout as it changes
+						if ( xhr.readyState === 4 ) {
+
+							// Allow onerror to be called first,
+							// but that will not handle a native abort
+							// Also, save errorCallback to a variable
+							// as xhr.onerror cannot be accessed
+							window.setTimeout( function() {
+								if ( callback ) {
+									errorCallback();
+								}
+							} );
+						}
+					};
+				}
+
+				// Create the abort callback
+				callback = callback( "abort" );
+
+				try {
+
+					// Do send the request (this may raise an exception)
+					xhr.send( options.hasContent && options.data || null );
+				} catch ( e ) {
+
+					// #14683: Only rethrow if this hasn't been notified as an error yet
+					if ( callback ) {
+						throw e;
+					}
+				}
+			},
+
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+	if ( s.crossDomain ) {
+		s.contents.script = false;
+	}
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+	accepts: {
+		script: "text/javascript, application/javascript, " +
+			"application/ecmascript, application/x-ecmascript"
+	},
+	contents: {
+		script: /\b(?:java|ecma)script\b/
+	},
+	converters: {
+		"text script": function( text ) {
+			jQuery.globalEval( text );
+			return text;
+		}
+	}
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+	if ( s.cache === undefined ) {
+		s.cache = false;
+	}
+	if ( s.crossDomain ) {
+		s.type = "GET";
+	}
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+	// This transport only deals with cross domain or forced-by-attrs requests
+	if ( s.crossDomain || s.scriptAttrs ) {
+		var script, callback;
+		return {
+			send: function( _, complete ) {
+				script = jQuery( "<script>" )
+					.attr( s.scriptAttrs || {} )
+					.prop( { charset: s.scriptCharset, src: s.url } )
+					.on( "load error", callback = function( evt ) {
+						script.remove();
+						callback = null;
+						if ( evt ) {
+							complete( evt.type === "error" ? 404 : 200, evt.type );
+						}
+					} );
+
+				// Use native DOM manipulation to avoid our domManip AJAX trickery
+				document.head.appendChild( script[ 0 ] );
+			},
+			abort: function() {
+				if ( callback ) {
+					callback();
+				}
+			}
+		};
+	}
+} );
+
+
+
+
+var oldCallbacks = [],
+	rjsonp = /(=)\?(?=&|$)|\?\?/;
+
+// Default jsonp settings
+jQuery.ajaxSetup( {
+	jsonp: "callback",
+	jsonpCallback: function() {
+		var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
+		this[ callback ] = true;
+		return callback;
+	}
+} );
+
+// Detect, normalize options and install callbacks for jsonp requests
+jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) {
+
+	var callbackName, overwritten, responseContainer,
+		jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ?
+			"url" :
+			typeof s.data === "string" &&
+				( s.contentType || "" )
+					.indexOf( "application/x-www-form-urlencoded" ) === 0 &&
+				rjsonp.test( s.data ) && "data"
+		);
+
+	// Handle iff the expected data type is "jsonp" or we have a parameter to set
+	if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) {
+
+		// Get callback name, remembering preexisting value associated with it
+		callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ?
+			s.jsonpCallback() :
+			s.jsonpCallback;
+
+		// Insert callback into url or form data
+		if ( jsonProp ) {
+			s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName );
+		} else if ( s.jsonp !== false ) {
+			s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName;
+		}
+
+		// Use data converter to retrieve json after script execution
+		s.converters[ "script json" ] = function() {
+			if ( !responseContainer ) {
+				jQuery.error( callbackName + " was not called" );
+			}
+			return responseContainer[ 0 ];
+		};
+
+		// Force json dataType
+		s.dataTypes[ 0 ] = "json";
+
+		// Install callback
+		overwritten = window[ callbackName ];
+		window[ callbackName ] = function() {
+			responseContainer = arguments;
+		};
+
+		// Clean-up function (fires after converters)
+		jqXHR.always( function() {
+
+			// If previous value didn't exist - remove it
+			if ( overwritten === undefined ) {
+				jQuery( window ).removeProp( callbackName );
+
+			// Otherwise restore preexisting value
+			} else {
+				window[ callbackName ] = overwritten;
+			}
+
+			// Save back as free
+			if ( s[ callbackName ] ) {
+
+				// Make sure that re-using the options doesn't screw things around
+				s.jsonpCallback = originalSettings.jsonpCallback;
+
+				// Save the callback name for future use
+				oldCallbacks.push( callbackName );
+			}
+
+			// Call if it was a function and we have a response
+			if ( responseContainer && isFunction( overwritten ) ) {
+				overwritten( responseContainer[ 0 ] );
+			}
+
+			responseContainer = overwritten = undefined;
+		} );
+
+		// Delegate to script
+		return "script";
+	}
+} );
+
+
+
+
+// Support: Safari 8 only
+// In Safari 8 documents created via document.implementation.createHTMLDocument
+// collapse sibling forms: the second one becomes a child of the first one.
+// Because of that, this security measure has to be disabled in Safari 8.
+// https://bugs.webkit.org/show_bug.cgi?id=137337
+support.createHTMLDocument = ( function() {
+	var body = document.implementation.createHTMLDocument( "" ).body;
+	body.innerHTML = "<form></form><form></form>";
+	return body.childNodes.length === 2;
+} )();
+
+
+// Argument "data" should be string of html
+// context (optional): If specified, the fragment will be created in this context,
+// defaults to document
+// keepScripts (optional): If true, will include scripts passed in the html string
+jQuery.parseHTML = function( data, context, keepScripts ) {
+	if ( typeof data !== "string" ) {
+		return [];
+	}
+	if ( typeof context === "boolean" ) {
+		keepScripts = context;
+		context = false;
+	}
+
+	var base, parsed, scripts;
+
+	if ( !context ) {
+
+		// Stop scripts or inline event handlers from being executed immediately
+		// by using document.implementation
+		if ( support.createHTMLDocument ) {
+			context = document.implementation.createHTMLDocument( "" );
+
+			// Set the base href for the created document
+			// so any parsed elements with URLs
+			// are based on the document's URL (gh-2965)
+			base = context.createElement( "base" );
+			base.href = document.location.href;
+			context.head.appendChild( base );
+		} else {
+			context = document;
+		}
+	}
+
+	parsed = rsingleTag.exec( data );
+	scripts = !keepScripts && [];
+
+	// Single tag
+	if ( parsed ) {
+		return [ context.createElement( parsed[ 1 ] ) ];
+	}
+
+	parsed = buildFragment( [ data ], context, scripts );
+
+	if ( scripts && scripts.length ) {
+		jQuery( scripts ).remove();
+	}
+
+	return jQuery.merge( [], parsed.childNodes );
+};
+
+
+/**
+ * Load a url into a page
+ */
+jQuery.fn.load = function( url, params, callback ) {
+	var selector, type, response,
+		self = this,
+		off = url.indexOf( " " );
+
+	if ( off > -1 ) {
+		selector = stripAndCollapse( url.slice( off ) );
+		url = url.slice( 0, off );
+	}
+
+	// If it's a function
+	if ( isFunction( params ) ) {
+
+		// We assume that it's the callback
+		callback = params;
+		params = undefined;
+
+	// Otherwise, build a param string
+	} else if ( params && typeof params === "object" ) {
+		type = "POST";
+	}
+
+	// If we have elements to modify, make the request
+	if ( self.length > 0 ) {
+		jQuery.ajax( {
+			url: url,
+
+			// If "type" variable is undefined, then "GET" method will be used.
+			// Make value of this field explicit since
+			// user can override it through ajaxSetup method
+			type: type || "GET",
+			dataType: "html",
+			data: params
+		} ).done( function( responseText ) {
+
+			// Save response for use in complete callback
+			response = arguments;
+
+			self.html( selector ?
+
+				// If a selector was specified, locate the right elements in a dummy div
+				// Exclude scripts to avoid IE 'Permission Denied' errors
+				jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+				// Otherwise use the full result
+				responseText );
+
+		// If the request succeeds, this function gets "data", "status", "jqXHR"
+		// but they are ignored because response was set above.
+		// If it fails, this function gets "jqXHR", "status", "error"
+		} ).always( callback && function( jqXHR, status ) {
+			self.each( function() {
+				callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] );
+			} );
+		} );
+	}
+
+	return this;
+};
+
+
+
+
+jQuery.expr.pseudos.animated = function( elem ) {
+	return jQuery.grep( jQuery.timers, function( fn ) {
+		return elem === fn.elem;
+	} ).length;
+};
+
+
+
+
+jQuery.offset = {
+	setOffset: function( elem, options, i ) {
+		var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+			position = jQuery.css( elem, "position" ),
+			curElem = jQuery( elem ),
+			props = {};
+
+		// Set position first, in-case top/left are set even on static elem
+		if ( position === "static" ) {
+			elem.style.position = "relative";
+		}
+
+		curOffset = curElem.offset();
+		curCSSTop = jQuery.css( elem, "top" );
+		curCSSLeft = jQuery.css( elem, "left" );
+		calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+			( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1;
+
+		// Need to be able to calculate position if either
+		// top or left is auto and position is either absolute or fixed
+		if ( calculatePosition ) {
+			curPosition = curElem.position();
+			curTop = curPosition.top;
+			curLeft = curPosition.left;
+
+		} else {
+			curTop = parseFloat( curCSSTop ) || 0;
+			curLeft = parseFloat( curCSSLeft ) || 0;
+		}
+
+		if ( isFunction( options ) ) {
+
+			// Use jQuery.extend here to allow modification of coordinates argument (gh-1848)
+			options = options.call( elem, i, jQuery.extend( {}, curOffset ) );
+		}
+
+		if ( options.top != null ) {
+			props.top = ( options.top - curOffset.top ) + curTop;
+		}
+		if ( options.left != null ) {
+			props.left = ( options.left - curOffset.left ) + curLeft;
+		}
+
+		if ( "using" in options ) {
+			options.using.call( elem, props );
+
+		} else {
+			curElem.css( props );
+		}
+	}
+};
+
+jQuery.fn.extend( {
+
+	// offset() relates an element's border box to the document origin
+	offset: function( options ) {
+
+		// Preserve chaining for setter
+		if ( arguments.length ) {
+			return options === undefined ?
+				this :
+				this.each( function( i ) {
+					jQuery.offset.setOffset( this, options, i );
+				} );
+		}
+
+		var rect, win,
+			elem = this[ 0 ];
+
+		if ( !elem ) {
+			return;
+		}
+
+		// Return zeros for disconnected and hidden (display: none) elements (gh-2310)
+		// Support: IE <=11 only
+		// Running getBoundingClientRect on a
+		// disconnected node in IE throws an error
+		if ( !elem.getClientRects().length ) {
+			return { top: 0, left: 0 };
+		}
+
+		// Get document-relative position by adding viewport scroll to viewport-relative gBCR
+		rect = elem.getBoundingClientRect();
+		win = elem.ownerDocument.defaultView;
+		return {
+			top: rect.top + win.pageYOffset,
+			left: rect.left + win.pageXOffset
+		};
+	},
+
+	// position() relates an element's margin box to its offset parent's padding box
+	// This corresponds to the behavior of CSS absolute positioning
+	position: function() {
+		if ( !this[ 0 ] ) {
+			return;
+		}
+
+		var offsetParent, offset, doc,
+			elem = this[ 0 ],
+			parentOffset = { top: 0, left: 0 };
+
+		// position:fixed elements are offset from the viewport, which itself always has zero offset
+		if ( jQuery.css( elem, "position" ) === "fixed" ) {
+
+			// Assume position:fixed implies availability of getBoundingClientRect
+			offset = elem.getBoundingClientRect();
+
+		} else {
+			offset = this.offset();
+
+			// Account for the *real* offset parent, which can be the document or its root element
+			// when a statically positioned element is identified
+			doc = elem.ownerDocument;
+			offsetParent = elem.offsetParent || doc.documentElement;
+			while ( offsetParent &&
+				( offsetParent === doc.body || offsetParent === doc.documentElement ) &&
+				jQuery.css( offsetParent, "position" ) === "static" ) {
+
+				offsetParent = offsetParent.parentNode;
+			}
+			if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) {
+
+				// Incorporate borders into its offset, since they are outside its content origin
+				parentOffset = jQuery( offsetParent ).offset();
+				parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true );
+				parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true );
+			}
+		}
+
+		// Subtract parent offsets and element margins
+		return {
+			top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+			left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true )
+		};
+	},
+
+	// This method will return documentElement in the following cases:
+	// 1) For the element inside the iframe without offsetParent, this method will return
+	//    documentElement of the parent window
+	// 2) For the hidden or detached element
+	// 3) For body or html element, i.e. in case of the html node - it will return itself
+	//
+	// but those exceptions were never presented as a real life use-cases
+	// and might be considered as more preferable results.
+	//
+	// This logic, however, is not guaranteed and can change at any point in the future
+	offsetParent: function() {
+		return this.map( function() {
+			var offsetParent = this.offsetParent;
+
+			while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) {
+				offsetParent = offsetParent.offsetParent;
+			}
+
+			return offsetParent || documentElement;
+		} );
+	}
+} );
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+	var top = "pageYOffset" === prop;
+
+	jQuery.fn[ method ] = function( val ) {
+		return access( this, function( elem, method, val ) {
+
+			// Coalesce documents and windows
+			var win;
+			if ( isWindow( elem ) ) {
+				win = elem;
+			} else if ( elem.nodeType === 9 ) {
+				win = elem.defaultView;
+			}
+
+			if ( val === undefined ) {
+				return win ? win[ prop ] : elem[ method ];
+			}
+
+			if ( win ) {
+				win.scrollTo(
+					!top ? val : win.pageXOffset,
+					top ? val : win.pageYOffset
+				);
+
+			} else {
+				elem[ method ] = val;
+			}
+		}, method, val, arguments.length );
+	};
+} );
+
+// Support: Safari <=7 - 9.1, Chrome <=37 - 49
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
+// getComputedStyle returns percent when specified for top/left/bottom/right;
+// rather than make the css module depend on the offset module, just check for it here
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
+	jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+		function( elem, computed ) {
+			if ( computed ) {
+				computed = curCSS( elem, prop );
+
+				// If curCSS returns percentage, fallback to offset
+				return rnumnonpx.test( computed ) ?
+					jQuery( elem ).position()[ prop ] + "px" :
+					computed;
+			}
+		}
+	);
+} );
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+	jQuery.each( {
+		padding: "inner" + name,
+		content: type,
+		"": "outer" + name
+	}, function( defaultExtra, funcName ) {
+
+		// Margin is only for outerHeight, outerWidth
+		jQuery.fn[ funcName ] = function( margin, value ) {
+			var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+				extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+			return access( this, function( elem, type, value ) {
+				var doc;
+
+				if ( isWindow( elem ) ) {
+
+					// $( window ).outerWidth/Height return w/h including scrollbars (gh-1729)
+					return funcName.indexOf( "outer" ) === 0 ?
+						elem[ "inner" + name ] :
+						elem.document.documentElement[ "client" + name ];
+				}
+
+				// Get document width or height
+				if ( elem.nodeType === 9 ) {
+					doc = elem.documentElement;
+
+					// Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height],
+					// whichever is greatest
+					return Math.max(
+						elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+						elem.body[ "offset" + name ], doc[ "offset" + name ],
+						doc[ "client" + name ]
+					);
+				}
+
+				return value === undefined ?
+
+					// Get width or height on the element, requesting but not forcing parseFloat
+					jQuery.css( elem, type, extra ) :
+
+					// Set width or height on the element
+					jQuery.style( elem, type, value, extra );
+			}, type, chainable ? margin : undefined, chainable );
+		};
+	} );
+} );
+
+
+jQuery.each( [
+	"ajaxStart",
+	"ajaxStop",
+	"ajaxComplete",
+	"ajaxError",
+	"ajaxSuccess",
+	"ajaxSend"
+], function( _i, type ) {
+	jQuery.fn[ type ] = function( fn ) {
+		return this.on( type, fn );
+	};
+} );
+
+
+
+
+jQuery.fn.extend( {
+
+	bind: function( types, data, fn ) {
+		return this.on( types, null, data, fn );
+	},
+	unbind: function( types, fn ) {
+		return this.off( types, null, fn );
+	},
+
+	delegate: function( selector, types, data, fn ) {
+		return this.on( types, selector, data, fn );
+	},
+	undelegate: function( selector, types, fn ) {
+
+		// ( namespace ) or ( selector, types [, fn] )
+		return arguments.length === 1 ?
+			this.off( selector, "**" ) :
+			this.off( types, selector || "**", fn );
+	},
+
+	hover: function( fnOver, fnOut ) {
+		return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
+	}
+} );
+
+jQuery.each(
+	( "blur focus focusin focusout resize scroll click dblclick " +
+	"mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+	"change select submit keydown keypress keyup contextmenu" ).split( " " ),
+	function( _i, name ) {
+
+		// Handle event binding
+		jQuery.fn[ name ] = function( data, fn ) {
+			return arguments.length > 0 ?
+				this.on( name, null, data, fn ) :
+				this.trigger( name );
+		};
+	}
+);
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
+// Bind a function to a context, optionally partially applying any
+// arguments.
+// jQuery.proxy is deprecated to promote standards (specifically Function#bind)
+// However, it is not slated for removal any time soon
+jQuery.proxy = function( fn, context ) {
+	var tmp, args, proxy;
+
+	if ( typeof context === "string" ) {
+		tmp = fn[ context ];
+		context = fn;
+		fn = tmp;
+	}
+
+	// Quick check to determine if target is callable, in the spec
+	// this throws a TypeError, but we will just return undefined.
+	if ( !isFunction( fn ) ) {
+		return undefined;
+	}
+
+	// Simulated bind
+	args = slice.call( arguments, 2 );
+	proxy = function() {
+		return fn.apply( context || this, args.concat( slice.call( arguments ) ) );
+	};
+
+	// Set the guid of unique handler to the same of original handler, so it can be removed
+	proxy.guid = fn.guid = fn.guid || jQuery.guid++;
+
+	return proxy;
+};
+
+jQuery.holdReady = function( hold ) {
+	if ( hold ) {
+		jQuery.readyWait++;
+	} else {
+		jQuery.ready( true );
+	}
+};
+jQuery.isArray = Array.isArray;
+jQuery.parseJSON = JSON.parse;
+jQuery.nodeName = nodeName;
+jQuery.isFunction = isFunction;
+jQuery.isWindow = isWindow;
+jQuery.camelCase = camelCase;
+jQuery.type = toType;
+
+jQuery.now = Date.now;
+
+jQuery.isNumeric = function( obj ) {
+
+	// As of jQuery 3.0, isNumeric is limited to
+	// strings and numbers (primitives or objects)
+	// that can be coerced to finite numbers (gh-2662)
+	var type = jQuery.type( obj );
+	return ( type === "number" || type === "string" ) &&
+
+		// parseFloat NaNs numeric-cast false positives ("")
+		// ...but misinterprets leading-number strings, particularly hex literals ("0x...")
+		// subtraction forces infinities to NaN
+		!isNaN( obj - parseFloat( obj ) );
+};
+
+jQuery.trim = function( text ) {
+	return text == null ?
+		"" :
+		( text + "" ).replace( rtrim, "" );
+};
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+	define( "jquery", [], function() {
+		return jQuery;
+	} );
+}
+
+
+
+
+var
+
+	// Map over jQuery in case of overwrite
+	_jQuery = window.jQuery,
+
+	// Map over the $ in case of overwrite
+	_$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+	if ( window.$ === jQuery ) {
+		window.$ = _$;
+	}
+
+	if ( deep && window.jQuery === jQuery ) {
+		window.jQuery = _jQuery;
+	}
+
+	return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in AMD
+// (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === "undefined" ) {
+	window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+} );
diff --git a/doc/LectureNotes/_build/html/_static/jquery.js b/doc/LectureNotes/_build/html/_static/jquery.js
index b0614034a..c4c6022f2 100644
--- a/doc/LectureNotes/_build/html/_static/jquery.js
+++ b/doc/LectureNotes/_build/html/_static/jquery.js
@@ -1,2 +1,2 @@
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diff --git a/doc/LectureNotes/_build/html/_static/language_data.js b/doc/LectureNotes/_build/html/_static/language_data.js
index ebe2f03bf..2e22b06ab 100644
--- a/doc/LectureNotes/_build/html/_static/language_data.js
+++ b/doc/LectureNotes/_build/html/_static/language_data.js
@@ -10,7 +10,7 @@
  *
  */
 
-var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+var stopwords = ["a", "and", "are", "as", "at", "be", "but", "by", "for", "if", "in", "into", "is", "it", "near", "no", "not", "of", "on", "or", "such", "that", "the", "their", "then", "there", "these", "they", "this", "to", "was", "will", "with"];
 
 
 /* Non-minified version is copied as a separate JS file, is available */
@@ -197,101 +197,3 @@ var Stemmer = function() {
   }
 }
 
-
-
-
-var splitChars = (function() {
-    var result = {};
-    var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
-         1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
-         2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
-         2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
-         3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
-         3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
-         4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
-         8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
-         11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
-         43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
-    var i, j, start, end;
-    for (i = 0; i < singles.length; i++) {
-        result[singles[i]] = true;
-    }
-    var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
-         [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
-         [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
-         [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
-         [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
-         [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
-         [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
-         [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
-         [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
-         [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
-         [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
-         [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
-         [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
-         [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
-         [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
-         [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
-         [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
-         [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
-         [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
-         [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
-         [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
-         [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
-         [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
-         [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
-         [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
-         [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
-         [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
-         [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
-         [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
-         [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
-         [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
-         [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
-         [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
-         [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
-         [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
-         [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
-         [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
-         [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
-         [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
-         [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
-         [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
-         [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
-         [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
-         [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
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diff --git a/doc/LectureNotes/_build/html/_static/locales/ar/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ar/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..15541a6a375f93efed3f410c2f892174ba91aaa0
GIT binary patch
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diff --git a/doc/LectureNotes/_build/html/_static/locales/ar/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ar/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..2e8d68202
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ar/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ar\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "أقترح تحرير"
+
+msgid "Last updated on"
+msgstr "آخر تحديث في"
+
+msgid "Edit this page"
+msgstr "قم بتحرير هذه الصفحة"
+
+msgid "Launch"
+msgstr "إطلاق"
+
+msgid "Print to PDF"
+msgstr "طباعة إلى PDF"
+
+msgid "open issue"
+msgstr "قضية مفتوحة"
+
+msgid "Download notebook file"
+msgstr "تنزيل ملف دفتر الملاحظات"
+
+msgid "Toggle navigation"
+msgstr "تبديل التنقل"
+
+msgid "Source repository"
+msgstr "مستودع المصدر"
+
+msgid "By the"
+msgstr "بواسطة"
+
+msgid "next page"
+msgstr "الصفحة التالية"
+
+msgid "repository"
+msgstr "مخزن"
+
+msgid "Sphinx Book Theme"
+msgstr "موضوع كتاب أبو الهول"
+
+msgid "Download source file"
+msgstr "تنزيل ملف المصدر"
+
+msgid "Contents"
+msgstr "محتويات"
+
+msgid "By"
+msgstr "بواسطة"
+
+msgid "Copyright"
+msgstr "حقوق النشر"
+
+msgid "Fullscreen mode"
+msgstr "وضع ملء الشاشة"
+
+msgid "Open an issue"
+msgstr "افتح قضية"
+
+msgid "previous page"
+msgstr "الصفحة السابقة"
+
+msgid "Download this page"
+msgstr "قم بتنزيل هذه الصفحة"
+
+msgid "Theme by the"
+msgstr "موضوع بواسطة"
diff --git a/doc/LectureNotes/_build/html/_static/locales/bg/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/bg/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..da95120037f8d7c52ad1f166a7682ea55ca47a01
GIT binary patch
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/bg/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/bg/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..56ef0ebdf
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/bg/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: bg\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "предложи редактиране"
+
+msgid "Last updated on"
+msgstr "Последна актуализация на"
+
+msgid "Edit this page"
+msgstr "Редактирайте тази страница"
+
+msgid "Launch"
+msgstr "Стартиране"
+
+msgid "Print to PDF"
+msgstr "Печат в PDF"
+
+msgid "open issue"
+msgstr "отворен брой"
+
+msgid "Download notebook file"
+msgstr "Изтеглете файла на бележника"
+
+msgid "Toggle navigation"
+msgstr "Превключване на навигацията"
+
+msgid "Source repository"
+msgstr "Хранилище на източника"
+
+msgid "By the"
+msgstr "По"
+
+msgid "next page"
+msgstr "Следваща страница"
+
+msgid "repository"
+msgstr "хранилище"
+
+msgid "Sphinx Book Theme"
+msgstr "Тема на книгата Sphinx"
+
+msgid "Download source file"
+msgstr "Изтеглете изходния файл"
+
+msgid "Contents"
+msgstr "Съдържание"
+
+msgid "By"
+msgstr "От"
+
+msgid "Copyright"
+msgstr "Авторско право"
+
+msgid "Fullscreen mode"
+msgstr "Режим на цял екран"
+
+msgid "Open an issue"
+msgstr "Отворете проблем"
+
+msgid "previous page"
+msgstr "предишна страница"
+
+msgid "Download this page"
+msgstr "Изтеглете тази страница"
+
+msgid "Theme by the"
+msgstr "Тема от"
diff --git a/doc/LectureNotes/_build/html/_static/locales/bn/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/bn/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..6b96639b726a2fa959a6419b6f8b7e0dfcce33ae
GIT binary patch
literal 1646
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/bn/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/bn/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..243ca31f7
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/bn/LC_MESSAGES/booktheme.po
@@ -0,0 +1,63 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: bn\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "Last updated on"
+msgstr "সর্বশেষ আপডেট"
+
+msgid "Edit this page"
+msgstr "এই পৃষ্ঠাটি সম্পাদনা করুন"
+
+msgid "Launch"
+msgstr "শুরু করা"
+
+msgid "Print to PDF"
+msgstr "পিডিএফ প্রিন্ট করুন"
+
+msgid "open issue"
+msgstr "খোলা সমস্যা"
+
+msgid "Download notebook file"
+msgstr "নোটবুক ফাইল ডাউনলোড করুন"
+
+msgid "Toggle navigation"
+msgstr "নেভিগেশন টগল করুন"
+
+msgid "Source repository"
+msgstr "উত্স সংগ্রহস্থল"
+
+msgid "By the"
+msgstr "দ্বারা"
+
+msgid "next page"
+msgstr "পরবর্তী পৃষ্ঠা"
+
+msgid "Sphinx Book Theme"
+msgstr "স্পিনিক্স বুক থিম"
+
+msgid "Download source file"
+msgstr "উত্স ফাইল ডাউনলোড করুন"
+
+msgid "By"
+msgstr "দ্বারা"
+
+msgid "Copyright"
+msgstr "কপিরাইট"
+
+msgid "Open an issue"
+msgstr "একটি সমস্যা খুলুন"
+
+msgid "previous page"
+msgstr "আগের পৃষ্ঠা"
+
+msgid "Download this page"
+msgstr "এই পৃষ্ঠাটি ডাউনলোড করুন"
+
+msgid "Theme by the"
+msgstr "থিম দ্বারা"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ca/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ca/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..a4dd30e9bd762578b119c4401d082ea4fa430613
GIT binary patch
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ca/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ca/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..b27a13db9
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ca/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ca\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "suggerir edició"
+
+msgid "Last updated on"
+msgstr "Darrera actualització el"
+
+msgid "Edit this page"
+msgstr "Editeu aquesta pàgina"
+
+msgid "Launch"
+msgstr "Llançament"
+
+msgid "Print to PDF"
+msgstr "Imprimeix a PDF"
+
+msgid "open issue"
+msgstr "número obert"
+
+msgid "Download notebook file"
+msgstr "Descarregar fitxer de quadern"
+
+msgid "Toggle navigation"
+msgstr "Commuta la navegació"
+
+msgid "Source repository"
+msgstr "Dipòsit de fonts"
+
+msgid "By the"
+msgstr "Per la"
+
+msgid "next page"
+msgstr "pàgina següent"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema del llibre Esfinx"
+
+msgid "Download source file"
+msgstr "Baixeu el fitxer font"
+
+msgid "By"
+msgstr "Per"
+
+msgid "Copyright"
+msgstr "Copyright"
+
+msgid "Open an issue"
+msgstr "Obriu un número"
+
+msgid "previous page"
+msgstr "Pàgina anterior"
+
+msgid "Download this page"
+msgstr "Descarregueu aquesta pàgina"
+
+msgid "Theme by the"
+msgstr "Tema del"
diff --git a/doc/LectureNotes/_build/html/_static/locales/cs/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/cs/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..c39e01a6ae9ae5242f04566ffa2cda96b328ca18
GIT binary patch
literal 1405
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/cs/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/cs/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..3818df976
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/cs/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: cs\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "navrhnout úpravy"
+
+msgid "Last updated on"
+msgstr "Naposledy aktualizováno"
+
+msgid "Edit this page"
+msgstr "Upravit tuto stránku"
+
+msgid "Launch"
+msgstr "Zahájení"
+
+msgid "Print to PDF"
+msgstr "Tisk do PDF"
+
+msgid "open issue"
+msgstr "otevřené číslo"
+
+msgid "Download notebook file"
+msgstr "Stáhnout soubor poznámkového bloku"
+
+msgid "Toggle navigation"
+msgstr "Přepnout navigaci"
+
+msgid "Source repository"
+msgstr "Zdrojové úložiště"
+
+msgid "By the"
+msgstr "Podle"
+
+msgid "next page"
+msgstr "další strana"
+
+msgid "repository"
+msgstr "úložiště"
+
+msgid "Sphinx Book Theme"
+msgstr "Téma knihy Sfinga"
+
+msgid "Download source file"
+msgstr "Stáhněte si zdrojový soubor"
+
+msgid "Contents"
+msgstr "Obsah"
+
+msgid "By"
+msgstr "Podle"
+
+msgid "Copyright"
+msgstr "autorská práva"
+
+msgid "Fullscreen mode"
+msgstr "Režim celé obrazovky"
+
+msgid "Open an issue"
+msgstr "Otevřete problém"
+
+msgid "previous page"
+msgstr "předchozí stránka"
+
+msgid "Download this page"
+msgstr "Stáhněte si tuto stránku"
+
+msgid "Theme by the"
+msgstr "Téma od"
diff --git a/doc/LectureNotes/_build/html/_static/locales/da/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/da/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..f43157d70c63ff21b4385dc36cb73f5b14eb6b01
GIT binary patch
literal 1304
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/da/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/da/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..7f20a3bd0
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/da/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: da\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "foreslå redigering"
+
+msgid "Last updated on"
+msgstr "Sidst opdateret den"
+
+msgid "Edit this page"
+msgstr "Rediger denne side"
+
+msgid "Launch"
+msgstr "Start"
+
+msgid "Print to PDF"
+msgstr "Udskriv til PDF"
+
+msgid "open issue"
+msgstr "åbent nummer"
+
+msgid "Download notebook file"
+msgstr "Download notesbog-fil"
+
+msgid "Toggle navigation"
+msgstr "Skift navigation"
+
+msgid "Source repository"
+msgstr "Kildelager"
+
+msgid "By the"
+msgstr "Ved"
+
+msgid "next page"
+msgstr "Næste side"
+
+msgid "repository"
+msgstr "lager"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx bogtema"
+
+msgid "Download source file"
+msgstr "Download kildefil"
+
+msgid "Contents"
+msgstr "Indhold"
+
+msgid "By"
+msgstr "Ved"
+
+msgid "Copyright"
+msgstr "ophavsret"
+
+msgid "Fullscreen mode"
+msgstr "Fuldskærmstilstand"
+
+msgid "Open an issue"
+msgstr "Åbn et problem"
+
+msgid "previous page"
+msgstr "forrige side"
+
+msgid "Download this page"
+msgstr "Download denne side"
+
+msgid "Theme by the"
+msgstr "Tema af"
diff --git a/doc/LectureNotes/_build/html/_static/locales/de/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/de/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..648b565c7829535bc5f26f86909f458d0cd0fe1b
GIT binary patch
literal 1388
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/de/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/de/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..c0027d3ab
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/de/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: de\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "vorschlagen zu bearbeiten"
+
+msgid "Last updated on"
+msgstr "Zuletzt aktualisiert am"
+
+msgid "Edit this page"
+msgstr "Bearbeite diese Seite"
+
+msgid "Launch"
+msgstr "Starten"
+
+msgid "Print to PDF"
+msgstr "In PDF drucken"
+
+msgid "open issue"
+msgstr "offenes Thema"
+
+msgid "Download notebook file"
+msgstr "Notebook-Datei herunterladen"
+
+msgid "Toggle navigation"
+msgstr "Navigation umschalten"
+
+msgid "Source repository"
+msgstr "Quell-Repository"
+
+msgid "By the"
+msgstr "Bis zum"
+
+msgid "next page"
+msgstr "Nächste Seite"
+
+msgid "repository"
+msgstr "Repository"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx-Buch-Thema"
+
+msgid "Download source file"
+msgstr "Quelldatei herunterladen"
+
+msgid "Contents"
+msgstr "Inhalt"
+
+msgid "By"
+msgstr "Durch"
+
+msgid "Copyright"
+msgstr "Urheberrechte ©"
+
+msgid "Fullscreen mode"
+msgstr "Vollbildmodus"
+
+msgid "Open an issue"
+msgstr "Öffnen Sie ein Problem"
+
+msgid "previous page"
+msgstr "vorherige Seite"
+
+msgid "Download this page"
+msgstr "Laden Sie diese Seite herunter"
+
+msgid "Theme by the"
+msgstr "Thema von der"
diff --git a/doc/LectureNotes/_build/html/_static/locales/el/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/el/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..fca6e9355f314677f2890f5679fd79dd67a7a5a2
GIT binary patch
literal 1722
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/el/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/el/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..bdeb3270a
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/el/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: el\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "προτείνω επεξεργασία"
+
+msgid "Last updated on"
+msgstr "Τελευταία ενημέρωση στις"
+
+msgid "Edit this page"
+msgstr "Επεξεργαστείτε αυτήν τη σελίδα"
+
+msgid "Launch"
+msgstr "Εκτόξευση"
+
+msgid "Print to PDF"
+msgstr "Εκτύπωση σε PDF"
+
+msgid "open issue"
+msgstr "ανοιχτό ζήτημα"
+
+msgid "Download notebook file"
+msgstr "Λήψη αρχείου σημειωματάριου"
+
+msgid "Toggle navigation"
+msgstr "Εναλλαγή πλοήγησης"
+
+msgid "Source repository"
+msgstr "Αποθήκη πηγής"
+
+msgid "By the"
+msgstr "Από το"
+
+msgid "next page"
+msgstr "επόμενη σελίδα"
+
+msgid "repository"
+msgstr "αποθήκη"
+
+msgid "Sphinx Book Theme"
+msgstr "Θέμα βιβλίου Sphinx"
+
+msgid "Download source file"
+msgstr "Λήψη αρχείου προέλευσης"
+
+msgid "Contents"
+msgstr "Περιεχόμενα"
+
+msgid "By"
+msgstr "Με"
+
+msgid "Copyright"
+msgstr "Πνευματική ιδιοκτησία"
+
+msgid "Fullscreen mode"
+msgstr "ΛΕΙΤΟΥΡΓΙΑ ΠΛΗΡΟΥΣ ΟΘΟΝΗΣ"
+
+msgid "Open an issue"
+msgstr "Ανοίξτε ένα ζήτημα"
+
+msgid "previous page"
+msgstr "προηγούμενη σελίδα"
+
+msgid "Download this page"
+msgstr "Λήψη αυτής της σελίδας"
+
+msgid "Theme by the"
+msgstr "Θέμα από το"
diff --git a/doc/LectureNotes/_build/html/_static/locales/eo/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/eo/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..d1072bbec62959524a87953d3f41b7c272ecbe37
GIT binary patch
literal 1337
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/eo/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/eo/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..6749f3a34
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/eo/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: eo\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "sugesti redaktadon"
+
+msgid "Last updated on"
+msgstr "Laste ĝisdatigita la"
+
+msgid "Edit this page"
+msgstr "Redaktu ĉi tiun paĝon"
+
+msgid "Launch"
+msgstr "Lanĉo"
+
+msgid "Print to PDF"
+msgstr "Presi al PDF"
+
+msgid "open issue"
+msgstr "malferma numero"
+
+msgid "Download notebook file"
+msgstr "Elŝutu kajeran dosieron"
+
+msgid "Toggle navigation"
+msgstr "Ŝalti navigadon"
+
+msgid "Source repository"
+msgstr "Fonto-deponejo"
+
+msgid "By the"
+msgstr "Per la"
+
+msgid "next page"
+msgstr "sekva paĝo"
+
+msgid "repository"
+msgstr "deponejo"
+
+msgid "Sphinx Book Theme"
+msgstr "Sfinksa Libro-Temo"
+
+msgid "Download source file"
+msgstr "Elŝutu fontodosieron"
+
+msgid "Contents"
+msgstr "Enhavo"
+
+msgid "By"
+msgstr "De"
+
+msgid "Copyright"
+msgstr "Kopirajto"
+
+msgid "Fullscreen mode"
+msgstr "Plenekrana reĝimo"
+
+msgid "Open an issue"
+msgstr "Malfermu numeron"
+
+msgid "previous page"
+msgstr "antaŭa paĝo"
+
+msgid "Download this page"
+msgstr "Elŝutu ĉi tiun paĝon"
+
+msgid "Theme by the"
+msgstr "Temo de la"
diff --git a/doc/LectureNotes/_build/html/_static/locales/es/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/es/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..ba2ee4dc22148ed53f2aeba32c5965654d4a5a2f
GIT binary patch
literal 1396
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/es/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/es/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..71dde37f2
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/es/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: es\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "sugerir editar"
+
+msgid "Last updated on"
+msgstr "Ultima actualización en"
+
+msgid "Edit this page"
+msgstr "Edita esta página"
+
+msgid "Launch"
+msgstr "Lanzamiento"
+
+msgid "Print to PDF"
+msgstr "Imprimir en PDF"
+
+msgid "open issue"
+msgstr "Tema abierto"
+
+msgid "Download notebook file"
+msgstr "Descargar archivo de cuaderno"
+
+msgid "Toggle navigation"
+msgstr "Navegación de palanca"
+
+msgid "Source repository"
+msgstr "Repositorio de origen"
+
+msgid "By the"
+msgstr "Por el"
+
+msgid "next page"
+msgstr "siguiente página"
+
+msgid "repository"
+msgstr "repositorio"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema del libro de la esfinge"
+
+msgid "Download source file"
+msgstr "Descargar archivo fuente"
+
+msgid "Contents"
+msgstr "Contenido"
+
+msgid "By"
+msgstr "Por"
+
+msgid "Copyright"
+msgstr "Derechos de autor"
+
+msgid "Fullscreen mode"
+msgstr "Modo de pantalla completa"
+
+msgid "Open an issue"
+msgstr "Abrir un problema"
+
+msgid "previous page"
+msgstr "pagina anterior"
+
+msgid "Download this page"
+msgstr "Descarga esta pagina"
+
+msgid "Theme by the"
+msgstr "Tema por el"
diff --git a/doc/LectureNotes/_build/html/_static/locales/et/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/et/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..983b82391f499b67a9046c15d0dd8744650ad925
GIT binary patch
literal 1341
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P_MW2m5}a<3ol*Y+f5$~k

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/et/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/et/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..cdcd07c7d
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/et/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: et\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "soovita muuta"
+
+msgid "Last updated on"
+msgstr "Viimati uuendatud"
+
+msgid "Edit this page"
+msgstr "Muutke seda lehte"
+
+msgid "Launch"
+msgstr "Käivitage"
+
+msgid "Print to PDF"
+msgstr "Prindi PDF-i"
+
+msgid "open issue"
+msgstr "avatud küsimus"
+
+msgid "Download notebook file"
+msgstr "Laadige sülearvuti fail alla"
+
+msgid "Toggle navigation"
+msgstr "Lülita navigeerimine sisse"
+
+msgid "Source repository"
+msgstr "Allikahoidla"
+
+msgid "By the"
+msgstr "Autor"
+
+msgid "next page"
+msgstr "järgmine leht"
+
+msgid "repository"
+msgstr "hoidla"
+
+msgid "Sphinx Book Theme"
+msgstr "Sfinksiraamatu teema"
+
+msgid "Download source file"
+msgstr "Laadige alla lähtefail"
+
+msgid "Contents"
+msgstr "Sisu"
+
+msgid "By"
+msgstr "Kõrval"
+
+msgid "Copyright"
+msgstr "Autoriõigus"
+
+msgid "Fullscreen mode"
+msgstr "Täisekraanirežiim"
+
+msgid "Open an issue"
+msgstr "Avage probleem"
+
+msgid "previous page"
+msgstr "eelmine leht"
+
+msgid "Download this page"
+msgstr "Laadige see leht alla"
+
+msgid "Theme by the"
+msgstr "Teema"
diff --git a/doc/LectureNotes/_build/html/_static/locales/fi/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/fi/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..d8ac054597c924e3010f629caeac1c748b7211cd
GIT binary patch
literal 1368
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H66VBTf3Z^G

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/fi/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/fi/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..3c3dd0896
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/fi/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: fi\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "ehdottaa muokkausta"
+
+msgid "Last updated on"
+msgstr "Viimeksi päivitetty"
+
+msgid "Edit this page"
+msgstr "Muokkaa tätä sivua"
+
+msgid "Launch"
+msgstr "Tuoda markkinoille"
+
+msgid "Print to PDF"
+msgstr "Tulosta PDF-tiedostoon"
+
+msgid "open issue"
+msgstr "avoin ongelma"
+
+msgid "Download notebook file"
+msgstr "Lataa muistikirjatiedosto"
+
+msgid "Toggle navigation"
+msgstr "Vaihda navigointia"
+
+msgid "Source repository"
+msgstr "Lähteen arkisto"
+
+msgid "By the"
+msgstr "Mukaan"
+
+msgid "next page"
+msgstr "seuraava sivu"
+
+msgid "repository"
+msgstr "arkisto"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx-kirjan teema"
+
+msgid "Download source file"
+msgstr "Lataa lähdetiedosto"
+
+msgid "Contents"
+msgstr "Sisällys"
+
+msgid "By"
+msgstr "Tekijä"
+
+msgid "Copyright"
+msgstr "Tekijänoikeus"
+
+msgid "Fullscreen mode"
+msgstr "Koko näytön tila"
+
+msgid "Open an issue"
+msgstr "Avaa ongelma"
+
+msgid "previous page"
+msgstr "Edellinen sivu"
+
+msgid "Download this page"
+msgstr "Lataa tämä sivu"
+
+msgid "Theme by the"
+msgstr "Teeman tekijä"
diff --git a/doc/LectureNotes/_build/html/_static/locales/fr/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/fr/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..f663d39f0faa76c5b9bd504c51252eef74cca5de
GIT binary patch
literal 1412
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T<A7>A2+cw{Vw>h7Yg+MtLz81?

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/fr/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/fr/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..b57d2fe74
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/fr/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: fr\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "suggestion de modification"
+
+msgid "Last updated on"
+msgstr "Dernière mise à jour le"
+
+msgid "Edit this page"
+msgstr "Modifier cette page"
+
+msgid "Launch"
+msgstr "lancement"
+
+msgid "Print to PDF"
+msgstr "Imprimer au format PDF"
+
+msgid "open issue"
+msgstr "signaler un problème"
+
+msgid "Download notebook file"
+msgstr "Télécharger le fichier notebook"
+
+msgid "Toggle navigation"
+msgstr "Basculer la navigation"
+
+msgid "Source repository"
+msgstr "Dépôt source"
+
+msgid "By the"
+msgstr "Par le"
+
+msgid "next page"
+msgstr "page suivante"
+
+msgid "repository"
+msgstr "dépôt"
+
+msgid "Sphinx Book Theme"
+msgstr "Thème du livre Sphinx"
+
+msgid "Download source file"
+msgstr "Télécharger le fichier source"
+
+msgid "Contents"
+msgstr "Contenu"
+
+msgid "By"
+msgstr "Par"
+
+msgid "Copyright"
+msgstr "droits d'auteur"
+
+msgid "Fullscreen mode"
+msgstr "Mode plein écran"
+
+msgid "Open an issue"
+msgstr "Ouvrez un problème"
+
+msgid "previous page"
+msgstr "page précédente"
+
+msgid "Download this page"
+msgstr "Téléchargez cette page"
+
+msgid "Theme by the"
+msgstr "Thème par le"
diff --git a/doc/LectureNotes/_build/html/_static/locales/hr/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/hr/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..eca4a1a2842830f06bd5f6235bf01d07bdd313d2
GIT binary patch
literal 1402
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/hr/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/hr/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..4c425e89a
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/hr/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: hr\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "predloži uređivanje"
+
+msgid "Last updated on"
+msgstr "Posljednje ažuriranje:"
+
+msgid "Edit this page"
+msgstr "Uredite ovu stranicu"
+
+msgid "Launch"
+msgstr "Pokrenite"
+
+msgid "Print to PDF"
+msgstr "Ispis u PDF"
+
+msgid "open issue"
+msgstr "otvoreno izdanje"
+
+msgid "Download notebook file"
+msgstr "Preuzmi datoteku bilježnice"
+
+msgid "Toggle navigation"
+msgstr "Uključi / isključi navigaciju"
+
+msgid "Source repository"
+msgstr "Izvorno spremište"
+
+msgid "By the"
+msgstr "Od strane"
+
+msgid "next page"
+msgstr "sljedeća stranica"
+
+msgid "repository"
+msgstr "spremište"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema knjige Sphinx"
+
+msgid "Download source file"
+msgstr "Preuzmi izvornu datoteku"
+
+msgid "Contents"
+msgstr "Sadržaj"
+
+msgid "By"
+msgstr "Po"
+
+msgid "Copyright"
+msgstr "Autorska prava"
+
+msgid "Fullscreen mode"
+msgstr "Način preko cijelog zaslona"
+
+msgid "Open an issue"
+msgstr "Otvorite izdanje"
+
+msgid "previous page"
+msgstr "Prethodna stranica"
+
+msgid "Download this page"
+msgstr "Preuzmite ovu stranicu"
+
+msgid "Theme by the"
+msgstr "Tema autora"
diff --git a/doc/LectureNotes/_build/html/_static/locales/id/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/id/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..d07a06a9d27aaf6d67234c227c22d61d5a23203b
GIT binary patch
literal 1323
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/id/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/id/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..5db2ae147
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/id/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: id\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "menyarankan edit"
+
+msgid "Last updated on"
+msgstr "Terakhir diperbarui saat"
+
+msgid "Edit this page"
+msgstr "Edit halaman ini"
+
+msgid "Launch"
+msgstr "Meluncurkan"
+
+msgid "Print to PDF"
+msgstr "Cetak ke PDF"
+
+msgid "open issue"
+msgstr "masalah terbuka"
+
+msgid "Download notebook file"
+msgstr "Unduh file notebook"
+
+msgid "Toggle navigation"
+msgstr "Alihkan navigasi"
+
+msgid "Source repository"
+msgstr "Repositori sumber"
+
+msgid "By the"
+msgstr "Oleh"
+
+msgid "next page"
+msgstr "halaman selanjutnya"
+
+msgid "repository"
+msgstr "gudang"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema Buku Sphinx"
+
+msgid "Download source file"
+msgstr "Unduh file sumber"
+
+msgid "Contents"
+msgstr "Isi"
+
+msgid "By"
+msgstr "Oleh"
+
+msgid "Copyright"
+msgstr "hak cipta"
+
+msgid "Fullscreen mode"
+msgstr "Mode layar penuh"
+
+msgid "Open an issue"
+msgstr "Buka masalah"
+
+msgid "previous page"
+msgstr "halaman sebelumnya"
+
+msgid "Download this page"
+msgstr "Unduh halaman ini"
+
+msgid "Theme by the"
+msgstr "Tema oleh"
diff --git a/doc/LectureNotes/_build/html/_static/locales/it/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/it/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..53ba476edd2df2a802917e9df402257ceca1a130
GIT binary patch
literal 1403
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/it/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/it/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..7d54fdefa
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/it/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: it\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "suggerisci modifica"
+
+msgid "Last updated on"
+msgstr "Ultimo aggiornamento il"
+
+msgid "Edit this page"
+msgstr "Modifica questa pagina"
+
+msgid "Launch"
+msgstr "Lanciare"
+
+msgid "Print to PDF"
+msgstr "Stampa in PDF"
+
+msgid "open issue"
+msgstr "questione aperta"
+
+msgid "Download notebook file"
+msgstr "Scarica il file del taccuino"
+
+msgid "Toggle navigation"
+msgstr "Attiva / disattiva la navigazione"
+
+msgid "Source repository"
+msgstr "Repository di origine"
+
+msgid "By the"
+msgstr "Dal"
+
+msgid "next page"
+msgstr "pagina successiva"
+
+msgid "repository"
+msgstr "repository"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema del libro della Sfinge"
+
+msgid "Download source file"
+msgstr "Scarica il file sorgente"
+
+msgid "Contents"
+msgstr "Contenuti"
+
+msgid "By"
+msgstr "Di"
+
+msgid "Copyright"
+msgstr "Diritto d'autore"
+
+msgid "Fullscreen mode"
+msgstr "Modalità schermo intero"
+
+msgid "Open an issue"
+msgstr "Apri un problema"
+
+msgid "previous page"
+msgstr "pagina precedente"
+
+msgid "Download this page"
+msgstr "Scarica questa pagina"
+
+msgid "Theme by the"
+msgstr "Tema di"
diff --git a/doc/LectureNotes/_build/html/_static/locales/iw/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/iw/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..a45c6575e469914582f8223ac54793afc2f26575
GIT binary patch
literal 1445
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F;x7>$;pPAU

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/iw/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/iw/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..32b017cf6
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/iw/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: iw\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "מציע לערוך"
+
+msgid "Last updated on"
+msgstr "עודכן לאחרונה ב"
+
+msgid "Edit this page"
+msgstr "ערוך דף זה"
+
+msgid "Launch"
+msgstr "לְהַשִׁיק"
+
+msgid "Print to PDF"
+msgstr "הדפס לקובץ PDF"
+
+msgid "open issue"
+msgstr "בעיה פתוחה"
+
+msgid "Download notebook file"
+msgstr "הורד קובץ מחברת"
+
+msgid "Toggle navigation"
+msgstr "החלף ניווט"
+
+msgid "Source repository"
+msgstr "מאגר המקורות"
+
+msgid "By the"
+msgstr "דרך"
+
+msgid "next page"
+msgstr "עמוד הבא"
+
+msgid "repository"
+msgstr "מאגר"
+
+msgid "Sphinx Book Theme"
+msgstr "נושא ספר ספינקס"
+
+msgid "Download source file"
+msgstr "הורד את קובץ המקור"
+
+msgid "Contents"
+msgstr "תוכן"
+
+msgid "By"
+msgstr "על ידי"
+
+msgid "Copyright"
+msgstr "זכויות יוצרים"
+
+msgid "Fullscreen mode"
+msgstr "מצב מסך מלא"
+
+msgid "Open an issue"
+msgstr "פתח גיליון"
+
+msgid "previous page"
+msgstr "עמוד קודם"
+
+msgid "Download this page"
+msgstr "הורד דף זה"
+
+msgid "Theme by the"
+msgstr "נושא מאת"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ja/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ja/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..1cefd29ce3cc08792667a82dc7ff47e9843107be
GIT binary patch
literal 1471
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Jb0#{<{sfT*^1J{5

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ja/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ja/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..16924e197
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ja/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ja\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "編集を提案する"
+
+msgid "Last updated on"
+msgstr "最終更新日"
+
+msgid "Edit this page"
+msgstr "このページを編集"
+
+msgid "Launch"
+msgstr "起動"
+
+msgid "Print to PDF"
+msgstr "PDFに印刷"
+
+msgid "open issue"
+msgstr "未解決の問題"
+
+msgid "Download notebook file"
+msgstr "ノートブックファイルをダウンロード"
+
+msgid "Toggle navigation"
+msgstr "ナビゲーションを切り替え"
+
+msgid "Source repository"
+msgstr "ソースリポジトリ"
+
+msgid "By the"
+msgstr "によって"
+
+msgid "next page"
+msgstr "次のページ"
+
+msgid "repository"
+msgstr "リポジトリ"
+
+msgid "Sphinx Book Theme"
+msgstr "スフィンクスの本のテーマ"
+
+msgid "Download source file"
+msgstr "ソースファイルをダウンロード"
+
+msgid "Contents"
+msgstr "目次"
+
+msgid "By"
+msgstr "著者"
+
+msgid "Copyright"
+msgstr "Copyright"
+
+msgid "Fullscreen mode"
+msgstr "全画面モード"
+
+msgid "Open an issue"
+msgstr "問題を報告"
+
+msgid "previous page"
+msgstr "前のページ"
+
+msgid "Download this page"
+msgstr "このページをダウンロード"
+
+msgid "Theme by the"
+msgstr "のテーマ"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ko/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ko/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..06c7ec938b4975c721caff60b956e343eef11570
GIT binary patch
literal 1375
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ko/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ko/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..69dd18f77
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ko/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ko\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "편집 제안"
+
+msgid "Last updated on"
+msgstr "마지막 업데이트"
+
+msgid "Edit this page"
+msgstr "이 페이지 편집"
+
+msgid "Launch"
+msgstr "시작하다"
+
+msgid "Print to PDF"
+msgstr "PDF로 인쇄"
+
+msgid "open issue"
+msgstr "열린 문제"
+
+msgid "Download notebook file"
+msgstr "노트북 파일 다운로드"
+
+msgid "Toggle navigation"
+msgstr "탐색 전환"
+
+msgid "Source repository"
+msgstr "소스 저장소"
+
+msgid "By the"
+msgstr "에 의해"
+
+msgid "next page"
+msgstr "다음 페이지"
+
+msgid "repository"
+msgstr "저장소"
+
+msgid "Sphinx Book Theme"
+msgstr "스핑크스 도서 테마"
+
+msgid "Download source file"
+msgstr "소스 파일 다운로드"
+
+msgid "Contents"
+msgstr "내용"
+
+msgid "By"
+msgstr "으로"
+
+msgid "Copyright"
+msgstr "저작권"
+
+msgid "Fullscreen mode"
+msgstr "전체 화면으로보기"
+
+msgid "Open an issue"
+msgstr "이슈 열기"
+
+msgid "previous page"
+msgstr "이전 페이지"
+
+msgid "Download this page"
+msgstr "이 페이지 다운로드"
+
+msgid "Theme by the"
+msgstr "테마별"
diff --git a/doc/LectureNotes/_build/html/_static/locales/lt/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/lt/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..4468ba04bc134a84fea5e3c973461cf02c9c2da3
GIT binary patch
literal 1413
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/lt/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/lt/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..9f037752c
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/lt/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: lt\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "pasiūlyti redaguoti"
+
+msgid "Last updated on"
+msgstr "Paskutinį kartą atnaujinta"
+
+msgid "Edit this page"
+msgstr "Redaguoti šį puslapį"
+
+msgid "Launch"
+msgstr "Paleiskite"
+
+msgid "Print to PDF"
+msgstr "Spausdinti į PDF"
+
+msgid "open issue"
+msgstr "atviras klausimas"
+
+msgid "Download notebook file"
+msgstr "Atsisiųsti nešiojamojo kompiuterio failą"
+
+msgid "Toggle navigation"
+msgstr "Perjungti naršymą"
+
+msgid "Source repository"
+msgstr "Šaltinio saugykla"
+
+msgid "By the"
+msgstr "Prie"
+
+msgid "next page"
+msgstr "Kitas puslapis"
+
+msgid "repository"
+msgstr "saugykla"
+
+msgid "Sphinx Book Theme"
+msgstr "Sfinkso knygos tema"
+
+msgid "Download source file"
+msgstr "Atsisiųsti šaltinio failą"
+
+msgid "Contents"
+msgstr "Turinys"
+
+msgid "By"
+msgstr "Iki"
+
+msgid "Copyright"
+msgstr "Autorių teisės"
+
+msgid "Fullscreen mode"
+msgstr "Pilno ekrano režimas"
+
+msgid "Open an issue"
+msgstr "Atidarykite problemą"
+
+msgid "previous page"
+msgstr "Ankstesnis puslapis"
+
+msgid "Download this page"
+msgstr "Atsisiųskite šį puslapį"
+
+msgid "Theme by the"
+msgstr "Tema"
diff --git a/doc/LectureNotes/_build/html/_static/locales/lv/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/lv/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..74aa4d8985d96a07c4c9be96f006f3b58d884342
GIT binary patch
literal 1404
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A2mk;8

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/lv/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/lv/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..c9633b545
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/lv/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: lv\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "ieteikt rediģēt"
+
+msgid "Last updated on"
+msgstr "Pēdējoreiz atjaunināts"
+
+msgid "Edit this page"
+msgstr "Rediģēt šo lapu"
+
+msgid "Launch"
+msgstr "Uzsākt"
+
+msgid "Print to PDF"
+msgstr "Drukāt PDF formātā"
+
+msgid "open issue"
+msgstr "atklāts jautājums"
+
+msgid "Download notebook file"
+msgstr "Lejupielādēt piezīmju grāmatiņu"
+
+msgid "Toggle navigation"
+msgstr "Pārslēgt navigāciju"
+
+msgid "Source repository"
+msgstr "Avota krātuve"
+
+msgid "By the"
+msgstr "Ar"
+
+msgid "next page"
+msgstr "nākamā lapaspuse"
+
+msgid "repository"
+msgstr "krātuve"
+
+msgid "Sphinx Book Theme"
+msgstr "Sfinksa grāmatas tēma"
+
+msgid "Download source file"
+msgstr "Lejupielādēt avota failu"
+
+msgid "Contents"
+msgstr "Saturs"
+
+msgid "By"
+msgstr "Autors"
+
+msgid "Copyright"
+msgstr "Autortiesības"
+
+msgid "Fullscreen mode"
+msgstr "Pilnekrāna režīms"
+
+msgid "Open an issue"
+msgstr "Atveriet problēmu"
+
+msgid "previous page"
+msgstr "iepriekšējā lapa"
+
+msgid "Download this page"
+msgstr "Lejupielādējiet šo lapu"
+
+msgid "Theme by the"
+msgstr "Autora tēma"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ml/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ml/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..2736e8fcf6f9e923c2403307f0b366086d37b335
GIT binary patch
literal 1883
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ml/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ml/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..9a6a41e8e
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ml/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ml\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "എഡിറ്റുചെയ്യാൻ നിർദ്ദേശിക്കുക"
+
+msgid "Last updated on"
+msgstr "അവസാനം അപ്‌ഡേറ്റുചെയ്‌തത്"
+
+msgid "Edit this page"
+msgstr "ഈ പേജ് എഡിറ്റുചെയ്യുക"
+
+msgid "Launch"
+msgstr "സമാരംഭിക്കുക"
+
+msgid "Print to PDF"
+msgstr "PDF- ലേക്ക് പ്രിന്റുചെയ്യുക"
+
+msgid "open issue"
+msgstr "തുറന്ന പ്രശ്നം"
+
+msgid "Download notebook file"
+msgstr "നോട്ട്ബുക്ക് ഫയൽ ഡൺലോഡ് ചെയ്യുക"
+
+msgid "Toggle navigation"
+msgstr "നാവിഗേഷൻ ടോഗിൾ ചെയ്യുക"
+
+msgid "Source repository"
+msgstr "ഉറവിട ശേഖരം"
+
+msgid "By the"
+msgstr "എഴുതിയത്"
+
+msgid "next page"
+msgstr "അടുത്ത പേജ്"
+
+msgid "Sphinx Book Theme"
+msgstr "സ്ഫിങ്ക്സ് പുസ്തക തീം"
+
+msgid "Download source file"
+msgstr "ഉറവിട ഫയൽ ഡൗൺലോഡുചെയ്യുക"
+
+msgid "By"
+msgstr "എഴുതിയത്"
+
+msgid "Copyright"
+msgstr "പകർപ്പവകാശം"
+
+msgid "Open an issue"
+msgstr "ഒരു പ്രശ്നം തുറക്കുക"
+
+msgid "previous page"
+msgstr "മുൻപത്തെ താൾ"
+
+msgid "Download this page"
+msgstr "ഈ പേജ് ഡൗൺലോഡുചെയ്യുക"
+
+msgid "Theme by the"
+msgstr "പ്രമേയം"
diff --git a/doc/LectureNotes/_build/html/_static/locales/mr/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/mr/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..fe530100d7715cdc19a6f9db33a971665835f3c4
GIT binary patch
literal 1674
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/mr/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/mr/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..ef72d8c6b
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/mr/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: mr\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "संपादन सुचवा"
+
+msgid "Last updated on"
+msgstr "अखेरचे अद्यतनित"
+
+msgid "Edit this page"
+msgstr "हे पृष्ठ संपादित करा"
+
+msgid "Launch"
+msgstr "लाँच करा"
+
+msgid "Print to PDF"
+msgstr "पीडीएफवर मुद्रित करा"
+
+msgid "open issue"
+msgstr "खुला मुद्दा"
+
+msgid "Download notebook file"
+msgstr "नोटबुक फाईल डाउनलोड करा"
+
+msgid "Toggle navigation"
+msgstr "नेव्हिगेशन टॉगल करा"
+
+msgid "Source repository"
+msgstr "स्त्रोत भांडार"
+
+msgid "By the"
+msgstr "द्वारा"
+
+msgid "next page"
+msgstr "पुढील पृष्ठ"
+
+msgid "Sphinx Book Theme"
+msgstr "स्फिंक्स बुक थीम"
+
+msgid "Download source file"
+msgstr "स्त्रोत फाइल डाउनलोड करा"
+
+msgid "By"
+msgstr "द्वारा"
+
+msgid "Copyright"
+msgstr "कॉपीराइट"
+
+msgid "Open an issue"
+msgstr "एक मुद्दा उघडा"
+
+msgid "previous page"
+msgstr "मागील पान"
+
+msgid "Download this page"
+msgstr "हे पृष्ठ डाउनलोड करा"
+
+msgid "Theme by the"
+msgstr "द्वारा थीम"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ms/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ms/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..f02603fa2522a40060bd3f1b5d65052c77530de6
GIT binary patch
literal 1213
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ms/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ms/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..e29cbe2ec
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ms/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ms\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "cadangkan edit"
+
+msgid "Last updated on"
+msgstr "Terakhir dikemas kini pada"
+
+msgid "Edit this page"
+msgstr "Edit halaman ini"
+
+msgid "Launch"
+msgstr "Lancarkan"
+
+msgid "Print to PDF"
+msgstr "Cetak ke PDF"
+
+msgid "open issue"
+msgstr "isu terbuka"
+
+msgid "Download notebook file"
+msgstr "Muat turun fail buku nota"
+
+msgid "Toggle navigation"
+msgstr "Togol navigasi"
+
+msgid "Source repository"
+msgstr "Repositori sumber"
+
+msgid "By the"
+msgstr "Oleh"
+
+msgid "next page"
+msgstr "muka surat seterusnya"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema Buku Sphinx"
+
+msgid "Download source file"
+msgstr "Muat turun fail sumber"
+
+msgid "By"
+msgstr "Oleh"
+
+msgid "Copyright"
+msgstr "hak cipta"
+
+msgid "Open an issue"
+msgstr "Buka masalah"
+
+msgid "previous page"
+msgstr "halaman sebelumnya"
+
+msgid "Download this page"
+msgstr "Muat turun halaman ini"
+
+msgid "Theme by the"
+msgstr "Tema oleh"
diff --git a/doc/LectureNotes/_build/html/_static/locales/nl/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/nl/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..e59e7ecb308a7648cd23aa6342a9ad98a61d0009
GIT binary patch
literal 1356
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/nl/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/nl/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..e4844d7c9
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/nl/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: nl\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "suggereren bewerken"
+
+msgid "Last updated on"
+msgstr "Laatst geupdate op"
+
+msgid "Edit this page"
+msgstr "bewerk deze pagina"
+
+msgid "Launch"
+msgstr "Lancering"
+
+msgid "Print to PDF"
+msgstr "Afdrukken naar pdf"
+
+msgid "open issue"
+msgstr "open probleem"
+
+msgid "Download notebook file"
+msgstr "Download notebookbestand"
+
+msgid "Toggle navigation"
+msgstr "Schakel navigatie"
+
+msgid "Source repository"
+msgstr "Bronopslagplaats"
+
+msgid "By the"
+msgstr "Door de"
+
+msgid "next page"
+msgstr "volgende bladzijde"
+
+msgid "repository"
+msgstr "repository"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx-boekthema"
+
+msgid "Download source file"
+msgstr "Download het bronbestand"
+
+msgid "Contents"
+msgstr "Inhoud"
+
+msgid "By"
+msgstr "Door"
+
+msgid "Copyright"
+msgstr "auteursrechten"
+
+msgid "Fullscreen mode"
+msgstr "Volledig scherm"
+
+msgid "Open an issue"
+msgstr "Open een probleem"
+
+msgid "previous page"
+msgstr "vorige pagina"
+
+msgid "Download this page"
+msgstr "Download deze pagina"
+
+msgid "Theme by the"
+msgstr "Thema door de"
diff --git a/doc/LectureNotes/_build/html/_static/locales/no/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/no/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..6cd15c88de675226c00ca4d0430171075e5559ff
GIT binary patch
literal 1317
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/no/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/no/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..d079dd9b0
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/no/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: no\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "foreslå redigering"
+
+msgid "Last updated on"
+msgstr "Sist oppdatert den"
+
+msgid "Edit this page"
+msgstr "Rediger denne siden"
+
+msgid "Launch"
+msgstr "Start"
+
+msgid "Print to PDF"
+msgstr "Skriv ut til PDF"
+
+msgid "open issue"
+msgstr "åpent nummer"
+
+msgid "Download notebook file"
+msgstr "Last ned notatbokfilen"
+
+msgid "Toggle navigation"
+msgstr "Bytt navigasjon"
+
+msgid "Source repository"
+msgstr "Kildedepot"
+
+msgid "By the"
+msgstr "Ved"
+
+msgid "next page"
+msgstr "neste side"
+
+msgid "repository"
+msgstr "oppbevaringssted"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx boktema"
+
+msgid "Download source file"
+msgstr "Last ned kildefilen"
+
+msgid "Contents"
+msgstr "Innhold"
+
+msgid "By"
+msgstr "Av"
+
+msgid "Copyright"
+msgstr "opphavsrett"
+
+msgid "Fullscreen mode"
+msgstr "Fullskjerm-modus"
+
+msgid "Open an issue"
+msgstr "Åpne et problem"
+
+msgid "previous page"
+msgstr "forrige side"
+
+msgid "Download this page"
+msgstr "Last ned denne siden"
+
+msgid "Theme by the"
+msgstr "Tema av"
diff --git a/doc/LectureNotes/_build/html/_static/locales/pl/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/pl/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..9ebb584f77091f5666db4194ecd4f707396cbbca
GIT binary patch
literal 1371
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/pl/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/pl/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..fcac51d32
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/pl/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: pl\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "zaproponuj edycję"
+
+msgid "Last updated on"
+msgstr "Ostatnia aktualizacja"
+
+msgid "Edit this page"
+msgstr "Edytuj tę strone"
+
+msgid "Launch"
+msgstr "Uruchomić"
+
+msgid "Print to PDF"
+msgstr "Drukuj do PDF"
+
+msgid "open issue"
+msgstr "otwarty problem"
+
+msgid "Download notebook file"
+msgstr "Pobierz plik notatnika"
+
+msgid "Toggle navigation"
+msgstr "Przełącz nawigację"
+
+msgid "Source repository"
+msgstr "Repozytorium źródłowe"
+
+msgid "By the"
+msgstr "Przez"
+
+msgid "next page"
+msgstr "Następna strona"
+
+msgid "repository"
+msgstr "magazyn"
+
+msgid "Sphinx Book Theme"
+msgstr "Motyw książki Sphinx"
+
+msgid "Download source file"
+msgstr "Pobierz plik źródłowy"
+
+msgid "Contents"
+msgstr "Zawartość"
+
+msgid "By"
+msgstr "Przez"
+
+msgid "Copyright"
+msgstr "prawa autorskie"
+
+msgid "Fullscreen mode"
+msgstr "Pełny ekran"
+
+msgid "Open an issue"
+msgstr "Otwórz problem"
+
+msgid "previous page"
+msgstr "Poprzednia strona"
+
+msgid "Download this page"
+msgstr "Pobierz tę stronę"
+
+msgid "Theme by the"
+msgstr "Motyw autorstwa"
diff --git a/doc/LectureNotes/_build/html/_static/locales/pt/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/pt/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..d0ddb8728e1d5ef72dddc1537f66aa32251a83c8
GIT binary patch
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/pt/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/pt/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..1761db08a
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/pt/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: pt\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "sugerir edição"
+
+msgid "Last updated on"
+msgstr "Última atualização em"
+
+msgid "Edit this page"
+msgstr "Edite essa página"
+
+msgid "Launch"
+msgstr "Lançamento"
+
+msgid "Print to PDF"
+msgstr "Imprimir em PDF"
+
+msgid "open issue"
+msgstr "questão aberta"
+
+msgid "Download notebook file"
+msgstr "Baixar arquivo de notebook"
+
+msgid "Toggle navigation"
+msgstr "Alternar de navegação"
+
+msgid "Source repository"
+msgstr "Repositório fonte"
+
+msgid "By the"
+msgstr "Pelo"
+
+msgid "next page"
+msgstr "próxima página"
+
+msgid "repository"
+msgstr "repositório"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema do livro Sphinx"
+
+msgid "Download source file"
+msgstr "Baixar arquivo fonte"
+
+msgid "Contents"
+msgstr "Conteúdo"
+
+msgid "By"
+msgstr "De"
+
+msgid "Copyright"
+msgstr "direito autoral"
+
+msgid "Fullscreen mode"
+msgstr "Modo tela cheia"
+
+msgid "Open an issue"
+msgstr "Abra um problema"
+
+msgid "previous page"
+msgstr "página anterior"
+
+msgid "Download this page"
+msgstr "Baixe esta página"
+
+msgid "Theme by the"
+msgstr "Tema por"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ro/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ro/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..3c36ab1df7c589ad82614599b8c91f072a25d4a6
GIT binary patch
literal 1390
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ro/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ro/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..db865c8f6
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ro/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ro\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "sugerează editare"
+
+msgid "Last updated on"
+msgstr "Ultima actualizare la"
+
+msgid "Edit this page"
+msgstr "Editați această pagină"
+
+msgid "Launch"
+msgstr "Lansa"
+
+msgid "Print to PDF"
+msgstr "Imprimați în PDF"
+
+msgid "open issue"
+msgstr "problema deschisă"
+
+msgid "Download notebook file"
+msgstr "Descărcați fișierul notebook"
+
+msgid "Toggle navigation"
+msgstr "Comutare navigare"
+
+msgid "Source repository"
+msgstr "Depozit sursă"
+
+msgid "By the"
+msgstr "Langa"
+
+msgid "next page"
+msgstr "pagina următoare"
+
+msgid "repository"
+msgstr "repertoriu"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema Sphinx Book"
+
+msgid "Download source file"
+msgstr "Descărcați fișierul sursă"
+
+msgid "Contents"
+msgstr "Cuprins"
+
+msgid "By"
+msgstr "De"
+
+msgid "Copyright"
+msgstr "Drepturi de autor"
+
+msgid "Fullscreen mode"
+msgstr "Modul ecran întreg"
+
+msgid "Open an issue"
+msgstr "Deschideți o problemă"
+
+msgid "previous page"
+msgstr "pagina anterioară"
+
+msgid "Download this page"
+msgstr "Descarcă această pagină"
+
+msgid "Theme by the"
+msgstr "Tema de"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ru/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ru/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..6b8ca41f36ebf869818399a9584cdb15619bea78
GIT binary patch
literal 1722
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ru/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ru/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..84ab6eb53
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ru/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ru\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "предложить редактировать"
+
+msgid "Last updated on"
+msgstr "Последнее обновление"
+
+msgid "Edit this page"
+msgstr "Редактировать эту страницу"
+
+msgid "Launch"
+msgstr "Запуск"
+
+msgid "Print to PDF"
+msgstr "Распечатать в PDF"
+
+msgid "open issue"
+msgstr "открытый вопрос"
+
+msgid "Download notebook file"
+msgstr "Скачать файл записной книжки"
+
+msgid "Toggle navigation"
+msgstr "Переключить навигацию"
+
+msgid "Source repository"
+msgstr "Исходный репозиторий"
+
+msgid "By the"
+msgstr "Посредством"
+
+msgid "next page"
+msgstr "Следующая страница"
+
+msgid "repository"
+msgstr "хранилище"
+
+msgid "Sphinx Book Theme"
+msgstr "Тема книги Сфинкс"
+
+msgid "Download source file"
+msgstr "Скачать исходный файл"
+
+msgid "Contents"
+msgstr "Содержание"
+
+msgid "By"
+msgstr "По"
+
+msgid "Copyright"
+msgstr "авторское право"
+
+msgid "Fullscreen mode"
+msgstr "Полноэкранный режим"
+
+msgid "Open an issue"
+msgstr "Открыть вопрос"
+
+msgid "previous page"
+msgstr "Предыдущая страница"
+
+msgid "Download this page"
+msgstr "Загрузите эту страницу"
+
+msgid "Theme by the"
+msgstr "Тема от"
diff --git a/doc/LectureNotes/_build/html/_static/locales/sk/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/sk/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..59bd0ddfa341477cf5ccfdc88f4c3e6127046f7a
GIT binary patch
literal 1393
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Di}h+h

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/sk/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/sk/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..e44878b50
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/sk/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: sk\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "navrhnúť úpravu"
+
+msgid "Last updated on"
+msgstr "Posledná aktualizácia dňa"
+
+msgid "Edit this page"
+msgstr "Upraviť túto stránku"
+
+msgid "Launch"
+msgstr "Spustiť"
+
+msgid "Print to PDF"
+msgstr "Tlač do PDF"
+
+msgid "open issue"
+msgstr "otvorené vydanie"
+
+msgid "Download notebook file"
+msgstr "Stiahnite si zošit"
+
+msgid "Toggle navigation"
+msgstr "Prepnúť navigáciu"
+
+msgid "Source repository"
+msgstr "Zdrojové úložisko"
+
+msgid "By the"
+msgstr "Podľa"
+
+msgid "next page"
+msgstr "ďalšia strana"
+
+msgid "repository"
+msgstr "Úložisko"
+
+msgid "Sphinx Book Theme"
+msgstr "Téma knihy Sfinga"
+
+msgid "Download source file"
+msgstr "Stiahnite si zdrojový súbor"
+
+msgid "Contents"
+msgstr "Obsah"
+
+msgid "By"
+msgstr "Autor:"
+
+msgid "Copyright"
+msgstr "Autorské práva"
+
+msgid "Fullscreen mode"
+msgstr "Režim celej obrazovky"
+
+msgid "Open an issue"
+msgstr "Otvorte problém"
+
+msgid "previous page"
+msgstr "predchádzajúca strana"
+
+msgid "Download this page"
+msgstr "Stiahnite si túto stránku"
+
+msgid "Theme by the"
+msgstr "Téma od"
diff --git a/doc/LectureNotes/_build/html/_static/locales/sl/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/sl/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..87bf26de683cb18c73bd23c2b4c57ef6a02545ec
GIT binary patch
literal 1374
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/sl/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/sl/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..228939bcd
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/sl/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: sl\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "predlagajte urejanje"
+
+msgid "Last updated on"
+msgstr "Nazadnje posodobljeno dne"
+
+msgid "Edit this page"
+msgstr "Uredite to stran"
+
+msgid "Launch"
+msgstr "Kosilo"
+
+msgid "Print to PDF"
+msgstr "Natisni v PDF"
+
+msgid "open issue"
+msgstr "odprto vprašanje"
+
+msgid "Download notebook file"
+msgstr "Prenesite datoteko zvezka"
+
+msgid "Toggle navigation"
+msgstr "Preklopi navigacijo"
+
+msgid "Source repository"
+msgstr "Izvorno skladišče"
+
+msgid "By the"
+msgstr "Avtor"
+
+msgid "next page"
+msgstr "Naslednja stran"
+
+msgid "repository"
+msgstr "odlagališče"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema knjige Sphinx"
+
+msgid "Download source file"
+msgstr "Prenesite izvorno datoteko"
+
+msgid "Contents"
+msgstr "Vsebina"
+
+msgid "By"
+msgstr "Avtor"
+
+msgid "Copyright"
+msgstr "avtorske pravice"
+
+msgid "Fullscreen mode"
+msgstr "Celozaslonski način"
+
+msgid "Open an issue"
+msgstr "Odprite številko"
+
+msgid "previous page"
+msgstr "Prejšnja stran"
+
+msgid "Download this page"
+msgstr "Prenesite to stran"
+
+msgid "Theme by the"
+msgstr "Tema avtorja"
diff --git a/doc/LectureNotes/_build/html/_static/locales/sr/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/sr/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..ec740f4852f3973fa72ed0c7f7cf59273b8dba41
GIT binary patch
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/sr/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/sr/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..1a712a18d
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/sr/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: sr\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "предложи уређивање"
+
+msgid "Last updated on"
+msgstr "Последње ажурирање"
+
+msgid "Edit this page"
+msgstr "Уредите ову страницу"
+
+msgid "Launch"
+msgstr "Лансирање"
+
+msgid "Print to PDF"
+msgstr "Испис у ПДФ"
+
+msgid "open issue"
+msgstr "отворено издање"
+
+msgid "Download notebook file"
+msgstr "Преузмите датотеку бележнице"
+
+msgid "Toggle navigation"
+msgstr "Укључи / искључи навигацију"
+
+msgid "Source repository"
+msgstr "Изворно спремиште"
+
+msgid "By the"
+msgstr "Од"
+
+msgid "next page"
+msgstr "Следећа страна"
+
+msgid "repository"
+msgstr "спремиште"
+
+msgid "Sphinx Book Theme"
+msgstr "Тема књиге Спхинк"
+
+msgid "Download source file"
+msgstr "Преузми изворну датотеку"
+
+msgid "Contents"
+msgstr "Садржај"
+
+msgid "By"
+msgstr "Од стране"
+
+msgid "Copyright"
+msgstr "Ауторско право"
+
+msgid "Fullscreen mode"
+msgstr "Режим целог екрана"
+
+msgid "Open an issue"
+msgstr "Отворите издање"
+
+msgid "previous page"
+msgstr "Претходна страница"
+
+msgid "Download this page"
+msgstr "Преузмите ову страницу"
+
+msgid "Theme by the"
+msgstr "Тхеме би"
diff --git a/doc/LectureNotes/_build/html/_static/locales/sv/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/sv/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..be951bec201ccd86d534499749af1df8938a14e3
GIT binary patch
literal 1349
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/sv/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/sv/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..7d2b56d94
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/sv/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: sv\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "föreslå redigering"
+
+msgid "Last updated on"
+msgstr "Senast uppdaterad den"
+
+msgid "Edit this page"
+msgstr "Redigera den här sidan"
+
+msgid "Launch"
+msgstr "Lansera"
+
+msgid "Print to PDF"
+msgstr "Skriv ut till PDF"
+
+msgid "open issue"
+msgstr "öppet problem"
+
+msgid "Download notebook file"
+msgstr "Ladda ner anteckningsbokfilen"
+
+msgid "Toggle navigation"
+msgstr "Växla navigering"
+
+msgid "Source repository"
+msgstr "Källförvar"
+
+msgid "By the"
+msgstr "Vid"
+
+msgid "next page"
+msgstr "nästa sida"
+
+msgid "repository"
+msgstr "förvar"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx boktema"
+
+msgid "Download source file"
+msgstr "Ladda ner källfil"
+
+msgid "Contents"
+msgstr "Innehåll"
+
+msgid "By"
+msgstr "Förbi"
+
+msgid "Copyright"
+msgstr "upphovsrätt"
+
+msgid "Fullscreen mode"
+msgstr "Fullskärmsläge"
+
+msgid "Open an issue"
+msgstr "Öppna ett problem"
+
+msgid "previous page"
+msgstr "föregående sida"
+
+msgid "Download this page"
+msgstr "Ladda ner den här sidan"
+
+msgid "Theme by the"
+msgstr "Tema av"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ta/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ta/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..29f52e1f6f1ec96aceb0f883d8ccc82c23eb35c2
GIT binary patch
literal 1928
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ta/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ta/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..c75ffe192
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ta/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ta\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "திருத்த பரிந்துரைக்கவும்"
+
+msgid "Last updated on"
+msgstr "கடைசியாக புதுப்பிக்கப்பட்டது"
+
+msgid "Edit this page"
+msgstr "இந்தப் பக்கத்தைத் திருத்தவும்"
+
+msgid "Launch"
+msgstr "தொடங்க"
+
+msgid "Print to PDF"
+msgstr "PDF இல் அச்சிடுக"
+
+msgid "open issue"
+msgstr "திறந்த பிரச்சினை"
+
+msgid "Download notebook file"
+msgstr "நோட்புக் கோப்பைப் பதிவிறக்கவும்"
+
+msgid "Toggle navigation"
+msgstr "வழிசெலுத்தலை நிலைமாற்று"
+
+msgid "Source repository"
+msgstr "மூல களஞ்சியம்"
+
+msgid "By the"
+msgstr "மூலம்"
+
+msgid "next page"
+msgstr "அடுத்த பக்கம்"
+
+msgid "Sphinx Book Theme"
+msgstr "ஸ்பிங்க்ஸ் புத்தக தீம்"
+
+msgid "Download source file"
+msgstr "மூல கோப்பைப் பதிவிறக்குக"
+
+msgid "By"
+msgstr "வழங்கியவர்"
+
+msgid "Copyright"
+msgstr "பதிப்புரிமை"
+
+msgid "Open an issue"
+msgstr "சிக்கலைத் திறக்கவும்"
+
+msgid "previous page"
+msgstr "முந்தைய பக்கம்"
+
+msgid "Download this page"
+msgstr "இந்தப் பக்கத்தைப் பதிவிறக்கவும்"
+
+msgid "Theme by the"
+msgstr "வழங்கிய தீம்"
diff --git a/doc/LectureNotes/_build/html/_static/locales/te/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/te/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..0a5f4b46adfda1551ae6791c3c3782525b61be04
GIT binary patch
literal 1806
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/te/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/te/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..2595c0359
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/te/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: te\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "సవరించమని సూచించండి"
+
+msgid "Last updated on"
+msgstr "చివరిగా నవీకరించబడింది"
+
+msgid "Edit this page"
+msgstr "ఈ పేజీని సవరించండి"
+
+msgid "Launch"
+msgstr "ప్రారంభించండి"
+
+msgid "Print to PDF"
+msgstr "PDF కి ముద్రించండి"
+
+msgid "open issue"
+msgstr "ఓపెన్ ఇష్యూ"
+
+msgid "Download notebook file"
+msgstr "నోట్బుక్ ఫైల్ను డౌన్లోడ్ చేయండి"
+
+msgid "Toggle navigation"
+msgstr "నావిగేషన్‌ను టోగుల్ చేయండి"
+
+msgid "Source repository"
+msgstr "మూల రిపోజిటరీ"
+
+msgid "By the"
+msgstr "ద్వారా"
+
+msgid "next page"
+msgstr "తరువాతి పేజీ"
+
+msgid "Sphinx Book Theme"
+msgstr "సింహిక పుస్తక థీమ్"
+
+msgid "Download source file"
+msgstr "మూల ఫైల్‌ను డౌన్‌లోడ్ చేయండి"
+
+msgid "By"
+msgstr "ద్వారా"
+
+msgid "Copyright"
+msgstr "కాపీరైట్"
+
+msgid "Open an issue"
+msgstr "సమస్యను తెరవండి"
+
+msgid "previous page"
+msgstr "ముందు పేజి"
+
+msgid "Download this page"
+msgstr "ఈ పేజీని డౌన్‌లోడ్ చేయండి"
+
+msgid "Theme by the"
+msgstr "ద్వారా థీమ్"
diff --git a/doc/LectureNotes/_build/html/_static/locales/tg/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/tg/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..b21c6c6340194fdf35f7e5660deb42479c8dbff9
GIT binary patch
literal 1628
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/tg/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/tg/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..73cd30ea9
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/tg/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: tg\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "пешниҳод вироиш"
+
+msgid "Last updated on"
+msgstr "Last навсозӣ дар"
+
+msgid "Edit this page"
+msgstr "Ин саҳифаро таҳрир кунед"
+
+msgid "Launch"
+msgstr "Оғоз"
+
+msgid "Print to PDF"
+msgstr "Чоп ба PDF"
+
+msgid "open issue"
+msgstr "барориши кушод"
+
+msgid "Download notebook file"
+msgstr "Файли дафтарро зеркашӣ кунед"
+
+msgid "Toggle navigation"
+msgstr "Гузаришро иваз кунед"
+
+msgid "Source repository"
+msgstr "Анбори манбаъ"
+
+msgid "By the"
+msgstr "Бо"
+
+msgid "next page"
+msgstr "саҳифаи оянда"
+
+msgid "repository"
+msgstr "анбор"
+
+msgid "Sphinx Book Theme"
+msgstr "Сфинкс Мавзӯи китоб"
+
+msgid "Download source file"
+msgstr "Файли манбаъро зеркашӣ кунед"
+
+msgid "Contents"
+msgstr "Мундариҷа"
+
+msgid "By"
+msgstr "Бо"
+
+msgid "Copyright"
+msgstr "Ҳуқуқи муаллиф"
+
+msgid "Fullscreen mode"
+msgstr "Ҳолати экрани пурра"
+
+msgid "Open an issue"
+msgstr "Масъаларо кушоед"
+
+msgid "previous page"
+msgstr "саҳифаи қаблӣ"
+
+msgid "Download this page"
+msgstr "Ин саҳифаро зеркашӣ кунед"
+
+msgid "Theme by the"
+msgstr "Мавзӯъи аз"
diff --git a/doc/LectureNotes/_build/html/_static/locales/th/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/th/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..abede98aa11b163e580a26b545980ace31e61ccf
GIT binary patch
literal 1766
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/th/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/th/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..0392b4ad3
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/th/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: th\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "แนะนำแก้ไข"
+
+msgid "Last updated on"
+msgstr "ปรับปรุงล่าสุดเมื่อ"
+
+msgid "Edit this page"
+msgstr "แก้ไขหน้านี้"
+
+msgid "Launch"
+msgstr "เปิด"
+
+msgid "Print to PDF"
+msgstr "พิมพ์เป็น PDF"
+
+msgid "open issue"
+msgstr "เปิดปัญหา"
+
+msgid "Download notebook file"
+msgstr "ดาวน์โหลดไฟล์สมุดบันทึก"
+
+msgid "Toggle navigation"
+msgstr "ไม่ต้องสลับช่องทาง"
+
+msgid "Source repository"
+msgstr "ที่เก็บซอร์ส"
+
+msgid "By the"
+msgstr "โดย"
+
+msgid "next page"
+msgstr "หน้าต่อไป"
+
+msgid "repository"
+msgstr "ที่เก็บ"
+
+msgid "Sphinx Book Theme"
+msgstr "ธีมหนังสือสฟิงซ์"
+
+msgid "Download source file"
+msgstr "ดาวน์โหลดไฟล์ต้นฉบับ"
+
+msgid "Contents"
+msgstr "สารบัญ"
+
+msgid "By"
+msgstr "โดย"
+
+msgid "Copyright"
+msgstr "ลิขสิทธิ์"
+
+msgid "Fullscreen mode"
+msgstr "โหมดเต็มหน้าจอ"
+
+msgid "Open an issue"
+msgstr "เปิดปัญหา"
+
+msgid "previous page"
+msgstr "หน้าที่แล้ว"
+
+msgid "Download this page"
+msgstr "ดาวน์โหลดหน้านี้"
+
+msgid "Theme by the"
+msgstr "ธีมโดย"
diff --git a/doc/LectureNotes/_build/html/_static/locales/tl/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/tl/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..8df1b73310e0c606251d1abff7e6033d1f6b273f
GIT binary patch
literal 1273
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/tl/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/tl/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..c8375b543
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/tl/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: tl\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "iminumungkahi i-edit"
+
+msgid "Last updated on"
+msgstr "Huling na-update noong"
+
+msgid "Edit this page"
+msgstr "I-edit ang pahinang ito"
+
+msgid "Launch"
+msgstr "Ilunsad"
+
+msgid "Print to PDF"
+msgstr "I-print sa PDF"
+
+msgid "open issue"
+msgstr "bukas na isyu"
+
+msgid "Download notebook file"
+msgstr "Mag-download ng file ng notebook"
+
+msgid "Toggle navigation"
+msgstr "I-toggle ang pag-navigate"
+
+msgid "Source repository"
+msgstr "Pinagmulan ng imbakan"
+
+msgid "By the"
+msgstr "Sa pamamagitan ng"
+
+msgid "next page"
+msgstr "Susunod na pahina"
+
+msgid "Sphinx Book Theme"
+msgstr "Tema ng Sphinx Book"
+
+msgid "Download source file"
+msgstr "Mag-download ng file ng pinagmulan"
+
+msgid "By"
+msgstr "Ni"
+
+msgid "Copyright"
+msgstr "Copyright"
+
+msgid "Open an issue"
+msgstr "Magbukas ng isyu"
+
+msgid "previous page"
+msgstr "Nakaraang pahina"
+
+msgid "Download this page"
+msgstr "I-download ang pahinang ito"
+
+msgid "Theme by the"
+msgstr "Tema ng"
diff --git a/doc/LectureNotes/_build/html/_static/locales/tr/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/tr/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..029ae18afb5360a8c238a052e8d3971761759d3d
GIT binary patch
literal 1373
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zo6h$Ap{&BCl*;`;;xXGI&@B^nMMIv5kwyPFiiuV?c-PnoHwMdQd*;PnG+qT~k=xL=
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/tr/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/tr/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..47d7bdf7f
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/tr/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: tr\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "düzenleme öner"
+
+msgid "Last updated on"
+msgstr "Son güncelleme tarihi"
+
+msgid "Edit this page"
+msgstr "Bu sayfayı düzenle"
+
+msgid "Launch"
+msgstr "Başlatmak"
+
+msgid "Print to PDF"
+msgstr "PDF olarak yazdır"
+
+msgid "open issue"
+msgstr "Açık konu"
+
+msgid "Download notebook file"
+msgstr "Defter dosyasını indirin"
+
+msgid "Toggle navigation"
+msgstr "Gezinmeyi değiştir"
+
+msgid "Source repository"
+msgstr "Kaynak kod deposu"
+
+msgid "By the"
+msgstr "Tarafından"
+
+msgid "next page"
+msgstr "sonraki Sayfa"
+
+msgid "repository"
+msgstr "depo"
+
+msgid "Sphinx Book Theme"
+msgstr "Sfenks Kitap Teması"
+
+msgid "Download source file"
+msgstr "Kaynak dosyayı indirin"
+
+msgid "Contents"
+msgstr "İçindekiler"
+
+msgid "By"
+msgstr "Tarafından"
+
+msgid "Copyright"
+msgstr "Telif hakkı"
+
+msgid "Fullscreen mode"
+msgstr "Tam ekran modu"
+
+msgid "Open an issue"
+msgstr "Bir sorunu açın"
+
+msgid "previous page"
+msgstr "önceki sayfa"
+
+msgid "Download this page"
+msgstr "Bu sayfayı indirin"
+
+msgid "Theme by the"
+msgstr "Tarafından tema"
diff --git a/doc/LectureNotes/_build/html/_static/locales/uk/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/uk/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..16ab78909cfbaba7fa199f47fdfc2934426ac699
GIT binary patch
literal 1681
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LPmM*`H%jps*u#;t

literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/uk/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/uk/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..e85f6f16a
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/uk/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: uk\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "запропонувати редагувати"
+
+msgid "Last updated on"
+msgstr "Останнє оновлення:"
+
+msgid "Edit this page"
+msgstr "Редагувати цю сторінку"
+
+msgid "Launch"
+msgstr "Запуск"
+
+msgid "Print to PDF"
+msgstr "Друк у форматі PDF"
+
+msgid "open issue"
+msgstr "відкритий випуск"
+
+msgid "Download notebook file"
+msgstr "Завантажте файл блокнота"
+
+msgid "Toggle navigation"
+msgstr "Переключити навігацію"
+
+msgid "Source repository"
+msgstr "Джерело сховища"
+
+msgid "By the"
+msgstr "По"
+
+msgid "next page"
+msgstr "Наступна сторінка"
+
+msgid "repository"
+msgstr "сховище"
+
+msgid "Sphinx Book Theme"
+msgstr "Тема книги \"Сфінкс\""
+
+msgid "Download source file"
+msgstr "Завантажити вихідний файл"
+
+msgid "Contents"
+msgstr "Зміст"
+
+msgid "By"
+msgstr "Автор"
+
+msgid "Copyright"
+msgstr "Авторське право"
+
+msgid "Fullscreen mode"
+msgstr "Повноекранний режим"
+
+msgid "Open an issue"
+msgstr "Відкрийте випуск"
+
+msgid "previous page"
+msgstr "Попередня сторінка"
+
+msgid "Download this page"
+msgstr "Завантажте цю сторінку"
+
+msgid "Theme by the"
+msgstr "Тема від"
diff --git a/doc/LectureNotes/_build/html/_static/locales/ur/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/ur/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..de8c84b935ed5c3db23e304015d45b638a3d2db3
GIT binary patch
literal 1462
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/ur/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/ur/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..0f90726c1
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/ur/LC_MESSAGES/booktheme.po
@@ -0,0 +1,66 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: ur\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "ترمیم کی تجویز کریں"
+
+msgid "Last updated on"
+msgstr "آخری بار تازہ کاری ہوئی"
+
+msgid "Edit this page"
+msgstr "اس صفحے میں ترمیم کریں"
+
+msgid "Launch"
+msgstr "لانچ کریں"
+
+msgid "Print to PDF"
+msgstr "پی ڈی ایف پرنٹ کریں"
+
+msgid "open issue"
+msgstr "کھلا مسئلہ"
+
+msgid "Download notebook file"
+msgstr "نوٹ بک فائل ڈاؤن لوڈ کریں"
+
+msgid "Toggle navigation"
+msgstr "نیویگیشن ٹوگل کریں"
+
+msgid "Source repository"
+msgstr "ماخذ ذخیرہ"
+
+msgid "By the"
+msgstr "کی طرف"
+
+msgid "next page"
+msgstr "اگلا صفحہ"
+
+msgid "Sphinx Book Theme"
+msgstr "سپنکس بک تھیم"
+
+msgid "Download source file"
+msgstr "سورس فائل ڈاؤن لوڈ کریں"
+
+msgid "By"
+msgstr "بذریعہ"
+
+msgid "Copyright"
+msgstr "کاپی رائٹ"
+
+msgid "Open an issue"
+msgstr "ایک مسئلہ کھولیں"
+
+msgid "previous page"
+msgstr "سابقہ ​​صفحہ"
+
+msgid "Download this page"
+msgstr "اس صفحے کو ڈاؤن لوڈ کریں"
+
+msgid "Theme by the"
+msgstr "کے ذریعہ تھیم"
diff --git a/doc/LectureNotes/_build/html/_static/locales/vi/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/vi/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..2bb32555c3ea0dab08ed37b71cb863fbe75698c6
GIT binary patch
literal 1431
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/vi/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/vi/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..2cb5cf3b8
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/vi/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: vi\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "đề nghị chỉnh sửa"
+
+msgid "Last updated on"
+msgstr "Cập nhật lần cuối vào"
+
+msgid "Edit this page"
+msgstr "chỉnh sửa trang này"
+
+msgid "Launch"
+msgstr "Phóng"
+
+msgid "Print to PDF"
+msgstr "In sang PDF"
+
+msgid "open issue"
+msgstr "vấn đề mở"
+
+msgid "Download notebook file"
+msgstr "Tải xuống tệp sổ tay"
+
+msgid "Toggle navigation"
+msgstr "Chuyển đổi điều hướng thành"
+
+msgid "Source repository"
+msgstr "Kho nguồn"
+
+msgid "By the"
+msgstr "Bằng"
+
+msgid "next page"
+msgstr "Trang tiếp theo"
+
+msgid "repository"
+msgstr "kho"
+
+msgid "Sphinx Book Theme"
+msgstr "Chủ đề sách nhân sư"
+
+msgid "Download source file"
+msgstr "Tải xuống tệp nguồn"
+
+msgid "Contents"
+msgstr "Nội dung"
+
+msgid "By"
+msgstr "Bởi"
+
+msgid "Copyright"
+msgstr "Bản quyền"
+
+msgid "Fullscreen mode"
+msgstr "Chế độ toàn màn hình"
+
+msgid "Open an issue"
+msgstr "Mở một vấn đề"
+
+msgid "previous page"
+msgstr "trang trước"
+
+msgid "Download this page"
+msgstr "Tải xuống trang này"
+
+msgid "Theme by the"
+msgstr "Chủ đề của"
diff --git a/doc/LectureNotes/_build/html/_static/locales/zh_CN/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/zh_CN/LC_MESSAGES/booktheme.mo
new file mode 100644
index 0000000000000000000000000000000000000000..0e3235d090c2a05c0e278d38520f0437847dc79f
GIT binary patch
literal 1310
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zVZLM|@+Cqff{+L(H9>+X*h#n|&YXJarQWrDsNf1G{?EIRgwekJ?VFu>|Np%Cx20*2
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literal 0
HcmV?d00001

diff --git a/doc/LectureNotes/_build/html/_static/locales/zh_CN/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/zh_CN/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..f91f3ba0a
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/zh_CN/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: zh_CN\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "提出修改建议"
+
+msgid "Last updated on"
+msgstr "上次更新时间："
+
+msgid "Edit this page"
+msgstr "编辑此页面"
+
+msgid "Launch"
+msgstr "启动"
+
+msgid "Print to PDF"
+msgstr "列印成 PDF"
+
+msgid "open issue"
+msgstr "创建议题"
+
+msgid "Download notebook file"
+msgstr "下载笔记本文件"
+
+msgid "Toggle navigation"
+msgstr "显示或隐藏导航栏"
+
+msgid "Source repository"
+msgstr "源码库"
+
+msgid "By the"
+msgstr "作者："
+
+msgid "next page"
+msgstr "下一页"
+
+msgid "repository"
+msgstr "仓库"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx Book 主题"
+
+msgid "Download source file"
+msgstr "下载源文件"
+
+msgid "Contents"
+msgstr "目录"
+
+msgid "By"
+msgstr "作者："
+
+msgid "Copyright"
+msgstr "版权"
+
+msgid "Fullscreen mode"
+msgstr "全屏模式"
+
+msgid "Open an issue"
+msgstr "创建议题"
+
+msgid "previous page"
+msgstr "上一页"
+
+msgid "Download this page"
+msgstr "下载此页面"
+
+msgid "Theme by the"
+msgstr "主题作者："
diff --git a/doc/LectureNotes/_build/html/_static/locales/zh_TW/LC_MESSAGES/booktheme.mo b/doc/LectureNotes/_build/html/_static/locales/zh_TW/LC_MESSAGES/booktheme.mo
new file mode 100644
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diff --git a/doc/LectureNotes/_build/html/_static/locales/zh_TW/LC_MESSAGES/booktheme.po b/doc/LectureNotes/_build/html/_static/locales/zh_TW/LC_MESSAGES/booktheme.po
new file mode 100644
index 000000000..7833d9043
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/locales/zh_TW/LC_MESSAGES/booktheme.po
@@ -0,0 +1,75 @@
+
+msgid ""
+msgstr ""
+"Project-Id-Version: Sphinx-Book-Theme\n"
+"MIME-Version: 1.0\n"
+"Content-Type: text/plain; charset=UTF-8\n"
+"Content-Transfer-Encoding: 8bit\n"
+"Language: zh_TW\n"
+"Plural-Forms: nplurals=2; plural=(n != 1);\n"
+
+msgid "suggest edit"
+msgstr "提出修改建議"
+
+msgid "Last updated on"
+msgstr "最後更新時間："
+
+msgid "Edit this page"
+msgstr "編輯此頁面"
+
+msgid "Launch"
+msgstr "啟動"
+
+msgid "Print to PDF"
+msgstr "列印成 PDF"
+
+msgid "open issue"
+msgstr "公開的問題"
+
+msgid "Download notebook file"
+msgstr "下載 Notebook 檔案"
+
+msgid "Toggle navigation"
+msgstr "顯示或隱藏導覽列"
+
+msgid "Source repository"
+msgstr "來源儲存庫"
+
+msgid "By the"
+msgstr "作者："
+
+msgid "next page"
+msgstr "下一頁"
+
+msgid "repository"
+msgstr "儲存庫"
+
+msgid "Sphinx Book Theme"
+msgstr "Sphinx Book 佈景主題"
+
+msgid "Download source file"
+msgstr "下載原始檔"
+
+msgid "Contents"
+msgstr "目錄"
+
+msgid "By"
+msgstr "作者："
+
+msgid "Copyright"
+msgstr "Copyright"
+
+msgid "Fullscreen mode"
+msgstr "全螢幕模式"
+
+msgid "Open an issue"
+msgstr "開啟議題"
+
+msgid "previous page"
+msgstr "上一頁"
+
+msgid "Download this page"
+msgstr "下載此頁面"
+
+msgid "Theme by the"
+msgstr "佈景主題作者："
diff --git a/doc/LectureNotes/_build/html/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css b/doc/LectureNotes/_build/html/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css
new file mode 100644
index 000000000..335663106
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/mystnb.4510f1fc1dee50b3e5859aac5469c37c29e427902b24a333a5f9fcb2f0b3ac41.css
@@ -0,0 +1,2342 @@
+/* Variables */
+:root {
+  --mystnb-source-bg-color: #f7f7f7;
+  --mystnb-stdout-bg-color: #fcfcfc;
+  --mystnb-stderr-bg-color: #fdd;
+  --mystnb-traceback-bg-color: #fcfcfc;
+  --mystnb-source-border-color: #ccc;
+  --mystnb-source-margin-color: green;
+  --mystnb-stdout-border-color: #f7f7f7;
+  --mystnb-stderr-border-color: #f7f7f7;
+  --mystnb-traceback-border-color: #ffd6d6;
+  --mystnb-hide-prompt-opacity: 70%;
+  --mystnb-source-border-radius: .4em;
+  --mystnb-source-border-width: 1px;
+}
+
+/* Whole cell */
+div.container.cell {
+  padding-left: 0;
+  margin-bottom: 1em;
+}
+
+/* Removing all background formatting so we can control at the div level */
+.cell_input div.highlight,
+.cell_output pre,
+.cell_input pre,
+.cell_output .output {
+  border: none;
+  box-shadow: none;
+}
+
+.cell_output .output pre,
+.cell_input pre {
+  margin: 0px;
+}
+
+/* Input cells */
+div.cell div.cell_input,
+div.cell details.above-input>summary {
+  padding-left: 0em;
+  padding-right: 0em;
+  border: var(--mystnb-source-border-width) var(--mystnb-source-border-color) solid;
+  background-color: var(--mystnb-source-bg-color);
+  border-left-color: var(--mystnb-source-margin-color);
+  border-left-width: medium;
+  border-radius: var(--mystnb-source-border-radius);
+}
+
+div.cell_input>div,
+div.cell_output div.output>div.highlight {
+  margin: 0em !important;
+  border: none !important;
+}
+
+/* All cell outputs */
+.cell_output {
+  padding-left: 1em;
+  padding-right: 0em;
+  margin-top: 1em;
+}
+
+/* Text outputs from cells */
+.cell_output .output.text_plain,
+.cell_output .output.traceback,
+.cell_output .output.stream,
+.cell_output .output.stderr {
+  margin-top: 1em;
+  margin-bottom: 0em;
+  box-shadow: none;
+}
+
+.cell_output .output.text_plain,
+.cell_output .output.stream {
+  background: var(--mystnb-stdout-bg-color);
+  border: 1px solid var(--mystnb-stdout-border-color);
+}
+
+.cell_output .output.stderr {
+  background: var(--mystnb-stderr-bg-color);
+  border: 1px solid var(--mystnb-stderr-border-color);
+}
+
+.cell_output .output.traceback {
+  background: var(--mystnb-traceback-bg-color);
+  border: 1px solid var(--mystnb-traceback-border-color);
+}
+
+/* Collapsible cell content */
+div.cell details.above-input div.cell_input {
+  border-top-left-radius: 0;
+  border-top-right-radius: 0;
+  border-top: var(--mystnb-source-border-width) var(--mystnb-source-border-color) dashed;
+}
+
+div.cell div.cell_input.above-output-prompt {
+  border-bottom-left-radius: 0;
+  border-bottom-right-radius: 0;
+}
+
+div.cell details.above-input>summary {
+  border-bottom-left-radius: 0;
+  border-bottom-right-radius: 0;
+  border-bottom: var(--mystnb-source-border-width) var(--mystnb-source-border-color) dashed;
+  padding-left: 1em;
+  margin-bottom: 0;
+}
+
+div.cell details.above-output>summary {
+  background-color: var(--mystnb-source-bg-color);
+  padding-left: 1em;
+  padding-right: 0em;
+  border: var(--mystnb-source-border-width) var(--mystnb-source-border-color) solid;
+  border-radius: var(--mystnb-source-border-radius);
+  border-left-color: var(--mystnb-source-margin-color);
+  border-left-width: medium;
+}
+
+div.cell details.below-input>summary {
+  background-color: var(--mystnb-source-bg-color);
+  padding-left: 1em;
+  padding-right: 0em;
+  border: var(--mystnb-source-border-width) var(--mystnb-source-border-color) solid;
+  border-top: none;
+  border-bottom-left-radius: var(--mystnb-source-border-radius);
+  border-bottom-right-radius: var(--mystnb-source-border-radius);
+  border-left-color: var(--mystnb-source-margin-color);
+  border-left-width: medium;
+}
+
+div.cell details.hide>summary>span {
+  opacity: var(--mystnb-hide-prompt-opacity);
+}
+
+div.cell details.hide[open]>summary>span.collapsed {
+  display: none;
+}
+
+div.cell details.hide:not([open])>summary>span.expanded {
+  display: none;
+}
+
+@keyframes collapsed-fade-in {
+  0% {
+    opacity: 0;
+  }
+
+  100% {
+    opacity: 1;
+  }
+}
+div.cell details.hide[open]>summary~* {
+  -moz-animation: collapsed-fade-in 0.3s ease-in-out;
+  -webkit-animation: collapsed-fade-in 0.3s ease-in-out;
+  animation: collapsed-fade-in 0.3s ease-in-out;
+}
+
+/* Math align to the left */
+.cell_output .MathJax_Display {
+  text-align: left !important;
+}
+
+/* Pandas tables. Pulled from the Jupyter / nbsphinx CSS */
+div.cell_output table {
+  border: none;
+  border-collapse: collapse;
+  border-spacing: 0;
+  color: black;
+  font-size: 1em;
+  table-layout: fixed;
+}
+
+div.cell_output thead {
+  border-bottom: 1px solid black;
+  vertical-align: bottom;
+}
+
+div.cell_output tr,
+div.cell_output th,
+div.cell_output td {
+  text-align: right;
+  vertical-align: middle;
+  padding: 0.5em 0.5em;
+  line-height: normal;
+  white-space: normal;
+  max-width: none;
+  border: none;
+}
+
+div.cell_output th {
+  font-weight: bold;
+}
+
+div.cell_output tbody tr:nth-child(odd) {
+  background: #f5f5f5;
+}
+
+div.cell_output tbody tr:hover {
+  background: rgba(66, 165, 245, 0.2);
+}
+
+/** source code line numbers **/
+span.linenos {
+  opacity: 0.5;
+}
+
+/* Inline text from `paste` operation */
+
+span.pasted-text {
+  font-weight: bold;
+}
+
+span.pasted-inline img {
+  max-height: 2em;
+}
+
+tbody span.pasted-inline img {
+  max-height: none;
+}
+
+/* Font colors for translated ANSI escape sequences
+Color values are copied from Jupyter Notebook
+https://github.com/jupyter/notebook/blob/52581f8eda9b319eb0390ac77fe5903c38f81e3e/notebook/static/notebook/less/ansicolors.less#L14-L21
+Background colors from
+https://nbsphinx.readthedocs.io/en/latest/code-cells.html#ANSI-Colors
+*/
+div.highlight .-Color-Bold {
+  font-weight: bold;
+}
+
+div.highlight .-Color[class*=-Black] {
+  color: #3E424D
+}
+
+div.highlight .-Color[class*=-Red] {
+  color: #E75C58
+}
+
+div.highlight .-Color[class*=-Green] {
+  color: #00A250
+}
+
+div.highlight .-Color[class*=-Yellow] {
+  color: #DDB62B
+}
+
+div.highlight .-Color[class*=-Blue] {
+  color: #208FFB
+}
+
+div.highlight .-Color[class*=-Magenta] {
+  color: #D160C4
+}
+
+div.highlight .-Color[class*=-Cyan] {
+  color: #60C6C8
+}
+
+div.highlight .-Color[class*=-White] {
+  color: #C5C1B4
+}
+
+div.highlight .-Color[class*=-BGBlack] {
+  background-color: #3E424D
+}
+
+div.highlight .-Color[class*=-BGRed] {
+  background-color: #E75C58
+}
+
+div.highlight .-Color[class*=-BGGreen] {
+  background-color: #00A250
+}
+
+div.highlight .-Color[class*=-BGYellow] {
+  background-color: #DDB62B
+}
+
+div.highlight .-Color[class*=-BGBlue] {
+  background-color: #208FFB
+}
+
+div.highlight .-Color[class*=-BGMagenta] {
+  background-color: #D160C4
+}
+
+div.highlight .-Color[class*=-BGCyan] {
+  background-color: #60C6C8
+}
+
+div.highlight .-Color[class*=-BGWhite] {
+  background-color: #C5C1B4
+}
+
+/* Font colors for 8-bit ANSI */
+
+div.highlight .-Color[class*=-C0] {
+  color: #000000
+}
+
+div.highlight .-Color[class*=-BGC0] {
+  background-color: #000000
+}
+
+div.highlight .-Color[class*=-C1] {
+  color: #800000
+}
+
+div.highlight .-Color[class*=-BGC1] {
+  background-color: #800000
+}
+
+div.highlight .-Color[class*=-C2] {
+  color: #008000
+}
+
+div.highlight .-Color[class*=-BGC2] {
+  background-color: #008000
+}
+
+div.highlight .-Color[class*=-C3] {
+  color: #808000
+}
+
+div.highlight .-Color[class*=-BGC3] {
+  background-color: #808000
+}
+
+div.highlight .-Color[class*=-C4] {
+  color: #000080
+}
+
+div.highlight .-Color[class*=-BGC4] {
+  background-color: #000080
+}
+
+div.highlight .-Color[class*=-C5] {
+  color: #800080
+}
+
+div.highlight .-Color[class*=-BGC5] {
+  background-color: #800080
+}
+
+div.highlight .-Color[class*=-C6] {
+  color: #008080
+}
+
+div.highlight .-Color[class*=-BGC6] {
+  background-color: #008080
+}
+
+div.highlight .-Color[class*=-C7] {
+  color: #C0C0C0
+}
+
+div.highlight .-Color[class*=-BGC7] {
+  background-color: #C0C0C0
+}
+
+div.highlight .-Color[class*=-C8] {
+  color: #808080
+}
+
+div.highlight .-Color[class*=-BGC8] {
+  background-color: #808080
+}
+
+div.highlight .-Color[class*=-C9] {
+  color: #FF0000
+}
+
+div.highlight .-Color[class*=-BGC9] {
+  background-color: #FF0000
+}
+
+div.highlight .-Color[class*=-C10] {
+  color: #00FF00
+}
+
+div.highlight .-Color[class*=-BGC10] {
+  background-color: #00FF00
+}
+
+div.highlight .-Color[class*=-C11] {
+  color: #FFFF00
+}
+
+div.highlight .-Color[class*=-BGC11] {
+  background-color: #FFFF00
+}
+
+div.highlight .-Color[class*=-C12] {
+  color: #0000FF
+}
+
+div.highlight .-Color[class*=-BGC12] {
+  background-color: #0000FF
+}
+
+div.highlight .-Color[class*=-C13] {
+  color: #FF00FF
+}
+
+div.highlight .-Color[class*=-BGC13] {
+  background-color: #FF00FF
+}
+
+div.highlight .-Color[class*=-C14] {
+  color: #00FFFF
+}
+
+div.highlight .-Color[class*=-BGC14] {
+  background-color: #00FFFF
+}
+
+div.highlight .-Color[class*=-C15] {
+  color: #FFFFFF
+}
+
+div.highlight .-Color[class*=-BGC15] {
+  background-color: #FFFFFF
+}
+
+div.highlight .-Color[class*=-C16] {
+  color: #000000
+}
+
+div.highlight .-Color[class*=-BGC16] {
+  background-color: #000000
+}
+
+div.highlight .-Color[class*=-C17] {
+  color: #00005F
+}
+
+div.highlight .-Color[class*=-BGC17] {
+  background-color: #00005F
+}
+
+div.highlight .-Color[class*=-C18] {
+  color: #000087
+}
+
+div.highlight .-Color[class*=-BGC18] {
+  background-color: #000087
+}
+
+div.highlight .-Color[class*=-C19] {
+  color: #0000AF
+}
+
+div.highlight .-Color[class*=-BGC19] {
+  background-color: #0000AF
+}
+
+div.highlight .-Color[class*=-C20] {
+  color: #0000D7
+}
+
+div.highlight .-Color[class*=-BGC20] {
+  background-color: #0000D7
+}
+
+div.highlight .-Color[class*=-C21] {
+  color: #0000FF
+}
+
+div.highlight .-Color[class*=-BGC21] {
+  background-color: #0000FF
+}
+
+div.highlight .-Color[class*=-C22] {
+  color: #005F00
+}
+
+div.highlight .-Color[class*=-BGC22] {
+  background-color: #005F00
+}
+
+div.highlight .-Color[class*=-C23] {
+  color: #005F5F
+}
+
+div.highlight .-Color[class*=-BGC23] {
+  background-color: #005F5F
+}
+
+div.highlight .-Color[class*=-C24] {
+  color: #005F87
+}
+
+div.highlight .-Color[class*=-BGC24] {
+  background-color: #005F87
+}
+
+div.highlight .-Color[class*=-C25] {
+  color: #005FAF
+}
+
+div.highlight .-Color[class*=-BGC25] {
+  background-color: #005FAF
+}
+
+div.highlight .-Color[class*=-C26] {
+  color: #005FD7
+}
+
+div.highlight .-Color[class*=-BGC26] {
+  background-color: #005FD7
+}
+
+div.highlight .-Color[class*=-C27] {
+  color: #005FFF
+}
+
+div.highlight .-Color[class*=-BGC27] {
+  background-color: #005FFF
+}
+
+div.highlight .-Color[class*=-C28] {
+  color: #008700
+}
+
+div.highlight .-Color[class*=-BGC28] {
+  background-color: #008700
+}
+
+div.highlight .-Color[class*=-C29] {
+  color: #00875F
+}
+
+div.highlight .-Color[class*=-BGC29] {
+  background-color: #00875F
+}
+
+div.highlight .-Color[class*=-C30] {
+  color: #008787
+}
+
+div.highlight .-Color[class*=-BGC30] {
+  background-color: #008787
+}
+
+div.highlight .-Color[class*=-C31] {
+  color: #0087AF
+}
+
+div.highlight .-Color[class*=-BGC31] {
+  background-color: #0087AF
+}
+
+div.highlight .-Color[class*=-C32] {
+  color: #0087D7
+}
+
+div.highlight .-Color[class*=-BGC32] {
+  background-color: #0087D7
+}
+
+div.highlight .-Color[class*=-C33] {
+  color: #0087FF
+}
+
+div.highlight .-Color[class*=-BGC33] {
+  background-color: #0087FF
+}
+
+div.highlight .-Color[class*=-C34] {
+  color: #00AF00
+}
+
+div.highlight .-Color[class*=-BGC34] {
+  background-color: #00AF00
+}
+
+div.highlight .-Color[class*=-C35] {
+  color: #00AF5F
+}
+
+div.highlight .-Color[class*=-BGC35] {
+  background-color: #00AF5F
+}
+
+div.highlight .-Color[class*=-C36] {
+  color: #00AF87
+}
+
+div.highlight .-Color[class*=-BGC36] {
+  background-color: #00AF87
+}
+
+div.highlight .-Color[class*=-C37] {
+  color: #00AFAF
+}
+
+div.highlight .-Color[class*=-BGC37] {
+  background-color: #00AFAF
+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
+
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+}
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+}
+
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+}
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+}
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+}
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+}
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+}
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+}
+
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+}
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+}
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+}
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+}
+
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+}
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+}
+
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+}
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+}
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+}
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+}
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+}
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+}
+
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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+}
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[data-bs-slide-to]",(function(t){const e=Pt(this);if(!e||!e.classList.contains(Je))return;t.preventDefault();const i=ri.getOrCreateInstance(e),n=this.getAttribute("data-bs-slide-to");return n?(i.to(n),void i._maybeEnableCycle()):"next"===be.getDataAttribute(this,"slide")?(i.next(),void i._maybeEnableCycle()):(i.prev(),void i._maybeEnableCycle())})),ue.on(window,Ue,(()=>{const t=ke.find('[data-bs-ride="carousel"]');for(const e of t)ri.getOrCreateInstance(e)})),Kt(ri);const ai=".bs.collapse",li=`show${ai}`,ci=`shown${ai}`,hi=`hide${ai}`,di=`hidden${ai}`,ui=`click${ai}.data-api`,fi="show",pi="collapse",gi="collapsing",mi=`:scope .${pi} .${pi}`,_i='[data-bs-toggle="collapse"]',bi={parent:null,toggle:!0},vi={parent:"(null|element)",toggle:"boolean"};class yi extends ye{constructor(t,e){super(t,e),this._isTransitioning=!1,this._triggerArray=[];const i=ke.find(_i);for(const t of i){const e=Nt(t),i=ke.find(e).filter((t=>t===this._element));null!==e&&i.length&&this._triggerArray.push(t)}this._initializeChildren(),this._config.parent||this._addAriaAndCollapsedClass(this._triggerArray,this._isShown()),this._config.toggle&&this.toggle()}static get Default(){return bi}static get DefaultType(){return vi}static get NAME(){return"collapse"}toggle(){this._isShown()?this.hide():this.show()}show(){if(this._isTransitioning||this._isShown())return;let t=[];if(this._config.parent&&(t=this._getFirstLevelChildren(".collapse.show, .collapse.collapsing").filter((t=>t!==this._element)).map((t=>yi.getOrCreateInstance(t,{toggle:!1})))),t.length&&t[0]._isTransitioning)return;if(ue.trigger(this._element,li).defaultPrevented)return;for(const e of t)e.hide();const e=this._getDimension();this._element.classList.remove(pi),this._element.classList.add(gi),this._element.style[e]=0,this._addAriaAndCollapsedClass(this._triggerArray,!0),this._isTransitioning=!0;const i=`scroll${e[0].toUpperCase()+e.slice(1)}`;this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(gi),this._element.classList.add(pi,fi),this._element.style[e]="",ue.trigger(this._element,ci)}),this._element,!0),this._element.style[e]=`${this._element[i]}px`}hide(){if(this._isTransitioning||!this._isShown())return;if(ue.trigger(this._element,hi).defaultPrevented)return;const t=this._getDimension();this._element.style[t]=`${this._element.getBoundingClientRect()[t]}px`,qt(this._element),this._element.classList.add(gi),this._element.classList.remove(pi,fi);for(const t of this._triggerArray){const e=Pt(t);e&&!this._isShown(e)&&this._addAriaAndCollapsedClass([t],!1)}this._isTransitioning=!0,this._element.style[t]="",this._queueCallback((()=>{this._isTransitioning=!1,this._element.classList.remove(gi),this._element.classList.add(pi),ue.trigger(this._element,di)}),this._element,!0)}_isShown(t=this._element){return t.classList.contains(fi)}_configAfterMerge(t){return t.toggle=Boolean(t.toggle),t.parent=Ht(t.parent),t}_getDimension(){return this._element.classList.contains("collapse-horizontal")?"width":"height"}_initializeChildren(){if(!this._config.parent)return;const t=this._getFirstLevelChildren(_i);for(const e of t){const t=Pt(e);t&&this._addAriaAndCollapsedClass([e],this._isShown(t))}}_getFirstLevelChildren(t){const e=ke.find(mi,this._config.parent);return ke.find(t,this._config.parent).filter((t=>!e.includes(t)))}_addAriaAndCollapsedClass(t,e){if(t.length)for(const i of t)i.classList.toggle("collapsed",!e),i.setAttribute("aria-expanded",e)}static jQueryInterface(t){const e={};return"string"==typeof t&&/show|hide/.test(t)&&(e.toggle=!1),this.each((function(){const i=yi.getOrCreateInstance(this,e);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t]()}}))}}ue.on(document,ui,_i,(function(t){("A"===t.target.tagName||t.delegateTarget&&"A"===t.delegateTarget.tagName)&&t.preventDefault();const e=Nt(this),i=ke.find(e);for(const t of i)yi.getOrCreateInstance(t,{toggle:!1}).toggle()})),Kt(yi);const wi="dropdown",Ai=".bs.dropdown",Ei=".data-api",Ci="ArrowUp",Ti="ArrowDown",Oi=`hide${Ai}`,xi=`hidden${Ai}`,ki=`show${Ai}`,Li=`shown${Ai}`,Di=`click${Ai}${Ei}`,$i=`keydown${Ai}${Ei}`,Si=`keyup${Ai}${Ei}`,Ii="show",Ni='[data-bs-toggle="dropdown"]:not(.disabled):not(:disabled)',Pi=`${Ni}.${Ii}`,ji=".dropdown-menu",Mi=Yt()?"top-end":"top-start",Hi=Yt()?"top-start":"top-end",Bi=Yt()?"bottom-end":"bottom-start",Wi=Yt()?"bottom-start":"bottom-end",Fi=Yt()?"left-start":"right-start",zi=Yt()?"right-start":"left-start",qi={autoClose:!0,boundary:"clippingParents",display:"dynamic",offset:[0,2],popperConfig:null,reference:"toggle"},Ri={autoClose:"(boolean|string)",boundary:"(string|element)",display:"string",offset:"(array|string|function)",popperConfig:"(null|object|function)",reference:"(string|element|object)"};class Vi extends ye{constructor(t,e){super(t,e),this._popper=null,this._parent=this._element.parentNode,this._menu=ke.next(this._element,ji)[0]||ke.prev(this._element,ji)[0]||ke.findOne(ji,this._parent),this._inNavbar=this._detectNavbar()}static get Default(){return qi}static get DefaultType(){return Ri}static get NAME(){return wi}toggle(){return this._isShown()?this.hide():this.show()}show(){if(Wt(this._element)||this._isShown())return;const t={relatedTarget:this._element};if(!ue.trigger(this._element,ki,t).defaultPrevented){if(this._createPopper(),"ontouchstart"in document.documentElement&&!this._parent.closest(".navbar-nav"))for(const t of[].concat(...document.body.children))ue.on(t,"mouseover",zt);this._element.focus(),this._element.setAttribute("aria-expanded",!0),this._menu.classList.add(Ii),this._element.classList.add(Ii),ue.trigger(this._element,Li,t)}}hide(){if(Wt(this._element)||!this._isShown())return;const t={relatedTarget:this._element};this._completeHide(t)}dispose(){this._popper&&this._popper.destroy(),super.dispose()}update(){this._inNavbar=this._detectNavbar(),this._popper&&this._popper.update()}_completeHide(t){if(!ue.trigger(this._element,Oi,t).defaultPrevented){if("ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))ue.off(t,"mouseover",zt);this._popper&&this._popper.destroy(),this._menu.classList.remove(Ii),this._element.classList.remove(Ii),this._element.setAttribute("aria-expanded","false"),be.removeDataAttribute(this._menu,"popper"),ue.trigger(this._element,xi,t)}}_getConfig(t){if("object"==typeof(t=super._getConfig(t)).reference&&!Mt(t.reference)&&"function"!=typeof t.reference.getBoundingClientRect)throw new TypeError(`${wi.toUpperCase()}: Option "reference" provided type "object" without a required "getBoundingClientRect" method.`);return t}_createPopper(){if(void 0===e)throw new TypeError("Bootstrap's dropdowns require Popper (https://popper.js.org)");let t=this._element;"parent"===this._config.reference?t=this._parent:Mt(this._config.reference)?t=Ht(this._config.reference):"object"==typeof this._config.reference&&(t=this._config.reference);const i=this._getPopperConfig();this._popper=Dt(t,this._menu,i)}_isShown(){return this._menu.classList.contains(Ii)}_getPlacement(){const t=this._parent;if(t.classList.contains("dropend"))return Fi;if(t.classList.contains("dropstart"))return zi;if(t.classList.contains("dropup-center"))return"top";if(t.classList.contains("dropdown-center"))return"bottom";const e="end"===getComputedStyle(this._menu).getPropertyValue("--bs-position").trim();return t.classList.contains("dropup")?e?Hi:Mi:e?Wi:Bi}_detectNavbar(){return null!==this._element.closest(".navbar")}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_getPopperConfig(){const t={placement:this._getPlacement(),modifiers:[{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"offset",options:{offset:this._getOffset()}}]};return(this._inNavbar||"static"===this._config.display)&&(be.setDataAttribute(this._menu,"popper","static"),t.modifiers=[{name:"applyStyles",enabled:!1}]),{...t,..."function"==typeof this._config.popperConfig?this._config.popperConfig(t):this._config.popperConfig}}_selectMenuItem({key:t,target:e}){const i=ke.find(".dropdown-menu .dropdown-item:not(.disabled):not(:disabled)",this._menu).filter((t=>Bt(t)));i.length&&Ut(i,e,t===Ti,!i.includes(e)).focus()}static jQueryInterface(t){return this.each((function(){const e=Vi.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}static clearMenus(t){if(2===t.button||"keyup"===t.type&&"Tab"!==t.key)return;const e=ke.find(Pi);for(const i of e){const e=Vi.getInstance(i);if(!e||!1===e._config.autoClose)continue;const n=t.composedPath(),s=n.includes(e._menu);if(n.includes(e._element)||"inside"===e._config.autoClose&&!s||"outside"===e._config.autoClose&&s)continue;if(e._menu.contains(t.target)&&("keyup"===t.type&&"Tab"===t.key||/input|select|option|textarea|form/i.test(t.target.tagName)))continue;const o={relatedTarget:e._element};"click"===t.type&&(o.clickEvent=t),e._completeHide(o)}}static dataApiKeydownHandler(t){const e=/input|textarea/i.test(t.target.tagName),i="Escape"===t.key,n=[Ci,Ti].includes(t.key);if(!n&&!i)return;if(e&&!i)return;t.preventDefault();const s=this.matches(Ni)?this:ke.prev(this,Ni)[0]||ke.next(this,Ni)[0]||ke.findOne(Ni,t.delegateTarget.parentNode),o=Vi.getOrCreateInstance(s);if(n)return t.stopPropagation(),o.show(),void o._selectMenuItem(t);o._isShown()&&(t.stopPropagation(),o.hide(),s.focus())}}ue.on(document,$i,Ni,Vi.dataApiKeydownHandler),ue.on(document,$i,ji,Vi.dataApiKeydownHandler),ue.on(document,Di,Vi.clearMenus),ue.on(document,Si,Vi.clearMenus),ue.on(document,Di,Ni,(function(t){t.preventDefault(),Vi.getOrCreateInstance(this).toggle()})),Kt(Vi);const Yi=".fixed-top, .fixed-bottom, .is-fixed, .sticky-top",Ki=".sticky-top",Qi="padding-right",Xi="margin-right";class Ui{constructor(){this._element=document.body}getWidth(){const t=document.documentElement.clientWidth;return Math.abs(window.innerWidth-t)}hide(){const t=this.getWidth();this._disableOverFlow(),this._setElementAttributes(this._element,Qi,(e=>e+t)),this._setElementAttributes(Yi,Qi,(e=>e+t)),this._setElementAttributes(Ki,Xi,(e=>e-t))}reset(){this._resetElementAttributes(this._element,"overflow"),this._resetElementAttributes(this._element,Qi),this._resetElementAttributes(Yi,Qi),this._resetElementAttributes(Ki,Xi)}isOverflowing(){return this.getWidth()>0}_disableOverFlow(){this._saveInitialAttribute(this._element,"overflow"),this._element.style.overflow="hidden"}_setElementAttributes(t,e,i){const n=this.getWidth();this._applyManipulationCallback(t,(t=>{if(t!==this._element&&window.innerWidth>t.clientWidth+n)return;this._saveInitialAttribute(t,e);const s=window.getComputedStyle(t).getPropertyValue(e);t.style.setProperty(e,`${i(Number.parseFloat(s))}px`)}))}_saveInitialAttribute(t,e){const i=t.style.getPropertyValue(e);i&&be.setDataAttribute(t,e,i)}_resetElementAttributes(t,e){this._applyManipulationCallback(t,(t=>{const i=be.getDataAttribute(t,e);null!==i?(be.removeDataAttribute(t,e),t.style.setProperty(e,i)):t.style.removeProperty(e)}))}_applyManipulationCallback(t,e){if(Mt(t))e(t);else for(const i of ke.find(t,this._element))e(i)}}const Gi="backdrop",Ji="show",Zi=`mousedown.bs.${Gi}`,tn={className:"modal-backdrop",clickCallback:null,isAnimated:!1,isVisible:!0,rootElement:"body"},en={className:"string",clickCallback:"(function|null)",isAnimated:"boolean",isVisible:"boolean",rootElement:"(element|string)"};class nn extends ve{constructor(t){super(),this._config=this._getConfig(t),this._isAppended=!1,this._element=null}static get Default(){return tn}static get DefaultType(){return en}static get NAME(){return Gi}show(t){if(!this._config.isVisible)return void Qt(t);this._append();const e=this._getElement();this._config.isAnimated&&qt(e),e.classList.add(Ji),this._emulateAnimation((()=>{Qt(t)}))}hide(t){this._config.isVisible?(this._getElement().classList.remove(Ji),this._emulateAnimation((()=>{this.dispose(),Qt(t)}))):Qt(t)}dispose(){this._isAppended&&(ue.off(this._element,Zi),this._element.remove(),this._isAppended=!1)}_getElement(){if(!this._element){const t=document.createElement("div");t.className=this._config.className,this._config.isAnimated&&t.classList.add("fade"),this._element=t}return this._element}_configAfterMerge(t){return t.rootElement=Ht(t.rootElement),t}_append(){if(this._isAppended)return;const t=this._getElement();this._config.rootElement.append(t),ue.on(t,Zi,(()=>{Qt(this._config.clickCallback)})),this._isAppended=!0}_emulateAnimation(t){Xt(t,this._getElement(),this._config.isAnimated)}}const sn=".bs.focustrap",on=`focusin${sn}`,rn=`keydown.tab${sn}`,an="backward",ln={autofocus:!0,trapElement:null},cn={autofocus:"boolean",trapElement:"element"};class hn extends ve{constructor(t){super(),this._config=this._getConfig(t),this._isActive=!1,this._lastTabNavDirection=null}static get Default(){return ln}static get DefaultType(){return cn}static get NAME(){return"focustrap"}activate(){this._isActive||(this._config.autofocus&&this._config.trapElement.focus(),ue.off(document,sn),ue.on(document,on,(t=>this._handleFocusin(t))),ue.on(document,rn,(t=>this._handleKeydown(t))),this._isActive=!0)}deactivate(){this._isActive&&(this._isActive=!1,ue.off(document,sn))}_handleFocusin(t){const{trapElement:e}=this._config;if(t.target===document||t.target===e||e.contains(t.target))return;const i=ke.focusableChildren(e);0===i.length?e.focus():this._lastTabNavDirection===an?i[i.length-1].focus():i[0].focus()}_handleKeydown(t){"Tab"===t.key&&(this._lastTabNavDirection=t.shiftKey?an:"forward")}}const dn=".bs.modal",un=`hide${dn}`,fn=`hidePrevented${dn}`,pn=`hidden${dn}`,gn=`show${dn}`,mn=`shown${dn}`,_n=`resize${dn}`,bn=`click.dismiss${dn}`,vn=`mousedown.dismiss${dn}`,yn=`keydown.dismiss${dn}`,wn=`click${dn}.data-api`,An="modal-open",En="show",Cn="modal-static",Tn={backdrop:!0,focus:!0,keyboard:!0},On={backdrop:"(boolean|string)",focus:"boolean",keyboard:"boolean"};class xn extends ye{constructor(t,e){super(t,e),this._dialog=ke.findOne(".modal-dialog",this._element),this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._isShown=!1,this._isTransitioning=!1,this._scrollBar=new Ui,this._addEventListeners()}static get Default(){return Tn}static get DefaultType(){return On}static get NAME(){return"modal"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||this._isTransitioning||ue.trigger(this._element,gn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._isTransitioning=!0,this._scrollBar.hide(),document.body.classList.add(An),this._adjustDialog(),this._backdrop.show((()=>this._showElement(t))))}hide(){this._isShown&&!this._isTransitioning&&(ue.trigger(this._element,un).defaultPrevented||(this._isShown=!1,this._isTransitioning=!0,this._focustrap.deactivate(),this._element.classList.remove(En),this._queueCallback((()=>this._hideModal()),this._element,this._isAnimated())))}dispose(){for(const t of[window,this._dialog])ue.off(t,dn);this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}handleUpdate(){this._adjustDialog()}_initializeBackDrop(){return new nn({isVisible:Boolean(this._config.backdrop),isAnimated:this._isAnimated()})}_initializeFocusTrap(){return new hn({trapElement:this._element})}_showElement(t){document.body.contains(this._element)||document.body.append(this._element),this._element.style.display="block",this._element.removeAttribute("aria-hidden"),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.scrollTop=0;const e=ke.findOne(".modal-body",this._dialog);e&&(e.scrollTop=0),qt(this._element),this._element.classList.add(En),this._queueCallback((()=>{this._config.focus&&this._focustrap.activate(),this._isTransitioning=!1,ue.trigger(this._element,mn,{relatedTarget:t})}),this._dialog,this._isAnimated())}_addEventListeners(){ue.on(this._element,yn,(t=>{if("Escape"===t.key)return this._config.keyboard?(t.preventDefault(),void this.hide()):void this._triggerBackdropTransition()})),ue.on(window,_n,(()=>{this._isShown&&!this._isTransitioning&&this._adjustDialog()})),ue.on(this._element,vn,(t=>{ue.one(this._element,bn,(e=>{this._element===t.target&&this._element===e.target&&("static"!==this._config.backdrop?this._config.backdrop&&this.hide():this._triggerBackdropTransition())}))}))}_hideModal(){this._element.style.display="none",this._element.setAttribute("aria-hidden",!0),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._isTransitioning=!1,this._backdrop.hide((()=>{document.body.classList.remove(An),this._resetAdjustments(),this._scrollBar.reset(),ue.trigger(this._element,pn)}))}_isAnimated(){return this._element.classList.contains("fade")}_triggerBackdropTransition(){if(ue.trigger(this._element,fn).defaultPrevented)return;const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._element.style.overflowY;"hidden"===e||this._element.classList.contains(Cn)||(t||(this._element.style.overflowY="hidden"),this._element.classList.add(Cn),this._queueCallback((()=>{this._element.classList.remove(Cn),this._queueCallback((()=>{this._element.style.overflowY=e}),this._dialog)}),this._dialog),this._element.focus())}_adjustDialog(){const t=this._element.scrollHeight>document.documentElement.clientHeight,e=this._scrollBar.getWidth(),i=e>0;if(i&&!t){const t=Yt()?"paddingLeft":"paddingRight";this._element.style[t]=`${e}px`}if(!i&&t){const t=Yt()?"paddingRight":"paddingLeft";this._element.style[t]=`${e}px`}}_resetAdjustments(){this._element.style.paddingLeft="",this._element.style.paddingRight=""}static jQueryInterface(t,e){return this.each((function(){const i=xn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===i[t])throw new TypeError(`No method named "${t}"`);i[t](e)}}))}}ue.on(document,wn,'[data-bs-toggle="modal"]',(function(t){const e=Pt(this);["A","AREA"].includes(this.tagName)&&t.preventDefault(),ue.one(e,gn,(t=>{t.defaultPrevented||ue.one(e,pn,(()=>{Bt(this)&&this.focus()}))}));const i=ke.findOne(".modal.show");i&&xn.getInstance(i).hide(),xn.getOrCreateInstance(e).toggle(this)})),we(xn),Kt(xn);const kn=".bs.offcanvas",Ln=".data-api",Dn=`load${kn}${Ln}`,$n="show",Sn="showing",In="hiding",Nn=".offcanvas.show",Pn=`show${kn}`,jn=`shown${kn}`,Mn=`hide${kn}`,Hn=`hidePrevented${kn}`,Bn=`hidden${kn}`,Wn=`resize${kn}`,Fn=`click${kn}${Ln}`,zn=`keydown.dismiss${kn}`,qn={backdrop:!0,keyboard:!0,scroll:!1},Rn={backdrop:"(boolean|string)",keyboard:"boolean",scroll:"boolean"};class Vn extends ye{constructor(t,e){super(t,e),this._isShown=!1,this._backdrop=this._initializeBackDrop(),this._focustrap=this._initializeFocusTrap(),this._addEventListeners()}static get Default(){return qn}static get DefaultType(){return Rn}static get NAME(){return"offcanvas"}toggle(t){return this._isShown?this.hide():this.show(t)}show(t){this._isShown||ue.trigger(this._element,Pn,{relatedTarget:t}).defaultPrevented||(this._isShown=!0,this._backdrop.show(),this._config.scroll||(new Ui).hide(),this._element.setAttribute("aria-modal",!0),this._element.setAttribute("role","dialog"),this._element.classList.add(Sn),this._queueCallback((()=>{this._config.scroll&&!this._config.backdrop||this._focustrap.activate(),this._element.classList.add($n),this._element.classList.remove(Sn),ue.trigger(this._element,jn,{relatedTarget:t})}),this._element,!0))}hide(){this._isShown&&(ue.trigger(this._element,Mn).defaultPrevented||(this._focustrap.deactivate(),this._element.blur(),this._isShown=!1,this._element.classList.add(In),this._backdrop.hide(),this._queueCallback((()=>{this._element.classList.remove($n,In),this._element.removeAttribute("aria-modal"),this._element.removeAttribute("role"),this._config.scroll||(new Ui).reset(),ue.trigger(this._element,Bn)}),this._element,!0)))}dispose(){this._backdrop.dispose(),this._focustrap.deactivate(),super.dispose()}_initializeBackDrop(){const t=Boolean(this._config.backdrop);return new nn({className:"offcanvas-backdrop",isVisible:t,isAnimated:!0,rootElement:this._element.parentNode,clickCallback:t?()=>{"static"!==this._config.backdrop?this.hide():ue.trigger(this._element,Hn)}:null})}_initializeFocusTrap(){return new hn({trapElement:this._element})}_addEventListeners(){ue.on(this._element,zn,(t=>{"Escape"===t.key&&(this._config.keyboard?this.hide():ue.trigger(this._element,Hn))}))}static jQueryInterface(t){return this.each((function(){const e=Vn.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}ue.on(document,Fn,'[data-bs-toggle="offcanvas"]',(function(t){const e=Pt(this);if(["A","AREA"].includes(this.tagName)&&t.preventDefault(),Wt(this))return;ue.one(e,Bn,(()=>{Bt(this)&&this.focus()}));const i=ke.findOne(Nn);i&&i!==e&&Vn.getInstance(i).hide(),Vn.getOrCreateInstance(e).toggle(this)})),ue.on(window,Dn,(()=>{for(const t of ke.find(Nn))Vn.getOrCreateInstance(t).show()})),ue.on(window,Wn,(()=>{for(const t of ke.find("[aria-modal][class*=show][class*=offcanvas-]"))"fixed"!==getComputedStyle(t).position&&Vn.getOrCreateInstance(t).hide()})),we(Vn),Kt(Vn);const Yn=new Set(["background","cite","href","itemtype","longdesc","poster","src","xlink:href"]),Kn=/^(?:(?:https?|mailto|ftp|tel|file|sms):|[^#&/:?]*(?:[#/?]|$))/i,Qn=/^data:(?:image\/(?:bmp|gif|jpeg|jpg|png|tiff|webp)|video\/(?:mpeg|mp4|ogg|webm)|audio\/(?:mp3|oga|ogg|opus));base64,[\d+/a-z]+=*$/i,Xn=(t,e)=>{const i=t.nodeName.toLowerCase();return e.includes(i)?!Yn.has(i)||Boolean(Kn.test(t.nodeValue)||Qn.test(t.nodeValue)):e.filter((t=>t instanceof RegExp)).some((t=>t.test(i)))},Un={"*":["class","dir","id","lang","role",/^aria-[\w-]*$/i],a:["target","href","title","rel"],area:[],b:[],br:[],col:[],code:[],div:[],em:[],hr:[],h1:[],h2:[],h3:[],h4:[],h5:[],h6:[],i:[],img:["src","srcset","alt","title","width","height"],li:[],ol:[],p:[],pre:[],s:[],small:[],span:[],sub:[],sup:[],strong:[],u:[],ul:[]},Gn={allowList:Un,content:{},extraClass:"",html:!1,sanitize:!0,sanitizeFn:null,template:"<div></div>"},Jn={allowList:"object",content:"object",extraClass:"(string|function)",html:"boolean",sanitize:"boolean",sanitizeFn:"(null|function)",template:"string"},Zn={entry:"(string|element|function|null)",selector:"(string|element)"};class ts extends ve{constructor(t){super(),this._config=this._getConfig(t)}static get Default(){return Gn}static get DefaultType(){return Jn}static get NAME(){return"TemplateFactory"}getContent(){return Object.values(this._config.content).map((t=>this._resolvePossibleFunction(t))).filter(Boolean)}hasContent(){return this.getContent().length>0}changeContent(t){return this._checkContent(t),this._config.content={...this._config.content,...t},this}toHtml(){const t=document.createElement("div");t.innerHTML=this._maybeSanitize(this._config.template);for(const[e,i]of Object.entries(this._config.content))this._setContent(t,i,e);const e=t.children[0],i=this._resolvePossibleFunction(this._config.extraClass);return i&&e.classList.add(...i.split(" ")),e}_typeCheckConfig(t){super._typeCheckConfig(t),this._checkContent(t.content)}_checkContent(t){for(const[e,i]of Object.entries(t))super._typeCheckConfig({selector:e,entry:i},Zn)}_setContent(t,e,i){const n=ke.findOne(i,t);n&&((e=this._resolvePossibleFunction(e))?Mt(e)?this._putElementInTemplate(Ht(e),n):this._config.html?n.innerHTML=this._maybeSanitize(e):n.textContent=e:n.remove())}_maybeSanitize(t){return this._config.sanitize?function(t,e,i){if(!t.length)return t;if(i&&"function"==typeof i)return i(t);const n=(new window.DOMParser).parseFromString(t,"text/html"),s=[].concat(...n.body.querySelectorAll("*"));for(const t of s){const i=t.nodeName.toLowerCase();if(!Object.keys(e).includes(i)){t.remove();continue}const n=[].concat(...t.attributes),s=[].concat(e["*"]||[],e[i]||[]);for(const e of n)Xn(e,s)||t.removeAttribute(e.nodeName)}return n.body.innerHTML}(t,this._config.allowList,this._config.sanitizeFn):t}_resolvePossibleFunction(t){return"function"==typeof t?t(this):t}_putElementInTemplate(t,e){if(this._config.html)return e.innerHTML="",void e.append(t);e.textContent=t.textContent}}const es=new Set(["sanitize","allowList","sanitizeFn"]),is="fade",ns="show",ss=".modal",os="hide.bs.modal",rs="hover",as="focus",ls={AUTO:"auto",TOP:"top",RIGHT:Yt()?"left":"right",BOTTOM:"bottom",LEFT:Yt()?"right":"left"},cs={allowList:Un,animation:!0,boundary:"clippingParents",container:!1,customClass:"",delay:0,fallbackPlacements:["top","right","bottom","left"],html:!1,offset:[0,0],placement:"top",popperConfig:null,sanitize:!0,sanitizeFn:null,selector:!1,template:'<div class="tooltip" role="tooltip"><div class="tooltip-arrow"></div><div class="tooltip-inner"></div></div>',title:"",trigger:"hover focus"},hs={allowList:"object",animation:"boolean",boundary:"(string|element)",container:"(string|element|boolean)",customClass:"(string|function)",delay:"(number|object)",fallbackPlacements:"array",html:"boolean",offset:"(array|string|function)",placement:"(string|function)",popperConfig:"(null|object|function)",sanitize:"boolean",sanitizeFn:"(null|function)",selector:"(string|boolean)",template:"string",title:"(string|element|function)",trigger:"string"};class ds extends ye{constructor(t,i){if(void 0===e)throw new TypeError("Bootstrap's tooltips require Popper (https://popper.js.org)");super(t,i),this._isEnabled=!0,this._timeout=0,this._isHovered=null,this._activeTrigger={},this._popper=null,this._templateFactory=null,this._newContent=null,this.tip=null,this._setListeners(),this._config.selector||this._fixTitle()}static get Default(){return cs}static get DefaultType(){return hs}static get NAME(){return"tooltip"}enable(){this._isEnabled=!0}disable(){this._isEnabled=!1}toggleEnabled(){this._isEnabled=!this._isEnabled}toggle(){this._isEnabled&&(this._activeTrigger.click=!this._activeTrigger.click,this._isShown()?this._leave():this._enter())}dispose(){clearTimeout(this._timeout),ue.off(this._element.closest(ss),os,this._hideModalHandler),this._element.getAttribute("data-bs-original-title")&&this._element.setAttribute("title",this._element.getAttribute("data-bs-original-title")),this._disposePopper(),super.dispose()}show(){if("none"===this._element.style.display)throw new Error("Please use show on visible elements");if(!this._isWithContent()||!this._isEnabled)return;const t=ue.trigger(this._element,this.constructor.eventName("show")),e=(Ft(this._element)||this._element.ownerDocument.documentElement).contains(this._element);if(t.defaultPrevented||!e)return;this._disposePopper();const i=this._getTipElement();this._element.setAttribute("aria-describedby",i.getAttribute("id"));const{container:n}=this._config;if(this._element.ownerDocument.documentElement.contains(this.tip)||(n.append(i),ue.trigger(this._element,this.constructor.eventName("inserted"))),this._popper=this._createPopper(i),i.classList.add(ns),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))ue.on(t,"mouseover",zt);this._queueCallback((()=>{ue.trigger(this._element,this.constructor.eventName("shown")),!1===this._isHovered&&this._leave(),this._isHovered=!1}),this.tip,this._isAnimated())}hide(){if(this._isShown()&&!ue.trigger(this._element,this.constructor.eventName("hide")).defaultPrevented){if(this._getTipElement().classList.remove(ns),"ontouchstart"in document.documentElement)for(const t of[].concat(...document.body.children))ue.off(t,"mouseover",zt);this._activeTrigger.click=!1,this._activeTrigger[as]=!1,this._activeTrigger[rs]=!1,this._isHovered=null,this._queueCallback((()=>{this._isWithActiveTrigger()||(this._isHovered||this._disposePopper(),this._element.removeAttribute("aria-describedby"),ue.trigger(this._element,this.constructor.eventName("hidden")))}),this.tip,this._isAnimated())}}update(){this._popper&&this._popper.update()}_isWithContent(){return Boolean(this._getTitle())}_getTipElement(){return this.tip||(this.tip=this._createTipElement(this._newContent||this._getContentForTemplate())),this.tip}_createTipElement(t){const e=this._getTemplateFactory(t).toHtml();if(!e)return null;e.classList.remove(is,ns),e.classList.add(`bs-${this.constructor.NAME}-auto`);const i=(t=>{do{t+=Math.floor(1e6*Math.random())}while(document.getElementById(t));return t})(this.constructor.NAME).toString();return e.setAttribute("id",i),this._isAnimated()&&e.classList.add(is),e}setContent(t){this._newContent=t,this._isShown()&&(this._disposePopper(),this.show())}_getTemplateFactory(t){return this._templateFactory?this._templateFactory.changeContent(t):this._templateFactory=new ts({...this._config,content:t,extraClass:this._resolvePossibleFunction(this._config.customClass)}),this._templateFactory}_getContentForTemplate(){return{".tooltip-inner":this._getTitle()}}_getTitle(){return this._resolvePossibleFunction(this._config.title)||this._element.getAttribute("data-bs-original-title")}_initializeOnDelegatedTarget(t){return this.constructor.getOrCreateInstance(t.delegateTarget,this._getDelegateConfig())}_isAnimated(){return this._config.animation||this.tip&&this.tip.classList.contains(is)}_isShown(){return this.tip&&this.tip.classList.contains(ns)}_createPopper(t){const e="function"==typeof this._config.placement?this._config.placement.call(this,t,this._element):this._config.placement,i=ls[e.toUpperCase()];return Dt(this._element,t,this._getPopperConfig(i))}_getOffset(){const{offset:t}=this._config;return"string"==typeof t?t.split(",").map((t=>Number.parseInt(t,10))):"function"==typeof t?e=>t(e,this._element):t}_resolvePossibleFunction(t){return"function"==typeof t?t.call(this._element):t}_getPopperConfig(t){const e={placement:t,modifiers:[{name:"flip",options:{fallbackPlacements:this._config.fallbackPlacements}},{name:"offset",options:{offset:this._getOffset()}},{name:"preventOverflow",options:{boundary:this._config.boundary}},{name:"arrow",options:{element:`.${this.constructor.NAME}-arrow`}},{name:"preSetPlacement",enabled:!0,phase:"beforeMain",fn:t=>{this._getTipElement().setAttribute("data-popper-placement",t.state.placement)}}]};return{...e,..."function"==typeof this._config.popperConfig?this._config.popperConfig(e):this._config.popperConfig}}_setListeners(){const t=this._config.trigger.split(" ");for(const e of t)if("click"===e)ue.on(this._element,this.constructor.eventName("click"),this._config.selector,(t=>{this._initializeOnDelegatedTarget(t).toggle()}));else if("manual"!==e){const t=e===rs?this.constructor.eventName("mouseenter"):this.constructor.eventName("focusin"),i=e===rs?this.constructor.eventName("mouseleave"):this.constructor.eventName("focusout");ue.on(this._element,t,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusin"===t.type?as:rs]=!0,e._enter()})),ue.on(this._element,i,this._config.selector,(t=>{const e=this._initializeOnDelegatedTarget(t);e._activeTrigger["focusout"===t.type?as:rs]=e._element.contains(t.relatedTarget),e._leave()}))}this._hideModalHandler=()=>{this._element&&this.hide()},ue.on(this._element.closest(ss),os,this._hideModalHandler)}_fixTitle(){const t=this._element.getAttribute("title");t&&(this._element.getAttribute("aria-label")||this._element.textContent.trim()||this._element.setAttribute("aria-label",t),this._element.setAttribute("data-bs-original-title",t),this._element.removeAttribute("title"))}_enter(){this._isShown()||this._isHovered?this._isHovered=!0:(this._isHovered=!0,this._setTimeout((()=>{this._isHovered&&this.show()}),this._config.delay.show))}_leave(){this._isWithActiveTrigger()||(this._isHovered=!1,this._setTimeout((()=>{this._isHovered||this.hide()}),this._config.delay.hide))}_setTimeout(t,e){clearTimeout(this._timeout),this._timeout=setTimeout(t,e)}_isWithActiveTrigger(){return Object.values(this._activeTrigger).includes(!0)}_getConfig(t){const e=be.getDataAttributes(this._element);for(const t of Object.keys(e))es.has(t)&&delete e[t];return t={...e,..."object"==typeof t&&t?t:{}},t=this._mergeConfigObj(t),t=this._configAfterMerge(t),this._typeCheckConfig(t),t}_configAfterMerge(t){return t.container=!1===t.container?document.body:Ht(t.container),"number"==typeof t.delay&&(t.delay={show:t.delay,hide:t.delay}),"number"==typeof t.title&&(t.title=t.title.toString()),"number"==typeof t.content&&(t.content=t.content.toString()),t}_getDelegateConfig(){const t={};for(const e in this._config)this.constructor.Default[e]!==this._config[e]&&(t[e]=this._config[e]);return t.selector=!1,t.trigger="manual",t}_disposePopper(){this._popper&&(this._popper.destroy(),this._popper=null),this.tip&&(this.tip.remove(),this.tip=null)}static jQueryInterface(t){return this.each((function(){const e=ds.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}Kt(ds);const us={...ds.Default,content:"",offset:[0,8],placement:"right",template:'<div class="popover" role="tooltip"><div class="popover-arrow"></div><h3 class="popover-header"></h3><div class="popover-body"></div></div>',trigger:"click"},fs={...ds.DefaultType,content:"(null|string|element|function)"};class ps extends ds{static get Default(){return us}static get DefaultType(){return fs}static get NAME(){return"popover"}_isWithContent(){return this._getTitle()||this._getContent()}_getContentForTemplate(){return{".popover-header":this._getTitle(),".popover-body":this._getContent()}}_getContent(){return this._resolvePossibleFunction(this._config.content)}static jQueryInterface(t){return this.each((function(){const e=ps.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t]()}}))}}Kt(ps);const gs=".bs.scrollspy",ms=`activate${gs}`,_s=`click${gs}`,bs=`load${gs}.data-api`,vs="active",ys="[href]",ws=".nav-link",As=`${ws}, .nav-item > ${ws}, .list-group-item`,Es={offset:null,rootMargin:"0px 0px -25%",smoothScroll:!1,target:null,threshold:[.1,.5,1]},Cs={offset:"(number|null)",rootMargin:"string",smoothScroll:"boolean",target:"element",threshold:"array"};class Ts extends ye{constructor(t,e){super(t,e),this._targetLinks=new Map,this._observableSections=new Map,this._rootElement="visible"===getComputedStyle(this._element).overflowY?null:this._element,this._activeTarget=null,this._observer=null,this._previousScrollData={visibleEntryTop:0,parentScrollTop:0},this.refresh()}static get Default(){return Es}static get DefaultType(){return Cs}static get NAME(){return"scrollspy"}refresh(){this._initializeTargetsAndObservables(),this._maybeEnableSmoothScroll(),this._observer?this._observer.disconnect():this._observer=this._getNewObserver();for(const t of this._observableSections.values())this._observer.observe(t)}dispose(){this._observer.disconnect(),super.dispose()}_configAfterMerge(t){return t.target=Ht(t.target)||document.body,t.rootMargin=t.offset?`${t.offset}px 0px -30%`:t.rootMargin,"string"==typeof t.threshold&&(t.threshold=t.threshold.split(",").map((t=>Number.parseFloat(t)))),t}_maybeEnableSmoothScroll(){this._config.smoothScroll&&(ue.off(this._config.target,_s),ue.on(this._config.target,_s,ys,(t=>{const e=this._observableSections.get(t.target.hash);if(e){t.preventDefault();const i=this._rootElement||window,n=e.offsetTop-this._element.offsetTop;if(i.scrollTo)return void i.scrollTo({top:n,behavior:"smooth"});i.scrollTop=n}})))}_getNewObserver(){const t={root:this._rootElement,threshold:this._config.threshold,rootMargin:this._config.rootMargin};return new IntersectionObserver((t=>this._observerCallback(t)),t)}_observerCallback(t){const e=t=>this._targetLinks.get(`#${t.target.id}`),i=t=>{this._previousScrollData.visibleEntryTop=t.target.offsetTop,this._process(e(t))},n=(this._rootElement||document.documentElement).scrollTop,s=n>=this._previousScrollData.parentScrollTop;this._previousScrollData.parentScrollTop=n;for(const o of t){if(!o.isIntersecting){this._activeTarget=null,this._clearActiveClass(e(o));continue}const t=o.target.offsetTop>=this._previousScrollData.visibleEntryTop;if(s&&t){if(i(o),!n)return}else s||t||i(o)}}_initializeTargetsAndObservables(){this._targetLinks=new Map,this._observableSections=new Map;const t=ke.find(ys,this._config.target);for(const e of t){if(!e.hash||Wt(e))continue;const t=ke.findOne(e.hash,this._element);Bt(t)&&(this._targetLinks.set(e.hash,e),this._observableSections.set(e.hash,t))}}_process(t){this._activeTarget!==t&&(this._clearActiveClass(this._config.target),this._activeTarget=t,t.classList.add(vs),this._activateParents(t),ue.trigger(this._element,ms,{relatedTarget:t}))}_activateParents(t){if(t.classList.contains("dropdown-item"))ke.findOne(".dropdown-toggle",t.closest(".dropdown")).classList.add(vs);else for(const e of ke.parents(t,".nav, .list-group"))for(const t of ke.prev(e,As))t.classList.add(vs)}_clearActiveClass(t){t.classList.remove(vs);const e=ke.find(`${ys}.${vs}`,t);for(const t of e)t.classList.remove(vs)}static jQueryInterface(t){return this.each((function(){const e=Ts.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}ue.on(window,bs,(()=>{for(const t of ke.find('[data-bs-spy="scroll"]'))Ts.getOrCreateInstance(t)})),Kt(Ts);const Os=".bs.tab",xs=`hide${Os}`,ks=`hidden${Os}`,Ls=`show${Os}`,Ds=`shown${Os}`,$s=`click${Os}`,Ss=`keydown${Os}`,Is=`load${Os}`,Ns="ArrowLeft",Ps="ArrowRight",js="ArrowUp",Ms="ArrowDown",Hs="active",Bs="fade",Ws="show",Fs=":not(.dropdown-toggle)",zs='[data-bs-toggle="tab"], [data-bs-toggle="pill"], [data-bs-toggle="list"]',qs=`.nav-link${Fs}, .list-group-item${Fs}, [role="tab"]${Fs}, ${zs}`,Rs=`.${Hs}[data-bs-toggle="tab"], .${Hs}[data-bs-toggle="pill"], .${Hs}[data-bs-toggle="list"]`;class Vs extends ye{constructor(t){super(t),this._parent=this._element.closest('.list-group, .nav, [role="tablist"]'),this._parent&&(this._setInitialAttributes(this._parent,this._getChildren()),ue.on(this._element,Ss,(t=>this._keydown(t))))}static get NAME(){return"tab"}show(){const t=this._element;if(this._elemIsActive(t))return;const e=this._getActiveElem(),i=e?ue.trigger(e,xs,{relatedTarget:t}):null;ue.trigger(t,Ls,{relatedTarget:e}).defaultPrevented||i&&i.defaultPrevented||(this._deactivate(e,t),this._activate(t,e))}_activate(t,e){t&&(t.classList.add(Hs),this._activate(Pt(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.removeAttribute("tabindex"),t.setAttribute("aria-selected",!0),this._toggleDropDown(t,!0),ue.trigger(t,Ds,{relatedTarget:e})):t.classList.add(Ws)}),t,t.classList.contains(Bs)))}_deactivate(t,e){t&&(t.classList.remove(Hs),t.blur(),this._deactivate(Pt(t)),this._queueCallback((()=>{"tab"===t.getAttribute("role")?(t.setAttribute("aria-selected",!1),t.setAttribute("tabindex","-1"),this._toggleDropDown(t,!1),ue.trigger(t,ks,{relatedTarget:e})):t.classList.remove(Ws)}),t,t.classList.contains(Bs)))}_keydown(t){if(![Ns,Ps,js,Ms].includes(t.key))return;t.stopPropagation(),t.preventDefault();const e=[Ps,Ms].includes(t.key),i=Ut(this._getChildren().filter((t=>!Wt(t))),t.target,e,!0);i&&(i.focus({preventScroll:!0}),Vs.getOrCreateInstance(i).show())}_getChildren(){return ke.find(qs,this._parent)}_getActiveElem(){return this._getChildren().find((t=>this._elemIsActive(t)))||null}_setInitialAttributes(t,e){this._setAttributeIfNotExists(t,"role","tablist");for(const t of e)this._setInitialAttributesOnChild(t)}_setInitialAttributesOnChild(t){t=this._getInnerElement(t);const e=this._elemIsActive(t),i=this._getOuterElement(t);t.setAttribute("aria-selected",e),i!==t&&this._setAttributeIfNotExists(i,"role","presentation"),e||t.setAttribute("tabindex","-1"),this._setAttributeIfNotExists(t,"role","tab"),this._setInitialAttributesOnTargetPanel(t)}_setInitialAttributesOnTargetPanel(t){const e=Pt(t);e&&(this._setAttributeIfNotExists(e,"role","tabpanel"),t.id&&this._setAttributeIfNotExists(e,"aria-labelledby",`#${t.id}`))}_toggleDropDown(t,e){const i=this._getOuterElement(t);if(!i.classList.contains("dropdown"))return;const n=(t,n)=>{const s=ke.findOne(t,i);s&&s.classList.toggle(n,e)};n(".dropdown-toggle",Hs),n(".dropdown-menu",Ws),i.setAttribute("aria-expanded",e)}_setAttributeIfNotExists(t,e,i){t.hasAttribute(e)||t.setAttribute(e,i)}_elemIsActive(t){return t.classList.contains(Hs)}_getInnerElement(t){return t.matches(qs)?t:ke.findOne(qs,t)}_getOuterElement(t){return t.closest(".nav-item, .list-group-item")||t}static jQueryInterface(t){return this.each((function(){const e=Vs.getOrCreateInstance(this);if("string"==typeof t){if(void 0===e[t]||t.startsWith("_")||"constructor"===t)throw new TypeError(`No method named "${t}"`);e[t]()}}))}}ue.on(document,$s,zs,(function(t){["A","AREA"].includes(this.tagName)&&t.preventDefault(),Wt(this)||Vs.getOrCreateInstance(this).show()})),ue.on(window,Is,(()=>{for(const t of ke.find(Rs))Vs.getOrCreateInstance(t)})),Kt(Vs);const Ys=".bs.toast",Ks=`mouseover${Ys}`,Qs=`mouseout${Ys}`,Xs=`focusin${Ys}`,Us=`focusout${Ys}`,Gs=`hide${Ys}`,Js=`hidden${Ys}`,Zs=`show${Ys}`,to=`shown${Ys}`,eo="hide",io="show",no="showing",so={animation:"boolean",autohide:"boolean",delay:"number"},oo={animation:!0,autohide:!0,delay:5e3};class ro extends ye{constructor(t,e){super(t,e),this._timeout=null,this._hasMouseInteraction=!1,this._hasKeyboardInteraction=!1,this._setListeners()}static get Default(){return oo}static get DefaultType(){return so}static get NAME(){return"toast"}show(){ue.trigger(this._element,Zs).defaultPrevented||(this._clearTimeout(),this._config.animation&&this._element.classList.add("fade"),this._element.classList.remove(eo),qt(this._element),this._element.classList.add(io,no),this._queueCallback((()=>{this._element.classList.remove(no),ue.trigger(this._element,to),this._maybeScheduleHide()}),this._element,this._config.animation))}hide(){this.isShown()&&(ue.trigger(this._element,Gs).defaultPrevented||(this._element.classList.add(no),this._queueCallback((()=>{this._element.classList.add(eo),this._element.classList.remove(no,io),ue.trigger(this._element,Js)}),this._element,this._config.animation)))}dispose(){this._clearTimeout(),this.isShown()&&this._element.classList.remove(io),super.dispose()}isShown(){return this._element.classList.contains(io)}_maybeScheduleHide(){this._config.autohide&&(this._hasMouseInteraction||this._hasKeyboardInteraction||(this._timeout=setTimeout((()=>{this.hide()}),this._config.delay)))}_onInteraction(t,e){switch(t.type){case"mouseover":case"mouseout":this._hasMouseInteraction=e;break;case"focusin":case"focusout":this._hasKeyboardInteraction=e}if(e)return void this._clearTimeout();const i=t.relatedTarget;this._element===i||this._element.contains(i)||this._maybeScheduleHide()}_setListeners(){ue.on(this._element,Ks,(t=>this._onInteraction(t,!0))),ue.on(this._element,Qs,(t=>this._onInteraction(t,!1))),ue.on(this._element,Xs,(t=>this._onInteraction(t,!0))),ue.on(this._element,Us,(t=>this._onInteraction(t,!1)))}_clearTimeout(){clearTimeout(this._timeout),this._timeout=null}static jQueryInterface(t){return this.each((function(){const e=ro.getOrCreateInstance(this,t);if("string"==typeof t){if(void 0===e[t])throw new TypeError(`No method named "${t}"`);e[t](this)}}))}}function ao(t){"loading"!=document.readyState?t():document.addEventListener("DOMContentLoaded",t)}we(ro),Kt(ro),ao((function(){[].slice.call(document.querySelectorAll('[data-bs-toggle="tooltip"]')).map((function(t){return new ds(t,{delay:{show:500,hide:100}})}))})),ao((function(){document.getElementById("pst-back-to-top").addEventListener("click",(function(){document.body.scrollTop=0,document.documentElement.scrollTop=0}))})),ao((function(){var t=document.getElementById("pst-back-to-top"),e=document.getElementsByClassName("bd-header")[0].getBoundingClientRect();window.addEventListener("scroll",(function(){this.oldScroll>this.scrollY&&this.scrollY>e.bottom?t.style.display="block":t.style.display="none",this.oldScroll=this.scrollY}))}))})();
+//# sourceMappingURL=bootstrap.js.map
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.LICENSE.txt b/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.LICENSE.txt
new file mode 100644
index 000000000..91ad10aa0
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.LICENSE.txt
@@ -0,0 +1,5 @@
+/*!
+  * Bootstrap v5.2.3 (https://getbootstrap.com/)
+  * Copyright 2011-2022 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)
+  * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+  */
diff --git a/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.map b/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.map
new file mode 100644
index 000000000..04c27d7bc
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/scripts/bootstrap.js.map
@@ -0,0 +1 @@
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The require scope\nvar __webpack_require__ = {};\n\n","// define getter functions for harmony exports\n__webpack_require__.d = (exports, definition) => {\n\tfor(var key in definition) {\n\t\tif(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {\n\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: definition[key] });\n\t\t}\n\t}\n};","__webpack_require__.o = (obj, prop) => (Object.prototype.hasOwnProperty.call(obj, prop))","// define __esModule on exports\n__webpack_require__.r = (exports) => {\n\tif(typeof Symbol !== 'undefined' && Symbol.toStringTag) {\n\t\tObject.defineProperty(exports, Symbol.toStringTag, { value: 'Module' });\n\t}\n\tObject.defineProperty(exports, '__esModule', { value: true });\n};","export var top = 'top';\nexport var bottom = 'bottom';\nexport var right = 'right';\nexport var left = 'left';\nexport var auto = 'auto';\nexport var basePlacements = [top, bottom, right, left];\nexport var start = 'start';\nexport var end = 'end';\nexport var clippingParents = 'clippingParents';\nexport var viewport = 'viewport';\nexport var popper = 'popper';\nexport var reference = 'reference';\nexport var variationPlacements = /*#__PURE__*/basePlacements.reduce(function (acc, placement) {\n  return acc.concat([placement + \"-\" + start, placement + \"-\" + end]);\n}, []);\nexport var placements = /*#__PURE__*/[].concat(basePlacements, [auto]).reduce(function (acc, placement) {\n  return acc.concat([placement, placement + \"-\" + start, placement + \"-\" + end]);\n}, []); // modifiers that need to read the DOM\n\nexport var beforeRead = 'beforeRead';\nexport var read = 'read';\nexport var afterRead = 'afterRead'; // pure-logic modifiers\n\nexport var beforeMain = 'beforeMain';\nexport var main = 'main';\nexport var afterMain = 'afterMain'; // modifier with the purpose to write to the DOM (or write into a framework state)\n\nexport var beforeWrite = 'beforeWrite';\nexport var write = 'write';\nexport var afterWrite = 'afterWrite';\nexport var modifierPhases = [beforeRead, read, afterRead, beforeMain, main, afterMain, beforeWrite, write, afterWrite];","export default function getNodeName(element) {\n  return element ? (element.nodeName || '').toLowerCase() : null;\n}","export default function getWindow(node) {\n  if (node == null) {\n    return window;\n  }\n\n  if (node.toString() !== '[object Window]') {\n    var ownerDocument = node.ownerDocument;\n    return ownerDocument ? ownerDocument.defaultView || window : window;\n  }\n\n  return node;\n}","import getWindow from \"./getWindow.js\";\n\nfunction isElement(node) {\n  var OwnElement = getWindow(node).Element;\n  return node instanceof OwnElement || node instanceof Element;\n}\n\nfunction isHTMLElement(node) {\n  var OwnElement = getWindow(node).HTMLElement;\n  return node instanceof OwnElement || node instanceof HTMLElement;\n}\n\nfunction isShadowRoot(node) {\n  // IE 11 has no ShadowRoot\n  if (typeof ShadowRoot === 'undefined') {\n    return false;\n  }\n\n  var OwnElement = getWindow(node).ShadowRoot;\n  return node instanceof OwnElement || node instanceof ShadowRoot;\n}\n\nexport { isElement, isHTMLElement, isShadowRoot };","import getNodeName from \"../dom-utils/getNodeName.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // This modifier takes the styles prepared by the `computeStyles` modifier\n// and applies them to the HTMLElements such as popper and arrow\n\nfunction applyStyles(_ref) {\n  var state = _ref.state;\n  Object.keys(state.elements).forEach(function (name) {\n    var style = state.styles[name] || {};\n    var attributes = state.attributes[name] || {};\n    var element = state.elements[name]; // arrow is optional + virtual elements\n\n    if (!isHTMLElement(element) || !getNodeName(element)) {\n      return;\n    } // Flow doesn't support to extend this property, but it's the most\n    // effective way to apply styles to an HTMLElement\n    // $FlowFixMe[cannot-write]\n\n\n    Object.assign(element.style, style);\n    Object.keys(attributes).forEach(function (name) {\n      var value = attributes[name];\n\n      if (value === false) {\n        element.removeAttribute(name);\n      } else {\n        element.setAttribute(name, value === true ? '' : value);\n      }\n    });\n  });\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state;\n  var initialStyles = {\n    popper: {\n      position: state.options.strategy,\n      left: '0',\n      top: '0',\n      margin: '0'\n    },\n    arrow: {\n      position: 'absolute'\n    },\n    reference: {}\n  };\n  Object.assign(state.elements.popper.style, initialStyles.popper);\n  state.styles = initialStyles;\n\n  if (state.elements.arrow) {\n    Object.assign(state.elements.arrow.style, initialStyles.arrow);\n  }\n\n  return function () {\n    Object.keys(state.elements).forEach(function (name) {\n      var element = state.elements[name];\n      var attributes = state.attributes[name] || {};\n      var styleProperties = Object.keys(state.styles.hasOwnProperty(name) ? state.styles[name] : initialStyles[name]); // Set all values to an empty string to unset them\n\n      var style = styleProperties.reduce(function (style, property) {\n        style[property] = '';\n        return style;\n      }, {}); // arrow is optional + virtual elements\n\n      if (!isHTMLElement(element) || !getNodeName(element)) {\n        return;\n      }\n\n      Object.assign(element.style, style);\n      Object.keys(attributes).forEach(function (attribute) {\n        element.removeAttribute(attribute);\n      });\n    });\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'applyStyles',\n  enabled: true,\n  phase: 'write',\n  fn: applyStyles,\n  effect: effect,\n  requires: ['computeStyles']\n};","import { auto } from \"../enums.js\";\nexport default function getBasePlacement(placement) {\n  return placement.split('-')[0];\n}","export var max = Math.max;\nexport var min = Math.min;\nexport var round = Math.round;","export default function getUAString() {\n  var uaData = navigator.userAgentData;\n\n  if (uaData != null && uaData.brands && Array.isArray(uaData.brands)) {\n    return uaData.brands.map(function (item) {\n      return item.brand + \"/\" + item.version;\n    }).join(' ');\n  }\n\n  return navigator.userAgent;\n}","import getUAString from \"../utils/userAgent.js\";\nexport default function isLayoutViewport() {\n  return !/^((?!chrome|android).)*safari/i.test(getUAString());\n}","import { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport { round } from \"../utils/math.js\";\nimport getWindow from \"./getWindow.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getBoundingClientRect(element, includeScale, isFixedStrategy) {\n  if (includeScale === void 0) {\n    includeScale = false;\n  }\n\n  if (isFixedStrategy === void 0) {\n    isFixedStrategy = false;\n  }\n\n  var clientRect = element.getBoundingClientRect();\n  var scaleX = 1;\n  var scaleY = 1;\n\n  if (includeScale && isHTMLElement(element)) {\n    scaleX = element.offsetWidth > 0 ? round(clientRect.width) / element.offsetWidth || 1 : 1;\n    scaleY = element.offsetHeight > 0 ? round(clientRect.height) / element.offsetHeight || 1 : 1;\n  }\n\n  var _ref = isElement(element) ? getWindow(element) : window,\n      visualViewport = _ref.visualViewport;\n\n  var addVisualOffsets = !isLayoutViewport() && isFixedStrategy;\n  var x = (clientRect.left + (addVisualOffsets && visualViewport ? visualViewport.offsetLeft : 0)) / scaleX;\n  var y = (clientRect.top + (addVisualOffsets && visualViewport ? visualViewport.offsetTop : 0)) / scaleY;\n  var width = clientRect.width / scaleX;\n  var height = clientRect.height / scaleY;\n  return {\n    width: width,\n    height: height,\n    top: y,\n    right: x + width,\n    bottom: y + height,\n    left: x,\n    x: x,\n    y: y\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\"; // Returns the layout rect of an element relative to its offsetParent. Layout\n// means it doesn't take into account transforms.\n\nexport default function getLayoutRect(element) {\n  var clientRect = getBoundingClientRect(element); // Use the clientRect sizes if it's not been transformed.\n  // Fixes https://github.com/popperjs/popper-core/issues/1223\n\n  var width = element.offsetWidth;\n  var height = element.offsetHeight;\n\n  if (Math.abs(clientRect.width - width) <= 1) {\n    width = clientRect.width;\n  }\n\n  if (Math.abs(clientRect.height - height) <= 1) {\n    height = clientRect.height;\n  }\n\n  return {\n    x: element.offsetLeft,\n    y: element.offsetTop,\n    width: width,\n    height: height\n  };\n}","import { isShadowRoot } from \"./instanceOf.js\";\nexport default function contains(parent, child) {\n  var rootNode = child.getRootNode && child.getRootNode(); // First, attempt with faster native method\n\n  if (parent.contains(child)) {\n    return true;\n  } // then fallback to custom implementation with Shadow DOM support\n  else if (rootNode && isShadowRoot(rootNode)) {\n      var next = child;\n\n      do {\n        if (next && parent.isSameNode(next)) {\n          return true;\n        } // $FlowFixMe[prop-missing]: need a better way to handle this...\n\n\n        next = next.parentNode || next.host;\n      } while (next);\n    } // Give up, the result is false\n\n\n  return false;\n}","import getWindow from \"./getWindow.js\";\nexport default function getComputedStyle(element) {\n  return getWindow(element).getComputedStyle(element);\n}","import getNodeName from \"./getNodeName.js\";\nexport default function isTableElement(element) {\n  return ['table', 'td', 'th'].indexOf(getNodeName(element)) >= 0;\n}","import { isElement } from \"./instanceOf.js\";\nexport default function getDocumentElement(element) {\n  // $FlowFixMe[incompatible-return]: assume body is always available\n  return ((isElement(element) ? element.ownerDocument : // $FlowFixMe[prop-missing]\n  element.document) || window.document).documentElement;\n}","import getNodeName from \"./getNodeName.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport { isShadowRoot } from \"./instanceOf.js\";\nexport default function getParentNode(element) {\n  if (getNodeName(element) === 'html') {\n    return element;\n  }\n\n  return (// this is a quicker (but less type safe) way to save quite some bytes from the bundle\n    // $FlowFixMe[incompatible-return]\n    // $FlowFixMe[prop-missing]\n    element.assignedSlot || // step into the shadow DOM of the parent of a slotted node\n    element.parentNode || ( // DOM Element detected\n    isShadowRoot(element) ? element.host : null) || // ShadowRoot detected\n    // $FlowFixMe[incompatible-call]: HTMLElement is a Node\n    getDocumentElement(element) // fallback\n\n  );\n}","import getWindow from \"./getWindow.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isHTMLElement, isShadowRoot } from \"./instanceOf.js\";\nimport isTableElement from \"./isTableElement.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getUAString from \"../utils/userAgent.js\";\n\nfunction getTrueOffsetParent(element) {\n  if (!isHTMLElement(element) || // https://github.com/popperjs/popper-core/issues/837\n  getComputedStyle(element).position === 'fixed') {\n    return null;\n  }\n\n  return element.offsetParent;\n} // `.offsetParent` reports `null` for fixed elements, while absolute elements\n// return the containing block\n\n\nfunction getContainingBlock(element) {\n  var isFirefox = /firefox/i.test(getUAString());\n  var isIE = /Trident/i.test(getUAString());\n\n  if (isIE && isHTMLElement(element)) {\n    // In IE 9, 10 and 11 fixed elements containing block is always established by the viewport\n    var elementCss = getComputedStyle(element);\n\n    if (elementCss.position === 'fixed') {\n      return null;\n    }\n  }\n\n  var currentNode = getParentNode(element);\n\n  if (isShadowRoot(currentNode)) {\n    currentNode = currentNode.host;\n  }\n\n  while (isHTMLElement(currentNode) && ['html', 'body'].indexOf(getNodeName(currentNode)) < 0) {\n    var css = getComputedStyle(currentNode); // This is non-exhaustive but covers the most common CSS properties that\n    // create a containing block.\n    // https://developer.mozilla.org/en-US/docs/Web/CSS/Containing_block#identifying_the_containing_block\n\n    if (css.transform !== 'none' || css.perspective !== 'none' || css.contain === 'paint' || ['transform', 'perspective'].indexOf(css.willChange) !== -1 || isFirefox && css.willChange === 'filter' || isFirefox && css.filter && css.filter !== 'none') {\n      return currentNode;\n    } else {\n      currentNode = currentNode.parentNode;\n    }\n  }\n\n  return null;\n} // Gets the closest ancestor positioned element. Handles some edge cases,\n// such as table ancestors and cross browser bugs.\n\n\nexport default function getOffsetParent(element) {\n  var window = getWindow(element);\n  var offsetParent = getTrueOffsetParent(element);\n\n  while (offsetParent && isTableElement(offsetParent) && getComputedStyle(offsetParent).position === 'static') {\n    offsetParent = getTrueOffsetParent(offsetParent);\n  }\n\n  if (offsetParent && (getNodeName(offsetParent) === 'html' || getNodeName(offsetParent) === 'body' && getComputedStyle(offsetParent).position === 'static')) {\n    return window;\n  }\n\n  return offsetParent || getContainingBlock(element) || window;\n}","export default function getMainAxisFromPlacement(placement) {\n  return ['top', 'bottom'].indexOf(placement) >= 0 ? 'x' : 'y';\n}","import { max as mathMax, min as mathMin } from \"./math.js\";\nexport function within(min, value, max) {\n  return mathMax(min, mathMin(value, max));\n}\nexport function withinMaxClamp(min, value, max) {\n  var v = within(min, value, max);\n  return v > max ? max : v;\n}","import getFreshSideObject from \"./getFreshSideObject.js\";\nexport default function mergePaddingObject(paddingObject) {\n  return Object.assign({}, getFreshSideObject(), paddingObject);\n}","export default function getFreshSideObject() {\n  return {\n    top: 0,\n    right: 0,\n    bottom: 0,\n    left: 0\n  };\n}","export default function expandToHashMap(value, keys) {\n  return keys.reduce(function (hashMap, key) {\n    hashMap[key] = value;\n    return hashMap;\n  }, {});\n}","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport contains from \"../dom-utils/contains.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport { within } from \"../utils/within.js\";\nimport mergePaddingObject from \"../utils/mergePaddingObject.js\";\nimport expandToHashMap from \"../utils/expandToHashMap.js\";\nimport { left, right, basePlacements, top, bottom } from \"../enums.js\";\nimport { isHTMLElement } from \"../dom-utils/instanceOf.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar toPaddingObject = function toPaddingObject(padding, state) {\n  padding = typeof padding === 'function' ? padding(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : padding;\n  return mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n};\n\nfunction arrow(_ref) {\n  var _state$modifiersData$;\n\n  var state = _ref.state,\n      name = _ref.name,\n      options = _ref.options;\n  var arrowElement = state.elements.arrow;\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var basePlacement = getBasePlacement(state.placement);\n  var axis = getMainAxisFromPlacement(basePlacement);\n  var isVertical = [left, right].indexOf(basePlacement) >= 0;\n  var len = isVertical ? 'height' : 'width';\n\n  if (!arrowElement || !popperOffsets) {\n    return;\n  }\n\n  var paddingObject = toPaddingObject(options.padding, state);\n  var arrowRect = getLayoutRect(arrowElement);\n  var minProp = axis === 'y' ? top : left;\n  var maxProp = axis === 'y' ? bottom : right;\n  var endDiff = state.rects.reference[len] + state.rects.reference[axis] - popperOffsets[axis] - state.rects.popper[len];\n  var startDiff = popperOffsets[axis] - state.rects.reference[axis];\n  var arrowOffsetParent = getOffsetParent(arrowElement);\n  var clientSize = arrowOffsetParent ? axis === 'y' ? arrowOffsetParent.clientHeight || 0 : arrowOffsetParent.clientWidth || 0 : 0;\n  var centerToReference = endDiff / 2 - startDiff / 2; // Make sure the arrow doesn't overflow the popper if the center point is\n  // outside of the popper bounds\n\n  var min = paddingObject[minProp];\n  var max = clientSize - arrowRect[len] - paddingObject[maxProp];\n  var center = clientSize / 2 - arrowRect[len] / 2 + centerToReference;\n  var offset = within(min, center, max); // Prevents breaking syntax highlighting...\n\n  var axisProp = axis;\n  state.modifiersData[name] = (_state$modifiersData$ = {}, _state$modifiersData$[axisProp] = offset, _state$modifiersData$.centerOffset = offset - center, _state$modifiersData$);\n}\n\nfunction effect(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options;\n  var _options$element = options.element,\n      arrowElement = _options$element === void 0 ? '[data-popper-arrow]' : _options$element;\n\n  if (arrowElement == null) {\n    return;\n  } // CSS selector\n\n\n  if (typeof arrowElement === 'string') {\n    arrowElement = state.elements.popper.querySelector(arrowElement);\n\n    if (!arrowElement) {\n      return;\n    }\n  }\n\n  if (process.env.NODE_ENV !== \"production\") {\n    if (!isHTMLElement(arrowElement)) {\n      console.error(['Popper: \"arrow\" element must be an HTMLElement (not an SVGElement).', 'To use an SVG arrow, wrap it in an HTMLElement that will be used as', 'the arrow.'].join(' '));\n    }\n  }\n\n  if (!contains(state.elements.popper, arrowElement)) {\n    if (process.env.NODE_ENV !== \"production\") {\n      console.error(['Popper: \"arrow\" modifier\\'s `element` must be a child of the popper', 'element.'].join(' '));\n    }\n\n    return;\n  }\n\n  state.elements.arrow = arrowElement;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'arrow',\n  enabled: true,\n  phase: 'main',\n  fn: arrow,\n  effect: effect,\n  requires: ['popperOffsets'],\n  requiresIfExists: ['preventOverflow']\n};","export default function getVariation(placement) {\n  return placement.split('-')[1];\n}","import { top, left, right, bottom, end } from \"../enums.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport getWindow from \"../dom-utils/getWindow.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getComputedStyle from \"../dom-utils/getComputedStyle.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport { round } from \"../utils/math.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar unsetSides = {\n  top: 'auto',\n  right: 'auto',\n  bottom: 'auto',\n  left: 'auto'\n}; // Round the offsets to the nearest suitable subpixel based on the DPR.\n// Zooming can change the DPR, but it seems to report a value that will\n// cleanly divide the values into the appropriate subpixels.\n\nfunction roundOffsetsByDPR(_ref, win) {\n  var x = _ref.x,\n      y = _ref.y;\n  var dpr = win.devicePixelRatio || 1;\n  return {\n    x: round(x * dpr) / dpr || 0,\n    y: round(y * dpr) / dpr || 0\n  };\n}\n\nexport function mapToStyles(_ref2) {\n  var _Object$assign2;\n\n  var popper = _ref2.popper,\n      popperRect = _ref2.popperRect,\n      placement = _ref2.placement,\n      variation = _ref2.variation,\n      offsets = _ref2.offsets,\n      position = _ref2.position,\n      gpuAcceleration = _ref2.gpuAcceleration,\n      adaptive = _ref2.adaptive,\n      roundOffsets = _ref2.roundOffsets,\n      isFixed = _ref2.isFixed;\n  var _offsets$x = offsets.x,\n      x = _offsets$x === void 0 ? 0 : _offsets$x,\n      _offsets$y = offsets.y,\n      y = _offsets$y === void 0 ? 0 : _offsets$y;\n\n  var _ref3 = typeof roundOffsets === 'function' ? roundOffsets({\n    x: x,\n    y: y\n  }) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref3.x;\n  y = _ref3.y;\n  var hasX = offsets.hasOwnProperty('x');\n  var hasY = offsets.hasOwnProperty('y');\n  var sideX = left;\n  var sideY = top;\n  var win = window;\n\n  if (adaptive) {\n    var offsetParent = getOffsetParent(popper);\n    var heightProp = 'clientHeight';\n    var widthProp = 'clientWidth';\n\n    if (offsetParent === getWindow(popper)) {\n      offsetParent = getDocumentElement(popper);\n\n      if (getComputedStyle(offsetParent).position !== 'static' && position === 'absolute') {\n        heightProp = 'scrollHeight';\n        widthProp = 'scrollWidth';\n      }\n    } // $FlowFixMe[incompatible-cast]: force type refinement, we compare offsetParent with window above, but Flow doesn't detect it\n\n\n    offsetParent = offsetParent;\n\n    if (placement === top || (placement === left || placement === right) && variation === end) {\n      sideY = bottom;\n      var offsetY = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.height : // $FlowFixMe[prop-missing]\n      offsetParent[heightProp];\n      y -= offsetY - popperRect.height;\n      y *= gpuAcceleration ? 1 : -1;\n    }\n\n    if (placement === left || (placement === top || placement === bottom) && variation === end) {\n      sideX = right;\n      var offsetX = isFixed && offsetParent === win && win.visualViewport ? win.visualViewport.width : // $FlowFixMe[prop-missing]\n      offsetParent[widthProp];\n      x -= offsetX - popperRect.width;\n      x *= gpuAcceleration ? 1 : -1;\n    }\n  }\n\n  var commonStyles = Object.assign({\n    position: position\n  }, adaptive && unsetSides);\n\n  var _ref4 = roundOffsets === true ? roundOffsetsByDPR({\n    x: x,\n    y: y\n  }, getWindow(popper)) : {\n    x: x,\n    y: y\n  };\n\n  x = _ref4.x;\n  y = _ref4.y;\n\n  if (gpuAcceleration) {\n    var _Object$assign;\n\n    return Object.assign({}, commonStyles, (_Object$assign = {}, _Object$assign[sideY] = hasY ? '0' : '', _Object$assign[sideX] = hasX ? '0' : '', _Object$assign.transform = (win.devicePixelRatio || 1) <= 1 ? \"translate(\" + x + \"px, \" + y + \"px)\" : \"translate3d(\" + x + \"px, \" + y + \"px, 0)\", _Object$assign));\n  }\n\n  return Object.assign({}, commonStyles, (_Object$assign2 = {}, _Object$assign2[sideY] = hasY ? y + \"px\" : '', _Object$assign2[sideX] = hasX ? x + \"px\" : '', _Object$assign2.transform = '', _Object$assign2));\n}\n\nfunction computeStyles(_ref5) {\n  var state = _ref5.state,\n      options = _ref5.options;\n  var _options$gpuAccelerat = options.gpuAcceleration,\n      gpuAcceleration = _options$gpuAccelerat === void 0 ? true : _options$gpuAccelerat,\n      _options$adaptive = options.adaptive,\n      adaptive = _options$adaptive === void 0 ? true : _options$adaptive,\n      _options$roundOffsets = options.roundOffsets,\n      roundOffsets = _options$roundOffsets === void 0 ? true : _options$roundOffsets;\n\n  if (process.env.NODE_ENV !== \"production\") {\n    var transitionProperty = getComputedStyle(state.elements.popper).transitionProperty || '';\n\n    if (adaptive && ['transform', 'top', 'right', 'bottom', 'left'].some(function (property) {\n      return transitionProperty.indexOf(property) >= 0;\n    })) {\n      console.warn(['Popper: Detected CSS transitions on at least one of the following', 'CSS properties: \"transform\", \"top\", \"right\", \"bottom\", \"left\".', '\\n\\n', 'Disable the \"computeStyles\" modifier\\'s `adaptive` option to allow', 'for smooth transitions, or remove these properties from the CSS', 'transition declaration on the popper element if only transitioning', 'opacity or background-color for example.', '\\n\\n', 'We recommend using the popper element as a wrapper around an inner', 'element that can have any CSS property transitioned for animations.'].join(' '));\n    }\n  }\n\n  var commonStyles = {\n    placement: getBasePlacement(state.placement),\n    variation: getVariation(state.placement),\n    popper: state.elements.popper,\n    popperRect: state.rects.popper,\n    gpuAcceleration: gpuAcceleration,\n    isFixed: state.options.strategy === 'fixed'\n  };\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.styles.popper = Object.assign({}, state.styles.popper, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.popperOffsets,\n      position: state.options.strategy,\n      adaptive: adaptive,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  if (state.modifiersData.arrow != null) {\n    state.styles.arrow = Object.assign({}, state.styles.arrow, mapToStyles(Object.assign({}, commonStyles, {\n      offsets: state.modifiersData.arrow,\n      position: 'absolute',\n      adaptive: false,\n      roundOffsets: roundOffsets\n    })));\n  }\n\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-placement': state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'computeStyles',\n  enabled: true,\n  phase: 'beforeWrite',\n  fn: computeStyles,\n  data: {}\n};","import getWindow from \"../dom-utils/getWindow.js\"; // eslint-disable-next-line import/no-unused-modules\n\nvar passive = {\n  passive: true\n};\n\nfunction effect(_ref) {\n  var state = _ref.state,\n      instance = _ref.instance,\n      options = _ref.options;\n  var _options$scroll = options.scroll,\n      scroll = _options$scroll === void 0 ? true : _options$scroll,\n      _options$resize = options.resize,\n      resize = _options$resize === void 0 ? true : _options$resize;\n  var window = getWindow(state.elements.popper);\n  var scrollParents = [].concat(state.scrollParents.reference, state.scrollParents.popper);\n\n  if (scroll) {\n    scrollParents.forEach(function (scrollParent) {\n      scrollParent.addEventListener('scroll', instance.update, passive);\n    });\n  }\n\n  if (resize) {\n    window.addEventListener('resize', instance.update, passive);\n  }\n\n  return function () {\n    if (scroll) {\n      scrollParents.forEach(function (scrollParent) {\n        scrollParent.removeEventListener('scroll', instance.update, passive);\n      });\n    }\n\n    if (resize) {\n      window.removeEventListener('resize', instance.update, passive);\n    }\n  };\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'eventListeners',\n  enabled: true,\n  phase: 'write',\n  fn: function fn() {},\n  effect: effect,\n  data: {}\n};","var hash = {\n  left: 'right',\n  right: 'left',\n  bottom: 'top',\n  top: 'bottom'\n};\nexport default function getOppositePlacement(placement) {\n  return placement.replace(/left|right|bottom|top/g, function (matched) {\n    return hash[matched];\n  });\n}","var hash = {\n  start: 'end',\n  end: 'start'\n};\nexport default function getOppositeVariationPlacement(placement) {\n  return placement.replace(/start|end/g, function (matched) {\n    return hash[matched];\n  });\n}","import getWindow from \"./getWindow.js\";\nexport default function getWindowScroll(node) {\n  var win = getWindow(node);\n  var scrollLeft = win.pageXOffset;\n  var scrollTop = win.pageYOffset;\n  return {\n    scrollLeft: scrollLeft,\n    scrollTop: scrollTop\n  };\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nexport default function getWindowScrollBarX(element) {\n  // If <html> has a CSS width greater than the viewport, then this will be\n  // incorrect for RTL.\n  // Popper 1 is broken in this case and never had a bug report so let's assume\n  // it's not an issue. I don't think anyone ever specifies width on <html>\n  // anyway.\n  // Browsers where the left scrollbar doesn't cause an issue report `0` for\n  // this (e.g. Edge 2019, IE11, Safari)\n  return getBoundingClientRect(getDocumentElement(element)).left + getWindowScroll(element).scrollLeft;\n}","import getComputedStyle from \"./getComputedStyle.js\";\nexport default function isScrollParent(element) {\n  // Firefox wants us to check `-x` and `-y` variations as well\n  var _getComputedStyle = getComputedStyle(element),\n      overflow = _getComputedStyle.overflow,\n      overflowX = _getComputedStyle.overflowX,\n      overflowY = _getComputedStyle.overflowY;\n\n  return /auto|scroll|overlay|hidden/.test(overflow + overflowY + overflowX);\n}","import getParentNode from \"./getParentNode.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nexport default function getScrollParent(node) {\n  if (['html', 'body', '#document'].indexOf(getNodeName(node)) >= 0) {\n    // $FlowFixMe[incompatible-return]: assume body is always available\n    return node.ownerDocument.body;\n  }\n\n  if (isHTMLElement(node) && isScrollParent(node)) {\n    return node;\n  }\n\n  return getScrollParent(getParentNode(node));\n}","import getScrollParent from \"./getScrollParent.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport getWindow from \"./getWindow.js\";\nimport isScrollParent from \"./isScrollParent.js\";\n/*\ngiven a DOM element, return the list of all scroll parents, up the list of ancesors\nuntil we get to the top window object. This list is what we attach scroll listeners\nto, because if any of these parent elements scroll, we'll need to re-calculate the\nreference element's position.\n*/\n\nexport default function listScrollParents(element, list) {\n  var _element$ownerDocumen;\n\n  if (list === void 0) {\n    list = [];\n  }\n\n  var scrollParent = getScrollParent(element);\n  var isBody = scrollParent === ((_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body);\n  var win = getWindow(scrollParent);\n  var target = isBody ? [win].concat(win.visualViewport || [], isScrollParent(scrollParent) ? scrollParent : []) : scrollParent;\n  var updatedList = list.concat(target);\n  return isBody ? updatedList : // $FlowFixMe[incompatible-call]: isBody tells us target will be an HTMLElement here\n  updatedList.concat(listScrollParents(getParentNode(target)));\n}","export default function rectToClientRect(rect) {\n  return Object.assign({}, rect, {\n    left: rect.x,\n    top: rect.y,\n    right: rect.x + rect.width,\n    bottom: rect.y + rect.height\n  });\n}","import { viewport } from \"../enums.js\";\nimport getViewportRect from \"./getViewportRect.js\";\nimport getDocumentRect from \"./getDocumentRect.js\";\nimport listScrollParents from \"./listScrollParents.js\";\nimport getOffsetParent from \"./getOffsetParent.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport { isElement, isHTMLElement } from \"./instanceOf.js\";\nimport getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getParentNode from \"./getParentNode.js\";\nimport contains from \"./contains.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport rectToClientRect from \"../utils/rectToClientRect.js\";\nimport { max, min } from \"../utils/math.js\";\n\nfunction getInnerBoundingClientRect(element, strategy) {\n  var rect = getBoundingClientRect(element, false, strategy === 'fixed');\n  rect.top = rect.top + element.clientTop;\n  rect.left = rect.left + element.clientLeft;\n  rect.bottom = rect.top + element.clientHeight;\n  rect.right = rect.left + element.clientWidth;\n  rect.width = element.clientWidth;\n  rect.height = element.clientHeight;\n  rect.x = rect.left;\n  rect.y = rect.top;\n  return rect;\n}\n\nfunction getClientRectFromMixedType(element, clippingParent, strategy) {\n  return clippingParent === viewport ? rectToClientRect(getViewportRect(element, strategy)) : isElement(clippingParent) ? getInnerBoundingClientRect(clippingParent, strategy) : rectToClientRect(getDocumentRect(getDocumentElement(element)));\n} // A \"clipping parent\" is an overflowable container with the characteristic of\n// clipping (or hiding) overflowing elements with a position different from\n// `initial`\n\n\nfunction getClippingParents(element) {\n  var clippingParents = listScrollParents(getParentNode(element));\n  var canEscapeClipping = ['absolute', 'fixed'].indexOf(getComputedStyle(element).position) >= 0;\n  var clipperElement = canEscapeClipping && isHTMLElement(element) ? getOffsetParent(element) : element;\n\n  if (!isElement(clipperElement)) {\n    return [];\n  } // $FlowFixMe[incompatible-return]: https://github.com/facebook/flow/issues/1414\n\n\n  return clippingParents.filter(function (clippingParent) {\n    return isElement(clippingParent) && contains(clippingParent, clipperElement) && getNodeName(clippingParent) !== 'body';\n  });\n} // Gets the maximum area that the element is visible in due to any number of\n// clipping parents\n\n\nexport default function getClippingRect(element, boundary, rootBoundary, strategy) {\n  var mainClippingParents = boundary === 'clippingParents' ? getClippingParents(element) : [].concat(boundary);\n  var clippingParents = [].concat(mainClippingParents, [rootBoundary]);\n  var firstClippingParent = clippingParents[0];\n  var clippingRect = clippingParents.reduce(function (accRect, clippingParent) {\n    var rect = getClientRectFromMixedType(element, clippingParent, strategy);\n    accRect.top = max(rect.top, accRect.top);\n    accRect.right = min(rect.right, accRect.right);\n    accRect.bottom = min(rect.bottom, accRect.bottom);\n    accRect.left = max(rect.left, accRect.left);\n    return accRect;\n  }, getClientRectFromMixedType(element, firstClippingParent, strategy));\n  clippingRect.width = clippingRect.right - clippingRect.left;\n  clippingRect.height = clippingRect.bottom - clippingRect.top;\n  clippingRect.x = clippingRect.left;\n  clippingRect.y = clippingRect.top;\n  return clippingRect;\n}","import getWindow from \"./getWindow.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport isLayoutViewport from \"./isLayoutViewport.js\";\nexport default function getViewportRect(element, strategy) {\n  var win = getWindow(element);\n  var html = getDocumentElement(element);\n  var visualViewport = win.visualViewport;\n  var width = html.clientWidth;\n  var height = html.clientHeight;\n  var x = 0;\n  var y = 0;\n\n  if (visualViewport) {\n    width = visualViewport.width;\n    height = visualViewport.height;\n    var layoutViewport = isLayoutViewport();\n\n    if (layoutViewport || !layoutViewport && strategy === 'fixed') {\n      x = visualViewport.offsetLeft;\n      y = visualViewport.offsetTop;\n    }\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x + getWindowScrollBarX(element),\n    y: y\n  };\n}","import getDocumentElement from \"./getDocumentElement.js\";\nimport getComputedStyle from \"./getComputedStyle.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getWindowScroll from \"./getWindowScroll.js\";\nimport { max } from \"../utils/math.js\"; // Gets the entire size of the scrollable document area, even extending outside\n// of the `<html>` and `<body>` rect bounds if horizontally scrollable\n\nexport default function getDocumentRect(element) {\n  var _element$ownerDocumen;\n\n  var html = getDocumentElement(element);\n  var winScroll = getWindowScroll(element);\n  var body = (_element$ownerDocumen = element.ownerDocument) == null ? void 0 : _element$ownerDocumen.body;\n  var width = max(html.scrollWidth, html.clientWidth, body ? body.scrollWidth : 0, body ? body.clientWidth : 0);\n  var height = max(html.scrollHeight, html.clientHeight, body ? body.scrollHeight : 0, body ? body.clientHeight : 0);\n  var x = -winScroll.scrollLeft + getWindowScrollBarX(element);\n  var y = -winScroll.scrollTop;\n\n  if (getComputedStyle(body || html).direction === 'rtl') {\n    x += max(html.clientWidth, body ? body.clientWidth : 0) - width;\n  }\n\n  return {\n    width: width,\n    height: height,\n    x: x,\n    y: y\n  };\n}","import getBasePlacement from \"./getBasePlacement.js\";\nimport getVariation from \"./getVariation.js\";\nimport getMainAxisFromPlacement from \"./getMainAxisFromPlacement.js\";\nimport { top, right, bottom, left, start, end } from \"../enums.js\";\nexport default function computeOffsets(_ref) {\n  var reference = _ref.reference,\n      element = _ref.element,\n      placement = _ref.placement;\n  var basePlacement = placement ? getBasePlacement(placement) : null;\n  var variation = placement ? getVariation(placement) : null;\n  var commonX = reference.x + reference.width / 2 - element.width / 2;\n  var commonY = reference.y + reference.height / 2 - element.height / 2;\n  var offsets;\n\n  switch (basePlacement) {\n    case top:\n      offsets = {\n        x: commonX,\n        y: reference.y - element.height\n      };\n      break;\n\n    case bottom:\n      offsets = {\n        x: commonX,\n        y: reference.y + reference.height\n      };\n      break;\n\n    case right:\n      offsets = {\n        x: reference.x + reference.width,\n        y: commonY\n      };\n      break;\n\n    case left:\n      offsets = {\n        x: reference.x - element.width,\n        y: commonY\n      };\n      break;\n\n    default:\n      offsets = {\n        x: reference.x,\n        y: reference.y\n      };\n  }\n\n  var mainAxis = basePlacement ? getMainAxisFromPlacement(basePlacement) : null;\n\n  if (mainAxis != null) {\n    var len = mainAxis === 'y' ? 'height' : 'width';\n\n    switch (variation) {\n      case start:\n        offsets[mainAxis] = offsets[mainAxis] - (reference[len] / 2 - element[len] / 2);\n        break;\n\n      case end:\n        offsets[mainAxis] = offsets[mainAxis] + (reference[len] / 2 - element[len] / 2);\n        break;\n\n      default:\n    }\n  }\n\n  return offsets;\n}","import getClippingRect from \"../dom-utils/getClippingRect.js\";\nimport getDocumentElement from \"../dom-utils/getDocumentElement.js\";\nimport getBoundingClientRect from \"../dom-utils/getBoundingClientRect.js\";\nimport computeOffsets from \"./computeOffsets.js\";\nimport rectToClientRect from \"./rectToClientRect.js\";\nimport { clippingParents, reference, popper, bottom, top, right, basePlacements, viewport } from \"../enums.js\";\nimport { isElement } from \"../dom-utils/instanceOf.js\";\nimport mergePaddingObject from \"./mergePaddingObject.js\";\nimport expandToHashMap from \"./expandToHashMap.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport default function detectOverflow(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      _options$placement = _options.placement,\n      placement = _options$placement === void 0 ? state.placement : _options$placement,\n      _options$strategy = _options.strategy,\n      strategy = _options$strategy === void 0 ? state.strategy : _options$strategy,\n      _options$boundary = _options.boundary,\n      boundary = _options$boundary === void 0 ? clippingParents : _options$boundary,\n      _options$rootBoundary = _options.rootBoundary,\n      rootBoundary = _options$rootBoundary === void 0 ? viewport : _options$rootBoundary,\n      _options$elementConte = _options.elementContext,\n      elementContext = _options$elementConte === void 0 ? popper : _options$elementConte,\n      _options$altBoundary = _options.altBoundary,\n      altBoundary = _options$altBoundary === void 0 ? false : _options$altBoundary,\n      _options$padding = _options.padding,\n      padding = _options$padding === void 0 ? 0 : _options$padding;\n  var paddingObject = mergePaddingObject(typeof padding !== 'number' ? padding : expandToHashMap(padding, basePlacements));\n  var altContext = elementContext === popper ? reference : popper;\n  var popperRect = state.rects.popper;\n  var element = state.elements[altBoundary ? altContext : elementContext];\n  var clippingClientRect = getClippingRect(isElement(element) ? element : element.contextElement || getDocumentElement(state.elements.popper), boundary, rootBoundary, strategy);\n  var referenceClientRect = getBoundingClientRect(state.elements.reference);\n  var popperOffsets = computeOffsets({\n    reference: referenceClientRect,\n    element: popperRect,\n    strategy: 'absolute',\n    placement: placement\n  });\n  var popperClientRect = rectToClientRect(Object.assign({}, popperRect, popperOffsets));\n  var elementClientRect = elementContext === popper ? popperClientRect : referenceClientRect; // positive = overflowing the clipping rect\n  // 0 or negative = within the clipping rect\n\n  var overflowOffsets = {\n    top: clippingClientRect.top - elementClientRect.top + paddingObject.top,\n    bottom: elementClientRect.bottom - clippingClientRect.bottom + paddingObject.bottom,\n    left: clippingClientRect.left - elementClientRect.left + paddingObject.left,\n    right: elementClientRect.right - clippingClientRect.right + paddingObject.right\n  };\n  var offsetData = state.modifiersData.offset; // Offsets can be applied only to the popper element\n\n  if (elementContext === popper && offsetData) {\n    var offset = offsetData[placement];\n    Object.keys(overflowOffsets).forEach(function (key) {\n      var multiply = [right, bottom].indexOf(key) >= 0 ? 1 : -1;\n      var axis = [top, bottom].indexOf(key) >= 0 ? 'y' : 'x';\n      overflowOffsets[key] += offset[axis] * multiply;\n    });\n  }\n\n  return overflowOffsets;\n}","import getOppositePlacement from \"../utils/getOppositePlacement.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getOppositeVariationPlacement from \"../utils/getOppositeVariationPlacement.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport computeAutoPlacement from \"../utils/computeAutoPlacement.js\";\nimport { bottom, top, start, right, left, auto } from \"../enums.js\";\nimport getVariation from \"../utils/getVariation.js\"; // eslint-disable-next-line import/no-unused-modules\n\nfunction getExpandedFallbackPlacements(placement) {\n  if (getBasePlacement(placement) === auto) {\n    return [];\n  }\n\n  var oppositePlacement = getOppositePlacement(placement);\n  return [getOppositeVariationPlacement(placement), oppositePlacement, getOppositeVariationPlacement(oppositePlacement)];\n}\n\nfunction flip(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n\n  if (state.modifiersData[name]._skip) {\n    return;\n  }\n\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? true : _options$altAxis,\n      specifiedFallbackPlacements = options.fallbackPlacements,\n      padding = options.padding,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      _options$flipVariatio = options.flipVariations,\n      flipVariations = _options$flipVariatio === void 0 ? true : _options$flipVariatio,\n      allowedAutoPlacements = options.allowedAutoPlacements;\n  var preferredPlacement = state.options.placement;\n  var basePlacement = getBasePlacement(preferredPlacement);\n  var isBasePlacement = basePlacement === preferredPlacement;\n  var fallbackPlacements = specifiedFallbackPlacements || (isBasePlacement || !flipVariations ? [getOppositePlacement(preferredPlacement)] : getExpandedFallbackPlacements(preferredPlacement));\n  var placements = [preferredPlacement].concat(fallbackPlacements).reduce(function (acc, placement) {\n    return acc.concat(getBasePlacement(placement) === auto ? computeAutoPlacement(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding,\n      flipVariations: flipVariations,\n      allowedAutoPlacements: allowedAutoPlacements\n    }) : placement);\n  }, []);\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var checksMap = new Map();\n  var makeFallbackChecks = true;\n  var firstFittingPlacement = placements[0];\n\n  for (var i = 0; i < placements.length; i++) {\n    var placement = placements[i];\n\n    var _basePlacement = getBasePlacement(placement);\n\n    var isStartVariation = getVariation(placement) === start;\n    var isVertical = [top, bottom].indexOf(_basePlacement) >= 0;\n    var len = isVertical ? 'width' : 'height';\n    var overflow = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      altBoundary: altBoundary,\n      padding: padding\n    });\n    var mainVariationSide = isVertical ? isStartVariation ? right : left : isStartVariation ? bottom : top;\n\n    if (referenceRect[len] > popperRect[len]) {\n      mainVariationSide = getOppositePlacement(mainVariationSide);\n    }\n\n    var altVariationSide = getOppositePlacement(mainVariationSide);\n    var checks = [];\n\n    if (checkMainAxis) {\n      checks.push(overflow[_basePlacement] <= 0);\n    }\n\n    if (checkAltAxis) {\n      checks.push(overflow[mainVariationSide] <= 0, overflow[altVariationSide] <= 0);\n    }\n\n    if (checks.every(function (check) {\n      return check;\n    })) {\n      firstFittingPlacement = placement;\n      makeFallbackChecks = false;\n      break;\n    }\n\n    checksMap.set(placement, checks);\n  }\n\n  if (makeFallbackChecks) {\n    // `2` may be desired in some cases – research later\n    var numberOfChecks = flipVariations ? 3 : 1;\n\n    var _loop = function _loop(_i) {\n      var fittingPlacement = placements.find(function (placement) {\n        var checks = checksMap.get(placement);\n\n        if (checks) {\n          return checks.slice(0, _i).every(function (check) {\n            return check;\n          });\n        }\n      });\n\n      if (fittingPlacement) {\n        firstFittingPlacement = fittingPlacement;\n        return \"break\";\n      }\n    };\n\n    for (var _i = numberOfChecks; _i > 0; _i--) {\n      var _ret = _loop(_i);\n\n      if (_ret === \"break\") break;\n    }\n  }\n\n  if (state.placement !== firstFittingPlacement) {\n    state.modifiersData[name]._skip = true;\n    state.placement = firstFittingPlacement;\n    state.reset = true;\n  }\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'flip',\n  enabled: true,\n  phase: 'main',\n  fn: flip,\n  requiresIfExists: ['offset'],\n  data: {\n    _skip: false\n  }\n};","import getVariation from \"./getVariation.js\";\nimport { variationPlacements, basePlacements, placements as allPlacements } from \"../enums.js\";\nimport detectOverflow from \"./detectOverflow.js\";\nimport getBasePlacement from \"./getBasePlacement.js\";\nexport default function computeAutoPlacement(state, options) {\n  if (options === void 0) {\n    options = {};\n  }\n\n  var _options = options,\n      placement = _options.placement,\n      boundary = _options.boundary,\n      rootBoundary = _options.rootBoundary,\n      padding = _options.padding,\n      flipVariations = _options.flipVariations,\n      _options$allowedAutoP = _options.allowedAutoPlacements,\n      allowedAutoPlacements = _options$allowedAutoP === void 0 ? allPlacements : _options$allowedAutoP;\n  var variation = getVariation(placement);\n  var placements = variation ? flipVariations ? variationPlacements : variationPlacements.filter(function (placement) {\n    return getVariation(placement) === variation;\n  }) : basePlacements;\n  var allowedPlacements = placements.filter(function (placement) {\n    return allowedAutoPlacements.indexOf(placement) >= 0;\n  });\n\n  if (allowedPlacements.length === 0) {\n    allowedPlacements = placements;\n\n    if (process.env.NODE_ENV !== \"production\") {\n      console.error(['Popper: The `allowedAutoPlacements` option did not allow any', 'placements. Ensure the `placement` option matches the variation', 'of the allowed placements.', 'For example, \"auto\" cannot be used to allow \"bottom-start\".', 'Use \"auto-start\" instead.'].join(' '));\n    }\n  } // $FlowFixMe[incompatible-type]: Flow seems to have problems with two array unions...\n\n\n  var overflows = allowedPlacements.reduce(function (acc, placement) {\n    acc[placement] = detectOverflow(state, {\n      placement: placement,\n      boundary: boundary,\n      rootBoundary: rootBoundary,\n      padding: padding\n    })[getBasePlacement(placement)];\n    return acc;\n  }, {});\n  return Object.keys(overflows).sort(function (a, b) {\n    return overflows[a] - overflows[b];\n  });\n}","import { top, bottom, left, right } from \"../enums.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\n\nfunction getSideOffsets(overflow, rect, preventedOffsets) {\n  if (preventedOffsets === void 0) {\n    preventedOffsets = {\n      x: 0,\n      y: 0\n    };\n  }\n\n  return {\n    top: overflow.top - rect.height - preventedOffsets.y,\n    right: overflow.right - rect.width + preventedOffsets.x,\n    bottom: overflow.bottom - rect.height + preventedOffsets.y,\n    left: overflow.left - rect.width - preventedOffsets.x\n  };\n}\n\nfunction isAnySideFullyClipped(overflow) {\n  return [top, right, bottom, left].some(function (side) {\n    return overflow[side] >= 0;\n  });\n}\n\nfunction hide(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var preventedOffsets = state.modifiersData.preventOverflow;\n  var referenceOverflow = detectOverflow(state, {\n    elementContext: 'reference'\n  });\n  var popperAltOverflow = detectOverflow(state, {\n    altBoundary: true\n  });\n  var referenceClippingOffsets = getSideOffsets(referenceOverflow, referenceRect);\n  var popperEscapeOffsets = getSideOffsets(popperAltOverflow, popperRect, preventedOffsets);\n  var isReferenceHidden = isAnySideFullyClipped(referenceClippingOffsets);\n  var hasPopperEscaped = isAnySideFullyClipped(popperEscapeOffsets);\n  state.modifiersData[name] = {\n    referenceClippingOffsets: referenceClippingOffsets,\n    popperEscapeOffsets: popperEscapeOffsets,\n    isReferenceHidden: isReferenceHidden,\n    hasPopperEscaped: hasPopperEscaped\n  };\n  state.attributes.popper = Object.assign({}, state.attributes.popper, {\n    'data-popper-reference-hidden': isReferenceHidden,\n    'data-popper-escaped': hasPopperEscaped\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'hide',\n  enabled: true,\n  phase: 'main',\n  requiresIfExists: ['preventOverflow'],\n  fn: hide\n};","import getBasePlacement from \"../utils/getBasePlacement.js\";\nimport { top, left, right, placements } from \"../enums.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport function distanceAndSkiddingToXY(placement, rects, offset) {\n  var basePlacement = getBasePlacement(placement);\n  var invertDistance = [left, top].indexOf(basePlacement) >= 0 ? -1 : 1;\n\n  var _ref = typeof offset === 'function' ? offset(Object.assign({}, rects, {\n    placement: placement\n  })) : offset,\n      skidding = _ref[0],\n      distance = _ref[1];\n\n  skidding = skidding || 0;\n  distance = (distance || 0) * invertDistance;\n  return [left, right].indexOf(basePlacement) >= 0 ? {\n    x: distance,\n    y: skidding\n  } : {\n    x: skidding,\n    y: distance\n  };\n}\n\nfunction offset(_ref2) {\n  var state = _ref2.state,\n      options = _ref2.options,\n      name = _ref2.name;\n  var _options$offset = options.offset,\n      offset = _options$offset === void 0 ? [0, 0] : _options$offset;\n  var data = placements.reduce(function (acc, placement) {\n    acc[placement] = distanceAndSkiddingToXY(placement, state.rects, offset);\n    return acc;\n  }, {});\n  var _data$state$placement = data[state.placement],\n      x = _data$state$placement.x,\n      y = _data$state$placement.y;\n\n  if (state.modifiersData.popperOffsets != null) {\n    state.modifiersData.popperOffsets.x += x;\n    state.modifiersData.popperOffsets.y += y;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'offset',\n  enabled: true,\n  phase: 'main',\n  requires: ['popperOffsets'],\n  fn: offset\n};","import computeOffsets from \"../utils/computeOffsets.js\";\n\nfunction popperOffsets(_ref) {\n  var state = _ref.state,\n      name = _ref.name;\n  // Offsets are the actual position the popper needs to have to be\n  // properly positioned near its reference element\n  // This is the most basic placement, and will be adjusted by\n  // the modifiers in the next step\n  state.modifiersData[name] = computeOffsets({\n    reference: state.rects.reference,\n    element: state.rects.popper,\n    strategy: 'absolute',\n    placement: state.placement\n  });\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'popperOffsets',\n  enabled: true,\n  phase: 'read',\n  fn: popperOffsets,\n  data: {}\n};","import { top, left, right, bottom, start } from \"../enums.js\";\nimport getBasePlacement from \"../utils/getBasePlacement.js\";\nimport getMainAxisFromPlacement from \"../utils/getMainAxisFromPlacement.js\";\nimport getAltAxis from \"../utils/getAltAxis.js\";\nimport { within, withinMaxClamp } from \"../utils/within.js\";\nimport getLayoutRect from \"../dom-utils/getLayoutRect.js\";\nimport getOffsetParent from \"../dom-utils/getOffsetParent.js\";\nimport detectOverflow from \"../utils/detectOverflow.js\";\nimport getVariation from \"../utils/getVariation.js\";\nimport getFreshSideObject from \"../utils/getFreshSideObject.js\";\nimport { min as mathMin, max as mathMax } from \"../utils/math.js\";\n\nfunction preventOverflow(_ref) {\n  var state = _ref.state,\n      options = _ref.options,\n      name = _ref.name;\n  var _options$mainAxis = options.mainAxis,\n      checkMainAxis = _options$mainAxis === void 0 ? true : _options$mainAxis,\n      _options$altAxis = options.altAxis,\n      checkAltAxis = _options$altAxis === void 0 ? false : _options$altAxis,\n      boundary = options.boundary,\n      rootBoundary = options.rootBoundary,\n      altBoundary = options.altBoundary,\n      padding = options.padding,\n      _options$tether = options.tether,\n      tether = _options$tether === void 0 ? true : _options$tether,\n      _options$tetherOffset = options.tetherOffset,\n      tetherOffset = _options$tetherOffset === void 0 ? 0 : _options$tetherOffset;\n  var overflow = detectOverflow(state, {\n    boundary: boundary,\n    rootBoundary: rootBoundary,\n    padding: padding,\n    altBoundary: altBoundary\n  });\n  var basePlacement = getBasePlacement(state.placement);\n  var variation = getVariation(state.placement);\n  var isBasePlacement = !variation;\n  var mainAxis = getMainAxisFromPlacement(basePlacement);\n  var altAxis = getAltAxis(mainAxis);\n  var popperOffsets = state.modifiersData.popperOffsets;\n  var referenceRect = state.rects.reference;\n  var popperRect = state.rects.popper;\n  var tetherOffsetValue = typeof tetherOffset === 'function' ? tetherOffset(Object.assign({}, state.rects, {\n    placement: state.placement\n  })) : tetherOffset;\n  var normalizedTetherOffsetValue = typeof tetherOffsetValue === 'number' ? {\n    mainAxis: tetherOffsetValue,\n    altAxis: tetherOffsetValue\n  } : Object.assign({\n    mainAxis: 0,\n    altAxis: 0\n  }, tetherOffsetValue);\n  var offsetModifierState = state.modifiersData.offset ? state.modifiersData.offset[state.placement] : null;\n  var data = {\n    x: 0,\n    y: 0\n  };\n\n  if (!popperOffsets) {\n    return;\n  }\n\n  if (checkMainAxis) {\n    var _offsetModifierState$;\n\n    var mainSide = mainAxis === 'y' ? top : left;\n    var altSide = mainAxis === 'y' ? bottom : right;\n    var len = mainAxis === 'y' ? 'height' : 'width';\n    var offset = popperOffsets[mainAxis];\n    var min = offset + overflow[mainSide];\n    var max = offset - overflow[altSide];\n    var additive = tether ? -popperRect[len] / 2 : 0;\n    var minLen = variation === start ? referenceRect[len] : popperRect[len];\n    var maxLen = variation === start ? -popperRect[len] : -referenceRect[len]; // We need to include the arrow in the calculation so the arrow doesn't go\n    // outside the reference bounds\n\n    var arrowElement = state.elements.arrow;\n    var arrowRect = tether && arrowElement ? getLayoutRect(arrowElement) : {\n      width: 0,\n      height: 0\n    };\n    var arrowPaddingObject = state.modifiersData['arrow#persistent'] ? state.modifiersData['arrow#persistent'].padding : getFreshSideObject();\n    var arrowPaddingMin = arrowPaddingObject[mainSide];\n    var arrowPaddingMax = arrowPaddingObject[altSide]; // If the reference length is smaller than the arrow length, we don't want\n    // to include its full size in the calculation. If the reference is small\n    // and near the edge of a boundary, the popper can overflow even if the\n    // reference is not overflowing as well (e.g. virtual elements with no\n    // width or height)\n\n    var arrowLen = within(0, referenceRect[len], arrowRect[len]);\n    var minOffset = isBasePlacement ? referenceRect[len] / 2 - additive - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis : minLen - arrowLen - arrowPaddingMin - normalizedTetherOffsetValue.mainAxis;\n    var maxOffset = isBasePlacement ? -referenceRect[len] / 2 + additive + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis : maxLen + arrowLen + arrowPaddingMax + normalizedTetherOffsetValue.mainAxis;\n    var arrowOffsetParent = state.elements.arrow && getOffsetParent(state.elements.arrow);\n    var clientOffset = arrowOffsetParent ? mainAxis === 'y' ? arrowOffsetParent.clientTop || 0 : arrowOffsetParent.clientLeft || 0 : 0;\n    var offsetModifierValue = (_offsetModifierState$ = offsetModifierState == null ? void 0 : offsetModifierState[mainAxis]) != null ? _offsetModifierState$ : 0;\n    var tetherMin = offset + minOffset - offsetModifierValue - clientOffset;\n    var tetherMax = offset + maxOffset - offsetModifierValue;\n    var preventedOffset = within(tether ? mathMin(min, tetherMin) : min, offset, tether ? mathMax(max, tetherMax) : max);\n    popperOffsets[mainAxis] = preventedOffset;\n    data[mainAxis] = preventedOffset - offset;\n  }\n\n  if (checkAltAxis) {\n    var _offsetModifierState$2;\n\n    var _mainSide = mainAxis === 'x' ? top : left;\n\n    var _altSide = mainAxis === 'x' ? bottom : right;\n\n    var _offset = popperOffsets[altAxis];\n\n    var _len = altAxis === 'y' ? 'height' : 'width';\n\n    var _min = _offset + overflow[_mainSide];\n\n    var _max = _offset - overflow[_altSide];\n\n    var isOriginSide = [top, left].indexOf(basePlacement) !== -1;\n\n    var _offsetModifierValue = (_offsetModifierState$2 = offsetModifierState == null ? void 0 : offsetModifierState[altAxis]) != null ? _offsetModifierState$2 : 0;\n\n    var _tetherMin = isOriginSide ? _min : _offset - referenceRect[_len] - popperRect[_len] - _offsetModifierValue + normalizedTetherOffsetValue.altAxis;\n\n    var _tetherMax = isOriginSide ? _offset + referenceRect[_len] + popperRect[_len] - _offsetModifierValue - normalizedTetherOffsetValue.altAxis : _max;\n\n    var _preventedOffset = tether && isOriginSide ? withinMaxClamp(_tetherMin, _offset, _tetherMax) : within(tether ? _tetherMin : _min, _offset, tether ? _tetherMax : _max);\n\n    popperOffsets[altAxis] = _preventedOffset;\n    data[altAxis] = _preventedOffset - _offset;\n  }\n\n  state.modifiersData[name] = data;\n} // eslint-disable-next-line import/no-unused-modules\n\n\nexport default {\n  name: 'preventOverflow',\n  enabled: true,\n  phase: 'main',\n  fn: preventOverflow,\n  requiresIfExists: ['offset']\n};","export default function getAltAxis(axis) {\n  return axis === 'x' ? 'y' : 'x';\n}","import getBoundingClientRect from \"./getBoundingClientRect.js\";\nimport getNodeScroll from \"./getNodeScroll.js\";\nimport getNodeName from \"./getNodeName.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getWindowScrollBarX from \"./getWindowScrollBarX.js\";\nimport getDocumentElement from \"./getDocumentElement.js\";\nimport isScrollParent from \"./isScrollParent.js\";\nimport { round } from \"../utils/math.js\";\n\nfunction isElementScaled(element) {\n  var rect = element.getBoundingClientRect();\n  var scaleX = round(rect.width) / element.offsetWidth || 1;\n  var scaleY = round(rect.height) / element.offsetHeight || 1;\n  return scaleX !== 1 || scaleY !== 1;\n} // Returns the composite rect of an element relative to its offsetParent.\n// Composite means it takes into account transforms as well as layout.\n\n\nexport default function getCompositeRect(elementOrVirtualElement, offsetParent, isFixed) {\n  if (isFixed === void 0) {\n    isFixed = false;\n  }\n\n  var isOffsetParentAnElement = isHTMLElement(offsetParent);\n  var offsetParentIsScaled = isHTMLElement(offsetParent) && isElementScaled(offsetParent);\n  var documentElement = getDocumentElement(offsetParent);\n  var rect = getBoundingClientRect(elementOrVirtualElement, offsetParentIsScaled, isFixed);\n  var scroll = {\n    scrollLeft: 0,\n    scrollTop: 0\n  };\n  var offsets = {\n    x: 0,\n    y: 0\n  };\n\n  if (isOffsetParentAnElement || !isOffsetParentAnElement && !isFixed) {\n    if (getNodeName(offsetParent) !== 'body' || // https://github.com/popperjs/popper-core/issues/1078\n    isScrollParent(documentElement)) {\n      scroll = getNodeScroll(offsetParent);\n    }\n\n    if (isHTMLElement(offsetParent)) {\n      offsets = getBoundingClientRect(offsetParent, true);\n      offsets.x += offsetParent.clientLeft;\n      offsets.y += offsetParent.clientTop;\n    } else if (documentElement) {\n      offsets.x = getWindowScrollBarX(documentElement);\n    }\n  }\n\n  return {\n    x: rect.left + scroll.scrollLeft - offsets.x,\n    y: rect.top + scroll.scrollTop - offsets.y,\n    width: rect.width,\n    height: rect.height\n  };\n}","import getWindowScroll from \"./getWindowScroll.js\";\nimport getWindow from \"./getWindow.js\";\nimport { isHTMLElement } from \"./instanceOf.js\";\nimport getHTMLElementScroll from \"./getHTMLElementScroll.js\";\nexport default function getNodeScroll(node) {\n  if (node === getWindow(node) || !isHTMLElement(node)) {\n    return getWindowScroll(node);\n  } else {\n    return getHTMLElementScroll(node);\n  }\n}","export default function getHTMLElementScroll(element) {\n  return {\n    scrollLeft: element.scrollLeft,\n    scrollTop: element.scrollTop\n  };\n}","import { modifierPhases } from \"../enums.js\"; // source: https://stackoverflow.com/questions/49875255\n\nfunction order(modifiers) {\n  var map = new Map();\n  var visited = new Set();\n  var result = [];\n  modifiers.forEach(function (modifier) {\n    map.set(modifier.name, modifier);\n  }); // On visiting object, check for its dependencies and visit them recursively\n\n  function sort(modifier) {\n    visited.add(modifier.name);\n    var requires = [].concat(modifier.requires || [], modifier.requiresIfExists || []);\n    requires.forEach(function (dep) {\n      if (!visited.has(dep)) {\n        var depModifier = map.get(dep);\n\n        if (depModifier) {\n          sort(depModifier);\n        }\n      }\n    });\n    result.push(modifier);\n  }\n\n  modifiers.forEach(function (modifier) {\n    if (!visited.has(modifier.name)) {\n      // check for visited object\n      sort(modifier);\n    }\n  });\n  return result;\n}\n\nexport default function orderModifiers(modifiers) {\n  // order based on dependencies\n  var orderedModifiers = order(modifiers); // order based on phase\n\n  return modifierPhases.reduce(function (acc, phase) {\n    return acc.concat(orderedModifiers.filter(function (modifier) {\n      return modifier.phase === phase;\n    }));\n  }, []);\n}","import getCompositeRect from \"./dom-utils/getCompositeRect.js\";\nimport getLayoutRect from \"./dom-utils/getLayoutRect.js\";\nimport listScrollParents from \"./dom-utils/listScrollParents.js\";\nimport getOffsetParent from \"./dom-utils/getOffsetParent.js\";\nimport getComputedStyle from \"./dom-utils/getComputedStyle.js\";\nimport orderModifiers from \"./utils/orderModifiers.js\";\nimport debounce from \"./utils/debounce.js\";\nimport validateModifiers from \"./utils/validateModifiers.js\";\nimport uniqueBy from \"./utils/uniqueBy.js\";\nimport getBasePlacement from \"./utils/getBasePlacement.js\";\nimport mergeByName from \"./utils/mergeByName.js\";\nimport detectOverflow from \"./utils/detectOverflow.js\";\nimport { isElement } from \"./dom-utils/instanceOf.js\";\nimport { auto } from \"./enums.js\";\nvar INVALID_ELEMENT_ERROR = 'Popper: Invalid reference or popper argument provided. They must be either a DOM element or virtual element.';\nvar INFINITE_LOOP_ERROR = 'Popper: An infinite loop in the modifiers cycle has been detected! The cycle has been interrupted to prevent a browser crash.';\nvar DEFAULT_OPTIONS = {\n  placement: 'bottom',\n  modifiers: [],\n  strategy: 'absolute'\n};\n\nfunction areValidElements() {\n  for (var _len = arguments.length, args = new Array(_len), _key = 0; _key < _len; _key++) {\n    args[_key] = arguments[_key];\n  }\n\n  return !args.some(function (element) {\n    return !(element && typeof element.getBoundingClientRect === 'function');\n  });\n}\n\nexport function popperGenerator(generatorOptions) {\n  if (generatorOptions === void 0) {\n    generatorOptions = {};\n  }\n\n  var _generatorOptions = generatorOptions,\n      _generatorOptions$def = _generatorOptions.defaultModifiers,\n      defaultModifiers = _generatorOptions$def === void 0 ? [] : _generatorOptions$def,\n      _generatorOptions$def2 = _generatorOptions.defaultOptions,\n      defaultOptions = _generatorOptions$def2 === void 0 ? DEFAULT_OPTIONS : _generatorOptions$def2;\n  return function createPopper(reference, popper, options) {\n    if (options === void 0) {\n      options = defaultOptions;\n    }\n\n    var state = {\n      placement: 'bottom',\n      orderedModifiers: [],\n      options: Object.assign({}, DEFAULT_OPTIONS, defaultOptions),\n      modifiersData: {},\n      elements: {\n        reference: reference,\n        popper: popper\n      },\n      attributes: {},\n      styles: {}\n    };\n    var effectCleanupFns = [];\n    var isDestroyed = false;\n    var instance = {\n      state: state,\n      setOptions: function setOptions(setOptionsAction) {\n        var options = typeof setOptionsAction === 'function' ? setOptionsAction(state.options) : setOptionsAction;\n        cleanupModifierEffects();\n        state.options = Object.assign({}, defaultOptions, state.options, options);\n        state.scrollParents = {\n          reference: isElement(reference) ? listScrollParents(reference) : reference.contextElement ? listScrollParents(reference.contextElement) : [],\n          popper: listScrollParents(popper)\n        }; // Orders the modifiers based on their dependencies and `phase`\n        // properties\n\n        var orderedModifiers = orderModifiers(mergeByName([].concat(defaultModifiers, state.options.modifiers))); // Strip out disabled modifiers\n\n        state.orderedModifiers = orderedModifiers.filter(function (m) {\n          return m.enabled;\n        }); // Validate the provided modifiers so that the consumer will get warned\n        // if one of the modifiers is invalid for any reason\n\n        if (process.env.NODE_ENV !== \"production\") {\n          var modifiers = uniqueBy([].concat(orderedModifiers, state.options.modifiers), function (_ref) {\n            var name = _ref.name;\n            return name;\n          });\n          validateModifiers(modifiers);\n\n          if (getBasePlacement(state.options.placement) === auto) {\n            var flipModifier = state.orderedModifiers.find(function (_ref2) {\n              var name = _ref2.name;\n              return name === 'flip';\n            });\n\n            if (!flipModifier) {\n              console.error(['Popper: \"auto\" placements require the \"flip\" modifier be', 'present and enabled to work.'].join(' '));\n            }\n          }\n\n          var _getComputedStyle = getComputedStyle(popper),\n              marginTop = _getComputedStyle.marginTop,\n              marginRight = _getComputedStyle.marginRight,\n              marginBottom = _getComputedStyle.marginBottom,\n              marginLeft = _getComputedStyle.marginLeft; // We no longer take into account `margins` on the popper, and it can\n          // cause bugs with positioning, so we'll warn the consumer\n\n\n          if ([marginTop, marginRight, marginBottom, marginLeft].some(function (margin) {\n            return parseFloat(margin);\n          })) {\n            console.warn(['Popper: CSS \"margin\" styles cannot be used to apply padding', 'between the popper and its reference element or boundary.', 'To replicate margin, use the `offset` modifier, as well as', 'the `padding` option in the `preventOverflow` and `flip`', 'modifiers.'].join(' '));\n          }\n        }\n\n        runModifierEffects();\n        return instance.update();\n      },\n      // Sync update – it will always be executed, even if not necessary. This\n      // is useful for low frequency updates where sync behavior simplifies the\n      // logic.\n      // For high frequency updates (e.g. `resize` and `scroll` events), always\n      // prefer the async Popper#update method\n      forceUpdate: function forceUpdate() {\n        if (isDestroyed) {\n          return;\n        }\n\n        var _state$elements = state.elements,\n            reference = _state$elements.reference,\n            popper = _state$elements.popper; // Don't proceed if `reference` or `popper` are not valid elements\n        // anymore\n\n        if (!areValidElements(reference, popper)) {\n          if (process.env.NODE_ENV !== \"production\") {\n            console.error(INVALID_ELEMENT_ERROR);\n          }\n\n          return;\n        } // Store the reference and popper rects to be read by modifiers\n\n\n        state.rects = {\n          reference: getCompositeRect(reference, getOffsetParent(popper), state.options.strategy === 'fixed'),\n          popper: getLayoutRect(popper)\n        }; // Modifiers have the ability to reset the current update cycle. The\n        // most common use case for this is the `flip` modifier changing the\n        // placement, which then needs to re-run all the modifiers, because the\n        // logic was previously ran for the previous placement and is therefore\n        // stale/incorrect\n\n        state.reset = false;\n        state.placement = state.options.placement; // On each update cycle, the `modifiersData` property for each modifier\n        // is filled with the initial data specified by the modifier. This means\n        // it doesn't persist and is fresh on each update.\n        // To ensure persistent data, use `${name}#persistent`\n\n        state.orderedModifiers.forEach(function (modifier) {\n          return state.modifiersData[modifier.name] = Object.assign({}, modifier.data);\n        });\n        var __debug_loops__ = 0;\n\n        for (var index = 0; index < state.orderedModifiers.length; index++) {\n          if (process.env.NODE_ENV !== \"production\") {\n            __debug_loops__ += 1;\n\n            if (__debug_loops__ > 100) {\n              console.error(INFINITE_LOOP_ERROR);\n              break;\n            }\n          }\n\n          if (state.reset === true) {\n            state.reset = false;\n            index = -1;\n            continue;\n          }\n\n          var _state$orderedModifie = state.orderedModifiers[index],\n              fn = _state$orderedModifie.fn,\n              _state$orderedModifie2 = _state$orderedModifie.options,\n              _options = _state$orderedModifie2 === void 0 ? {} : _state$orderedModifie2,\n              name = _state$orderedModifie.name;\n\n          if (typeof fn === 'function') {\n            state = fn({\n              state: state,\n              options: _options,\n              name: name,\n              instance: instance\n            }) || state;\n          }\n        }\n      },\n      // Async and optimistically optimized update – it will not be executed if\n      // not necessary (debounced to run at most once-per-tick)\n      update: debounce(function () {\n        return new Promise(function (resolve) {\n          instance.forceUpdate();\n          resolve(state);\n        });\n      }),\n      destroy: function destroy() {\n        cleanupModifierEffects();\n        isDestroyed = true;\n      }\n    };\n\n    if (!areValidElements(reference, popper)) {\n      if (process.env.NODE_ENV !== \"production\") {\n        console.error(INVALID_ELEMENT_ERROR);\n      }\n\n      return instance;\n    }\n\n    instance.setOptions(options).then(function (state) {\n      if (!isDestroyed && options.onFirstUpdate) {\n        options.onFirstUpdate(state);\n      }\n    }); // Modifiers have the ability to execute arbitrary code before the first\n    // update cycle runs. They will be executed in the same order as the update\n    // cycle. This is useful when a modifier adds some persistent data that\n    // other modifiers need to use, but the modifier is run after the dependent\n    // one.\n\n    function runModifierEffects() {\n      state.orderedModifiers.forEach(function (_ref3) {\n        var name = _ref3.name,\n            _ref3$options = _ref3.options,\n            options = _ref3$options === void 0 ? {} : _ref3$options,\n            effect = _ref3.effect;\n\n        if (typeof effect === 'function') {\n          var cleanupFn = effect({\n            state: state,\n            name: name,\n            instance: instance,\n            options: options\n          });\n\n          var noopFn = function noopFn() {};\n\n          effectCleanupFns.push(cleanupFn || noopFn);\n        }\n      });\n    }\n\n    function cleanupModifierEffects() {\n      effectCleanupFns.forEach(function (fn) {\n        return fn();\n      });\n      effectCleanupFns = [];\n    }\n\n    return instance;\n  };\n}\nexport var createPopper = /*#__PURE__*/popperGenerator(); // eslint-disable-next-line import/no-unused-modules\n\nexport { detectOverflow };","export default function debounce(fn) {\n  var pending;\n  return function () {\n    if (!pending) {\n      pending = new Promise(function (resolve) {\n        Promise.resolve().then(function () {\n          pending = undefined;\n          resolve(fn());\n        });\n      });\n    }\n\n    return pending;\n  };\n}","export default function mergeByName(modifiers) {\n  var merged = modifiers.reduce(function (merged, current) {\n    var existing = merged[current.name];\n    merged[current.name] = existing ? Object.assign({}, existing, current, {\n      options: Object.assign({}, existing.options, current.options),\n      data: Object.assign({}, existing.data, current.data)\n    }) : current;\n    return merged;\n  }, {}); // IE11 does not support Object.values\n\n  return Object.keys(merged).map(function (key) {\n    return merged[key];\n  });\n}","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nimport offset from \"./modifiers/offset.js\";\nimport flip from \"./modifiers/flip.js\";\nimport preventOverflow from \"./modifiers/preventOverflow.js\";\nimport arrow from \"./modifiers/arrow.js\";\nimport hide from \"./modifiers/hide.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles, offset, flip, preventOverflow, arrow, hide];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow }; // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper as createPopperLite } from \"./popper-lite.js\"; // eslint-disable-next-line import/no-unused-modules\n\nexport * from \"./modifiers/index.js\";","import { popperGenerator, detectOverflow } from \"./createPopper.js\";\nimport eventListeners from \"./modifiers/eventListeners.js\";\nimport popperOffsets from \"./modifiers/popperOffsets.js\";\nimport computeStyles from \"./modifiers/computeStyles.js\";\nimport applyStyles from \"./modifiers/applyStyles.js\";\nvar defaultModifiers = [eventListeners, popperOffsets, computeStyles, applyStyles];\nvar createPopper = /*#__PURE__*/popperGenerator({\n  defaultModifiers: defaultModifiers\n}); // eslint-disable-next-line import/no-unused-modules\n\nexport { createPopper, popperGenerator, defaultModifiers, detectOverflow };","/*!\n  * Bootstrap v5.2.3 (https://getbootstrap.com/)\n  * Copyright 2011-2022 The Bootstrap Authors (https://github.com/twbs/bootstrap/graphs/contributors)\n  * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n  */\nimport * as Popper from '@popperjs/core';\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/index.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\nconst MAX_UID = 1000000;\nconst MILLISECONDS_MULTIPLIER = 1000;\nconst TRANSITION_END = 'transitionend'; // Shout-out Angus Croll (https://goo.gl/pxwQGp)\n\nconst toType = object => {\n  if (object === null || object === undefined) {\n    return `${object}`;\n  }\n\n  return Object.prototype.toString.call(object).match(/\\s([a-z]+)/i)[1].toLowerCase();\n};\n/**\n * Public Util API\n */\n\n\nconst getUID = prefix => {\n  do {\n    prefix += Math.floor(Math.random() * MAX_UID);\n  } while (document.getElementById(prefix));\n\n  return prefix;\n};\n\nconst getSelector = element => {\n  let selector = element.getAttribute('data-bs-target');\n\n  if (!selector || selector === '#') {\n    let hrefAttribute = element.getAttribute('href'); // The only valid content that could double as a selector are IDs or classes,\n    // so everything starting with `#` or `.`. If a \"real\" URL is used as the selector,\n    // `document.querySelector` will rightfully complain it is invalid.\n    // See https://github.com/twbs/bootstrap/issues/32273\n\n    if (!hrefAttribute || !hrefAttribute.includes('#') && !hrefAttribute.startsWith('.')) {\n      return null;\n    } // Just in case some CMS puts out a full URL with the anchor appended\n\n\n    if (hrefAttribute.includes('#') && !hrefAttribute.startsWith('#')) {\n      hrefAttribute = `#${hrefAttribute.split('#')[1]}`;\n    }\n\n    selector = hrefAttribute && hrefAttribute !== '#' ? hrefAttribute.trim() : null;\n  }\n\n  return selector;\n};\n\nconst getSelectorFromElement = element => {\n  const selector = getSelector(element);\n\n  if (selector) {\n    return document.querySelector(selector) ? selector : null;\n  }\n\n  return null;\n};\n\nconst getElementFromSelector = element => {\n  const selector = getSelector(element);\n  return selector ? document.querySelector(selector) : null;\n};\n\nconst getTransitionDurationFromElement = element => {\n  if (!element) {\n    return 0;\n  } // Get transition-duration of the element\n\n\n  let {\n    transitionDuration,\n    transitionDelay\n  } = window.getComputedStyle(element);\n  const floatTransitionDuration = Number.parseFloat(transitionDuration);\n  const floatTransitionDelay = Number.parseFloat(transitionDelay); // Return 0 if element or transition duration is not found\n\n  if (!floatTransitionDuration && !floatTransitionDelay) {\n    return 0;\n  } // If multiple durations are defined, take the first\n\n\n  transitionDuration = transitionDuration.split(',')[0];\n  transitionDelay = transitionDelay.split(',')[0];\n  return (Number.parseFloat(transitionDuration) + Number.parseFloat(transitionDelay)) * MILLISECONDS_MULTIPLIER;\n};\n\nconst triggerTransitionEnd = element => {\n  element.dispatchEvent(new Event(TRANSITION_END));\n};\n\nconst isElement = object => {\n  if (!object || typeof object !== 'object') {\n    return false;\n  }\n\n  if (typeof object.jquery !== 'undefined') {\n    object = object[0];\n  }\n\n  return typeof object.nodeType !== 'undefined';\n};\n\nconst getElement = object => {\n  // it's a jQuery object or a node element\n  if (isElement(object)) {\n    return object.jquery ? object[0] : object;\n  }\n\n  if (typeof object === 'string' && object.length > 0) {\n    return document.querySelector(object);\n  }\n\n  return null;\n};\n\nconst isVisible = element => {\n  if (!isElement(element) || element.getClientRects().length === 0) {\n    return false;\n  }\n\n  const elementIsVisible = getComputedStyle(element).getPropertyValue('visibility') === 'visible'; // Handle `details` element as its content may falsie appear visible when it is closed\n\n  const closedDetails = element.closest('details:not([open])');\n\n  if (!closedDetails) {\n    return elementIsVisible;\n  }\n\n  if (closedDetails !== element) {\n    const summary = element.closest('summary');\n\n    if (summary && summary.parentNode !== closedDetails) {\n      return false;\n    }\n\n    if (summary === null) {\n      return false;\n    }\n  }\n\n  return elementIsVisible;\n};\n\nconst isDisabled = element => {\n  if (!element || element.nodeType !== Node.ELEMENT_NODE) {\n    return true;\n  }\n\n  if (element.classList.contains('disabled')) {\n    return true;\n  }\n\n  if (typeof element.disabled !== 'undefined') {\n    return element.disabled;\n  }\n\n  return element.hasAttribute('disabled') && element.getAttribute('disabled') !== 'false';\n};\n\nconst findShadowRoot = element => {\n  if (!document.documentElement.attachShadow) {\n    return null;\n  } // Can find the shadow root otherwise it'll return the document\n\n\n  if (typeof element.getRootNode === 'function') {\n    const root = element.getRootNode();\n    return root instanceof ShadowRoot ? root : null;\n  }\n\n  if (element instanceof ShadowRoot) {\n    return element;\n  } // when we don't find a shadow root\n\n\n  if (!element.parentNode) {\n    return null;\n  }\n\n  return findShadowRoot(element.parentNode);\n};\n\nconst noop = () => {};\n/**\n * Trick to restart an element's animation\n *\n * @param {HTMLElement} element\n * @return void\n *\n * @see https://www.charistheo.io/blog/2021/02/restart-a-css-animation-with-javascript/#restarting-a-css-animation\n */\n\n\nconst reflow = element => {\n  element.offsetHeight; // eslint-disable-line no-unused-expressions\n};\n\nconst getjQuery = () => {\n  if (window.jQuery && !document.body.hasAttribute('data-bs-no-jquery')) {\n    return window.jQuery;\n  }\n\n  return null;\n};\n\nconst DOMContentLoadedCallbacks = [];\n\nconst onDOMContentLoaded = callback => {\n  if (document.readyState === 'loading') {\n    // add listener on the first call when the document is in loading state\n    if (!DOMContentLoadedCallbacks.length) {\n      document.addEventListener('DOMContentLoaded', () => {\n        for (const callback of DOMContentLoadedCallbacks) {\n          callback();\n        }\n      });\n    }\n\n    DOMContentLoadedCallbacks.push(callback);\n  } else {\n    callback();\n  }\n};\n\nconst isRTL = () => document.documentElement.dir === 'rtl';\n\nconst defineJQueryPlugin = plugin => {\n  onDOMContentLoaded(() => {\n    const $ = getjQuery();\n    /* istanbul ignore if */\n\n    if ($) {\n      const name = plugin.NAME;\n      const JQUERY_NO_CONFLICT = $.fn[name];\n      $.fn[name] = plugin.jQueryInterface;\n      $.fn[name].Constructor = plugin;\n\n      $.fn[name].noConflict = () => {\n        $.fn[name] = JQUERY_NO_CONFLICT;\n        return plugin.jQueryInterface;\n      };\n    }\n  });\n};\n\nconst execute = callback => {\n  if (typeof callback === 'function') {\n    callback();\n  }\n};\n\nconst executeAfterTransition = (callback, transitionElement, waitForTransition = true) => {\n  if (!waitForTransition) {\n    execute(callback);\n    return;\n  }\n\n  const durationPadding = 5;\n  const emulatedDuration = getTransitionDurationFromElement(transitionElement) + durationPadding;\n  let called = false;\n\n  const handler = ({\n    target\n  }) => {\n    if (target !== transitionElement) {\n      return;\n    }\n\n    called = true;\n    transitionElement.removeEventListener(TRANSITION_END, handler);\n    execute(callback);\n  };\n\n  transitionElement.addEventListener(TRANSITION_END, handler);\n  setTimeout(() => {\n    if (!called) {\n      triggerTransitionEnd(transitionElement);\n    }\n  }, emulatedDuration);\n};\n/**\n * Return the previous/next element of a list.\n *\n * @param {array} list    The list of elements\n * @param activeElement   The active element\n * @param shouldGetNext   Choose to get next or previous element\n * @param isCycleAllowed\n * @return {Element|elem} The proper element\n */\n\n\nconst getNextActiveElement = (list, activeElement, shouldGetNext, isCycleAllowed) => {\n  const listLength = list.length;\n  let index = list.indexOf(activeElement); // if the element does not exist in the list return an element\n  // depending on the direction and if cycle is allowed\n\n  if (index === -1) {\n    return !shouldGetNext && isCycleAllowed ? list[listLength - 1] : list[0];\n  }\n\n  index += shouldGetNext ? 1 : -1;\n\n  if (isCycleAllowed) {\n    index = (index + listLength) % listLength;\n  }\n\n  return list[Math.max(0, Math.min(index, listLength - 1))];\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): dom/event-handler.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst namespaceRegex = /[^.]*(?=\\..*)\\.|.*/;\nconst stripNameRegex = /\\..*/;\nconst stripUidRegex = /::\\d+$/;\nconst eventRegistry = {}; // Events storage\n\nlet uidEvent = 1;\nconst customEvents = {\n  mouseenter: 'mouseover',\n  mouseleave: 'mouseout'\n};\nconst nativeEvents = new Set(['click', 'dblclick', 'mouseup', 'mousedown', 'contextmenu', 'mousewheel', 'DOMMouseScroll', 'mouseover', 'mouseout', 'mousemove', 'selectstart', 'selectend', 'keydown', 'keypress', 'keyup', 'orientationchange', 'touchstart', 'touchmove', 'touchend', 'touchcancel', 'pointerdown', 'pointermove', 'pointerup', 'pointerleave', 'pointercancel', 'gesturestart', 'gesturechange', 'gestureend', 'focus', 'blur', 'change', 'reset', 'select', 'submit', 'focusin', 'focusout', 'load', 'unload', 'beforeunload', 'resize', 'move', 'DOMContentLoaded', 'readystatechange', 'error', 'abort', 'scroll']);\n/**\n * Private methods\n */\n\nfunction makeEventUid(element, uid) {\n  return uid && `${uid}::${uidEvent++}` || element.uidEvent || uidEvent++;\n}\n\nfunction getElementEvents(element) {\n  const uid = makeEventUid(element);\n  element.uidEvent = uid;\n  eventRegistry[uid] = eventRegistry[uid] || {};\n  return eventRegistry[uid];\n}\n\nfunction bootstrapHandler(element, fn) {\n  return function handler(event) {\n    hydrateObj(event, {\n      delegateTarget: element\n    });\n\n    if (handler.oneOff) {\n      EventHandler.off(element, event.type, fn);\n    }\n\n    return fn.apply(element, [event]);\n  };\n}\n\nfunction bootstrapDelegationHandler(element, selector, fn) {\n  return function handler(event) {\n    const domElements = element.querySelectorAll(selector);\n\n    for (let {\n      target\n    } = event; target && target !== this; target = target.parentNode) {\n      for (const domElement of domElements) {\n        if (domElement !== target) {\n          continue;\n        }\n\n        hydrateObj(event, {\n          delegateTarget: target\n        });\n\n        if (handler.oneOff) {\n          EventHandler.off(element, event.type, selector, fn);\n        }\n\n        return fn.apply(target, [event]);\n      }\n    }\n  };\n}\n\nfunction findHandler(events, callable, delegationSelector = null) {\n  return Object.values(events).find(event => event.callable === callable && event.delegationSelector === delegationSelector);\n}\n\nfunction normalizeParameters(originalTypeEvent, handler, delegationFunction) {\n  const isDelegated = typeof handler === 'string'; // todo: tooltip passes `false` instead of selector, so we need to check\n\n  const callable = isDelegated ? delegationFunction : handler || delegationFunction;\n  let typeEvent = getTypeEvent(originalTypeEvent);\n\n  if (!nativeEvents.has(typeEvent)) {\n    typeEvent = originalTypeEvent;\n  }\n\n  return [isDelegated, callable, typeEvent];\n}\n\nfunction addHandler(element, originalTypeEvent, handler, delegationFunction, oneOff) {\n  if (typeof originalTypeEvent !== 'string' || !element) {\n    return;\n  }\n\n  let [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction); // in case of mouseenter or mouseleave wrap the handler within a function that checks for its DOM position\n  // this prevents the handler from being dispatched the same way as mouseover or mouseout does\n\n  if (originalTypeEvent in customEvents) {\n    const wrapFunction = fn => {\n      return function (event) {\n        if (!event.relatedTarget || event.relatedTarget !== event.delegateTarget && !event.delegateTarget.contains(event.relatedTarget)) {\n          return fn.call(this, event);\n        }\n      };\n    };\n\n    callable = wrapFunction(callable);\n  }\n\n  const events = getElementEvents(element);\n  const handlers = events[typeEvent] || (events[typeEvent] = {});\n  const previousFunction = findHandler(handlers, callable, isDelegated ? handler : null);\n\n  if (previousFunction) {\n    previousFunction.oneOff = previousFunction.oneOff && oneOff;\n    return;\n  }\n\n  const uid = makeEventUid(callable, originalTypeEvent.replace(namespaceRegex, ''));\n  const fn = isDelegated ? bootstrapDelegationHandler(element, handler, callable) : bootstrapHandler(element, callable);\n  fn.delegationSelector = isDelegated ? handler : null;\n  fn.callable = callable;\n  fn.oneOff = oneOff;\n  fn.uidEvent = uid;\n  handlers[uid] = fn;\n  element.addEventListener(typeEvent, fn, isDelegated);\n}\n\nfunction removeHandler(element, events, typeEvent, handler, delegationSelector) {\n  const fn = findHandler(events[typeEvent], handler, delegationSelector);\n\n  if (!fn) {\n    return;\n  }\n\n  element.removeEventListener(typeEvent, fn, Boolean(delegationSelector));\n  delete events[typeEvent][fn.uidEvent];\n}\n\nfunction removeNamespacedHandlers(element, events, typeEvent, namespace) {\n  const storeElementEvent = events[typeEvent] || {};\n\n  for (const handlerKey of Object.keys(storeElementEvent)) {\n    if (handlerKey.includes(namespace)) {\n      const event = storeElementEvent[handlerKey];\n      removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n    }\n  }\n}\n\nfunction getTypeEvent(event) {\n  // allow to get the native events from namespaced events ('click.bs.button' --> 'click')\n  event = event.replace(stripNameRegex, '');\n  return customEvents[event] || event;\n}\n\nconst EventHandler = {\n  on(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, false);\n  },\n\n  one(element, event, handler, delegationFunction) {\n    addHandler(element, event, handler, delegationFunction, true);\n  },\n\n  off(element, originalTypeEvent, handler, delegationFunction) {\n    if (typeof originalTypeEvent !== 'string' || !element) {\n      return;\n    }\n\n    const [isDelegated, callable, typeEvent] = normalizeParameters(originalTypeEvent, handler, delegationFunction);\n    const inNamespace = typeEvent !== originalTypeEvent;\n    const events = getElementEvents(element);\n    const storeElementEvent = events[typeEvent] || {};\n    const isNamespace = originalTypeEvent.startsWith('.');\n\n    if (typeof callable !== 'undefined') {\n      // Simplest case: handler is passed, remove that listener ONLY.\n      if (!Object.keys(storeElementEvent).length) {\n        return;\n      }\n\n      removeHandler(element, events, typeEvent, callable, isDelegated ? handler : null);\n      return;\n    }\n\n    if (isNamespace) {\n      for (const elementEvent of Object.keys(events)) {\n        removeNamespacedHandlers(element, events, elementEvent, originalTypeEvent.slice(1));\n      }\n    }\n\n    for (const keyHandlers of Object.keys(storeElementEvent)) {\n      const handlerKey = keyHandlers.replace(stripUidRegex, '');\n\n      if (!inNamespace || originalTypeEvent.includes(handlerKey)) {\n        const event = storeElementEvent[keyHandlers];\n        removeHandler(element, events, typeEvent, event.callable, event.delegationSelector);\n      }\n    }\n  },\n\n  trigger(element, event, args) {\n    if (typeof event !== 'string' || !element) {\n      return null;\n    }\n\n    const $ = getjQuery();\n    const typeEvent = getTypeEvent(event);\n    const inNamespace = event !== typeEvent;\n    let jQueryEvent = null;\n    let bubbles = true;\n    let nativeDispatch = true;\n    let defaultPrevented = false;\n\n    if (inNamespace && $) {\n      jQueryEvent = $.Event(event, args);\n      $(element).trigger(jQueryEvent);\n      bubbles = !jQueryEvent.isPropagationStopped();\n      nativeDispatch = !jQueryEvent.isImmediatePropagationStopped();\n      defaultPrevented = jQueryEvent.isDefaultPrevented();\n    }\n\n    let evt = new Event(event, {\n      bubbles,\n      cancelable: true\n    });\n    evt = hydrateObj(evt, args);\n\n    if (defaultPrevented) {\n      evt.preventDefault();\n    }\n\n    if (nativeDispatch) {\n      element.dispatchEvent(evt);\n    }\n\n    if (evt.defaultPrevented && jQueryEvent) {\n      jQueryEvent.preventDefault();\n    }\n\n    return evt;\n  }\n\n};\n\nfunction hydrateObj(obj, meta) {\n  for (const [key, value] of Object.entries(meta || {})) {\n    try {\n      obj[key] = value;\n    } catch (_unused) {\n      Object.defineProperty(obj, key, {\n        configurable: true,\n\n        get() {\n          return value;\n        }\n\n      });\n    }\n  }\n\n  return obj;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): dom/data.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\n/**\n * Constants\n */\nconst elementMap = new Map();\nconst Data = {\n  set(element, key, instance) {\n    if (!elementMap.has(element)) {\n      elementMap.set(element, new Map());\n    }\n\n    const instanceMap = elementMap.get(element); // make it clear we only want one instance per element\n    // can be removed later when multiple key/instances are fine to be used\n\n    if (!instanceMap.has(key) && instanceMap.size !== 0) {\n      // eslint-disable-next-line no-console\n      console.error(`Bootstrap doesn't allow more than one instance per element. Bound instance: ${Array.from(instanceMap.keys())[0]}.`);\n      return;\n    }\n\n    instanceMap.set(key, instance);\n  },\n\n  get(element, key) {\n    if (elementMap.has(element)) {\n      return elementMap.get(element).get(key) || null;\n    }\n\n    return null;\n  },\n\n  remove(element, key) {\n    if (!elementMap.has(element)) {\n      return;\n    }\n\n    const instanceMap = elementMap.get(element);\n    instanceMap.delete(key); // free up element references if there are no instances left for an element\n\n    if (instanceMap.size === 0) {\n      elementMap.delete(element);\n    }\n  }\n\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): dom/manipulator.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\nfunction normalizeData(value) {\n  if (value === 'true') {\n    return true;\n  }\n\n  if (value === 'false') {\n    return false;\n  }\n\n  if (value === Number(value).toString()) {\n    return Number(value);\n  }\n\n  if (value === '' || value === 'null') {\n    return null;\n  }\n\n  if (typeof value !== 'string') {\n    return value;\n  }\n\n  try {\n    return JSON.parse(decodeURIComponent(value));\n  } catch (_unused) {\n    return value;\n  }\n}\n\nfunction normalizeDataKey(key) {\n  return key.replace(/[A-Z]/g, chr => `-${chr.toLowerCase()}`);\n}\n\nconst Manipulator = {\n  setDataAttribute(element, key, value) {\n    element.setAttribute(`data-bs-${normalizeDataKey(key)}`, value);\n  },\n\n  removeDataAttribute(element, key) {\n    element.removeAttribute(`data-bs-${normalizeDataKey(key)}`);\n  },\n\n  getDataAttributes(element) {\n    if (!element) {\n      return {};\n    }\n\n    const attributes = {};\n    const bsKeys = Object.keys(element.dataset).filter(key => key.startsWith('bs') && !key.startsWith('bsConfig'));\n\n    for (const key of bsKeys) {\n      let pureKey = key.replace(/^bs/, '');\n      pureKey = pureKey.charAt(0).toLowerCase() + pureKey.slice(1, pureKey.length);\n      attributes[pureKey] = normalizeData(element.dataset[key]);\n    }\n\n    return attributes;\n  },\n\n  getDataAttribute(element, key) {\n    return normalizeData(element.getAttribute(`data-bs-${normalizeDataKey(key)}`));\n  }\n\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/config.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Class definition\n */\n\nclass Config {\n  // Getters\n  static get Default() {\n    return {};\n  }\n\n  static get DefaultType() {\n    return {};\n  }\n\n  static get NAME() {\n    throw new Error('You have to implement the static method \"NAME\", for each component!');\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config);\n    config = this._configAfterMerge(config);\n\n    this._typeCheckConfig(config);\n\n    return config;\n  }\n\n  _configAfterMerge(config) {\n    return config;\n  }\n\n  _mergeConfigObj(config, element) {\n    const jsonConfig = isElement(element) ? Manipulator.getDataAttribute(element, 'config') : {}; // try to parse\n\n    return { ...this.constructor.Default,\n      ...(typeof jsonConfig === 'object' ? jsonConfig : {}),\n      ...(isElement(element) ? Manipulator.getDataAttributes(element) : {}),\n      ...(typeof config === 'object' ? config : {})\n    };\n  }\n\n  _typeCheckConfig(config, configTypes = this.constructor.DefaultType) {\n    for (const property of Object.keys(configTypes)) {\n      const expectedTypes = configTypes[property];\n      const value = config[property];\n      const valueType = isElement(value) ? 'element' : toType(value);\n\n      if (!new RegExp(expectedTypes).test(valueType)) {\n        throw new TypeError(`${this.constructor.NAME.toUpperCase()}: Option \"${property}\" provided type \"${valueType}\" but expected type \"${expectedTypes}\".`);\n      }\n    }\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): base-component.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst VERSION = '5.2.3';\n/**\n * Class definition\n */\n\nclass BaseComponent extends Config {\n  constructor(element, config) {\n    super();\n    element = getElement(element);\n\n    if (!element) {\n      return;\n    }\n\n    this._element = element;\n    this._config = this._getConfig(config);\n    Data.set(this._element, this.constructor.DATA_KEY, this);\n  } // Public\n\n\n  dispose() {\n    Data.remove(this._element, this.constructor.DATA_KEY);\n    EventHandler.off(this._element, this.constructor.EVENT_KEY);\n\n    for (const propertyName of Object.getOwnPropertyNames(this)) {\n      this[propertyName] = null;\n    }\n  }\n\n  _queueCallback(callback, element, isAnimated = true) {\n    executeAfterTransition(callback, element, isAnimated);\n  }\n\n  _getConfig(config) {\n    config = this._mergeConfigObj(config, this._element);\n    config = this._configAfterMerge(config);\n\n    this._typeCheckConfig(config);\n\n    return config;\n  } // Static\n\n\n  static getInstance(element) {\n    return Data.get(getElement(element), this.DATA_KEY);\n  }\n\n  static getOrCreateInstance(element, config = {}) {\n    return this.getInstance(element) || new this(element, typeof config === 'object' ? config : null);\n  }\n\n  static get VERSION() {\n    return VERSION;\n  }\n\n  static get DATA_KEY() {\n    return `bs.${this.NAME}`;\n  }\n\n  static get EVENT_KEY() {\n    return `.${this.DATA_KEY}`;\n  }\n\n  static eventName(name) {\n    return `${name}${this.EVENT_KEY}`;\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/component-functions.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n\nconst enableDismissTrigger = (component, method = 'hide') => {\n  const clickEvent = `click.dismiss${component.EVENT_KEY}`;\n  const name = component.NAME;\n  EventHandler.on(document, clickEvent, `[data-bs-dismiss=\"${name}\"]`, function (event) {\n    if (['A', 'AREA'].includes(this.tagName)) {\n      event.preventDefault();\n    }\n\n    if (isDisabled(this)) {\n      return;\n    }\n\n    const target = getElementFromSelector(this) || this.closest(`.${name}`);\n    const instance = component.getOrCreateInstance(target); // Method argument is left, for Alert and only, as it doesn't implement the 'hide' method\n\n    instance[method]();\n  });\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): alert.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$f = 'alert';\nconst DATA_KEY$a = 'bs.alert';\nconst EVENT_KEY$b = `.${DATA_KEY$a}`;\nconst EVENT_CLOSE = `close${EVENT_KEY$b}`;\nconst EVENT_CLOSED = `closed${EVENT_KEY$b}`;\nconst CLASS_NAME_FADE$5 = 'fade';\nconst CLASS_NAME_SHOW$8 = 'show';\n/**\n * Class definition\n */\n\nclass Alert extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME$f;\n  } // Public\n\n\n  close() {\n    const closeEvent = EventHandler.trigger(this._element, EVENT_CLOSE);\n\n    if (closeEvent.defaultPrevented) {\n      return;\n    }\n\n    this._element.classList.remove(CLASS_NAME_SHOW$8);\n\n    const isAnimated = this._element.classList.contains(CLASS_NAME_FADE$5);\n\n    this._queueCallback(() => this._destroyElement(), this._element, isAnimated);\n  } // Private\n\n\n  _destroyElement() {\n    this._element.remove();\n\n    EventHandler.trigger(this._element, EVENT_CLOSED);\n    this.dispose();\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Alert.getOrCreateInstance(this);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config](this);\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nenableDismissTrigger(Alert, 'close');\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Alert);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): button.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$e = 'button';\nconst DATA_KEY$9 = 'bs.button';\nconst EVENT_KEY$a = `.${DATA_KEY$9}`;\nconst DATA_API_KEY$6 = '.data-api';\nconst CLASS_NAME_ACTIVE$3 = 'active';\nconst SELECTOR_DATA_TOGGLE$5 = '[data-bs-toggle=\"button\"]';\nconst EVENT_CLICK_DATA_API$6 = `click${EVENT_KEY$a}${DATA_API_KEY$6}`;\n/**\n * Class definition\n */\n\nclass Button extends BaseComponent {\n  // Getters\n  static get NAME() {\n    return NAME$e;\n  } // Public\n\n\n  toggle() {\n    // Toggle class and sync the `aria-pressed` attribute with the return value of the `.toggle()` method\n    this._element.setAttribute('aria-pressed', this._element.classList.toggle(CLASS_NAME_ACTIVE$3));\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Button.getOrCreateInstance(this);\n\n      if (config === 'toggle') {\n        data[config]();\n      }\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$6, SELECTOR_DATA_TOGGLE$5, event => {\n  event.preventDefault();\n  const button = event.target.closest(SELECTOR_DATA_TOGGLE$5);\n  const data = Button.getOrCreateInstance(button);\n  data.toggle();\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Button);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): dom/selector-engine.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst SelectorEngine = {\n  find(selector, element = document.documentElement) {\n    return [].concat(...Element.prototype.querySelectorAll.call(element, selector));\n  },\n\n  findOne(selector, element = document.documentElement) {\n    return Element.prototype.querySelector.call(element, selector);\n  },\n\n  children(element, selector) {\n    return [].concat(...element.children).filter(child => child.matches(selector));\n  },\n\n  parents(element, selector) {\n    const parents = [];\n    let ancestor = element.parentNode.closest(selector);\n\n    while (ancestor) {\n      parents.push(ancestor);\n      ancestor = ancestor.parentNode.closest(selector);\n    }\n\n    return parents;\n  },\n\n  prev(element, selector) {\n    let previous = element.previousElementSibling;\n\n    while (previous) {\n      if (previous.matches(selector)) {\n        return [previous];\n      }\n\n      previous = previous.previousElementSibling;\n    }\n\n    return [];\n  },\n\n  // TODO: this is now unused; remove later along with prev()\n  next(element, selector) {\n    let next = element.nextElementSibling;\n\n    while (next) {\n      if (next.matches(selector)) {\n        return [next];\n      }\n\n      next = next.nextElementSibling;\n    }\n\n    return [];\n  },\n\n  focusableChildren(element) {\n    const focusables = ['a', 'button', 'input', 'textarea', 'select', 'details', '[tabindex]', '[contenteditable=\"true\"]'].map(selector => `${selector}:not([tabindex^=\"-\"])`).join(',');\n    return this.find(focusables, element).filter(el => !isDisabled(el) && isVisible(el));\n  }\n\n};\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/swipe.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$d = 'swipe';\nconst EVENT_KEY$9 = '.bs.swipe';\nconst EVENT_TOUCHSTART = `touchstart${EVENT_KEY$9}`;\nconst EVENT_TOUCHMOVE = `touchmove${EVENT_KEY$9}`;\nconst EVENT_TOUCHEND = `touchend${EVENT_KEY$9}`;\nconst EVENT_POINTERDOWN = `pointerdown${EVENT_KEY$9}`;\nconst EVENT_POINTERUP = `pointerup${EVENT_KEY$9}`;\nconst POINTER_TYPE_TOUCH = 'touch';\nconst POINTER_TYPE_PEN = 'pen';\nconst CLASS_NAME_POINTER_EVENT = 'pointer-event';\nconst SWIPE_THRESHOLD = 40;\nconst Default$c = {\n  endCallback: null,\n  leftCallback: null,\n  rightCallback: null\n};\nconst DefaultType$c = {\n  endCallback: '(function|null)',\n  leftCallback: '(function|null)',\n  rightCallback: '(function|null)'\n};\n/**\n * Class definition\n */\n\nclass Swipe extends Config {\n  constructor(element, config) {\n    super();\n    this._element = element;\n\n    if (!element || !Swipe.isSupported()) {\n      return;\n    }\n\n    this._config = this._getConfig(config);\n    this._deltaX = 0;\n    this._supportPointerEvents = Boolean(window.PointerEvent);\n\n    this._initEvents();\n  } // Getters\n\n\n  static get Default() {\n    return Default$c;\n  }\n\n  static get DefaultType() {\n    return DefaultType$c;\n  }\n\n  static get NAME() {\n    return NAME$d;\n  } // Public\n\n\n  dispose() {\n    EventHandler.off(this._element, EVENT_KEY$9);\n  } // Private\n\n\n  _start(event) {\n    if (!this._supportPointerEvents) {\n      this._deltaX = event.touches[0].clientX;\n      return;\n    }\n\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX;\n    }\n  }\n\n  _end(event) {\n    if (this._eventIsPointerPenTouch(event)) {\n      this._deltaX = event.clientX - this._deltaX;\n    }\n\n    this._handleSwipe();\n\n    execute(this._config.endCallback);\n  }\n\n  _move(event) {\n    this._deltaX = event.touches && event.touches.length > 1 ? 0 : event.touches[0].clientX - this._deltaX;\n  }\n\n  _handleSwipe() {\n    const absDeltaX = Math.abs(this._deltaX);\n\n    if (absDeltaX <= SWIPE_THRESHOLD) {\n      return;\n    }\n\n    const direction = absDeltaX / this._deltaX;\n    this._deltaX = 0;\n\n    if (!direction) {\n      return;\n    }\n\n    execute(direction > 0 ? this._config.rightCallback : this._config.leftCallback);\n  }\n\n  _initEvents() {\n    if (this._supportPointerEvents) {\n      EventHandler.on(this._element, EVENT_POINTERDOWN, event => this._start(event));\n      EventHandler.on(this._element, EVENT_POINTERUP, event => this._end(event));\n\n      this._element.classList.add(CLASS_NAME_POINTER_EVENT);\n    } else {\n      EventHandler.on(this._element, EVENT_TOUCHSTART, event => this._start(event));\n      EventHandler.on(this._element, EVENT_TOUCHMOVE, event => this._move(event));\n      EventHandler.on(this._element, EVENT_TOUCHEND, event => this._end(event));\n    }\n  }\n\n  _eventIsPointerPenTouch(event) {\n    return this._supportPointerEvents && (event.pointerType === POINTER_TYPE_PEN || event.pointerType === POINTER_TYPE_TOUCH);\n  } // Static\n\n\n  static isSupported() {\n    return 'ontouchstart' in document.documentElement || navigator.maxTouchPoints > 0;\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): carousel.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$c = 'carousel';\nconst DATA_KEY$8 = 'bs.carousel';\nconst EVENT_KEY$8 = `.${DATA_KEY$8}`;\nconst DATA_API_KEY$5 = '.data-api';\nconst ARROW_LEFT_KEY$1 = 'ArrowLeft';\nconst ARROW_RIGHT_KEY$1 = 'ArrowRight';\nconst TOUCHEVENT_COMPAT_WAIT = 500; // Time for mouse compat events to fire after touch\n\nconst ORDER_NEXT = 'next';\nconst ORDER_PREV = 'prev';\nconst DIRECTION_LEFT = 'left';\nconst DIRECTION_RIGHT = 'right';\nconst EVENT_SLIDE = `slide${EVENT_KEY$8}`;\nconst EVENT_SLID = `slid${EVENT_KEY$8}`;\nconst EVENT_KEYDOWN$1 = `keydown${EVENT_KEY$8}`;\nconst EVENT_MOUSEENTER$1 = `mouseenter${EVENT_KEY$8}`;\nconst EVENT_MOUSELEAVE$1 = `mouseleave${EVENT_KEY$8}`;\nconst EVENT_DRAG_START = `dragstart${EVENT_KEY$8}`;\nconst EVENT_LOAD_DATA_API$3 = `load${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst EVENT_CLICK_DATA_API$5 = `click${EVENT_KEY$8}${DATA_API_KEY$5}`;\nconst CLASS_NAME_CAROUSEL = 'carousel';\nconst CLASS_NAME_ACTIVE$2 = 'active';\nconst CLASS_NAME_SLIDE = 'slide';\nconst CLASS_NAME_END = 'carousel-item-end';\nconst CLASS_NAME_START = 'carousel-item-start';\nconst CLASS_NAME_NEXT = 'carousel-item-next';\nconst CLASS_NAME_PREV = 'carousel-item-prev';\nconst SELECTOR_ACTIVE = '.active';\nconst SELECTOR_ITEM = '.carousel-item';\nconst SELECTOR_ACTIVE_ITEM = SELECTOR_ACTIVE + SELECTOR_ITEM;\nconst SELECTOR_ITEM_IMG = '.carousel-item img';\nconst SELECTOR_INDICATORS = '.carousel-indicators';\nconst SELECTOR_DATA_SLIDE = '[data-bs-slide], [data-bs-slide-to]';\nconst SELECTOR_DATA_RIDE = '[data-bs-ride=\"carousel\"]';\nconst KEY_TO_DIRECTION = {\n  [ARROW_LEFT_KEY$1]: DIRECTION_RIGHT,\n  [ARROW_RIGHT_KEY$1]: DIRECTION_LEFT\n};\nconst Default$b = {\n  interval: 5000,\n  keyboard: true,\n  pause: 'hover',\n  ride: false,\n  touch: true,\n  wrap: true\n};\nconst DefaultType$b = {\n  interval: '(number|boolean)',\n  // TODO:v6 remove boolean support\n  keyboard: 'boolean',\n  pause: '(string|boolean)',\n  ride: '(boolean|string)',\n  touch: 'boolean',\n  wrap: 'boolean'\n};\n/**\n * Class definition\n */\n\nclass Carousel extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._interval = null;\n    this._activeElement = null;\n    this._isSliding = false;\n    this.touchTimeout = null;\n    this._swipeHelper = null;\n    this._indicatorsElement = SelectorEngine.findOne(SELECTOR_INDICATORS, this._element);\n\n    this._addEventListeners();\n\n    if (this._config.ride === CLASS_NAME_CAROUSEL) {\n      this.cycle();\n    }\n  } // Getters\n\n\n  static get Default() {\n    return Default$b;\n  }\n\n  static get DefaultType() {\n    return DefaultType$b;\n  }\n\n  static get NAME() {\n    return NAME$c;\n  } // Public\n\n\n  next() {\n    this._slide(ORDER_NEXT);\n  }\n\n  nextWhenVisible() {\n    // FIXME TODO use `document.visibilityState`\n    // Don't call next when the page isn't visible\n    // or the carousel or its parent isn't visible\n    if (!document.hidden && isVisible(this._element)) {\n      this.next();\n    }\n  }\n\n  prev() {\n    this._slide(ORDER_PREV);\n  }\n\n  pause() {\n    if (this._isSliding) {\n      triggerTransitionEnd(this._element);\n    }\n\n    this._clearInterval();\n  }\n\n  cycle() {\n    this._clearInterval();\n\n    this._updateInterval();\n\n    this._interval = setInterval(() => this.nextWhenVisible(), this._config.interval);\n  }\n\n  _maybeEnableCycle() {\n    if (!this._config.ride) {\n      return;\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.cycle());\n      return;\n    }\n\n    this.cycle();\n  }\n\n  to(index) {\n    const items = this._getItems();\n\n    if (index > items.length - 1 || index < 0) {\n      return;\n    }\n\n    if (this._isSliding) {\n      EventHandler.one(this._element, EVENT_SLID, () => this.to(index));\n      return;\n    }\n\n    const activeIndex = this._getItemIndex(this._getActive());\n\n    if (activeIndex === index) {\n      return;\n    }\n\n    const order = index > activeIndex ? ORDER_NEXT : ORDER_PREV;\n\n    this._slide(order, items[index]);\n  }\n\n  dispose() {\n    if (this._swipeHelper) {\n      this._swipeHelper.dispose();\n    }\n\n    super.dispose();\n  } // Private\n\n\n  _configAfterMerge(config) {\n    config.defaultInterval = config.interval;\n    return config;\n  }\n\n  _addEventListeners() {\n    if (this._config.keyboard) {\n      EventHandler.on(this._element, EVENT_KEYDOWN$1, event => this._keydown(event));\n    }\n\n    if (this._config.pause === 'hover') {\n      EventHandler.on(this._element, EVENT_MOUSEENTER$1, () => this.pause());\n      EventHandler.on(this._element, EVENT_MOUSELEAVE$1, () => this._maybeEnableCycle());\n    }\n\n    if (this._config.touch && Swipe.isSupported()) {\n      this._addTouchEventListeners();\n    }\n  }\n\n  _addTouchEventListeners() {\n    for (const img of SelectorEngine.find(SELECTOR_ITEM_IMG, this._element)) {\n      EventHandler.on(img, EVENT_DRAG_START, event => event.preventDefault());\n    }\n\n    const endCallBack = () => {\n      if (this._config.pause !== 'hover') {\n        return;\n      } // If it's a touch-enabled device, mouseenter/leave are fired as\n      // part of the mouse compatibility events on first tap - the carousel\n      // would stop cycling until user tapped out of it;\n      // here, we listen for touchend, explicitly pause the carousel\n      // (as if it's the second time we tap on it, mouseenter compat event\n      // is NOT fired) and after a timeout (to allow for mouse compatibility\n      // events to fire) we explicitly restart cycling\n\n\n      this.pause();\n\n      if (this.touchTimeout) {\n        clearTimeout(this.touchTimeout);\n      }\n\n      this.touchTimeout = setTimeout(() => this._maybeEnableCycle(), TOUCHEVENT_COMPAT_WAIT + this._config.interval);\n    };\n\n    const swipeConfig = {\n      leftCallback: () => this._slide(this._directionToOrder(DIRECTION_LEFT)),\n      rightCallback: () => this._slide(this._directionToOrder(DIRECTION_RIGHT)),\n      endCallback: endCallBack\n    };\n    this._swipeHelper = new Swipe(this._element, swipeConfig);\n  }\n\n  _keydown(event) {\n    if (/input|textarea/i.test(event.target.tagName)) {\n      return;\n    }\n\n    const direction = KEY_TO_DIRECTION[event.key];\n\n    if (direction) {\n      event.preventDefault();\n\n      this._slide(this._directionToOrder(direction));\n    }\n  }\n\n  _getItemIndex(element) {\n    return this._getItems().indexOf(element);\n  }\n\n  _setActiveIndicatorElement(index) {\n    if (!this._indicatorsElement) {\n      return;\n    }\n\n    const activeIndicator = SelectorEngine.findOne(SELECTOR_ACTIVE, this._indicatorsElement);\n    activeIndicator.classList.remove(CLASS_NAME_ACTIVE$2);\n    activeIndicator.removeAttribute('aria-current');\n    const newActiveIndicator = SelectorEngine.findOne(`[data-bs-slide-to=\"${index}\"]`, this._indicatorsElement);\n\n    if (newActiveIndicator) {\n      newActiveIndicator.classList.add(CLASS_NAME_ACTIVE$2);\n      newActiveIndicator.setAttribute('aria-current', 'true');\n    }\n  }\n\n  _updateInterval() {\n    const element = this._activeElement || this._getActive();\n\n    if (!element) {\n      return;\n    }\n\n    const elementInterval = Number.parseInt(element.getAttribute('data-bs-interval'), 10);\n    this._config.interval = elementInterval || this._config.defaultInterval;\n  }\n\n  _slide(order, element = null) {\n    if (this._isSliding) {\n      return;\n    }\n\n    const activeElement = this._getActive();\n\n    const isNext = order === ORDER_NEXT;\n    const nextElement = element || getNextActiveElement(this._getItems(), activeElement, isNext, this._config.wrap);\n\n    if (nextElement === activeElement) {\n      return;\n    }\n\n    const nextElementIndex = this._getItemIndex(nextElement);\n\n    const triggerEvent = eventName => {\n      return EventHandler.trigger(this._element, eventName, {\n        relatedTarget: nextElement,\n        direction: this._orderToDirection(order),\n        from: this._getItemIndex(activeElement),\n        to: nextElementIndex\n      });\n    };\n\n    const slideEvent = triggerEvent(EVENT_SLIDE);\n\n    if (slideEvent.defaultPrevented) {\n      return;\n    }\n\n    if (!activeElement || !nextElement) {\n      // Some weirdness is happening, so we bail\n      // todo: change tests that use empty divs to avoid this check\n      return;\n    }\n\n    const isCycling = Boolean(this._interval);\n    this.pause();\n    this._isSliding = true;\n\n    this._setActiveIndicatorElement(nextElementIndex);\n\n    this._activeElement = nextElement;\n    const directionalClassName = isNext ? CLASS_NAME_START : CLASS_NAME_END;\n    const orderClassName = isNext ? CLASS_NAME_NEXT : CLASS_NAME_PREV;\n    nextElement.classList.add(orderClassName);\n    reflow(nextElement);\n    activeElement.classList.add(directionalClassName);\n    nextElement.classList.add(directionalClassName);\n\n    const completeCallBack = () => {\n      nextElement.classList.remove(directionalClassName, orderClassName);\n      nextElement.classList.add(CLASS_NAME_ACTIVE$2);\n      activeElement.classList.remove(CLASS_NAME_ACTIVE$2, orderClassName, directionalClassName);\n      this._isSliding = false;\n      triggerEvent(EVENT_SLID);\n    };\n\n    this._queueCallback(completeCallBack, activeElement, this._isAnimated());\n\n    if (isCycling) {\n      this.cycle();\n    }\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_SLIDE);\n  }\n\n  _getActive() {\n    return SelectorEngine.findOne(SELECTOR_ACTIVE_ITEM, this._element);\n  }\n\n  _getItems() {\n    return SelectorEngine.find(SELECTOR_ITEM, this._element);\n  }\n\n  _clearInterval() {\n    if (this._interval) {\n      clearInterval(this._interval);\n      this._interval = null;\n    }\n  }\n\n  _directionToOrder(direction) {\n    if (isRTL()) {\n      return direction === DIRECTION_LEFT ? ORDER_PREV : ORDER_NEXT;\n    }\n\n    return direction === DIRECTION_LEFT ? ORDER_NEXT : ORDER_PREV;\n  }\n\n  _orderToDirection(order) {\n    if (isRTL()) {\n      return order === ORDER_PREV ? DIRECTION_LEFT : DIRECTION_RIGHT;\n    }\n\n    return order === ORDER_PREV ? DIRECTION_RIGHT : DIRECTION_LEFT;\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Carousel.getOrCreateInstance(this, config);\n\n      if (typeof config === 'number') {\n        data.to(config);\n        return;\n      }\n\n      if (typeof config === 'string') {\n        if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n          throw new TypeError(`No method named \"${config}\"`);\n        }\n\n        data[config]();\n      }\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$5, SELECTOR_DATA_SLIDE, function (event) {\n  const target = getElementFromSelector(this);\n\n  if (!target || !target.classList.contains(CLASS_NAME_CAROUSEL)) {\n    return;\n  }\n\n  event.preventDefault();\n  const carousel = Carousel.getOrCreateInstance(target);\n  const slideIndex = this.getAttribute('data-bs-slide-to');\n\n  if (slideIndex) {\n    carousel.to(slideIndex);\n\n    carousel._maybeEnableCycle();\n\n    return;\n  }\n\n  if (Manipulator.getDataAttribute(this, 'slide') === 'next') {\n    carousel.next();\n\n    carousel._maybeEnableCycle();\n\n    return;\n  }\n\n  carousel.prev();\n\n  carousel._maybeEnableCycle();\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$3, () => {\n  const carousels = SelectorEngine.find(SELECTOR_DATA_RIDE);\n\n  for (const carousel of carousels) {\n    Carousel.getOrCreateInstance(carousel);\n  }\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Carousel);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): collapse.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$b = 'collapse';\nconst DATA_KEY$7 = 'bs.collapse';\nconst EVENT_KEY$7 = `.${DATA_KEY$7}`;\nconst DATA_API_KEY$4 = '.data-api';\nconst EVENT_SHOW$6 = `show${EVENT_KEY$7}`;\nconst EVENT_SHOWN$6 = `shown${EVENT_KEY$7}`;\nconst EVENT_HIDE$6 = `hide${EVENT_KEY$7}`;\nconst EVENT_HIDDEN$6 = `hidden${EVENT_KEY$7}`;\nconst EVENT_CLICK_DATA_API$4 = `click${EVENT_KEY$7}${DATA_API_KEY$4}`;\nconst CLASS_NAME_SHOW$7 = 'show';\nconst CLASS_NAME_COLLAPSE = 'collapse';\nconst CLASS_NAME_COLLAPSING = 'collapsing';\nconst CLASS_NAME_COLLAPSED = 'collapsed';\nconst CLASS_NAME_DEEPER_CHILDREN = `:scope .${CLASS_NAME_COLLAPSE} .${CLASS_NAME_COLLAPSE}`;\nconst CLASS_NAME_HORIZONTAL = 'collapse-horizontal';\nconst WIDTH = 'width';\nconst HEIGHT = 'height';\nconst SELECTOR_ACTIVES = '.collapse.show, .collapse.collapsing';\nconst SELECTOR_DATA_TOGGLE$4 = '[data-bs-toggle=\"collapse\"]';\nconst Default$a = {\n  parent: null,\n  toggle: true\n};\nconst DefaultType$a = {\n  parent: '(null|element)',\n  toggle: 'boolean'\n};\n/**\n * Class definition\n */\n\nclass Collapse extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._isTransitioning = false;\n    this._triggerArray = [];\n    const toggleList = SelectorEngine.find(SELECTOR_DATA_TOGGLE$4);\n\n    for (const elem of toggleList) {\n      const selector = getSelectorFromElement(elem);\n      const filterElement = SelectorEngine.find(selector).filter(foundElement => foundElement === this._element);\n\n      if (selector !== null && filterElement.length) {\n        this._triggerArray.push(elem);\n      }\n    }\n\n    this._initializeChildren();\n\n    if (!this._config.parent) {\n      this._addAriaAndCollapsedClass(this._triggerArray, this._isShown());\n    }\n\n    if (this._config.toggle) {\n      this.toggle();\n    }\n  } // Getters\n\n\n  static get Default() {\n    return Default$a;\n  }\n\n  static get DefaultType() {\n    return DefaultType$a;\n  }\n\n  static get NAME() {\n    return NAME$b;\n  } // Public\n\n\n  toggle() {\n    if (this._isShown()) {\n      this.hide();\n    } else {\n      this.show();\n    }\n  }\n\n  show() {\n    if (this._isTransitioning || this._isShown()) {\n      return;\n    }\n\n    let activeChildren = []; // find active children\n\n    if (this._config.parent) {\n      activeChildren = this._getFirstLevelChildren(SELECTOR_ACTIVES).filter(element => element !== this._element).map(element => Collapse.getOrCreateInstance(element, {\n        toggle: false\n      }));\n    }\n\n    if (activeChildren.length && activeChildren[0]._isTransitioning) {\n      return;\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_SHOW$6);\n\n    if (startEvent.defaultPrevented) {\n      return;\n    }\n\n    for (const activeInstance of activeChildren) {\n      activeInstance.hide();\n    }\n\n    const dimension = this._getDimension();\n\n    this._element.classList.remove(CLASS_NAME_COLLAPSE);\n\n    this._element.classList.add(CLASS_NAME_COLLAPSING);\n\n    this._element.style[dimension] = 0;\n\n    this._addAriaAndCollapsedClass(this._triggerArray, true);\n\n    this._isTransitioning = true;\n\n    const complete = () => {\n      this._isTransitioning = false;\n\n      this._element.classList.remove(CLASS_NAME_COLLAPSING);\n\n      this._element.classList.add(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n\n      this._element.style[dimension] = '';\n      EventHandler.trigger(this._element, EVENT_SHOWN$6);\n    };\n\n    const capitalizedDimension = dimension[0].toUpperCase() + dimension.slice(1);\n    const scrollSize = `scroll${capitalizedDimension}`;\n\n    this._queueCallback(complete, this._element, true);\n\n    this._element.style[dimension] = `${this._element[scrollSize]}px`;\n  }\n\n  hide() {\n    if (this._isTransitioning || !this._isShown()) {\n      return;\n    }\n\n    const startEvent = EventHandler.trigger(this._element, EVENT_HIDE$6);\n\n    if (startEvent.defaultPrevented) {\n      return;\n    }\n\n    const dimension = this._getDimension();\n\n    this._element.style[dimension] = `${this._element.getBoundingClientRect()[dimension]}px`;\n    reflow(this._element);\n\n    this._element.classList.add(CLASS_NAME_COLLAPSING);\n\n    this._element.classList.remove(CLASS_NAME_COLLAPSE, CLASS_NAME_SHOW$7);\n\n    for (const trigger of this._triggerArray) {\n      const element = getElementFromSelector(trigger);\n\n      if (element && !this._isShown(element)) {\n        this._addAriaAndCollapsedClass([trigger], false);\n      }\n    }\n\n    this._isTransitioning = true;\n\n    const complete = () => {\n      this._isTransitioning = false;\n\n      this._element.classList.remove(CLASS_NAME_COLLAPSING);\n\n      this._element.classList.add(CLASS_NAME_COLLAPSE);\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN$6);\n    };\n\n    this._element.style[dimension] = '';\n\n    this._queueCallback(complete, this._element, true);\n  }\n\n  _isShown(element = this._element) {\n    return element.classList.contains(CLASS_NAME_SHOW$7);\n  } // Private\n\n\n  _configAfterMerge(config) {\n    config.toggle = Boolean(config.toggle); // Coerce string values\n\n    config.parent = getElement(config.parent);\n    return config;\n  }\n\n  _getDimension() {\n    return this._element.classList.contains(CLASS_NAME_HORIZONTAL) ? WIDTH : HEIGHT;\n  }\n\n  _initializeChildren() {\n    if (!this._config.parent) {\n      return;\n    }\n\n    const children = this._getFirstLevelChildren(SELECTOR_DATA_TOGGLE$4);\n\n    for (const element of children) {\n      const selected = getElementFromSelector(element);\n\n      if (selected) {\n        this._addAriaAndCollapsedClass([element], this._isShown(selected));\n      }\n    }\n  }\n\n  _getFirstLevelChildren(selector) {\n    const children = SelectorEngine.find(CLASS_NAME_DEEPER_CHILDREN, this._config.parent); // remove children if greater depth\n\n    return SelectorEngine.find(selector, this._config.parent).filter(element => !children.includes(element));\n  }\n\n  _addAriaAndCollapsedClass(triggerArray, isOpen) {\n    if (!triggerArray.length) {\n      return;\n    }\n\n    for (const element of triggerArray) {\n      element.classList.toggle(CLASS_NAME_COLLAPSED, !isOpen);\n      element.setAttribute('aria-expanded', isOpen);\n    }\n  } // Static\n\n\n  static jQueryInterface(config) {\n    const _config = {};\n\n    if (typeof config === 'string' && /show|hide/.test(config)) {\n      _config.toggle = false;\n    }\n\n    return this.each(function () {\n      const data = Collapse.getOrCreateInstance(this, _config);\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`);\n        }\n\n        data[config]();\n      }\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$4, SELECTOR_DATA_TOGGLE$4, function (event) {\n  // preventDefault only for <a> elements (which change the URL) not inside the collapsible element\n  if (event.target.tagName === 'A' || event.delegateTarget && event.delegateTarget.tagName === 'A') {\n    event.preventDefault();\n  }\n\n  const selector = getSelectorFromElement(this);\n  const selectorElements = SelectorEngine.find(selector);\n\n  for (const element of selectorElements) {\n    Collapse.getOrCreateInstance(element, {\n      toggle: false\n    }).toggle();\n  }\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Collapse);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): dropdown.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$a = 'dropdown';\nconst DATA_KEY$6 = 'bs.dropdown';\nconst EVENT_KEY$6 = `.${DATA_KEY$6}`;\nconst DATA_API_KEY$3 = '.data-api';\nconst ESCAPE_KEY$2 = 'Escape';\nconst TAB_KEY$1 = 'Tab';\nconst ARROW_UP_KEY$1 = 'ArrowUp';\nconst ARROW_DOWN_KEY$1 = 'ArrowDown';\nconst RIGHT_MOUSE_BUTTON = 2; // MouseEvent.button value for the secondary button, usually the right button\n\nconst EVENT_HIDE$5 = `hide${EVENT_KEY$6}`;\nconst EVENT_HIDDEN$5 = `hidden${EVENT_KEY$6}`;\nconst EVENT_SHOW$5 = `show${EVENT_KEY$6}`;\nconst EVENT_SHOWN$5 = `shown${EVENT_KEY$6}`;\nconst EVENT_CLICK_DATA_API$3 = `click${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYDOWN_DATA_API = `keydown${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst EVENT_KEYUP_DATA_API = `keyup${EVENT_KEY$6}${DATA_API_KEY$3}`;\nconst CLASS_NAME_SHOW$6 = 'show';\nconst CLASS_NAME_DROPUP = 'dropup';\nconst CLASS_NAME_DROPEND = 'dropend';\nconst CLASS_NAME_DROPSTART = 'dropstart';\nconst CLASS_NAME_DROPUP_CENTER = 'dropup-center';\nconst CLASS_NAME_DROPDOWN_CENTER = 'dropdown-center';\nconst SELECTOR_DATA_TOGGLE$3 = '[data-bs-toggle=\"dropdown\"]:not(.disabled):not(:disabled)';\nconst SELECTOR_DATA_TOGGLE_SHOWN = `${SELECTOR_DATA_TOGGLE$3}.${CLASS_NAME_SHOW$6}`;\nconst SELECTOR_MENU = '.dropdown-menu';\nconst SELECTOR_NAVBAR = '.navbar';\nconst SELECTOR_NAVBAR_NAV = '.navbar-nav';\nconst SELECTOR_VISIBLE_ITEMS = '.dropdown-menu .dropdown-item:not(.disabled):not(:disabled)';\nconst PLACEMENT_TOP = isRTL() ? 'top-end' : 'top-start';\nconst PLACEMENT_TOPEND = isRTL() ? 'top-start' : 'top-end';\nconst PLACEMENT_BOTTOM = isRTL() ? 'bottom-end' : 'bottom-start';\nconst PLACEMENT_BOTTOMEND = isRTL() ? 'bottom-start' : 'bottom-end';\nconst PLACEMENT_RIGHT = isRTL() ? 'left-start' : 'right-start';\nconst PLACEMENT_LEFT = isRTL() ? 'right-start' : 'left-start';\nconst PLACEMENT_TOPCENTER = 'top';\nconst PLACEMENT_BOTTOMCENTER = 'bottom';\nconst Default$9 = {\n  autoClose: true,\n  boundary: 'clippingParents',\n  display: 'dynamic',\n  offset: [0, 2],\n  popperConfig: null,\n  reference: 'toggle'\n};\nconst DefaultType$9 = {\n  autoClose: '(boolean|string)',\n  boundary: '(string|element)',\n  display: 'string',\n  offset: '(array|string|function)',\n  popperConfig: '(null|object|function)',\n  reference: '(string|element|object)'\n};\n/**\n * Class definition\n */\n\nclass Dropdown extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._popper = null;\n    this._parent = this._element.parentNode; // dropdown wrapper\n    // todo: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.2/forms/input-group/\n\n    this._menu = SelectorEngine.next(this._element, SELECTOR_MENU)[0] || SelectorEngine.prev(this._element, SELECTOR_MENU)[0] || SelectorEngine.findOne(SELECTOR_MENU, this._parent);\n    this._inNavbar = this._detectNavbar();\n  } // Getters\n\n\n  static get Default() {\n    return Default$9;\n  }\n\n  static get DefaultType() {\n    return DefaultType$9;\n  }\n\n  static get NAME() {\n    return NAME$a;\n  } // Public\n\n\n  toggle() {\n    return this._isShown() ? this.hide() : this.show();\n  }\n\n  show() {\n    if (isDisabled(this._element) || this._isShown()) {\n      return;\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    };\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$5, relatedTarget);\n\n    if (showEvent.defaultPrevented) {\n      return;\n    }\n\n    this._createPopper(); // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n\n\n    if ('ontouchstart' in document.documentElement && !this._parent.closest(SELECTOR_NAVBAR_NAV)) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop);\n      }\n    }\n\n    this._element.focus();\n\n    this._element.setAttribute('aria-expanded', true);\n\n    this._menu.classList.add(CLASS_NAME_SHOW$6);\n\n    this._element.classList.add(CLASS_NAME_SHOW$6);\n\n    EventHandler.trigger(this._element, EVENT_SHOWN$5, relatedTarget);\n  }\n\n  hide() {\n    if (isDisabled(this._element) || !this._isShown()) {\n      return;\n    }\n\n    const relatedTarget = {\n      relatedTarget: this._element\n    };\n\n    this._completeHide(relatedTarget);\n  }\n\n  dispose() {\n    if (this._popper) {\n      this._popper.destroy();\n    }\n\n    super.dispose();\n  }\n\n  update() {\n    this._inNavbar = this._detectNavbar();\n\n    if (this._popper) {\n      this._popper.update();\n    }\n  } // Private\n\n\n  _completeHide(relatedTarget) {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$5, relatedTarget);\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    } // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n\n\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop);\n      }\n    }\n\n    if (this._popper) {\n      this._popper.destroy();\n    }\n\n    this._menu.classList.remove(CLASS_NAME_SHOW$6);\n\n    this._element.classList.remove(CLASS_NAME_SHOW$6);\n\n    this._element.setAttribute('aria-expanded', 'false');\n\n    Manipulator.removeDataAttribute(this._menu, 'popper');\n    EventHandler.trigger(this._element, EVENT_HIDDEN$5, relatedTarget);\n  }\n\n  _getConfig(config) {\n    config = super._getConfig(config);\n\n    if (typeof config.reference === 'object' && !isElement(config.reference) && typeof config.reference.getBoundingClientRect !== 'function') {\n      // Popper virtual elements require a getBoundingClientRect method\n      throw new TypeError(`${NAME$a.toUpperCase()}: Option \"reference\" provided type \"object\" without a required \"getBoundingClientRect\" method.`);\n    }\n\n    return config;\n  }\n\n  _createPopper() {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s dropdowns require Popper (https://popper.js.org)');\n    }\n\n    let referenceElement = this._element;\n\n    if (this._config.reference === 'parent') {\n      referenceElement = this._parent;\n    } else if (isElement(this._config.reference)) {\n      referenceElement = getElement(this._config.reference);\n    } else if (typeof this._config.reference === 'object') {\n      referenceElement = this._config.reference;\n    }\n\n    const popperConfig = this._getPopperConfig();\n\n    this._popper = Popper.createPopper(referenceElement, this._menu, popperConfig);\n  }\n\n  _isShown() {\n    return this._menu.classList.contains(CLASS_NAME_SHOW$6);\n  }\n\n  _getPlacement() {\n    const parentDropdown = this._parent;\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPEND)) {\n      return PLACEMENT_RIGHT;\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPSTART)) {\n      return PLACEMENT_LEFT;\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP_CENTER)) {\n      return PLACEMENT_TOPCENTER;\n    }\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPDOWN_CENTER)) {\n      return PLACEMENT_BOTTOMCENTER;\n    } // We need to trim the value because custom properties can also include spaces\n\n\n    const isEnd = getComputedStyle(this._menu).getPropertyValue('--bs-position').trim() === 'end';\n\n    if (parentDropdown.classList.contains(CLASS_NAME_DROPUP)) {\n      return isEnd ? PLACEMENT_TOPEND : PLACEMENT_TOP;\n    }\n\n    return isEnd ? PLACEMENT_BOTTOMEND : PLACEMENT_BOTTOM;\n  }\n\n  _detectNavbar() {\n    return this._element.closest(SELECTOR_NAVBAR) !== null;\n  }\n\n  _getOffset() {\n    const {\n      offset\n    } = this._config;\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10));\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element);\n    }\n\n    return offset;\n  }\n\n  _getPopperConfig() {\n    const defaultBsPopperConfig = {\n      placement: this._getPlacement(),\n      modifiers: [{\n        name: 'preventOverflow',\n        options: {\n          boundary: this._config.boundary\n        }\n      }, {\n        name: 'offset',\n        options: {\n          offset: this._getOffset()\n        }\n      }]\n    }; // Disable Popper if we have a static display or Dropdown is in Navbar\n\n    if (this._inNavbar || this._config.display === 'static') {\n      Manipulator.setDataAttribute(this._menu, 'popper', 'static'); // todo:v6 remove\n\n      defaultBsPopperConfig.modifiers = [{\n        name: 'applyStyles',\n        enabled: false\n      }];\n    }\n\n    return { ...defaultBsPopperConfig,\n      ...(typeof this._config.popperConfig === 'function' ? this._config.popperConfig(defaultBsPopperConfig) : this._config.popperConfig)\n    };\n  }\n\n  _selectMenuItem({\n    key,\n    target\n  }) {\n    const items = SelectorEngine.find(SELECTOR_VISIBLE_ITEMS, this._menu).filter(element => isVisible(element));\n\n    if (!items.length) {\n      return;\n    } // if target isn't included in items (e.g. when expanding the dropdown)\n    // allow cycling to get the last item in case key equals ARROW_UP_KEY\n\n\n    getNextActiveElement(items, target, key === ARROW_DOWN_KEY$1, !items.includes(target)).focus();\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Dropdown.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config]();\n    });\n  }\n\n  static clearMenus(event) {\n    if (event.button === RIGHT_MOUSE_BUTTON || event.type === 'keyup' && event.key !== TAB_KEY$1) {\n      return;\n    }\n\n    const openToggles = SelectorEngine.find(SELECTOR_DATA_TOGGLE_SHOWN);\n\n    for (const toggle of openToggles) {\n      const context = Dropdown.getInstance(toggle);\n\n      if (!context || context._config.autoClose === false) {\n        continue;\n      }\n\n      const composedPath = event.composedPath();\n      const isMenuTarget = composedPath.includes(context._menu);\n\n      if (composedPath.includes(context._element) || context._config.autoClose === 'inside' && !isMenuTarget || context._config.autoClose === 'outside' && isMenuTarget) {\n        continue;\n      } // Tab navigation through the dropdown menu or events from contained inputs shouldn't close the menu\n\n\n      if (context._menu.contains(event.target) && (event.type === 'keyup' && event.key === TAB_KEY$1 || /input|select|option|textarea|form/i.test(event.target.tagName))) {\n        continue;\n      }\n\n      const relatedTarget = {\n        relatedTarget: context._element\n      };\n\n      if (event.type === 'click') {\n        relatedTarget.clickEvent = event;\n      }\n\n      context._completeHide(relatedTarget);\n    }\n  }\n\n  static dataApiKeydownHandler(event) {\n    // If not an UP | DOWN | ESCAPE key => not a dropdown command\n    // If input/textarea && if key is other than ESCAPE => not a dropdown command\n    const isInput = /input|textarea/i.test(event.target.tagName);\n    const isEscapeEvent = event.key === ESCAPE_KEY$2;\n    const isUpOrDownEvent = [ARROW_UP_KEY$1, ARROW_DOWN_KEY$1].includes(event.key);\n\n    if (!isUpOrDownEvent && !isEscapeEvent) {\n      return;\n    }\n\n    if (isInput && !isEscapeEvent) {\n      return;\n    }\n\n    event.preventDefault(); // todo: v6 revert #37011 & change markup https://getbootstrap.com/docs/5.2/forms/input-group/\n\n    const getToggleButton = this.matches(SELECTOR_DATA_TOGGLE$3) ? this : SelectorEngine.prev(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.next(this, SELECTOR_DATA_TOGGLE$3)[0] || SelectorEngine.findOne(SELECTOR_DATA_TOGGLE$3, event.delegateTarget.parentNode);\n    const instance = Dropdown.getOrCreateInstance(getToggleButton);\n\n    if (isUpOrDownEvent) {\n      event.stopPropagation();\n      instance.show();\n\n      instance._selectMenuItem(event);\n\n      return;\n    }\n\n    if (instance._isShown()) {\n      // else is escape and we check if it is shown\n      event.stopPropagation();\n      instance.hide();\n      getToggleButton.focus();\n    }\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_DATA_TOGGLE$3, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_KEYDOWN_DATA_API, SELECTOR_MENU, Dropdown.dataApiKeydownHandler);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_KEYUP_DATA_API, Dropdown.clearMenus);\nEventHandler.on(document, EVENT_CLICK_DATA_API$3, SELECTOR_DATA_TOGGLE$3, function (event) {\n  event.preventDefault();\n  Dropdown.getOrCreateInstance(this).toggle();\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Dropdown);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/scrollBar.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst SELECTOR_FIXED_CONTENT = '.fixed-top, .fixed-bottom, .is-fixed, .sticky-top';\nconst SELECTOR_STICKY_CONTENT = '.sticky-top';\nconst PROPERTY_PADDING = 'padding-right';\nconst PROPERTY_MARGIN = 'margin-right';\n/**\n * Class definition\n */\n\nclass ScrollBarHelper {\n  constructor() {\n    this._element = document.body;\n  } // Public\n\n\n  getWidth() {\n    // https://developer.mozilla.org/en-US/docs/Web/API/Window/innerWidth#usage_notes\n    const documentWidth = document.documentElement.clientWidth;\n    return Math.abs(window.innerWidth - documentWidth);\n  }\n\n  hide() {\n    const width = this.getWidth();\n\n    this._disableOverFlow(); // give padding to element to balance the hidden scrollbar width\n\n\n    this._setElementAttributes(this._element, PROPERTY_PADDING, calculatedValue => calculatedValue + width); // trick: We adjust positive paddingRight and negative marginRight to sticky-top elements to keep showing fullwidth\n\n\n    this._setElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING, calculatedValue => calculatedValue + width);\n\n    this._setElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN, calculatedValue => calculatedValue - width);\n  }\n\n  reset() {\n    this._resetElementAttributes(this._element, 'overflow');\n\n    this._resetElementAttributes(this._element, PROPERTY_PADDING);\n\n    this._resetElementAttributes(SELECTOR_FIXED_CONTENT, PROPERTY_PADDING);\n\n    this._resetElementAttributes(SELECTOR_STICKY_CONTENT, PROPERTY_MARGIN);\n  }\n\n  isOverflowing() {\n    return this.getWidth() > 0;\n  } // Private\n\n\n  _disableOverFlow() {\n    this._saveInitialAttribute(this._element, 'overflow');\n\n    this._element.style.overflow = 'hidden';\n  }\n\n  _setElementAttributes(selector, styleProperty, callback) {\n    const scrollbarWidth = this.getWidth();\n\n    const manipulationCallBack = element => {\n      if (element !== this._element && window.innerWidth > element.clientWidth + scrollbarWidth) {\n        return;\n      }\n\n      this._saveInitialAttribute(element, styleProperty);\n\n      const calculatedValue = window.getComputedStyle(element).getPropertyValue(styleProperty);\n      element.style.setProperty(styleProperty, `${callback(Number.parseFloat(calculatedValue))}px`);\n    };\n\n    this._applyManipulationCallback(selector, manipulationCallBack);\n  }\n\n  _saveInitialAttribute(element, styleProperty) {\n    const actualValue = element.style.getPropertyValue(styleProperty);\n\n    if (actualValue) {\n      Manipulator.setDataAttribute(element, styleProperty, actualValue);\n    }\n  }\n\n  _resetElementAttributes(selector, styleProperty) {\n    const manipulationCallBack = element => {\n      const value = Manipulator.getDataAttribute(element, styleProperty); // We only want to remove the property if the value is `null`; the value can also be zero\n\n      if (value === null) {\n        element.style.removeProperty(styleProperty);\n        return;\n      }\n\n      Manipulator.removeDataAttribute(element, styleProperty);\n      element.style.setProperty(styleProperty, value);\n    };\n\n    this._applyManipulationCallback(selector, manipulationCallBack);\n  }\n\n  _applyManipulationCallback(selector, callBack) {\n    if (isElement(selector)) {\n      callBack(selector);\n      return;\n    }\n\n    for (const sel of SelectorEngine.find(selector, this._element)) {\n      callBack(sel);\n    }\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/backdrop.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$9 = 'backdrop';\nconst CLASS_NAME_FADE$4 = 'fade';\nconst CLASS_NAME_SHOW$5 = 'show';\nconst EVENT_MOUSEDOWN = `mousedown.bs.${NAME$9}`;\nconst Default$8 = {\n  className: 'modal-backdrop',\n  clickCallback: null,\n  isAnimated: false,\n  isVisible: true,\n  // if false, we use the backdrop helper without adding any element to the dom\n  rootElement: 'body' // give the choice to place backdrop under different elements\n\n};\nconst DefaultType$8 = {\n  className: 'string',\n  clickCallback: '(function|null)',\n  isAnimated: 'boolean',\n  isVisible: 'boolean',\n  rootElement: '(element|string)'\n};\n/**\n * Class definition\n */\n\nclass Backdrop extends Config {\n  constructor(config) {\n    super();\n    this._config = this._getConfig(config);\n    this._isAppended = false;\n    this._element = null;\n  } // Getters\n\n\n  static get Default() {\n    return Default$8;\n  }\n\n  static get DefaultType() {\n    return DefaultType$8;\n  }\n\n  static get NAME() {\n    return NAME$9;\n  } // Public\n\n\n  show(callback) {\n    if (!this._config.isVisible) {\n      execute(callback);\n      return;\n    }\n\n    this._append();\n\n    const element = this._getElement();\n\n    if (this._config.isAnimated) {\n      reflow(element);\n    }\n\n    element.classList.add(CLASS_NAME_SHOW$5);\n\n    this._emulateAnimation(() => {\n      execute(callback);\n    });\n  }\n\n  hide(callback) {\n    if (!this._config.isVisible) {\n      execute(callback);\n      return;\n    }\n\n    this._getElement().classList.remove(CLASS_NAME_SHOW$5);\n\n    this._emulateAnimation(() => {\n      this.dispose();\n      execute(callback);\n    });\n  }\n\n  dispose() {\n    if (!this._isAppended) {\n      return;\n    }\n\n    EventHandler.off(this._element, EVENT_MOUSEDOWN);\n\n    this._element.remove();\n\n    this._isAppended = false;\n  } // Private\n\n\n  _getElement() {\n    if (!this._element) {\n      const backdrop = document.createElement('div');\n      backdrop.className = this._config.className;\n\n      if (this._config.isAnimated) {\n        backdrop.classList.add(CLASS_NAME_FADE$4);\n      }\n\n      this._element = backdrop;\n    }\n\n    return this._element;\n  }\n\n  _configAfterMerge(config) {\n    // use getElement() with the default \"body\" to get a fresh Element on each instantiation\n    config.rootElement = getElement(config.rootElement);\n    return config;\n  }\n\n  _append() {\n    if (this._isAppended) {\n      return;\n    }\n\n    const element = this._getElement();\n\n    this._config.rootElement.append(element);\n\n    EventHandler.on(element, EVENT_MOUSEDOWN, () => {\n      execute(this._config.clickCallback);\n    });\n    this._isAppended = true;\n  }\n\n  _emulateAnimation(callback) {\n    executeAfterTransition(callback, this._getElement(), this._config.isAnimated);\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/focustrap.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$8 = 'focustrap';\nconst DATA_KEY$5 = 'bs.focustrap';\nconst EVENT_KEY$5 = `.${DATA_KEY$5}`;\nconst EVENT_FOCUSIN$2 = `focusin${EVENT_KEY$5}`;\nconst EVENT_KEYDOWN_TAB = `keydown.tab${EVENT_KEY$5}`;\nconst TAB_KEY = 'Tab';\nconst TAB_NAV_FORWARD = 'forward';\nconst TAB_NAV_BACKWARD = 'backward';\nconst Default$7 = {\n  autofocus: true,\n  trapElement: null // The element to trap focus inside of\n\n};\nconst DefaultType$7 = {\n  autofocus: 'boolean',\n  trapElement: 'element'\n};\n/**\n * Class definition\n */\n\nclass FocusTrap extends Config {\n  constructor(config) {\n    super();\n    this._config = this._getConfig(config);\n    this._isActive = false;\n    this._lastTabNavDirection = null;\n  } // Getters\n\n\n  static get Default() {\n    return Default$7;\n  }\n\n  static get DefaultType() {\n    return DefaultType$7;\n  }\n\n  static get NAME() {\n    return NAME$8;\n  } // Public\n\n\n  activate() {\n    if (this._isActive) {\n      return;\n    }\n\n    if (this._config.autofocus) {\n      this._config.trapElement.focus();\n    }\n\n    EventHandler.off(document, EVENT_KEY$5); // guard against infinite focus loop\n\n    EventHandler.on(document, EVENT_FOCUSIN$2, event => this._handleFocusin(event));\n    EventHandler.on(document, EVENT_KEYDOWN_TAB, event => this._handleKeydown(event));\n    this._isActive = true;\n  }\n\n  deactivate() {\n    if (!this._isActive) {\n      return;\n    }\n\n    this._isActive = false;\n    EventHandler.off(document, EVENT_KEY$5);\n  } // Private\n\n\n  _handleFocusin(event) {\n    const {\n      trapElement\n    } = this._config;\n\n    if (event.target === document || event.target === trapElement || trapElement.contains(event.target)) {\n      return;\n    }\n\n    const elements = SelectorEngine.focusableChildren(trapElement);\n\n    if (elements.length === 0) {\n      trapElement.focus();\n    } else if (this._lastTabNavDirection === TAB_NAV_BACKWARD) {\n      elements[elements.length - 1].focus();\n    } else {\n      elements[0].focus();\n    }\n  }\n\n  _handleKeydown(event) {\n    if (event.key !== TAB_KEY) {\n      return;\n    }\n\n    this._lastTabNavDirection = event.shiftKey ? TAB_NAV_BACKWARD : TAB_NAV_FORWARD;\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): modal.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$7 = 'modal';\nconst DATA_KEY$4 = 'bs.modal';\nconst EVENT_KEY$4 = `.${DATA_KEY$4}`;\nconst DATA_API_KEY$2 = '.data-api';\nconst ESCAPE_KEY$1 = 'Escape';\nconst EVENT_HIDE$4 = `hide${EVENT_KEY$4}`;\nconst EVENT_HIDE_PREVENTED$1 = `hidePrevented${EVENT_KEY$4}`;\nconst EVENT_HIDDEN$4 = `hidden${EVENT_KEY$4}`;\nconst EVENT_SHOW$4 = `show${EVENT_KEY$4}`;\nconst EVENT_SHOWN$4 = `shown${EVENT_KEY$4}`;\nconst EVENT_RESIZE$1 = `resize${EVENT_KEY$4}`;\nconst EVENT_CLICK_DISMISS = `click.dismiss${EVENT_KEY$4}`;\nconst EVENT_MOUSEDOWN_DISMISS = `mousedown.dismiss${EVENT_KEY$4}`;\nconst EVENT_KEYDOWN_DISMISS$1 = `keydown.dismiss${EVENT_KEY$4}`;\nconst EVENT_CLICK_DATA_API$2 = `click${EVENT_KEY$4}${DATA_API_KEY$2}`;\nconst CLASS_NAME_OPEN = 'modal-open';\nconst CLASS_NAME_FADE$3 = 'fade';\nconst CLASS_NAME_SHOW$4 = 'show';\nconst CLASS_NAME_STATIC = 'modal-static';\nconst OPEN_SELECTOR$1 = '.modal.show';\nconst SELECTOR_DIALOG = '.modal-dialog';\nconst SELECTOR_MODAL_BODY = '.modal-body';\nconst SELECTOR_DATA_TOGGLE$2 = '[data-bs-toggle=\"modal\"]';\nconst Default$6 = {\n  backdrop: true,\n  focus: true,\n  keyboard: true\n};\nconst DefaultType$6 = {\n  backdrop: '(boolean|string)',\n  focus: 'boolean',\n  keyboard: 'boolean'\n};\n/**\n * Class definition\n */\n\nclass Modal extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._dialog = SelectorEngine.findOne(SELECTOR_DIALOG, this._element);\n    this._backdrop = this._initializeBackDrop();\n    this._focustrap = this._initializeFocusTrap();\n    this._isShown = false;\n    this._isTransitioning = false;\n    this._scrollBar = new ScrollBarHelper();\n\n    this._addEventListeners();\n  } // Getters\n\n\n  static get Default() {\n    return Default$6;\n  }\n\n  static get DefaultType() {\n    return DefaultType$6;\n  }\n\n  static get NAME() {\n    return NAME$7;\n  } // Public\n\n\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget);\n  }\n\n  show(relatedTarget) {\n    if (this._isShown || this._isTransitioning) {\n      return;\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$4, {\n      relatedTarget\n    });\n\n    if (showEvent.defaultPrevented) {\n      return;\n    }\n\n    this._isShown = true;\n    this._isTransitioning = true;\n\n    this._scrollBar.hide();\n\n    document.body.classList.add(CLASS_NAME_OPEN);\n\n    this._adjustDialog();\n\n    this._backdrop.show(() => this._showElement(relatedTarget));\n  }\n\n  hide() {\n    if (!this._isShown || this._isTransitioning) {\n      return;\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$4);\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    }\n\n    this._isShown = false;\n    this._isTransitioning = true;\n\n    this._focustrap.deactivate();\n\n    this._element.classList.remove(CLASS_NAME_SHOW$4);\n\n    this._queueCallback(() => this._hideModal(), this._element, this._isAnimated());\n  }\n\n  dispose() {\n    for (const htmlElement of [window, this._dialog]) {\n      EventHandler.off(htmlElement, EVENT_KEY$4);\n    }\n\n    this._backdrop.dispose();\n\n    this._focustrap.deactivate();\n\n    super.dispose();\n  }\n\n  handleUpdate() {\n    this._adjustDialog();\n  } // Private\n\n\n  _initializeBackDrop() {\n    return new Backdrop({\n      isVisible: Boolean(this._config.backdrop),\n      // 'static' option will be translated to true, and booleans will keep their value,\n      isAnimated: this._isAnimated()\n    });\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    });\n  }\n\n  _showElement(relatedTarget) {\n    // try to append dynamic modal\n    if (!document.body.contains(this._element)) {\n      document.body.append(this._element);\n    }\n\n    this._element.style.display = 'block';\n\n    this._element.removeAttribute('aria-hidden');\n\n    this._element.setAttribute('aria-modal', true);\n\n    this._element.setAttribute('role', 'dialog');\n\n    this._element.scrollTop = 0;\n    const modalBody = SelectorEngine.findOne(SELECTOR_MODAL_BODY, this._dialog);\n\n    if (modalBody) {\n      modalBody.scrollTop = 0;\n    }\n\n    reflow(this._element);\n\n    this._element.classList.add(CLASS_NAME_SHOW$4);\n\n    const transitionComplete = () => {\n      if (this._config.focus) {\n        this._focustrap.activate();\n      }\n\n      this._isTransitioning = false;\n      EventHandler.trigger(this._element, EVENT_SHOWN$4, {\n        relatedTarget\n      });\n    };\n\n    this._queueCallback(transitionComplete, this._dialog, this._isAnimated());\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS$1, event => {\n      if (event.key !== ESCAPE_KEY$1) {\n        return;\n      }\n\n      if (this._config.keyboard) {\n        event.preventDefault();\n        this.hide();\n        return;\n      }\n\n      this._triggerBackdropTransition();\n    });\n    EventHandler.on(window, EVENT_RESIZE$1, () => {\n      if (this._isShown && !this._isTransitioning) {\n        this._adjustDialog();\n      }\n    });\n    EventHandler.on(this._element, EVENT_MOUSEDOWN_DISMISS, event => {\n      // a bad trick to segregate clicks that may start inside dialog but end outside, and avoid listen to scrollbar clicks\n      EventHandler.one(this._element, EVENT_CLICK_DISMISS, event2 => {\n        if (this._element !== event.target || this._element !== event2.target) {\n          return;\n        }\n\n        if (this._config.backdrop === 'static') {\n          this._triggerBackdropTransition();\n\n          return;\n        }\n\n        if (this._config.backdrop) {\n          this.hide();\n        }\n      });\n    });\n  }\n\n  _hideModal() {\n    this._element.style.display = 'none';\n\n    this._element.setAttribute('aria-hidden', true);\n\n    this._element.removeAttribute('aria-modal');\n\n    this._element.removeAttribute('role');\n\n    this._isTransitioning = false;\n\n    this._backdrop.hide(() => {\n      document.body.classList.remove(CLASS_NAME_OPEN);\n\n      this._resetAdjustments();\n\n      this._scrollBar.reset();\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN$4);\n    });\n  }\n\n  _isAnimated() {\n    return this._element.classList.contains(CLASS_NAME_FADE$3);\n  }\n\n  _triggerBackdropTransition() {\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED$1);\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    }\n\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n    const initialOverflowY = this._element.style.overflowY; // return if the following background transition hasn't yet completed\n\n    if (initialOverflowY === 'hidden' || this._element.classList.contains(CLASS_NAME_STATIC)) {\n      return;\n    }\n\n    if (!isModalOverflowing) {\n      this._element.style.overflowY = 'hidden';\n    }\n\n    this._element.classList.add(CLASS_NAME_STATIC);\n\n    this._queueCallback(() => {\n      this._element.classList.remove(CLASS_NAME_STATIC);\n\n      this._queueCallback(() => {\n        this._element.style.overflowY = initialOverflowY;\n      }, this._dialog);\n    }, this._dialog);\n\n    this._element.focus();\n  }\n  /**\n   * The following methods are used to handle overflowing modals\n   */\n\n\n  _adjustDialog() {\n    const isModalOverflowing = this._element.scrollHeight > document.documentElement.clientHeight;\n\n    const scrollbarWidth = this._scrollBar.getWidth();\n\n    const isBodyOverflowing = scrollbarWidth > 0;\n\n    if (isBodyOverflowing && !isModalOverflowing) {\n      const property = isRTL() ? 'paddingLeft' : 'paddingRight';\n      this._element.style[property] = `${scrollbarWidth}px`;\n    }\n\n    if (!isBodyOverflowing && isModalOverflowing) {\n      const property = isRTL() ? 'paddingRight' : 'paddingLeft';\n      this._element.style[property] = `${scrollbarWidth}px`;\n    }\n  }\n\n  _resetAdjustments() {\n    this._element.style.paddingLeft = '';\n    this._element.style.paddingRight = '';\n  } // Static\n\n\n  static jQueryInterface(config, relatedTarget) {\n    return this.each(function () {\n      const data = Modal.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config](relatedTarget);\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$2, SELECTOR_DATA_TOGGLE$2, function (event) {\n  const target = getElementFromSelector(this);\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault();\n  }\n\n  EventHandler.one(target, EVENT_SHOW$4, showEvent => {\n    if (showEvent.defaultPrevented) {\n      // only register focus restorer if modal will actually get shown\n      return;\n    }\n\n    EventHandler.one(target, EVENT_HIDDEN$4, () => {\n      if (isVisible(this)) {\n        this.focus();\n      }\n    });\n  }); // avoid conflict when clicking modal toggler while another one is open\n\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR$1);\n\n  if (alreadyOpen) {\n    Modal.getInstance(alreadyOpen).hide();\n  }\n\n  const data = Modal.getOrCreateInstance(target);\n  data.toggle(this);\n});\nenableDismissTrigger(Modal);\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Modal);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): offcanvas.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$6 = 'offcanvas';\nconst DATA_KEY$3 = 'bs.offcanvas';\nconst EVENT_KEY$3 = `.${DATA_KEY$3}`;\nconst DATA_API_KEY$1 = '.data-api';\nconst EVENT_LOAD_DATA_API$2 = `load${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst ESCAPE_KEY = 'Escape';\nconst CLASS_NAME_SHOW$3 = 'show';\nconst CLASS_NAME_SHOWING$1 = 'showing';\nconst CLASS_NAME_HIDING = 'hiding';\nconst CLASS_NAME_BACKDROP = 'offcanvas-backdrop';\nconst OPEN_SELECTOR = '.offcanvas.show';\nconst EVENT_SHOW$3 = `show${EVENT_KEY$3}`;\nconst EVENT_SHOWN$3 = `shown${EVENT_KEY$3}`;\nconst EVENT_HIDE$3 = `hide${EVENT_KEY$3}`;\nconst EVENT_HIDE_PREVENTED = `hidePrevented${EVENT_KEY$3}`;\nconst EVENT_HIDDEN$3 = `hidden${EVENT_KEY$3}`;\nconst EVENT_RESIZE = `resize${EVENT_KEY$3}`;\nconst EVENT_CLICK_DATA_API$1 = `click${EVENT_KEY$3}${DATA_API_KEY$1}`;\nconst EVENT_KEYDOWN_DISMISS = `keydown.dismiss${EVENT_KEY$3}`;\nconst SELECTOR_DATA_TOGGLE$1 = '[data-bs-toggle=\"offcanvas\"]';\nconst Default$5 = {\n  backdrop: true,\n  keyboard: true,\n  scroll: false\n};\nconst DefaultType$5 = {\n  backdrop: '(boolean|string)',\n  keyboard: 'boolean',\n  scroll: 'boolean'\n};\n/**\n * Class definition\n */\n\nclass Offcanvas extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._isShown = false;\n    this._backdrop = this._initializeBackDrop();\n    this._focustrap = this._initializeFocusTrap();\n\n    this._addEventListeners();\n  } // Getters\n\n\n  static get Default() {\n    return Default$5;\n  }\n\n  static get DefaultType() {\n    return DefaultType$5;\n  }\n\n  static get NAME() {\n    return NAME$6;\n  } // Public\n\n\n  toggle(relatedTarget) {\n    return this._isShown ? this.hide() : this.show(relatedTarget);\n  }\n\n  show(relatedTarget) {\n    if (this._isShown) {\n      return;\n    }\n\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW$3, {\n      relatedTarget\n    });\n\n    if (showEvent.defaultPrevented) {\n      return;\n    }\n\n    this._isShown = true;\n\n    this._backdrop.show();\n\n    if (!this._config.scroll) {\n      new ScrollBarHelper().hide();\n    }\n\n    this._element.setAttribute('aria-modal', true);\n\n    this._element.setAttribute('role', 'dialog');\n\n    this._element.classList.add(CLASS_NAME_SHOWING$1);\n\n    const completeCallBack = () => {\n      if (!this._config.scroll || this._config.backdrop) {\n        this._focustrap.activate();\n      }\n\n      this._element.classList.add(CLASS_NAME_SHOW$3);\n\n      this._element.classList.remove(CLASS_NAME_SHOWING$1);\n\n      EventHandler.trigger(this._element, EVENT_SHOWN$3, {\n        relatedTarget\n      });\n    };\n\n    this._queueCallback(completeCallBack, this._element, true);\n  }\n\n  hide() {\n    if (!this._isShown) {\n      return;\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE$3);\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    }\n\n    this._focustrap.deactivate();\n\n    this._element.blur();\n\n    this._isShown = false;\n\n    this._element.classList.add(CLASS_NAME_HIDING);\n\n    this._backdrop.hide();\n\n    const completeCallback = () => {\n      this._element.classList.remove(CLASS_NAME_SHOW$3, CLASS_NAME_HIDING);\n\n      this._element.removeAttribute('aria-modal');\n\n      this._element.removeAttribute('role');\n\n      if (!this._config.scroll) {\n        new ScrollBarHelper().reset();\n      }\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN$3);\n    };\n\n    this._queueCallback(completeCallback, this._element, true);\n  }\n\n  dispose() {\n    this._backdrop.dispose();\n\n    this._focustrap.deactivate();\n\n    super.dispose();\n  } // Private\n\n\n  _initializeBackDrop() {\n    const clickCallback = () => {\n      if (this._config.backdrop === 'static') {\n        EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n        return;\n      }\n\n      this.hide();\n    }; // 'static' option will be translated to true, and booleans will keep their value\n\n\n    const isVisible = Boolean(this._config.backdrop);\n    return new Backdrop({\n      className: CLASS_NAME_BACKDROP,\n      isVisible,\n      isAnimated: true,\n      rootElement: this._element.parentNode,\n      clickCallback: isVisible ? clickCallback : null\n    });\n  }\n\n  _initializeFocusTrap() {\n    return new FocusTrap({\n      trapElement: this._element\n    });\n  }\n\n  _addEventListeners() {\n    EventHandler.on(this._element, EVENT_KEYDOWN_DISMISS, event => {\n      if (event.key !== ESCAPE_KEY) {\n        return;\n      }\n\n      if (!this._config.keyboard) {\n        EventHandler.trigger(this._element, EVENT_HIDE_PREVENTED);\n        return;\n      }\n\n      this.hide();\n    });\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Offcanvas.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config](this);\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API$1, SELECTOR_DATA_TOGGLE$1, function (event) {\n  const target = getElementFromSelector(this);\n\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault();\n  }\n\n  if (isDisabled(this)) {\n    return;\n  }\n\n  EventHandler.one(target, EVENT_HIDDEN$3, () => {\n    // focus on trigger when it is closed\n    if (isVisible(this)) {\n      this.focus();\n    }\n  }); // avoid conflict when clicking a toggler of an offcanvas, while another is open\n\n  const alreadyOpen = SelectorEngine.findOne(OPEN_SELECTOR);\n\n  if (alreadyOpen && alreadyOpen !== target) {\n    Offcanvas.getInstance(alreadyOpen).hide();\n  }\n\n  const data = Offcanvas.getOrCreateInstance(target);\n  data.toggle(this);\n});\nEventHandler.on(window, EVENT_LOAD_DATA_API$2, () => {\n  for (const selector of SelectorEngine.find(OPEN_SELECTOR)) {\n    Offcanvas.getOrCreateInstance(selector).show();\n  }\n});\nEventHandler.on(window, EVENT_RESIZE, () => {\n  for (const element of SelectorEngine.find('[aria-modal][class*=show][class*=offcanvas-]')) {\n    if (getComputedStyle(element).position !== 'fixed') {\n      Offcanvas.getOrCreateInstance(element).hide();\n    }\n  }\n});\nenableDismissTrigger(Offcanvas);\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Offcanvas);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/sanitizer.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\nconst uriAttributes = new Set(['background', 'cite', 'href', 'itemtype', 'longdesc', 'poster', 'src', 'xlink:href']);\nconst ARIA_ATTRIBUTE_PATTERN = /^aria-[\\w-]*$/i;\n/**\n * A pattern that recognizes a commonly useful subset of URLs that are safe.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/12.2.x/packages/core/src/sanitization/url_sanitizer.ts\n */\n\nconst SAFE_URL_PATTERN = /^(?:(?:https?|mailto|ftp|tel|file|sms):|[^#&/:?]*(?:[#/?]|$))/i;\n/**\n * A pattern that matches safe data URLs. Only matches image, video and audio types.\n *\n * Shout-out to Angular https://github.com/angular/angular/blob/12.2.x/packages/core/src/sanitization/url_sanitizer.ts\n */\n\nconst DATA_URL_PATTERN = /^data:(?:image\\/(?:bmp|gif|jpeg|jpg|png|tiff|webp)|video\\/(?:mpeg|mp4|ogg|webm)|audio\\/(?:mp3|oga|ogg|opus));base64,[\\d+/a-z]+=*$/i;\n\nconst allowedAttribute = (attribute, allowedAttributeList) => {\n  const attributeName = attribute.nodeName.toLowerCase();\n\n  if (allowedAttributeList.includes(attributeName)) {\n    if (uriAttributes.has(attributeName)) {\n      return Boolean(SAFE_URL_PATTERN.test(attribute.nodeValue) || DATA_URL_PATTERN.test(attribute.nodeValue));\n    }\n\n    return true;\n  } // Check if a regular expression validates the attribute.\n\n\n  return allowedAttributeList.filter(attributeRegex => attributeRegex instanceof RegExp).some(regex => regex.test(attributeName));\n};\n\nconst DefaultAllowlist = {\n  // Global attributes allowed on any supplied element below.\n  '*': ['class', 'dir', 'id', 'lang', 'role', ARIA_ATTRIBUTE_PATTERN],\n  a: ['target', 'href', 'title', 'rel'],\n  area: [],\n  b: [],\n  br: [],\n  col: [],\n  code: [],\n  div: [],\n  em: [],\n  hr: [],\n  h1: [],\n  h2: [],\n  h3: [],\n  h4: [],\n  h5: [],\n  h6: [],\n  i: [],\n  img: ['src', 'srcset', 'alt', 'title', 'width', 'height'],\n  li: [],\n  ol: [],\n  p: [],\n  pre: [],\n  s: [],\n  small: [],\n  span: [],\n  sub: [],\n  sup: [],\n  strong: [],\n  u: [],\n  ul: []\n};\nfunction sanitizeHtml(unsafeHtml, allowList, sanitizeFunction) {\n  if (!unsafeHtml.length) {\n    return unsafeHtml;\n  }\n\n  if (sanitizeFunction && typeof sanitizeFunction === 'function') {\n    return sanitizeFunction(unsafeHtml);\n  }\n\n  const domParser = new window.DOMParser();\n  const createdDocument = domParser.parseFromString(unsafeHtml, 'text/html');\n  const elements = [].concat(...createdDocument.body.querySelectorAll('*'));\n\n  for (const element of elements) {\n    const elementName = element.nodeName.toLowerCase();\n\n    if (!Object.keys(allowList).includes(elementName)) {\n      element.remove();\n      continue;\n    }\n\n    const attributeList = [].concat(...element.attributes);\n    const allowedAttributes = [].concat(allowList['*'] || [], allowList[elementName] || []);\n\n    for (const attribute of attributeList) {\n      if (!allowedAttribute(attribute, allowedAttributes)) {\n        element.removeAttribute(attribute.nodeName);\n      }\n    }\n  }\n\n  return createdDocument.body.innerHTML;\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): util/template-factory.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$5 = 'TemplateFactory';\nconst Default$4 = {\n  allowList: DefaultAllowlist,\n  content: {},\n  // { selector : text ,  selector2 : text2 , }\n  extraClass: '',\n  html: false,\n  sanitize: true,\n  sanitizeFn: null,\n  template: '<div></div>'\n};\nconst DefaultType$4 = {\n  allowList: 'object',\n  content: 'object',\n  extraClass: '(string|function)',\n  html: 'boolean',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  template: 'string'\n};\nconst DefaultContentType = {\n  entry: '(string|element|function|null)',\n  selector: '(string|element)'\n};\n/**\n * Class definition\n */\n\nclass TemplateFactory extends Config {\n  constructor(config) {\n    super();\n    this._config = this._getConfig(config);\n  } // Getters\n\n\n  static get Default() {\n    return Default$4;\n  }\n\n  static get DefaultType() {\n    return DefaultType$4;\n  }\n\n  static get NAME() {\n    return NAME$5;\n  } // Public\n\n\n  getContent() {\n    return Object.values(this._config.content).map(config => this._resolvePossibleFunction(config)).filter(Boolean);\n  }\n\n  hasContent() {\n    return this.getContent().length > 0;\n  }\n\n  changeContent(content) {\n    this._checkContent(content);\n\n    this._config.content = { ...this._config.content,\n      ...content\n    };\n    return this;\n  }\n\n  toHtml() {\n    const templateWrapper = document.createElement('div');\n    templateWrapper.innerHTML = this._maybeSanitize(this._config.template);\n\n    for (const [selector, text] of Object.entries(this._config.content)) {\n      this._setContent(templateWrapper, text, selector);\n    }\n\n    const template = templateWrapper.children[0];\n\n    const extraClass = this._resolvePossibleFunction(this._config.extraClass);\n\n    if (extraClass) {\n      template.classList.add(...extraClass.split(' '));\n    }\n\n    return template;\n  } // Private\n\n\n  _typeCheckConfig(config) {\n    super._typeCheckConfig(config);\n\n    this._checkContent(config.content);\n  }\n\n  _checkContent(arg) {\n    for (const [selector, content] of Object.entries(arg)) {\n      super._typeCheckConfig({\n        selector,\n        entry: content\n      }, DefaultContentType);\n    }\n  }\n\n  _setContent(template, content, selector) {\n    const templateElement = SelectorEngine.findOne(selector, template);\n\n    if (!templateElement) {\n      return;\n    }\n\n    content = this._resolvePossibleFunction(content);\n\n    if (!content) {\n      templateElement.remove();\n      return;\n    }\n\n    if (isElement(content)) {\n      this._putElementInTemplate(getElement(content), templateElement);\n\n      return;\n    }\n\n    if (this._config.html) {\n      templateElement.innerHTML = this._maybeSanitize(content);\n      return;\n    }\n\n    templateElement.textContent = content;\n  }\n\n  _maybeSanitize(arg) {\n    return this._config.sanitize ? sanitizeHtml(arg, this._config.allowList, this._config.sanitizeFn) : arg;\n  }\n\n  _resolvePossibleFunction(arg) {\n    return typeof arg === 'function' ? arg(this) : arg;\n  }\n\n  _putElementInTemplate(element, templateElement) {\n    if (this._config.html) {\n      templateElement.innerHTML = '';\n      templateElement.append(element);\n      return;\n    }\n\n    templateElement.textContent = element.textContent;\n  }\n\n}\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): tooltip.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$4 = 'tooltip';\nconst DISALLOWED_ATTRIBUTES = new Set(['sanitize', 'allowList', 'sanitizeFn']);\nconst CLASS_NAME_FADE$2 = 'fade';\nconst CLASS_NAME_MODAL = 'modal';\nconst CLASS_NAME_SHOW$2 = 'show';\nconst SELECTOR_TOOLTIP_INNER = '.tooltip-inner';\nconst SELECTOR_MODAL = `.${CLASS_NAME_MODAL}`;\nconst EVENT_MODAL_HIDE = 'hide.bs.modal';\nconst TRIGGER_HOVER = 'hover';\nconst TRIGGER_FOCUS = 'focus';\nconst TRIGGER_CLICK = 'click';\nconst TRIGGER_MANUAL = 'manual';\nconst EVENT_HIDE$2 = 'hide';\nconst EVENT_HIDDEN$2 = 'hidden';\nconst EVENT_SHOW$2 = 'show';\nconst EVENT_SHOWN$2 = 'shown';\nconst EVENT_INSERTED = 'inserted';\nconst EVENT_CLICK$1 = 'click';\nconst EVENT_FOCUSIN$1 = 'focusin';\nconst EVENT_FOCUSOUT$1 = 'focusout';\nconst EVENT_MOUSEENTER = 'mouseenter';\nconst EVENT_MOUSELEAVE = 'mouseleave';\nconst AttachmentMap = {\n  AUTO: 'auto',\n  TOP: 'top',\n  RIGHT: isRTL() ? 'left' : 'right',\n  BOTTOM: 'bottom',\n  LEFT: isRTL() ? 'right' : 'left'\n};\nconst Default$3 = {\n  allowList: DefaultAllowlist,\n  animation: true,\n  boundary: 'clippingParents',\n  container: false,\n  customClass: '',\n  delay: 0,\n  fallbackPlacements: ['top', 'right', 'bottom', 'left'],\n  html: false,\n  offset: [0, 0],\n  placement: 'top',\n  popperConfig: null,\n  sanitize: true,\n  sanitizeFn: null,\n  selector: false,\n  template: '<div class=\"tooltip\" role=\"tooltip\">' + '<div class=\"tooltip-arrow\"></div>' + '<div class=\"tooltip-inner\"></div>' + '</div>',\n  title: '',\n  trigger: 'hover focus'\n};\nconst DefaultType$3 = {\n  allowList: 'object',\n  animation: 'boolean',\n  boundary: '(string|element)',\n  container: '(string|element|boolean)',\n  customClass: '(string|function)',\n  delay: '(number|object)',\n  fallbackPlacements: 'array',\n  html: 'boolean',\n  offset: '(array|string|function)',\n  placement: '(string|function)',\n  popperConfig: '(null|object|function)',\n  sanitize: 'boolean',\n  sanitizeFn: '(null|function)',\n  selector: '(string|boolean)',\n  template: 'string',\n  title: '(string|element|function)',\n  trigger: 'string'\n};\n/**\n * Class definition\n */\n\nclass Tooltip extends BaseComponent {\n  constructor(element, config) {\n    if (typeof Popper === 'undefined') {\n      throw new TypeError('Bootstrap\\'s tooltips require Popper (https://popper.js.org)');\n    }\n\n    super(element, config); // Private\n\n    this._isEnabled = true;\n    this._timeout = 0;\n    this._isHovered = null;\n    this._activeTrigger = {};\n    this._popper = null;\n    this._templateFactory = null;\n    this._newContent = null; // Protected\n\n    this.tip = null;\n\n    this._setListeners();\n\n    if (!this._config.selector) {\n      this._fixTitle();\n    }\n  } // Getters\n\n\n  static get Default() {\n    return Default$3;\n  }\n\n  static get DefaultType() {\n    return DefaultType$3;\n  }\n\n  static get NAME() {\n    return NAME$4;\n  } // Public\n\n\n  enable() {\n    this._isEnabled = true;\n  }\n\n  disable() {\n    this._isEnabled = false;\n  }\n\n  toggleEnabled() {\n    this._isEnabled = !this._isEnabled;\n  }\n\n  toggle() {\n    if (!this._isEnabled) {\n      return;\n    }\n\n    this._activeTrigger.click = !this._activeTrigger.click;\n\n    if (this._isShown()) {\n      this._leave();\n\n      return;\n    }\n\n    this._enter();\n  }\n\n  dispose() {\n    clearTimeout(this._timeout);\n    EventHandler.off(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n\n    if (this._element.getAttribute('data-bs-original-title')) {\n      this._element.setAttribute('title', this._element.getAttribute('data-bs-original-title'));\n    }\n\n    this._disposePopper();\n\n    super.dispose();\n  }\n\n  show() {\n    if (this._element.style.display === 'none') {\n      throw new Error('Please use show on visible elements');\n    }\n\n    if (!(this._isWithContent() && this._isEnabled)) {\n      return;\n    }\n\n    const showEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOW$2));\n    const shadowRoot = findShadowRoot(this._element);\n\n    const isInTheDom = (shadowRoot || this._element.ownerDocument.documentElement).contains(this._element);\n\n    if (showEvent.defaultPrevented || !isInTheDom) {\n      return;\n    } // todo v6 remove this OR make it optional\n\n\n    this._disposePopper();\n\n    const tip = this._getTipElement();\n\n    this._element.setAttribute('aria-describedby', tip.getAttribute('id'));\n\n    const {\n      container\n    } = this._config;\n\n    if (!this._element.ownerDocument.documentElement.contains(this.tip)) {\n      container.append(tip);\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_INSERTED));\n    }\n\n    this._popper = this._createPopper(tip);\n    tip.classList.add(CLASS_NAME_SHOW$2); // If this is a touch-enabled device we add extra\n    // empty mouseover listeners to the body's immediate children;\n    // only needed because of broken event delegation on iOS\n    // https://www.quirksmode.org/blog/archives/2014/02/mouse_event_bub.html\n\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.on(element, 'mouseover', noop);\n      }\n    }\n\n    const complete = () => {\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_SHOWN$2));\n\n      if (this._isHovered === false) {\n        this._leave();\n      }\n\n      this._isHovered = false;\n    };\n\n    this._queueCallback(complete, this.tip, this._isAnimated());\n  }\n\n  hide() {\n    if (!this._isShown()) {\n      return;\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDE$2));\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    }\n\n    const tip = this._getTipElement();\n\n    tip.classList.remove(CLASS_NAME_SHOW$2); // If this is a touch-enabled device we remove the extra\n    // empty mouseover listeners we added for iOS support\n\n    if ('ontouchstart' in document.documentElement) {\n      for (const element of [].concat(...document.body.children)) {\n        EventHandler.off(element, 'mouseover', noop);\n      }\n    }\n\n    this._activeTrigger[TRIGGER_CLICK] = false;\n    this._activeTrigger[TRIGGER_FOCUS] = false;\n    this._activeTrigger[TRIGGER_HOVER] = false;\n    this._isHovered = null; // it is a trick to support manual triggering\n\n    const complete = () => {\n      if (this._isWithActiveTrigger()) {\n        return;\n      }\n\n      if (!this._isHovered) {\n        this._disposePopper();\n      }\n\n      this._element.removeAttribute('aria-describedby');\n\n      EventHandler.trigger(this._element, this.constructor.eventName(EVENT_HIDDEN$2));\n    };\n\n    this._queueCallback(complete, this.tip, this._isAnimated());\n  }\n\n  update() {\n    if (this._popper) {\n      this._popper.update();\n    }\n  } // Protected\n\n\n  _isWithContent() {\n    return Boolean(this._getTitle());\n  }\n\n  _getTipElement() {\n    if (!this.tip) {\n      this.tip = this._createTipElement(this._newContent || this._getContentForTemplate());\n    }\n\n    return this.tip;\n  }\n\n  _createTipElement(content) {\n    const tip = this._getTemplateFactory(content).toHtml(); // todo: remove this check on v6\n\n\n    if (!tip) {\n      return null;\n    }\n\n    tip.classList.remove(CLASS_NAME_FADE$2, CLASS_NAME_SHOW$2); // todo: on v6 the following can be achieved with CSS only\n\n    tip.classList.add(`bs-${this.constructor.NAME}-auto`);\n    const tipId = getUID(this.constructor.NAME).toString();\n    tip.setAttribute('id', tipId);\n\n    if (this._isAnimated()) {\n      tip.classList.add(CLASS_NAME_FADE$2);\n    }\n\n    return tip;\n  }\n\n  setContent(content) {\n    this._newContent = content;\n\n    if (this._isShown()) {\n      this._disposePopper();\n\n      this.show();\n    }\n  }\n\n  _getTemplateFactory(content) {\n    if (this._templateFactory) {\n      this._templateFactory.changeContent(content);\n    } else {\n      this._templateFactory = new TemplateFactory({ ...this._config,\n        // the `content` var has to be after `this._config`\n        // to override config.content in case of popover\n        content,\n        extraClass: this._resolvePossibleFunction(this._config.customClass)\n      });\n    }\n\n    return this._templateFactory;\n  }\n\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TOOLTIP_INNER]: this._getTitle()\n    };\n  }\n\n  _getTitle() {\n    return this._resolvePossibleFunction(this._config.title) || this._element.getAttribute('data-bs-original-title');\n  } // Private\n\n\n  _initializeOnDelegatedTarget(event) {\n    return this.constructor.getOrCreateInstance(event.delegateTarget, this._getDelegateConfig());\n  }\n\n  _isAnimated() {\n    return this._config.animation || this.tip && this.tip.classList.contains(CLASS_NAME_FADE$2);\n  }\n\n  _isShown() {\n    return this.tip && this.tip.classList.contains(CLASS_NAME_SHOW$2);\n  }\n\n  _createPopper(tip) {\n    const placement = typeof this._config.placement === 'function' ? this._config.placement.call(this, tip, this._element) : this._config.placement;\n    const attachment = AttachmentMap[placement.toUpperCase()];\n    return Popper.createPopper(this._element, tip, this._getPopperConfig(attachment));\n  }\n\n  _getOffset() {\n    const {\n      offset\n    } = this._config;\n\n    if (typeof offset === 'string') {\n      return offset.split(',').map(value => Number.parseInt(value, 10));\n    }\n\n    if (typeof offset === 'function') {\n      return popperData => offset(popperData, this._element);\n    }\n\n    return offset;\n  }\n\n  _resolvePossibleFunction(arg) {\n    return typeof arg === 'function' ? arg.call(this._element) : arg;\n  }\n\n  _getPopperConfig(attachment) {\n    const defaultBsPopperConfig = {\n      placement: attachment,\n      modifiers: [{\n        name: 'flip',\n        options: {\n          fallbackPlacements: this._config.fallbackPlacements\n        }\n      }, {\n        name: 'offset',\n        options: {\n          offset: this._getOffset()\n        }\n      }, {\n        name: 'preventOverflow',\n        options: {\n          boundary: this._config.boundary\n        }\n      }, {\n        name: 'arrow',\n        options: {\n          element: `.${this.constructor.NAME}-arrow`\n        }\n      }, {\n        name: 'preSetPlacement',\n        enabled: true,\n        phase: 'beforeMain',\n        fn: data => {\n          // Pre-set Popper's placement attribute in order to read the arrow sizes properly.\n          // Otherwise, Popper mixes up the width and height dimensions since the initial arrow style is for top placement\n          this._getTipElement().setAttribute('data-popper-placement', data.state.placement);\n        }\n      }]\n    };\n    return { ...defaultBsPopperConfig,\n      ...(typeof this._config.popperConfig === 'function' ? this._config.popperConfig(defaultBsPopperConfig) : this._config.popperConfig)\n    };\n  }\n\n  _setListeners() {\n    const triggers = this._config.trigger.split(' ');\n\n    for (const trigger of triggers) {\n      if (trigger === 'click') {\n        EventHandler.on(this._element, this.constructor.eventName(EVENT_CLICK$1), this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event);\n\n          context.toggle();\n        });\n      } else if (trigger !== TRIGGER_MANUAL) {\n        const eventIn = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSEENTER) : this.constructor.eventName(EVENT_FOCUSIN$1);\n        const eventOut = trigger === TRIGGER_HOVER ? this.constructor.eventName(EVENT_MOUSELEAVE) : this.constructor.eventName(EVENT_FOCUSOUT$1);\n        EventHandler.on(this._element, eventIn, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event);\n\n          context._activeTrigger[event.type === 'focusin' ? TRIGGER_FOCUS : TRIGGER_HOVER] = true;\n\n          context._enter();\n        });\n        EventHandler.on(this._element, eventOut, this._config.selector, event => {\n          const context = this._initializeOnDelegatedTarget(event);\n\n          context._activeTrigger[event.type === 'focusout' ? TRIGGER_FOCUS : TRIGGER_HOVER] = context._element.contains(event.relatedTarget);\n\n          context._leave();\n        });\n      }\n    }\n\n    this._hideModalHandler = () => {\n      if (this._element) {\n        this.hide();\n      }\n    };\n\n    EventHandler.on(this._element.closest(SELECTOR_MODAL), EVENT_MODAL_HIDE, this._hideModalHandler);\n  }\n\n  _fixTitle() {\n    const title = this._element.getAttribute('title');\n\n    if (!title) {\n      return;\n    }\n\n    if (!this._element.getAttribute('aria-label') && !this._element.textContent.trim()) {\n      this._element.setAttribute('aria-label', title);\n    }\n\n    this._element.setAttribute('data-bs-original-title', title); // DO NOT USE IT. Is only for backwards compatibility\n\n\n    this._element.removeAttribute('title');\n  }\n\n  _enter() {\n    if (this._isShown() || this._isHovered) {\n      this._isHovered = true;\n      return;\n    }\n\n    this._isHovered = true;\n\n    this._setTimeout(() => {\n      if (this._isHovered) {\n        this.show();\n      }\n    }, this._config.delay.show);\n  }\n\n  _leave() {\n    if (this._isWithActiveTrigger()) {\n      return;\n    }\n\n    this._isHovered = false;\n\n    this._setTimeout(() => {\n      if (!this._isHovered) {\n        this.hide();\n      }\n    }, this._config.delay.hide);\n  }\n\n  _setTimeout(handler, timeout) {\n    clearTimeout(this._timeout);\n    this._timeout = setTimeout(handler, timeout);\n  }\n\n  _isWithActiveTrigger() {\n    return Object.values(this._activeTrigger).includes(true);\n  }\n\n  _getConfig(config) {\n    const dataAttributes = Manipulator.getDataAttributes(this._element);\n\n    for (const dataAttribute of Object.keys(dataAttributes)) {\n      if (DISALLOWED_ATTRIBUTES.has(dataAttribute)) {\n        delete dataAttributes[dataAttribute];\n      }\n    }\n\n    config = { ...dataAttributes,\n      ...(typeof config === 'object' && config ? config : {})\n    };\n    config = this._mergeConfigObj(config);\n    config = this._configAfterMerge(config);\n\n    this._typeCheckConfig(config);\n\n    return config;\n  }\n\n  _configAfterMerge(config) {\n    config.container = config.container === false ? document.body : getElement(config.container);\n\n    if (typeof config.delay === 'number') {\n      config.delay = {\n        show: config.delay,\n        hide: config.delay\n      };\n    }\n\n    if (typeof config.title === 'number') {\n      config.title = config.title.toString();\n    }\n\n    if (typeof config.content === 'number') {\n      config.content = config.content.toString();\n    }\n\n    return config;\n  }\n\n  _getDelegateConfig() {\n    const config = {};\n\n    for (const key in this._config) {\n      if (this.constructor.Default[key] !== this._config[key]) {\n        config[key] = this._config[key];\n      }\n    }\n\n    config.selector = false;\n    config.trigger = 'manual'; // In the future can be replaced with:\n    // const keysWithDifferentValues = Object.entries(this._config).filter(entry => this.constructor.Default[entry[0]] !== this._config[entry[0]])\n    // `Object.fromEntries(keysWithDifferentValues)`\n\n    return config;\n  }\n\n  _disposePopper() {\n    if (this._popper) {\n      this._popper.destroy();\n\n      this._popper = null;\n    }\n\n    if (this.tip) {\n      this.tip.remove();\n      this.tip = null;\n    }\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tooltip.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config]();\n    });\n  }\n\n}\n/**\n * jQuery\n */\n\n\ndefineJQueryPlugin(Tooltip);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): popover.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$3 = 'popover';\nconst SELECTOR_TITLE = '.popover-header';\nconst SELECTOR_CONTENT = '.popover-body';\nconst Default$2 = { ...Tooltip.Default,\n  content: '',\n  offset: [0, 8],\n  placement: 'right',\n  template: '<div class=\"popover\" role=\"tooltip\">' + '<div class=\"popover-arrow\"></div>' + '<h3 class=\"popover-header\"></h3>' + '<div class=\"popover-body\"></div>' + '</div>',\n  trigger: 'click'\n};\nconst DefaultType$2 = { ...Tooltip.DefaultType,\n  content: '(null|string|element|function)'\n};\n/**\n * Class definition\n */\n\nclass Popover extends Tooltip {\n  // Getters\n  static get Default() {\n    return Default$2;\n  }\n\n  static get DefaultType() {\n    return DefaultType$2;\n  }\n\n  static get NAME() {\n    return NAME$3;\n  } // Overrides\n\n\n  _isWithContent() {\n    return this._getTitle() || this._getContent();\n  } // Private\n\n\n  _getContentForTemplate() {\n    return {\n      [SELECTOR_TITLE]: this._getTitle(),\n      [SELECTOR_CONTENT]: this._getContent()\n    };\n  }\n\n  _getContent() {\n    return this._resolvePossibleFunction(this._config.content);\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Popover.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (typeof data[config] === 'undefined') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config]();\n    });\n  }\n\n}\n/**\n * jQuery\n */\n\n\ndefineJQueryPlugin(Popover);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): scrollspy.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$2 = 'scrollspy';\nconst DATA_KEY$2 = 'bs.scrollspy';\nconst EVENT_KEY$2 = `.${DATA_KEY$2}`;\nconst DATA_API_KEY = '.data-api';\nconst EVENT_ACTIVATE = `activate${EVENT_KEY$2}`;\nconst EVENT_CLICK = `click${EVENT_KEY$2}`;\nconst EVENT_LOAD_DATA_API$1 = `load${EVENT_KEY$2}${DATA_API_KEY}`;\nconst CLASS_NAME_DROPDOWN_ITEM = 'dropdown-item';\nconst CLASS_NAME_ACTIVE$1 = 'active';\nconst SELECTOR_DATA_SPY = '[data-bs-spy=\"scroll\"]';\nconst SELECTOR_TARGET_LINKS = '[href]';\nconst SELECTOR_NAV_LIST_GROUP = '.nav, .list-group';\nconst SELECTOR_NAV_LINKS = '.nav-link';\nconst SELECTOR_NAV_ITEMS = '.nav-item';\nconst SELECTOR_LIST_ITEMS = '.list-group-item';\nconst SELECTOR_LINK_ITEMS = `${SELECTOR_NAV_LINKS}, ${SELECTOR_NAV_ITEMS} > ${SELECTOR_NAV_LINKS}, ${SELECTOR_LIST_ITEMS}`;\nconst SELECTOR_DROPDOWN = '.dropdown';\nconst SELECTOR_DROPDOWN_TOGGLE$1 = '.dropdown-toggle';\nconst Default$1 = {\n  offset: null,\n  // TODO: v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: '0px 0px -25%',\n  smoothScroll: false,\n  target: null,\n  threshold: [0.1, 0.5, 1]\n};\nconst DefaultType$1 = {\n  offset: '(number|null)',\n  // TODO v6 @deprecated, keep it for backwards compatibility reasons\n  rootMargin: 'string',\n  smoothScroll: 'boolean',\n  target: 'element',\n  threshold: 'array'\n};\n/**\n * Class definition\n */\n\nclass ScrollSpy extends BaseComponent {\n  constructor(element, config) {\n    super(element, config); // this._element is the observablesContainer and config.target the menu links wrapper\n\n    this._targetLinks = new Map();\n    this._observableSections = new Map();\n    this._rootElement = getComputedStyle(this._element).overflowY === 'visible' ? null : this._element;\n    this._activeTarget = null;\n    this._observer = null;\n    this._previousScrollData = {\n      visibleEntryTop: 0,\n      parentScrollTop: 0\n    };\n    this.refresh(); // initialize\n  } // Getters\n\n\n  static get Default() {\n    return Default$1;\n  }\n\n  static get DefaultType() {\n    return DefaultType$1;\n  }\n\n  static get NAME() {\n    return NAME$2;\n  } // Public\n\n\n  refresh() {\n    this._initializeTargetsAndObservables();\n\n    this._maybeEnableSmoothScroll();\n\n    if (this._observer) {\n      this._observer.disconnect();\n    } else {\n      this._observer = this._getNewObserver();\n    }\n\n    for (const section of this._observableSections.values()) {\n      this._observer.observe(section);\n    }\n  }\n\n  dispose() {\n    this._observer.disconnect();\n\n    super.dispose();\n  } // Private\n\n\n  _configAfterMerge(config) {\n    // TODO: on v6 target should be given explicitly & remove the {target: 'ss-target'} case\n    config.target = getElement(config.target) || document.body; // TODO: v6 Only for backwards compatibility reasons. Use rootMargin only\n\n    config.rootMargin = config.offset ? `${config.offset}px 0px -30%` : config.rootMargin;\n\n    if (typeof config.threshold === 'string') {\n      config.threshold = config.threshold.split(',').map(value => Number.parseFloat(value));\n    }\n\n    return config;\n  }\n\n  _maybeEnableSmoothScroll() {\n    if (!this._config.smoothScroll) {\n      return;\n    } // unregister any previous listeners\n\n\n    EventHandler.off(this._config.target, EVENT_CLICK);\n    EventHandler.on(this._config.target, EVENT_CLICK, SELECTOR_TARGET_LINKS, event => {\n      const observableSection = this._observableSections.get(event.target.hash);\n\n      if (observableSection) {\n        event.preventDefault();\n        const root = this._rootElement || window;\n        const height = observableSection.offsetTop - this._element.offsetTop;\n\n        if (root.scrollTo) {\n          root.scrollTo({\n            top: height,\n            behavior: 'smooth'\n          });\n          return;\n        } // Chrome 60 doesn't support `scrollTo`\n\n\n        root.scrollTop = height;\n      }\n    });\n  }\n\n  _getNewObserver() {\n    const options = {\n      root: this._rootElement,\n      threshold: this._config.threshold,\n      rootMargin: this._config.rootMargin\n    };\n    return new IntersectionObserver(entries => this._observerCallback(entries), options);\n  } // The logic of selection\n\n\n  _observerCallback(entries) {\n    const targetElement = entry => this._targetLinks.get(`#${entry.target.id}`);\n\n    const activate = entry => {\n      this._previousScrollData.visibleEntryTop = entry.target.offsetTop;\n\n      this._process(targetElement(entry));\n    };\n\n    const parentScrollTop = (this._rootElement || document.documentElement).scrollTop;\n    const userScrollsDown = parentScrollTop >= this._previousScrollData.parentScrollTop;\n    this._previousScrollData.parentScrollTop = parentScrollTop;\n\n    for (const entry of entries) {\n      if (!entry.isIntersecting) {\n        this._activeTarget = null;\n\n        this._clearActiveClass(targetElement(entry));\n\n        continue;\n      }\n\n      const entryIsLowerThanPrevious = entry.target.offsetTop >= this._previousScrollData.visibleEntryTop; // if we are scrolling down, pick the bigger offsetTop\n\n      if (userScrollsDown && entryIsLowerThanPrevious) {\n        activate(entry); // if parent isn't scrolled, let's keep the first visible item, breaking the iteration\n\n        if (!parentScrollTop) {\n          return;\n        }\n\n        continue;\n      } // if we are scrolling up, pick the smallest offsetTop\n\n\n      if (!userScrollsDown && !entryIsLowerThanPrevious) {\n        activate(entry);\n      }\n    }\n  }\n\n  _initializeTargetsAndObservables() {\n    this._targetLinks = new Map();\n    this._observableSections = new Map();\n    const targetLinks = SelectorEngine.find(SELECTOR_TARGET_LINKS, this._config.target);\n\n    for (const anchor of targetLinks) {\n      // ensure that the anchor has an id and is not disabled\n      if (!anchor.hash || isDisabled(anchor)) {\n        continue;\n      }\n\n      const observableSection = SelectorEngine.findOne(anchor.hash, this._element); // ensure that the observableSection exists & is visible\n\n      if (isVisible(observableSection)) {\n        this._targetLinks.set(anchor.hash, anchor);\n\n        this._observableSections.set(anchor.hash, observableSection);\n      }\n    }\n  }\n\n  _process(target) {\n    if (this._activeTarget === target) {\n      return;\n    }\n\n    this._clearActiveClass(this._config.target);\n\n    this._activeTarget = target;\n    target.classList.add(CLASS_NAME_ACTIVE$1);\n\n    this._activateParents(target);\n\n    EventHandler.trigger(this._element, EVENT_ACTIVATE, {\n      relatedTarget: target\n    });\n  }\n\n  _activateParents(target) {\n    // Activate dropdown parents\n    if (target.classList.contains(CLASS_NAME_DROPDOWN_ITEM)) {\n      SelectorEngine.findOne(SELECTOR_DROPDOWN_TOGGLE$1, target.closest(SELECTOR_DROPDOWN)).classList.add(CLASS_NAME_ACTIVE$1);\n      return;\n    }\n\n    for (const listGroup of SelectorEngine.parents(target, SELECTOR_NAV_LIST_GROUP)) {\n      // Set triggered links parents as active\n      // With both <ul> and <nav> markup a parent is the previous sibling of any nav ancestor\n      for (const item of SelectorEngine.prev(listGroup, SELECTOR_LINK_ITEMS)) {\n        item.classList.add(CLASS_NAME_ACTIVE$1);\n      }\n    }\n  }\n\n  _clearActiveClass(parent) {\n    parent.classList.remove(CLASS_NAME_ACTIVE$1);\n    const activeNodes = SelectorEngine.find(`${SELECTOR_TARGET_LINKS}.${CLASS_NAME_ACTIVE$1}`, parent);\n\n    for (const node of activeNodes) {\n      node.classList.remove(CLASS_NAME_ACTIVE$1);\n    }\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = ScrollSpy.getOrCreateInstance(this, config);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config]();\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(window, EVENT_LOAD_DATA_API$1, () => {\n  for (const spy of SelectorEngine.find(SELECTOR_DATA_SPY)) {\n    ScrollSpy.getOrCreateInstance(spy);\n  }\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(ScrollSpy);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): tab.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME$1 = 'tab';\nconst DATA_KEY$1 = 'bs.tab';\nconst EVENT_KEY$1 = `.${DATA_KEY$1}`;\nconst EVENT_HIDE$1 = `hide${EVENT_KEY$1}`;\nconst EVENT_HIDDEN$1 = `hidden${EVENT_KEY$1}`;\nconst EVENT_SHOW$1 = `show${EVENT_KEY$1}`;\nconst EVENT_SHOWN$1 = `shown${EVENT_KEY$1}`;\nconst EVENT_CLICK_DATA_API = `click${EVENT_KEY$1}`;\nconst EVENT_KEYDOWN = `keydown${EVENT_KEY$1}`;\nconst EVENT_LOAD_DATA_API = `load${EVENT_KEY$1}`;\nconst ARROW_LEFT_KEY = 'ArrowLeft';\nconst ARROW_RIGHT_KEY = 'ArrowRight';\nconst ARROW_UP_KEY = 'ArrowUp';\nconst ARROW_DOWN_KEY = 'ArrowDown';\nconst CLASS_NAME_ACTIVE = 'active';\nconst CLASS_NAME_FADE$1 = 'fade';\nconst CLASS_NAME_SHOW$1 = 'show';\nconst CLASS_DROPDOWN = 'dropdown';\nconst SELECTOR_DROPDOWN_TOGGLE = '.dropdown-toggle';\nconst SELECTOR_DROPDOWN_MENU = '.dropdown-menu';\nconst NOT_SELECTOR_DROPDOWN_TOGGLE = ':not(.dropdown-toggle)';\nconst SELECTOR_TAB_PANEL = '.list-group, .nav, [role=\"tablist\"]';\nconst SELECTOR_OUTER = '.nav-item, .list-group-item';\nconst SELECTOR_INNER = `.nav-link${NOT_SELECTOR_DROPDOWN_TOGGLE}, .list-group-item${NOT_SELECTOR_DROPDOWN_TOGGLE}, [role=\"tab\"]${NOT_SELECTOR_DROPDOWN_TOGGLE}`;\nconst SELECTOR_DATA_TOGGLE = '[data-bs-toggle=\"tab\"], [data-bs-toggle=\"pill\"], [data-bs-toggle=\"list\"]'; // todo:v6: could be only `tab`\n\nconst SELECTOR_INNER_ELEM = `${SELECTOR_INNER}, ${SELECTOR_DATA_TOGGLE}`;\nconst SELECTOR_DATA_TOGGLE_ACTIVE = `.${CLASS_NAME_ACTIVE}[data-bs-toggle=\"tab\"], .${CLASS_NAME_ACTIVE}[data-bs-toggle=\"pill\"], .${CLASS_NAME_ACTIVE}[data-bs-toggle=\"list\"]`;\n/**\n * Class definition\n */\n\nclass Tab extends BaseComponent {\n  constructor(element) {\n    super(element);\n    this._parent = this._element.closest(SELECTOR_TAB_PANEL);\n\n    if (!this._parent) {\n      return; // todo: should Throw exception on v6\n      // throw new TypeError(`${element.outerHTML} has not a valid parent ${SELECTOR_INNER_ELEM}`)\n    } // Set up initial aria attributes\n\n\n    this._setInitialAttributes(this._parent, this._getChildren());\n\n    EventHandler.on(this._element, EVENT_KEYDOWN, event => this._keydown(event));\n  } // Getters\n\n\n  static get NAME() {\n    return NAME$1;\n  } // Public\n\n\n  show() {\n    // Shows this elem and deactivate the active sibling if exists\n    const innerElem = this._element;\n\n    if (this._elemIsActive(innerElem)) {\n      return;\n    } // Search for active tab on same parent to deactivate it\n\n\n    const active = this._getActiveElem();\n\n    const hideEvent = active ? EventHandler.trigger(active, EVENT_HIDE$1, {\n      relatedTarget: innerElem\n    }) : null;\n    const showEvent = EventHandler.trigger(innerElem, EVENT_SHOW$1, {\n      relatedTarget: active\n    });\n\n    if (showEvent.defaultPrevented || hideEvent && hideEvent.defaultPrevented) {\n      return;\n    }\n\n    this._deactivate(active, innerElem);\n\n    this._activate(innerElem, active);\n  } // Private\n\n\n  _activate(element, relatedElem) {\n    if (!element) {\n      return;\n    }\n\n    element.classList.add(CLASS_NAME_ACTIVE);\n\n    this._activate(getElementFromSelector(element)); // Search and activate/show the proper section\n\n\n    const complete = () => {\n      if (element.getAttribute('role') !== 'tab') {\n        element.classList.add(CLASS_NAME_SHOW$1);\n        return;\n      }\n\n      element.removeAttribute('tabindex');\n      element.setAttribute('aria-selected', true);\n\n      this._toggleDropDown(element, true);\n\n      EventHandler.trigger(element, EVENT_SHOWN$1, {\n        relatedTarget: relatedElem\n      });\n    };\n\n    this._queueCallback(complete, element, element.classList.contains(CLASS_NAME_FADE$1));\n  }\n\n  _deactivate(element, relatedElem) {\n    if (!element) {\n      return;\n    }\n\n    element.classList.remove(CLASS_NAME_ACTIVE);\n    element.blur();\n\n    this._deactivate(getElementFromSelector(element)); // Search and deactivate the shown section too\n\n\n    const complete = () => {\n      if (element.getAttribute('role') !== 'tab') {\n        element.classList.remove(CLASS_NAME_SHOW$1);\n        return;\n      }\n\n      element.setAttribute('aria-selected', false);\n      element.setAttribute('tabindex', '-1');\n\n      this._toggleDropDown(element, false);\n\n      EventHandler.trigger(element, EVENT_HIDDEN$1, {\n        relatedTarget: relatedElem\n      });\n    };\n\n    this._queueCallback(complete, element, element.classList.contains(CLASS_NAME_FADE$1));\n  }\n\n  _keydown(event) {\n    if (![ARROW_LEFT_KEY, ARROW_RIGHT_KEY, ARROW_UP_KEY, ARROW_DOWN_KEY].includes(event.key)) {\n      return;\n    }\n\n    event.stopPropagation(); // stopPropagation/preventDefault both added to support up/down keys without scrolling the page\n\n    event.preventDefault();\n    const isNext = [ARROW_RIGHT_KEY, ARROW_DOWN_KEY].includes(event.key);\n    const nextActiveElement = getNextActiveElement(this._getChildren().filter(element => !isDisabled(element)), event.target, isNext, true);\n\n    if (nextActiveElement) {\n      nextActiveElement.focus({\n        preventScroll: true\n      });\n      Tab.getOrCreateInstance(nextActiveElement).show();\n    }\n  }\n\n  _getChildren() {\n    // collection of inner elements\n    return SelectorEngine.find(SELECTOR_INNER_ELEM, this._parent);\n  }\n\n  _getActiveElem() {\n    return this._getChildren().find(child => this._elemIsActive(child)) || null;\n  }\n\n  _setInitialAttributes(parent, children) {\n    this._setAttributeIfNotExists(parent, 'role', 'tablist');\n\n    for (const child of children) {\n      this._setInitialAttributesOnChild(child);\n    }\n  }\n\n  _setInitialAttributesOnChild(child) {\n    child = this._getInnerElement(child);\n\n    const isActive = this._elemIsActive(child);\n\n    const outerElem = this._getOuterElement(child);\n\n    child.setAttribute('aria-selected', isActive);\n\n    if (outerElem !== child) {\n      this._setAttributeIfNotExists(outerElem, 'role', 'presentation');\n    }\n\n    if (!isActive) {\n      child.setAttribute('tabindex', '-1');\n    }\n\n    this._setAttributeIfNotExists(child, 'role', 'tab'); // set attributes to the related panel too\n\n\n    this._setInitialAttributesOnTargetPanel(child);\n  }\n\n  _setInitialAttributesOnTargetPanel(child) {\n    const target = getElementFromSelector(child);\n\n    if (!target) {\n      return;\n    }\n\n    this._setAttributeIfNotExists(target, 'role', 'tabpanel');\n\n    if (child.id) {\n      this._setAttributeIfNotExists(target, 'aria-labelledby', `#${child.id}`);\n    }\n  }\n\n  _toggleDropDown(element, open) {\n    const outerElem = this._getOuterElement(element);\n\n    if (!outerElem.classList.contains(CLASS_DROPDOWN)) {\n      return;\n    }\n\n    const toggle = (selector, className) => {\n      const element = SelectorEngine.findOne(selector, outerElem);\n\n      if (element) {\n        element.classList.toggle(className, open);\n      }\n    };\n\n    toggle(SELECTOR_DROPDOWN_TOGGLE, CLASS_NAME_ACTIVE);\n    toggle(SELECTOR_DROPDOWN_MENU, CLASS_NAME_SHOW$1);\n    outerElem.setAttribute('aria-expanded', open);\n  }\n\n  _setAttributeIfNotExists(element, attribute, value) {\n    if (!element.hasAttribute(attribute)) {\n      element.setAttribute(attribute, value);\n    }\n  }\n\n  _elemIsActive(elem) {\n    return elem.classList.contains(CLASS_NAME_ACTIVE);\n  } // Try to get the inner element (usually the .nav-link)\n\n\n  _getInnerElement(elem) {\n    return elem.matches(SELECTOR_INNER_ELEM) ? elem : SelectorEngine.findOne(SELECTOR_INNER_ELEM, elem);\n  } // Try to get the outer element (usually the .nav-item)\n\n\n  _getOuterElement(elem) {\n    return elem.closest(SELECTOR_OUTER) || elem;\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Tab.getOrCreateInstance(this);\n\n      if (typeof config !== 'string') {\n        return;\n      }\n\n      if (data[config] === undefined || config.startsWith('_') || config === 'constructor') {\n        throw new TypeError(`No method named \"${config}\"`);\n      }\n\n      data[config]();\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nEventHandler.on(document, EVENT_CLICK_DATA_API, SELECTOR_DATA_TOGGLE, function (event) {\n  if (['A', 'AREA'].includes(this.tagName)) {\n    event.preventDefault();\n  }\n\n  if (isDisabled(this)) {\n    return;\n  }\n\n  Tab.getOrCreateInstance(this).show();\n});\n/**\n * Initialize on focus\n */\n\nEventHandler.on(window, EVENT_LOAD_DATA_API, () => {\n  for (const element of SelectorEngine.find(SELECTOR_DATA_TOGGLE_ACTIVE)) {\n    Tab.getOrCreateInstance(element);\n  }\n});\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Tab);\n\n/**\n * --------------------------------------------------------------------------\n * Bootstrap (v5.2.3): toast.js\n * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)\n * --------------------------------------------------------------------------\n */\n/**\n * Constants\n */\n\nconst NAME = 'toast';\nconst DATA_KEY = 'bs.toast';\nconst EVENT_KEY = `.${DATA_KEY}`;\nconst EVENT_MOUSEOVER = `mouseover${EVENT_KEY}`;\nconst EVENT_MOUSEOUT = `mouseout${EVENT_KEY}`;\nconst EVENT_FOCUSIN = `focusin${EVENT_KEY}`;\nconst EVENT_FOCUSOUT = `focusout${EVENT_KEY}`;\nconst EVENT_HIDE = `hide${EVENT_KEY}`;\nconst EVENT_HIDDEN = `hidden${EVENT_KEY}`;\nconst EVENT_SHOW = `show${EVENT_KEY}`;\nconst EVENT_SHOWN = `shown${EVENT_KEY}`;\nconst CLASS_NAME_FADE = 'fade';\nconst CLASS_NAME_HIDE = 'hide'; // @deprecated - kept here only for backwards compatibility\n\nconst CLASS_NAME_SHOW = 'show';\nconst CLASS_NAME_SHOWING = 'showing';\nconst DefaultType = {\n  animation: 'boolean',\n  autohide: 'boolean',\n  delay: 'number'\n};\nconst Default = {\n  animation: true,\n  autohide: true,\n  delay: 5000\n};\n/**\n * Class definition\n */\n\nclass Toast extends BaseComponent {\n  constructor(element, config) {\n    super(element, config);\n    this._timeout = null;\n    this._hasMouseInteraction = false;\n    this._hasKeyboardInteraction = false;\n\n    this._setListeners();\n  } // Getters\n\n\n  static get Default() {\n    return Default;\n  }\n\n  static get DefaultType() {\n    return DefaultType;\n  }\n\n  static get NAME() {\n    return NAME;\n  } // Public\n\n\n  show() {\n    const showEvent = EventHandler.trigger(this._element, EVENT_SHOW);\n\n    if (showEvent.defaultPrevented) {\n      return;\n    }\n\n    this._clearTimeout();\n\n    if (this._config.animation) {\n      this._element.classList.add(CLASS_NAME_FADE);\n    }\n\n    const complete = () => {\n      this._element.classList.remove(CLASS_NAME_SHOWING);\n\n      EventHandler.trigger(this._element, EVENT_SHOWN);\n\n      this._maybeScheduleHide();\n    };\n\n    this._element.classList.remove(CLASS_NAME_HIDE); // @deprecated\n\n\n    reflow(this._element);\n\n    this._element.classList.add(CLASS_NAME_SHOW, CLASS_NAME_SHOWING);\n\n    this._queueCallback(complete, this._element, this._config.animation);\n  }\n\n  hide() {\n    if (!this.isShown()) {\n      return;\n    }\n\n    const hideEvent = EventHandler.trigger(this._element, EVENT_HIDE);\n\n    if (hideEvent.defaultPrevented) {\n      return;\n    }\n\n    const complete = () => {\n      this._element.classList.add(CLASS_NAME_HIDE); // @deprecated\n\n\n      this._element.classList.remove(CLASS_NAME_SHOWING, CLASS_NAME_SHOW);\n\n      EventHandler.trigger(this._element, EVENT_HIDDEN);\n    };\n\n    this._element.classList.add(CLASS_NAME_SHOWING);\n\n    this._queueCallback(complete, this._element, this._config.animation);\n  }\n\n  dispose() {\n    this._clearTimeout();\n\n    if (this.isShown()) {\n      this._element.classList.remove(CLASS_NAME_SHOW);\n    }\n\n    super.dispose();\n  }\n\n  isShown() {\n    return this._element.classList.contains(CLASS_NAME_SHOW);\n  } // Private\n\n\n  _maybeScheduleHide() {\n    if (!this._config.autohide) {\n      return;\n    }\n\n    if (this._hasMouseInteraction || this._hasKeyboardInteraction) {\n      return;\n    }\n\n    this._timeout = setTimeout(() => {\n      this.hide();\n    }, this._config.delay);\n  }\n\n  _onInteraction(event, isInteracting) {\n    switch (event.type) {\n      case 'mouseover':\n      case 'mouseout':\n        {\n          this._hasMouseInteraction = isInteracting;\n          break;\n        }\n\n      case 'focusin':\n      case 'focusout':\n        {\n          this._hasKeyboardInteraction = isInteracting;\n          break;\n        }\n    }\n\n    if (isInteracting) {\n      this._clearTimeout();\n\n      return;\n    }\n\n    const nextElement = event.relatedTarget;\n\n    if (this._element === nextElement || this._element.contains(nextElement)) {\n      return;\n    }\n\n    this._maybeScheduleHide();\n  }\n\n  _setListeners() {\n    EventHandler.on(this._element, EVENT_MOUSEOVER, event => this._onInteraction(event, true));\n    EventHandler.on(this._element, EVENT_MOUSEOUT, event => this._onInteraction(event, false));\n    EventHandler.on(this._element, EVENT_FOCUSIN, event => this._onInteraction(event, true));\n    EventHandler.on(this._element, EVENT_FOCUSOUT, event => this._onInteraction(event, false));\n  }\n\n  _clearTimeout() {\n    clearTimeout(this._timeout);\n    this._timeout = null;\n  } // Static\n\n\n  static jQueryInterface(config) {\n    return this.each(function () {\n      const data = Toast.getOrCreateInstance(this, config);\n\n      if (typeof config === 'string') {\n        if (typeof data[config] === 'undefined') {\n          throw new TypeError(`No method named \"${config}\"`);\n        }\n\n        data[config](this);\n      }\n    });\n  }\n\n}\n/**\n * Data API implementation\n */\n\n\nenableDismissTrigger(Toast);\n/**\n * jQuery\n */\n\ndefineJQueryPlugin(Toast);\n\nexport { Alert, Button, Carousel, Collapse, Dropdown, Modal, Offcanvas, Popover, ScrollSpy, Tab, Toast, Tooltip };\n//# sourceMappingURL=bootstrap.esm.js.map\n","/* define several functions to replace jQuery methods\n * inspired by https://tobiasahlin.com/blog/move-from-jquery-to-vanilla-javascript/\n */\n\n/**\n * Execute a method if DOM has finished loading\n *\n * @param {function} callback the method to execute\n */\nexport function documentReady(callback) {\n  if (document.readyState != \"loading\") callback();\n  else document.addEventListener(\"DOMContentLoaded\", callback);\n}\n","// Import and setup functions to control Bootstrap's behavior.\nimport \"@popperjs/core\";\nimport { Tooltip } from \"bootstrap\";\nimport { documentReady } from \"./mixin\";\n\nimport \"../styles/bootstrap.scss\";\n\n/*******************************************************************************\n * Trigger tooltips\n */\n\n/**\n * Add tooltip to each element with the \"tooltip\" data-bs-toogle class\n */\nfunction TriggerTooltip() {\n  var tooltipTriggerList = [].slice.call(\n    document.querySelectorAll('[data-bs-toggle=\"tooltip\"]')\n  );\n  tooltipTriggerList.map(function (tooltipTriggerEl) {\n    return new Tooltip(tooltipTriggerEl, { delay: { show: 500, hide: 100 } });\n  });\n}\n\n/*******************************************************************************\n * back to top button\n */\nfunction backToTop() {\n  var btn = document.getElementById(\"pst-back-to-top\");\n  btn.addEventListener(\"click\", function () {\n    document.body.scrollTop = 0;\n    document.documentElement.scrollTop = 0;\n  });\n}\n\nfunction showBackToTop() {\n  var btn 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promise : getResult();\n\t}, (err) => ((err ? reject(promise[webpackError] = err) : outerResolve(exports)), resolveQueue(queue)));\n\tqueue && (queue.d = 0);\n};","/**\n * Compare [semver](https://semver.org/) version strings to find greater, equal or lesser.\n * This library supports the full semver specification, including comparing versions with different number of digits like `1.0.0`, `1.0`, `1`, and pre-release versions like `1.0.0-alpha`.\n * @param v1 - First version to compare\n * @param v2 - Second version to compare\n * @returns Numeric value compatible with the [Array.sort(fn) interface](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/sort#Parameters).\n */\nexport const compareVersions = (v1, v2) => {\n    // validate input and split into segments\n    const n1 = validateAndParse(v1);\n    const n2 = validateAndParse(v2);\n    // pop off the patch\n    const p1 = n1.pop();\n    const p2 = n2.pop();\n    // validate numbers\n    const r = compareSegments(n1, n2);\n    if (r !== 0)\n        return r;\n    // validate pre-release\n    if (p1 && p2) {\n        return compareSegments(p1.split('.'), p2.split('.'));\n    }\n    else if (p1 || p2) {\n        return p1 ? -1 : 1;\n    }\n    return 0;\n};\n/**\n * Validate [semver](https://semver.org/) version strings.\n *\n * @param version Version number to validate\n * @returns `true` if the version number is a valid semver version number, `false` otherwise.\n *\n * @example\n * ```\n * validate('1.0.0-rc.1'); // return true\n * validate('1.0-rc.1'); // return false\n * validate('foo'); // return false\n * ```\n */\nexport const validate = (version) => typeof version === 'string' && /^[v\\d]/.test(version) && semver.test(version);\n/**\n * Compare [semver](https://semver.org/) version strings using the specified operator.\n *\n * @param v1 First version to compare\n * @param v2 Second version to compare\n * @param operator Allowed arithmetic operator to use\n * @returns `true` if the comparison between the firstVersion and the secondVersion satisfies the operator, `false` otherwise.\n *\n * @example\n * ```\n * compare('10.1.8', '10.0.4', '>'); // return true\n * compare('10.0.1', '10.0.1', '='); // return true\n * compare('10.1.1', '10.2.2', '<'); // return true\n * compare('10.1.1', '10.2.2', '<='); // return true\n * compare('10.1.1', '10.2.2', '>='); // return false\n * ```\n */\nexport const compare = (v1, v2, operator) => {\n    // validate input operator\n    assertValidOperator(operator);\n    // since result of compareVersions can only be -1 or 0 or 1\n    // a simple map can be used to replace switch\n    const res = compareVersions(v1, v2);\n    return operatorResMap[operator].includes(res);\n};\n/**\n * Match [npm semver](https://docs.npmjs.com/cli/v6/using-npm/semver) version range.\n *\n * @param version Version number to match\n * @param range Range pattern for version\n * @returns `true` if the version number is within the range, `false` otherwise.\n *\n * @example\n * ```\n * satisfies('1.1.0', '^1.0.0'); // return true\n * satisfies('1.1.0', '~1.0.0'); // return false\n * ```\n */\nexport const satisfies = (version, range) => {\n    // if no range operator then \"=\"\n    const m = range.match(/^([<>=~^]+)/);\n    const op = m ? m[1] : '=';\n    // if gt/lt/eq then operator compare\n    if (op !== '^' && op !== '~')\n        return compare(version, range, op);\n    // else range of either \"~\" or \"^\" is assumed\n    const [v1, v2, v3, , vp] = validateAndParse(version);\n    const [r1, r2, r3, , rp] = validateAndParse(range);\n    const v = [v1, v2, v3];\n    const r = [r1, r2 !== null && r2 !== void 0 ? r2 : 'x', r3 !== null && r3 !== void 0 ? r3 : 'x'];\n    // validate pre-release\n    if (rp) {\n        if (!vp)\n            return false;\n        if (compareSegments(v, r) !== 0)\n            return false;\n        if (compareSegments(vp.split('.'), rp.split('.')) === -1)\n            return false;\n    }\n    // first non-zero number\n    const nonZero = r.findIndex((v) => v !== '0') + 1;\n    // pointer to where segments can be >=\n    const i = op === '~' ? 2 : nonZero > 1 ? nonZero : 1;\n    // before pointer must be equal\n    if (compareSegments(v.slice(0, i), r.slice(0, i)) !== 0)\n        return false;\n    // after pointer must be >=\n    if (compareSegments(v.slice(i), r.slice(i)) === -1)\n        return false;\n    return true;\n};\nconst semver = /^[v^~<>=]*?(\\d+)(?:\\.([x*]|\\d+)(?:\\.([x*]|\\d+)(?:\\.([x*]|\\d+))?(?:-([\\da-z\\-]+(?:\\.[\\da-z\\-]+)*))?(?:\\+[\\da-z\\-]+(?:\\.[\\da-z\\-]+)*)?)?)?$/i;\nconst validateAndParse = (version) => {\n    if (typeof version !== 'string') {\n        throw new TypeError('Invalid argument expected string');\n    }\n    const match = version.match(semver);\n    if (!match) {\n        throw new Error(`Invalid argument not valid semver ('${version}' received)`);\n    }\n    match.shift();\n    return match;\n};\nconst isWildcard = (s) => s === '*' || s === 'x' || s === 'X';\nconst tryParse = (v) => {\n    const n = parseInt(v, 10);\n    return isNaN(n) ? v : n;\n};\nconst forceType = (a, b) => typeof a !== typeof b ? [String(a), String(b)] : [a, b];\nconst compareStrings = (a, b) => {\n    if (isWildcard(a) || isWildcard(b))\n        return 0;\n    const [ap, bp] = forceType(tryParse(a), tryParse(b));\n    if (ap > bp)\n        return 1;\n    if (ap < bp)\n        return -1;\n    return 0;\n};\nconst compareSegments = (a, b) => {\n    for (let i = 0; i < Math.max(a.length, b.length); i++) {\n        const r = compareStrings(a[i] || '0', b[i] || '0');\n        if (r !== 0)\n            return r;\n    }\n    return 0;\n};\nconst operatorResMap = {\n    '>': [1],\n    '>=': [0, 1],\n    '=': [0],\n    '<=': [-1, 0],\n    '<': [-1],\n};\nconst allowedOperators = Object.keys(operatorResMap);\nconst assertValidOperator = (op) => {\n    if (typeof op !== 'string') {\n        throw new TypeError(`Invalid operator type, expected string but got ${typeof op}`);\n    }\n    if (allowedOperators.indexOf(op) === -1) {\n        throw new Error(`Invalid operator, expected one of ${allowedOperators.join('|')}`);\n    }\n};\n//# sourceMappingURL=index.js.map","/* define several functions to replace jQuery methods\n * inspired by https://tobiasahlin.com/blog/move-from-jquery-to-vanilla-javascript/\n */\n\n/**\n * Execute a method if DOM has finished loading\n *\n * @param {function} callback the method to execute\n */\nexport function documentReady(callback) {\n  if (document.readyState != \"loading\") callback();\n  else document.addEventListener(\"DOMContentLoaded\", callback);\n}\n","// Define the custom behavior of the page\nimport { documentReady } from \"./mixin\";\nimport { compare, validate } from \"compare-versions\";\n\nimport \"../styles/pydata-sphinx-theme.scss\";\n\n/*******************************************************************************\n * Theme interaction\n */\n\nvar prefersDark = window.matchMedia(\"(prefers-color-scheme: dark)\");\n\n/**\n * set the the body theme to the one specified by the user browser\n *\n * @param {event} e\n */\nfunction autoTheme(e) {\n  document.documentElement.dataset.theme = prefersDark.matches\n    ? \"dark\"\n    : \"light\";\n}\n\n/**\n * Set the theme using the specified mode.\n * It can be one of [\"auto\", \"dark\", \"light\"]\n *\n * @param {str} mode\n */\nfunction setTheme(mode) {\n  if (mode !== \"light\" && mode !== \"dark\" && mode !== \"auto\") {\n    console.error(`Got invalid theme mode: ${mode}. Resetting to auto.`);\n    mode = \"auto\";\n  }\n\n  // get the theme\n  var colorScheme = prefersDark.matches ? \"dark\" : \"light\";\n  document.documentElement.dataset.mode = mode;\n  var theme = mode == \"auto\" ? colorScheme : mode;\n  document.documentElement.dataset.theme = theme;\n  // TODO: remove this line after Bootstrap upgrade\n  // v5.3 has a colors mode: https://getbootstrap.com/docs/5.3/customize/color-modes/\n  document.querySelectorAll(\".dropdown-menu\").forEach((el) => {\n    if (theme === \"dark\") {\n      el.classList.add(\"dropdown-menu-dark\");\n    } else {\n      el.classList.remove(\"dropdown-menu-dark\");\n    }\n  });\n\n  // save mode and theme\n  localStorage.setItem(\"mode\", mode);\n  localStorage.setItem(\"theme\", theme);\n  console.log(`[PST]: Changed to ${mode} mode using the ${theme} theme.`);\n\n  // add a listener if set on auto\n  prefersDark.onchange = mode == \"auto\" ? autoTheme : \"\";\n}\n\n/**\n * Change the theme option order so that clicking on the btn is always a change\n * from \"auto\"\n */\nfunction cycleMode() {\n  const defaultMode = document.documentElement.dataset.defaultMode || \"auto\";\n  const currentMode = localStorage.getItem(\"mode\") || defaultMode;\n\n  var loopArray = (arr, current) => {\n    var nextPosition = arr.indexOf(current) + 1;\n    if (nextPosition === arr.length) {\n      nextPosition = 0;\n    }\n    return arr[nextPosition];\n  };\n\n  // make sure the next theme after auto is always a change\n  var modeList = prefersDark.matches\n    ? [\"auto\", \"light\", \"dark\"]\n    : [\"auto\", \"dark\", \"light\"];\n  var newMode = loopArray(modeList, currentMode);\n  setTheme(newMode);\n}\n\n/**\n * add the theme listener on the btns of the navbar\n */\nfunction addModeListener() {\n  // the theme was set a first time using the initial mini-script\n  // running setMode will ensure the use of the dark mode if auto is selected\n  setTheme(document.documentElement.dataset.mode);\n\n  // Attach event handlers for toggling themes colors\n  document.querySelectorAll(\".theme-switch-button\").forEach((el) => {\n    el.addEventListener(\"click\", cycleMode);\n  });\n}\n\n/*******************************************************************************\n * TOC interactivity\n */\n\n/**\n * TOC sidebar - add \"active\" class to parent list\n *\n * Bootstrap's scrollspy adds the active class to the <a> link,\n * but for the automatic collapsing we need this on the parent list item.\n *\n * The event is triggered on \"window\" (and not the nav item as documented),\n * see https://github.com/twbs/bootstrap/issues/20086\n */\nfunction addTOCInteractivity() {\n  window.addEventListener(\"activate.bs.scrollspy\", function () {\n    const navLinks = document.querySelectorAll(\".bd-toc-nav a\");\n\n    navLinks.forEach((navLink) => {\n      navLink.parentElement.classList.remove(\"active\");\n    });\n\n    const activeNavLinks = document.querySelectorAll(\".bd-toc-nav a.active\");\n    activeNavLinks.forEach((navLink) => {\n      navLink.parentElement.classList.add(\"active\");\n    });\n  });\n}\n\n/*******************************************************************************\n * Scroll\n */\n\n/**\n * Navigation sidebar scrolling to active page\n */\nfunction scrollToActive() {\n  // If the docs nav doesn't exist, do nothing (e.g., on search page)\n  if (!document.querySelector(\".bd-docs-nav\")) {\n    return;\n  }\n\n  var sidebar = document.querySelector(\"div.bd-sidebar\");\n\n  // Remember the sidebar scroll position between page loads\n  // Inspired on source of revealjs.com\n  let storedScrollTop = parseInt(\n    sessionStorage.getItem(\"sidebar-scroll-top\"),\n    10\n  );\n\n  if (!isNaN(storedScrollTop)) {\n    // If we've got a saved scroll position, just use that\n    sidebar.scrollTop = storedScrollTop;\n    console.log(\"[PST]: Scrolled sidebar using stored browser position...\");\n  } else {\n    // Otherwise, calculate a position to scroll to based on the lowest `active` link\n    var sidebarNav = document.querySelector(\".bd-docs-nav\");\n    var active_pages = sidebarNav.querySelectorAll(\".active\");\n    if (active_pages.length > 0) {\n      // Use the last active page as the offset since it's the page we're on\n      var latest_active = active_pages[active_pages.length - 1];\n      var offset =\n        latest_active.getBoundingClientRect().y -\n        sidebar.getBoundingClientRect().y;\n      // Only scroll the navbar if the active link is lower than 50% of the page\n      if (latest_active.getBoundingClientRect().y > window.innerHeight * 0.5) {\n        let buffer = 0.25; // Buffer so we have some space above the scrolled item\n        sidebar.scrollTop = offset - sidebar.clientHeight * buffer;\n        console.log(\"[PST]: Scrolled sidebar using last active link...\");\n      }\n    }\n  }\n\n  // Store the sidebar scroll position\n  window.addEventListener(\"beforeunload\", () => {\n    sessionStorage.setItem(\"sidebar-scroll-top\", sidebar.scrollTop);\n  });\n}\n\n/*******************************************************************************\n * Search\n */\n\n/**\n * Find any search forms on the page and return their input element\n */\nvar findSearchInput = () => {\n  let forms = document.querySelectorAll(\"form.bd-search\");\n  if (!forms.length) {\n    // no search form found\n    return;\n  } else {\n    var form;\n    if (forms.length == 1) {\n      // there is exactly one search form (persistent or hidden)\n      form = forms[0];\n    } else {\n      // must be at least one persistent form, use the first persistent one\n      form = document.querySelector(\n        \"div:not(.search-button__search-container) > form.bd-search\"\n      );\n    }\n    return form.querySelector(\"input\");\n  }\n};\n\n/**\n * Activate the search field on the page.\n * - If there is a search field already visible it will be activated.\n * - If not, then a search field will pop up.\n */\nvar toggleSearchField = () => {\n  // Find the search input to highlight\n  let input = findSearchInput();\n\n  // if the input field is the hidden one (the one associated with the\n  // search button) then toggle the button state (to show/hide the field)\n  let searchPopupWrapper = document.querySelector(\".search-button__wrapper\");\n  let hiddenInput = searchPopupWrapper.querySelector(\"input\");\n  if (input === hiddenInput) {\n    searchPopupWrapper.classList.toggle(\"show\");\n  }\n  // when toggling off the search field, remove its focus\n  if (document.activeElement === input) {\n    input.blur();\n  } else {\n    input.focus();\n    input.select();\n    input.scrollIntoView({ block: \"center\" });\n  }\n};\n\n/**\n * Add an event listener for toggleSearchField() for Ctrl/Cmd + K\n */\nvar addEventListenerForSearchKeyboard = () => {\n  window.addEventListener(\n    \"keydown\",\n    (event) => {\n      let input = findSearchInput();\n      // toggle on Ctrl+k or ⌘+k\n      if ((event.ctrlKey || event.metaKey) && event.code == \"KeyK\") {\n        event.preventDefault();\n        toggleSearchField();\n      }\n      // also allow Escape key to hide (but not show) the dynamic search field\n      else if (document.activeElement === input && event.code == \"Escape\") {\n        toggleSearchField();\n      }\n    },\n    true\n  );\n};\n\n/**\n * Find out if we're on a Mac\n */\nvar isMac = (navigator) => {\n  var platform = \"\";\n  if (\n    typeof navigator.userAgentData !== \"undefined\" &&\n    navigator.userAgentData != null\n  ) {\n    platform = navigator.userAgentData.platform;\n  } else if (typeof navigator.platform !== \"undefined\") {\n    platform = navigator.platform;\n  }\n  return /mac.?os/.test(platform.toLowerCase());\n};\n\n/**\n * Change the search hint to `meta key` if we are a Mac\n */\n\nvar changeSearchShortcutKey = () => {\n  let shortcuts = document.querySelectorAll(\".search-button__kbd-shortcut\");\n  if (isMac(window.navigator)) {\n    shortcuts.forEach(\n      (f) => (f.querySelector(\"kbd.kbd-shortcut__modifier\").innerText = \"⌘\")\n    );\n  }\n};\n\n/**\n * Activate callbacks for search button popup\n */\nvar setupSearchButtons = () => {\n  changeSearchShortcutKey();\n  addEventListenerForSearchKeyboard();\n\n  // Add the search button trigger event callback\n  document.querySelectorAll(\".search-button__button\").forEach((btn) => {\n    btn.onclick = toggleSearchField;\n  });\n\n  // Add the search button overlay event callback\n  let overlay = document.querySelector(\".search-button__overlay\");\n  if (overlay) {\n    overlay.onclick = toggleSearchField;\n  }\n};\n\n/*******************************************************************************\n * Version Switcher\n * Note that this depends on two variables existing that are defined in\n * and `html-page-context` hook:\n *\n * - DOCUMENTATION_OPTIONS.pagename\n * - DOCUMENTATION_OPTIONS.theme_switcher_url\n */\n\n/**\n * Check if corresponding page path exists in other version of docs\n * and, if so, go there instead of the homepage of the other docs version\n *\n * @param {event} event the event that trigger the check\n */\nasync function checkPageExistsAndRedirect(event) {\n  // ensure we don't follow the initial link\n  event.preventDefault();\n  let currentFilePath = `${DOCUMENTATION_OPTIONS.pagename}.html`;\n  let tryUrl = event.currentTarget.getAttribute(\"href\");\n  let otherDocsHomepage = tryUrl.replace(currentFilePath, \"\");\n  try {\n    let head = await fetch(tryUrl, { method: \"HEAD\" });\n    if (head.ok) {\n      location.href = tryUrl; // the page exists, go there\n    } else {\n      location.href = otherDocsHomepage;\n    }\n  } catch (err) {\n    // something went wrong, probably CORS restriction, fallback to other docs homepage\n    location.href = otherDocsHomepage;\n  }\n}\n\n/**\n * Load and parse the version switcher JSON file from an absolute or relative URL.\n *\n * @param {string} url The URL to load version switcher entries from.\n */\nasync function fetchVersionSwitcherJSON(url) {\n  // first check if it's a valid URL\n  try {\n    var result = new URL(url);\n  } catch (err) {\n    if (err instanceof TypeError) {\n      // assume we got a relative path, and fix accordingly. But first, we need to\n      // use `fetch()` to follow redirects so we get the correct final base URL\n      const origin = await fetch(window.location.origin, { method: \"HEAD\" });\n      result = new URL(url, origin.url);\n    } else {\n      // something unexpected happened\n      throw err;\n    }\n  }\n  // load and return the JSON\n  const response = await fetch(result);\n  const data = await response.json();\n  return data;\n}\n\n// Populate the version switcher from the JSON data\nfunction populateVersionSwitcher(data, versionSwitcherBtns) {\n  const currentFilePath = `${DOCUMENTATION_OPTIONS.pagename}.html`;\n  versionSwitcherBtns.forEach((btn) => {\n    // Set empty strings by default so that these attributes exist and can be used in CSS selectors\n    btn.dataset[\"activeVersionName\"] = \"\";\n    btn.dataset[\"activeVersion\"] = \"\";\n  });\n  // in case there are multiple entries with the same version string, this helps us\n  // decide which entry's `name` to put on the button itself. Without this, it would\n  // always be the *last* version-matching entry; now it will be either the\n  // version-matching entry that is also marked as `\"preferred\": true`, or if that\n  // doesn't exist: the *first* version-matching entry.\n  data = data.map((entry) => {\n    // does this entry match the version that we're currently building/viewing?\n    entry.match =\n      entry.version == DOCUMENTATION_OPTIONS.theme_switcher_version_match;\n    entry.preferred = entry.preferred || false;\n    // if no custom name specified (e.g., \"latest\"), use version string\n    if (!(\"name\" in entry)) {\n      entry.name = entry.version;\n    }\n    return entry;\n  });\n  const hasMatchingPreferredEntry = data\n    .map((entry) => entry.preferred && entry.match)\n    .some(Boolean);\n  var foundMatch = false;\n  // create links to the corresponding page in the other docs versions\n  data.forEach((entry) => {\n    // create the node\n    const anchor = document.createElement(\"a\");\n    anchor.setAttribute(\n      \"class\",\n      \"dropdown-item list-group-item list-group-item-action py-1\"\n    );\n    anchor.setAttribute(\"href\", `${entry.url}${currentFilePath}`);\n    anchor.setAttribute(\"role\", \"option\");\n    const span = document.createElement(\"span\");\n    span.textContent = `${entry.name}`;\n    anchor.appendChild(span);\n    // Add dataset values for the version and name in case people want\n    // to apply CSS styling based on this information.\n    anchor.dataset[\"versionName\"] = entry.name;\n    anchor.dataset[\"version\"] = entry.version;\n    // replace dropdown button text with the preferred display name of the\n    // currently-viewed version, rather than using sphinx's {{ version }} variable.\n    // also highlight the dropdown entry for the currently-viewed version's entry\n    let matchesAndIsPreferred = hasMatchingPreferredEntry && entry.preferred;\n    let matchesAndIsFirst =\n      !hasMatchingPreferredEntry && !foundMatch && entry.match;\n    if (matchesAndIsPreferred || matchesAndIsFirst) {\n      anchor.classList.add(\"active\");\n      versionSwitcherBtns.forEach((btn) => {\n        btn.innerText = entry.name;\n        btn.dataset[\"activeVersionName\"] = entry.name;\n        btn.dataset[\"activeVersion\"] = entry.version;\n      });\n      foundMatch = true;\n    }\n    // There may be multiple version-switcher elements, e.g. one\n    // in a slide-over panel displayed on smaller screens.\n    document.querySelectorAll(\".version-switcher__menu\").forEach((menu) => {\n      // we need to clone the node for each menu, but onclick attributes are not\n      // preserved by `.cloneNode()` so we add onclick here after cloning.\n      let node = anchor.cloneNode(true);\n      node.onclick = checkPageExistsAndRedirect;\n      // on click, AJAX calls will check if the linked page exists before\n      // trying to redirect, and if not, will redirect to the homepage\n      // for that version of the docs.\n      menu.append(node);\n    });\n  });\n}\n\n/*******************************************************************************\n * Warning banner when viewing non-stable version of the docs.\n */\n\n/**\n * Show a warning banner when viewing a non-stable version of the docs.\n *\n * adapted 2023-06 from https://mne.tools/versionwarning.js, which was\n * originally adapted 2020-05 from https://scikit-learn.org/versionwarning.js\n *\n * @param {Array} data The version data used to populate the switcher menu.\n */\nfunction showVersionWarningBanner(data) {\n  var version = DOCUMENTATION_OPTIONS.VERSION;\n  // figure out what latest stable version is\n  var preferredEntries = data.filter((entry) => entry.preferred);\n  if (preferredEntries.length !== 1) {\n    const howMany = preferredEntries.length == 0 ? \"No\" : \"Multiple\";\n    console.log(\n      `[PST] ${howMany} versions marked \"preferred\" found in versions JSON, ignoring.`\n    );\n    return;\n  }\n  const preferredVersion = preferredEntries[0].version;\n  const preferredURL = preferredEntries[0].url;\n  // if already on preferred version, nothing to do\n  const versionsAreComparable = validate(version) && validate(preferredVersion);\n  if (versionsAreComparable && compare(version, preferredVersion, \"=\")) {\n    return;\n  }\n  // now construct the warning banner\n  var outer = document.createElement(\"div\");\n  const middle = document.createElement(\"div\");\n  const inner = document.createElement(\"div\");\n  const bold = document.createElement(\"strong\");\n  const button = document.createElement(\"a\");\n  // these classes exist since pydata-sphinx-theme v0.10.0\n  outer.classList = \"bd-header-version-warning container-fluid\";\n  middle.classList = \"bd-header-announcement__content\";\n  inner.classList = \"sidebar-message\";\n  button.classList =\n    \"sd-btn sd-btn-danger sd-shadow-sm sd-text-wrap font-weight-bold ms-3 my-1 align-baseline\";\n  button.href = 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index 000000000..be9fa44d6
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/scripts/sphinx-book-theme.js
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index 000000000..b8abcf860
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https://developer.mozilla.org/en-US/docs/Web/API/Fullscreen_API\n */\nvar toggleFullScreen = () => {\n  var isInFullScreen =\n    (document.fullscreenElement && document.fullscreenElement !== null) ||\n    (document.webkitFullscreenElement &&\n      document.webkitFullscreenElement !== null);\n  let docElm = document.documentElement;\n  if (!isInFullScreen) {\n    console.log(\"[SBT]: Entering full screen\");\n    if (docElm.requestFullscreen) {\n      docElm.requestFullscreen();\n    } else if (docElm.webkitRequestFullscreen) {\n      docElm.webkitRequestFullscreen();\n    }\n  } else {\n    console.log(\"[SBT]: Exiting full screen\");\n    if (document.exitFullscreen) {\n      document.exitFullscreen();\n    } else if (document.webkitExitFullscreen) {\n      document.webkitExitFullscreen();\n    }\n  }\n};\n\n/**\n * Manage scrolling behavior. This is primarily two things:\n *\n * 1. Hide the Table of Contents any time sidebar content is on the screen.\n *\n * This will be triggered any time a sidebar item enters or exits the screen.\n * It adds/removes items from an array if they have entered the screen, and\n * removes them when they exit the screen. It hides the TOC if anything is\n * on-screen.\n *\n * ref: https://developer.mozilla.org/en-US/docs/Web/API/Intersection_Observer_API\n *\n * 2. Add a `scrolled` class to <body> to trigger CSS changes.\n */\nvar initTocHide = () => {\n  var onScreenItems = [];\n  let hideTocCallback = (entries, observer) => {\n    // Check whether any sidebar item is displayed\n    entries.forEach((entry) => {\n      if (entry.isIntersecting) {\n        // If an element just came on screen, add it our list\n        onScreenItems.push(entry.target);\n      } else {\n        // Otherwise, if it's in our list then remove it\n        for (let ii = 0; ii < onScreenItems.length; ii++) {\n          if (onScreenItems[ii] === entry.target) {\n            onScreenItems.splice(ii, 1);\n            break;\n          }\n        }\n      }\n    });\n\n    // Hide the TOC if any margin content is displayed on the screen\n    if (onScreenItems.length > 0) {\n      document.querySelector(\"div.bd-sidebar-secondary\").classList.add(\"hide\");\n    } else {\n      document\n        .querySelector(\"div.bd-sidebar-secondary\")\n        .classList.remove(\"hide\");\n    }\n  };\n  let manageScrolledClassOnBody = (entries, observer) => {\n    // The pixel is at the top, so if we're < 0 that it means we've scrolled\n    if (entries[0].boundingClientRect.y < 0) {\n      document.body.classList.add(\"scrolled\");\n    } else {\n      document.body.classList.remove(\"scrolled\");\n    }\n  };\n\n  // Set up the intersection observer to watch all margin content\n  let options = {\n    // Trigger callback when the top of a margin item is 1/3 up the screen\n    rootMargin: \"0px 0px -33% 0px\",\n  };\n  let tocObserver = new IntersectionObserver(hideTocCallback, options);\n  // TODO: deprecate popout after v0.5.0\n  const selectorClasses = [\n    \"marginnote\",\n    \"sidenote\",\n    \"margin\",\n    \"margin-caption\",\n    \"full-width\",\n    \"sidebar\",\n    \"popout\",\n  ];\n  let marginSelector = [];\n  selectorClasses.forEach((ii) => {\n    // Use three permutations of each class name because `tag_` and `_` used to be supported\n    marginSelector.push(\n      ...[\n        `.${ii}`,\n        `.tag_${ii}`,\n        `.${ii.replace(\"-\", \"_\")}`,\n        `.tag_${ii.replace(\"-\", \"_\")}`,\n      ],\n    );\n  });\n  document.querySelectorAll(marginSelector.join(\", \")).forEach((ii) => {\n    tocObserver.observe(ii);\n  });\n\n  // Set up the observer to check if we've scrolled from top of page\n  let scrollObserver = new IntersectionObserver(manageScrolledClassOnBody);\n  scrollObserver.observe(document.querySelector(\".sbt-scroll-pixel-helper\"));\n};\n\n/**\n * Activate Thebe with a custom button click.\n */\nvar initThebeSBT = () => {\n  var title = document.querySelector(\"section h1\");\n  var sibling = title.nextElementSibling;\n  // If the next element after the title isn't a thebe button, add one now.\n  // That way it is initiatlized when thebe is first-clicked and isn't re-added after.\n  if (!sibling.classList.contains(\"thebe-launch-button\")) {\n    title.insertAdjacentHTML(\n      \"afterend\",\n      \"<button class='thebe-launch-button'></button>\",\n    );\n  }\n  // This function is provided by sphinx-thebe\n  initThebe();\n};\n\n/**\n * Add no print class to certain DOM elements\n */\n\nfunction addNoPrint() {\n  var noPrintSelector = [\n    \".bd-header-announcement\",\n    \".bd-header\",\n    \".bd-header-article\",\n    \".bd-sidebar-primary\",\n    \".bd-sidebar-secondary\",\n    \".bd-footer-article\",\n    \".bd-footer-content\",\n    \".bd-footer\",\n  ].join(\",\");\n  document.querySelectorAll(noPrintSelector).forEach((ii) => {\n    ii.classList.add(\"noprint\");\n  });\n}\n\n/**\n * Set up callback functions for UI click actions\n */\nwindow.initThebeSBT = initThebeSBT;\nwindow.toggleFullScreen = toggleFullScreen;\n\n/**\n * Set up functions to load when the DOM is ready\n */\nsbRunWhenDOMLoaded(initTocHide);\nsbRunWhenDOMLoaded(addNoPrint);\n"],"sourceRoot":""}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/_static/searchtools.js b/doc/LectureNotes/_build/html/_static/searchtools.js
index 2d7785937..ac4d5861f 100644
--- a/doc/LectureNotes/_build/html/_static/searchtools.js
+++ b/doc/LectureNotes/_build/html/_static/searchtools.js
@@ -8,18 +8,20 @@
  * :license: BSD, see LICENSE for details.
  *
  */
+"use strict";
 
-if (!Scorer) {
-  /**
-   * Simple result scoring code.
-   */
+/**
+ * Simple result scoring code.
+ */
+if (typeof Scorer === "undefined") {
   var Scorer = {
     // Implement the following function to further tweak the score for each result
-    // The function takes a result array [filename, title, anchor, descr, score]
+    // The function takes a result array [docname, title, anchor, descr, score, filename]
     // and returns the new score.
     /*
-    score: function(result) {
-      return result[4];
+    score: result => {
+      const [docname, title, anchor, descr, score, filename] = result
+      return score
     },
     */
 
@@ -28,9 +30,11 @@ if (!Scorer) {
     // or matches in the last dotted part of the object name
     objPartialMatch: 6,
     // Additive scores depending on the priority of the object
-    objPrio: {0:  15,   // used to be importantResults
-              1:  5,   // used to be objectResults
-              2: -5},  // used to be unimportantResults
+    objPrio: {
+      0: 15, // used to be importantResults
+      1: 5, // used to be objectResults
+      2: -5, // used to be unimportantResults
+    },
     //  Used when the priority is not in the mapping.
     objPrioDefault: 0,
 
@@ -39,456 +43,455 @@ if (!Scorer) {
     partialTitle: 7,
     // query found in terms
     term: 5,
-    partialTerm: 2
+    partialTerm: 2,
   };
 }
 
-if (!splitQuery) {
-  function splitQuery(query) {
-    return query.split(/\s+/);
+const _removeChildren = (element) => {
+  while (element && element.lastChild) element.removeChild(element.lastChild);
+};
+
+/**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping
+ */
+const _escapeRegExp = (string) =>
+  string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string
+
+const _displayItem = (item, highlightTerms, searchTerms) => {
+  const docBuilder = DOCUMENTATION_OPTIONS.BUILDER;
+  const docUrlRoot = DOCUMENTATION_OPTIONS.URL_ROOT;
+  const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+  const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+  const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY;
+
+  const [docName, title, anchor, descr] = item;
+
+  let listItem = document.createElement("li");
+  let requestUrl;
+  let linkUrl;
+  if (docBuilder === "dirhtml") {
+    // dirhtml builder
+    let dirname = docName + "/";
+    if (dirname.match(/\/index\/$/))
+      dirname = dirname.substring(0, dirname.length - 6);
+    else if (dirname === "index/") dirname = "";
+    requestUrl = docUrlRoot + dirname;
+    linkUrl = requestUrl;
+  } else {
+    // normal html builders
+    requestUrl = docUrlRoot + docName + docFileSuffix;
+    linkUrl = docName + docLinkSuffix;
   }
+  const params = new URLSearchParams();
+  params.set("highlight", [...highlightTerms].join(" "));
+  let linkEl = listItem.appendChild(document.createElement("a"));
+  linkEl.href = linkUrl + "?" + params.toString() + anchor;
+  linkEl.innerHTML = title;
+  if (descr)
+    listItem.appendChild(document.createElement("span")).innerText =
+      " (" + descr + ")";
+  else if (showSearchSummary)
+    fetch(requestUrl)
+      .then((responseData) => responseData.text())
+      .then((data) => {
+        if (data)
+          listItem.appendChild(
+            Search.makeSearchSummary(data, searchTerms, highlightTerms)
+          );
+      });
+  Search.output.appendChild(listItem);
+};
+const _finishSearch = (resultCount) => {
+  Search.stopPulse();
+  Search.title.innerText = _("Search Results");
+  if (!resultCount)
+    Search.status.innerText = Documentation.gettext(
+      "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories."
+    );
+  else
+    Search.status.innerText = _(
+      `Search finished, found ${resultCount} page(s) matching the search query.`
+    );
+};
+const _displayNextItem = (
+  results,
+  resultCount,
+  highlightTerms,
+  searchTerms
+) => {
+  // results left, load the summary and display it
+  // this is intended to be dynamic (don't sub resultsCount)
+  if (results.length) {
+    _displayItem(results.pop(), highlightTerms, searchTerms);
+    setTimeout(
+      () => _displayNextItem(results, resultCount, highlightTerms, searchTerms),
+      5
+    );
+  }
+  // search finished, update title and status message
+  else _finishSearch(resultCount);
+};
+
+/**
+ * Default splitQuery function. Can be overridden in ``sphinx.search`` with a
+ * custom function per language.
+ *
+ * The regular expression works by splitting the string on consecutive characters
+ * that are not Unicode letters, numbers, underscores, or emoji characters.
+ * This is the same as ``\W+`` in Python, preserving the surrogate pair area.
+ */
+if (typeof splitQuery === "undefined") {
+  var splitQuery = (query) => query
+      .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu)
+      .filter(term => term)  // remove remaining empty strings
 }
 
 /**
  * Search Module
  */
-var Search = {
+const Search = {
+  _index: null,
+  _queued_query: null,
+  _pulse_status: -1,
 
-  _index : null,
-  _queued_query : null,
-  _pulse_status : -1,
-
-  htmlToText : function(htmlString) {
-      var virtualDocument = document.implementation.createHTMLDocument('virtual');
-      var htmlElement = $(htmlString, virtualDocument);
-      htmlElement.find('.headerlink').remove();
-      docContent = htmlElement.find('[role=main]')[0];
-      if(docContent === undefined) {
-          console.warn("Content block not found. Sphinx search tries to obtain it " +
-                       "via '[role=main]'. Could you check your theme or template.");
-          return "";
-      }
-      return docContent.textContent || docContent.innerText;
+  htmlToText: (htmlString) => {
+    const htmlElement = document
+      .createRange()
+      .createContextualFragment(htmlString);
+    _removeChildren(htmlElement.querySelectorAll(".headerlink"));
+    const docContent = htmlElement.querySelector('[role="main"]');
+    if (docContent !== undefined) return docContent.textContent;
+    console.warn(
+      "Content block not found. Sphinx search tries to obtain it via '[role=main]'. Could you check your theme or template."
+    );
+    return "";
   },
 
-  init : function() {
-      var params = $.getQueryParameters();
-      if (params.q) {
-          var query = params.q[0];
-          $('input[name="q"]')[0].value = query;
-          this.performSearch(query);
-      }
+  init: () => {
+    const query = new URLSearchParams(window.location.search).get("q");
+    document
+      .querySelectorAll('input[name="q"]')
+      .forEach((el) => (el.value = query));
+    if (query) Search.performSearch(query);
   },
 
-  loadIndex : function(url) {
-    $.ajax({type: "GET", url: url, data: null,
-            dataType: "script", cache: true,
-            complete: function(jqxhr, textstatus) {
-              if (textstatus != "success") {
-                document.getElementById("searchindexloader").src = url;
-              }
-            }});
-  },
+  loadIndex: (url) =>
+    (document.body.appendChild(document.createElement("script")).src = url),
 
-  setIndex : function(index) {
-    var q;
-    this._index = index;
-    if ((q = this._queued_query) !== null) {
-      this._queued_query = null;
-      Search.query(q);
+  setIndex: (index) => {
+    Search._index = index;
+    if (Search._queued_query !== null) {
+      const query = Search._queued_query;
+      Search._queued_query = null;
+      Search.query(query);
     }
   },
 
-  hasIndex : function() {
-      return this._index !== null;
-  },
+  hasIndex: () => Search._index !== null,
 
-  deferQuery : function(query) {
-      this._queued_query = query;
-  },
+  deferQuery: (query) => (Search._queued_query = query),
 
-  stopPulse : function() {
-      this._pulse_status = 0;
-  },
+  stopPulse: () => (Search._pulse_status = -1),
 
-  startPulse : function() {
-    if (this._pulse_status >= 0)
-        return;
-    function pulse() {
-      var i;
+  startPulse: () => {
+    if (Search._pulse_status >= 0) return;
+
+    const pulse = () => {
       Search._pulse_status = (Search._pulse_status + 1) % 4;
-      var dotString = '';
-      for (i = 0; i < Search._pulse_status; i++)
-        dotString += '.';
-      Search.dots.text(dotString);
-      if (Search._pulse_status > -1)
-        window.setTimeout(pulse, 500);
-    }
+      Search.dots.innerText = ".".repeat(Search._pulse_status);
+      if (Search._pulse_status >= 0) window.setTimeout(pulse, 500);
+    };
     pulse();
   },
 
   /**
    * perform a search for something (or wait until index is loaded)
    */
-  performSearch : function(query) {
+  performSearch: (query) => {
     // create the required interface elements
-    this.out = $('#search-results');
-    this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
-    this.dots = $('<span></span>').appendTo(this.title);
-    this.status = $('<p class="search-summary">&nbsp;</p>').appendTo(this.out);
-    this.output = $('<ul class="search"/>').appendTo(this.out);
+    const searchText = document.createElement("h2");
+    searchText.textContent = _("Searching");
+    const searchSummary = document.createElement("p");
+    searchSummary.classList.add("search-summary");
+    searchSummary.innerText = "";
+    const searchList = document.createElement("ul");
+    searchList.classList.add("search");
 
-    $('#search-progress').text(_('Preparing search...'));
-    this.startPulse();
+    const out = document.getElementById("search-results");
+    Search.title = out.appendChild(searchText);
+    Search.dots = Search.title.appendChild(document.createElement("span"));
+    Search.status = out.appendChild(searchSummary);
+    Search.output = out.appendChild(searchList);
+
+    const searchProgress = document.getElementById("search-progress");
+    // Some themes don't use the search progress node
+    if (searchProgress) {
+      searchProgress.innerText = _("Preparing search...");
+    }
+    Search.startPulse();
 
     // index already loaded, the browser was quick!
-    if (this.hasIndex())
-      this.query(query);
-    else
-      this.deferQuery(query);
+    if (Search.hasIndex()) Search.query(query);
+    else Search.deferQuery(query);
   },
 
   /**
    * execute search (requires search index to be loaded)
    */
-  query : function(query) {
-    var i;
+  query: (query) => {
+    // stem the search terms and add them to the correct list
+    const stemmer = new Stemmer();
+    const searchTerms = new Set();
+    const excludedTerms = new Set();
+    const highlightTerms = new Set();
+    const objectTerms = new Set(splitQuery(query.toLowerCase().trim()));
+    splitQuery(query.trim()).forEach((queryTerm) => {
+      const queryTermLower = queryTerm.toLowerCase();
 
-    // stem the searchterms and add them to the correct list
-    var stemmer = new Stemmer();
-    var searchterms = [];
-    var excluded = [];
-    var hlterms = [];
-    var tmp = splitQuery(query);
-    var objectterms = [];
-    for (i = 0; i < tmp.length; i++) {
-      if (tmp[i] !== "") {
-          objectterms.push(tmp[i].toLowerCase());
-      }
+      // maybe skip this "word"
+      // stopwords array is from language_data.js
+      if (
+        stopwords.indexOf(queryTermLower) !== -1 ||
+        queryTerm.match(/^\d+$/)
+      )
+        return;
 
-      if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") {
-        // skip this "word"
-        continue;
-      }
       // stem the word
-      var word = stemmer.stemWord(tmp[i].toLowerCase());
-      // prevent stemmer from cutting word smaller than two chars
-      if(word.length < 3 && tmp[i].length >= 3) {
-        word = tmp[i];
-      }
-      var toAppend;
+      let word = stemmer.stemWord(queryTermLower);
       // select the correct list
-      if (word[0] == '-') {
-        toAppend = excluded;
-        word = word.substr(1);
-      }
+      if (word[0] === "-") excludedTerms.add(word.substr(1));
       else {
-        toAppend = searchterms;
-        hlterms.push(tmp[i].toLowerCase());
+        searchTerms.add(word);
+        highlightTerms.add(queryTermLower);
       }
-      // only add if not already in the list
-      if (!$u.contains(toAppend, word))
-        toAppend.push(word);
-    }
-    var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+    });
 
-    // console.debug('SEARCH: searching for:');
-    // console.info('required: ', searchterms);
-    // console.info('excluded: ', excluded);
+    // console.debug("SEARCH: searching for:");
+    // console.info("required: ", [...searchTerms]);
+    // console.info("excluded: ", [...excludedTerms]);
 
-    // prepare search
-    var terms = this._index.terms;
-    var titleterms = this._index.titleterms;
-
-    // array of [filename, title, anchor, descr, score]
-    var results = [];
-    $('#search-progress').empty();
+    // array of [docname, title, anchor, descr, score, filename]
+    let results = [];
+    _removeChildren(document.getElementById("search-progress"));
 
     // lookup as object
-    for (i = 0; i < objectterms.length; i++) {
-      var others = [].concat(objectterms.slice(0, i),
-                             objectterms.slice(i+1, objectterms.length));
-      results = results.concat(this.performObjectSearch(objectterms[i], others));
-    }
+    objectTerms.forEach((term) =>
+      results.push(...Search.performObjectSearch(term, objectTerms))
+    );
 
     // lookup as search terms in fulltext
-    results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+    results.push(...Search.performTermsSearch(searchTerms, excludedTerms));
 
     // let the scorer override scores with a custom scoring function
-    if (Scorer.score) {
-      for (i = 0; i < results.length; i++)
-        results[i][4] = Scorer.score(results[i]);
-    }
+    if (Scorer.score) results.forEach((item) => (item[4] = Scorer.score(item)));
 
     // now sort the results by score (in opposite order of appearance, since the
     // display function below uses pop() to retrieve items) and then
     // alphabetically
-    results.sort(function(a, b) {
-      var left = a[4];
-      var right = b[4];
-      if (left > right) {
-        return 1;
-      } else if (left < right) {
-        return -1;
-      } else {
+    results.sort((a, b) => {
+      const leftScore = a[4];
+      const rightScore = b[4];
+      if (leftScore === rightScore) {
         // same score: sort alphabetically
-        left = a[1].toLowerCase();
-        right = b[1].toLowerCase();
-        return (left > right) ? -1 : ((left < right) ? 1 : 0);
+        const leftTitle = a[1].toLowerCase();
+        const rightTitle = b[1].toLowerCase();
+        if (leftTitle === rightTitle) return 0;
+        return leftTitle > rightTitle ? -1 : 1; // inverted is intentional
       }
+      return leftScore > rightScore ? 1 : -1;
     });
 
+    // remove duplicate search results
+    // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept
+    let seen = new Set();
+    results = results.reverse().reduce((acc, result) => {
+      let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(',');
+      if (!seen.has(resultStr)) {
+        acc.push(result);
+        seen.add(resultStr);
+      }
+      return acc;
+    }, []);
+
+    results = results.reverse();
+
     // for debugging
     //Search.lastresults = results.slice();  // a copy
-    //console.info('search results:', Search.lastresults);
+    // console.info("search results:", Search.lastresults);
 
     // print the results
-    var resultCount = results.length;
-    function displayNextItem() {
-      // results left, load the summary and display it
-      if (results.length) {
-        var item = results.pop();
-        var listItem = $('<li></li>');
-        var requestUrl = "";
-        var linkUrl = "";
-        if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
-          // dirhtml builder
-          var dirname = item[0] + '/';
-          if (dirname.match(/\/index\/$/)) {
-            dirname = dirname.substring(0, dirname.length-6);
-          } else if (dirname == 'index/') {
-            dirname = '';
-          }
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
-          linkUrl = requestUrl;
-
-        } else {
-          // normal html builders
-          requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
-          linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
-        }
-        listItem.append($('<a/>').attr('href',
-            linkUrl +
-            highlightstring + item[2]).html(item[1]));
-        if (item[3]) {
-          listItem.append($('<span> (' + item[3] + ')</span>'));
-          Search.output.append(listItem);
-          setTimeout(function() {
-            displayNextItem();
-          }, 5);
-        } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
-          $.ajax({url: requestUrl,
-                  dataType: "text",
-                  complete: function(jqxhr, textstatus) {
-                    var data = jqxhr.responseText;
-                    if (data !== '' && data !== undefined) {
-                      var summary = Search.makeSearchSummary(data, searchterms, hlterms);
-                      if (summary) {
-                        listItem.append(summary);
-                      }
-                    }
-                    Search.output.append(listItem);
-                    setTimeout(function() {
-                      displayNextItem();
-                    }, 5);
-                  }});
-        } else {
-          // no source available, just display title
-          Search.output.append(listItem);
-          setTimeout(function() {
-            displayNextItem();
-          }, 5);
-        }
-      }
-      // search finished, update title and status message
-      else {
-        Search.stopPulse();
-        Search.title.text(_('Search Results'));
-        if (!resultCount)
-          Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
-        else
-            Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
-        Search.status.fadeIn(500);
-      }
-    }
-    displayNextItem();
+    _displayNextItem(results, results.length, highlightTerms, searchTerms);
   },
 
   /**
    * search for object names
    */
-  performObjectSearch : function(object, otherterms) {
-    var filenames = this._index.filenames;
-    var docnames = this._index.docnames;
-    var objects = this._index.objects;
-    var objnames = this._index.objnames;
-    var titles = this._index.titles;
+  performObjectSearch: (object, objectTerms) => {
+    const filenames = Search._index.filenames;
+    const docNames = Search._index.docnames;
+    const objects = Search._index.objects;
+    const objNames = Search._index.objnames;
+    const titles = Search._index.titles;
 
-    var i;
-    var results = [];
+    const results = [];
 
-    for (var prefix in objects) {
-      for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) {
-        var match = objects[prefix][iMatch];
-        var name = match[4];
-        var fullname = (prefix ? prefix + '.' : '') + name;
-        var fullnameLower = fullname.toLowerCase()
-        if (fullnameLower.indexOf(object) > -1) {
-          var score = 0;
-          var parts = fullnameLower.split('.');
-          // check for different match types: exact matches of full name or
-          // "last name" (i.e. last dotted part)
-          if (fullnameLower == object || parts[parts.length - 1] == object) {
-            score += Scorer.objNameMatch;
-          // matches in last name
-          } else if (parts[parts.length - 1].indexOf(object) > -1) {
-            score += Scorer.objPartialMatch;
-          }
-          var objname = objnames[match[1]][2];
-          var title = titles[match[0]];
-          // If more than one term searched for, we require other words to be
-          // found in the name/title/description
-          if (otherterms.length > 0) {
-            var haystack = (prefix + ' ' + name + ' ' +
-                            objname + ' ' + title).toLowerCase();
-            var allfound = true;
-            for (i = 0; i < otherterms.length; i++) {
-              if (haystack.indexOf(otherterms[i]) == -1) {
-                allfound = false;
-                break;
-              }
-            }
-            if (!allfound) {
-              continue;
-            }
-          }
-          var descr = objname + _(', in ') + title;
+    const objectSearchCallback = (prefix, match) => {
+      const name = match[4]
+      const fullname = (prefix ? prefix + "." : "") + name;
+      const fullnameLower = fullname.toLowerCase();
+      if (fullnameLower.indexOf(object) < 0) return;
 
-          var anchor = match[3];
-          if (anchor === '')
-            anchor = fullname;
-          else if (anchor == '-')
-            anchor = objnames[match[1]][1] + '-' + fullname;
-          // add custom score for some objects according to scorer
-          if (Scorer.objPrio.hasOwnProperty(match[2])) {
-            score += Scorer.objPrio[match[2]];
-          } else {
-            score += Scorer.objPrioDefault;
-          }
-          results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
-        }
+      let score = 0;
+      const parts = fullnameLower.split(".");
+
+      // check for different match types: exact matches of full name or
+      // "last name" (i.e. last dotted part)
+      if (fullnameLower === object || parts.slice(-1)[0] === object)
+        score += Scorer.objNameMatch;
+      else if (parts.slice(-1)[0].indexOf(object) > -1)
+        score += Scorer.objPartialMatch; // matches in last name
+
+      const objName = objNames[match[1]][2];
+      const title = titles[match[0]];
+
+      // If more than one term searched for, we require other words to be
+      // found in the name/title/description
+      const otherTerms = new Set(objectTerms);
+      otherTerms.delete(object);
+      if (otherTerms.size > 0) {
+        const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase();
+        if (
+          [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0)
+        )
+          return;
       }
-    }
 
+      let anchor = match[3];
+      if (anchor === "") anchor = fullname;
+      else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname;
+
+      const descr = objName + _(", in ") + title;
+
+      // add custom score for some objects according to scorer
+      if (Scorer.objPrio.hasOwnProperty(match[2]))
+        score += Scorer.objPrio[match[2]];
+      else score += Scorer.objPrioDefault;
+
+      results.push([
+        docNames[match[0]],
+        fullname,
+        "#" + anchor,
+        descr,
+        score,
+        filenames[match[0]],
+      ]);
+    };
+    Object.keys(objects).forEach((prefix) =>
+      objects[prefix].forEach((array) =>
+        objectSearchCallback(prefix, array)
+      )
+    );
     return results;
   },
 
-  /**
-   * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
-   */
-  escapeRegExp : function(string) {
-    return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
-  },
-
   /**
    * search for full-text terms in the index
    */
-  performTermsSearch : function(searchterms, excluded, terms, titleterms) {
-    var docnames = this._index.docnames;
-    var filenames = this._index.filenames;
-    var titles = this._index.titles;
+  performTermsSearch: (searchTerms, excludedTerms) => {
+    // prepare search
+    const terms = Search._index.terms;
+    const titleTerms = Search._index.titleterms;
+    const docNames = Search._index.docnames;
+    const filenames = Search._index.filenames;
+    const titles = Search._index.titles;
 
-    var i, j, file;
-    var fileMap = {};
-    var scoreMap = {};
-    var results = [];
+    const scoreMap = new Map();
+    const fileMap = new Map();
 
     // perform the search on the required terms
-    for (i = 0; i < searchterms.length; i++) {
-      var word = searchterms[i];
-      var files = [];
-      var _o = [
-        {files: terms[word], score: Scorer.term},
-        {files: titleterms[word], score: Scorer.title}
+    searchTerms.forEach((word) => {
+      const files = [];
+      const arr = [
+        { files: terms[word], score: Scorer.term },
+        { files: titleTerms[word], score: Scorer.title },
       ];
       // add support for partial matches
       if (word.length > 2) {
-        var word_regex = this.escapeRegExp(word);
-        for (var w in terms) {
-          if (w.match(word_regex) && !terms[word]) {
-            _o.push({files: terms[w], score: Scorer.partialTerm})
-          }
-        }
-        for (var w in titleterms) {
-          if (w.match(word_regex) && !titleterms[word]) {
-              _o.push({files: titleterms[w], score: Scorer.partialTitle})
-          }
-        }
+        const escapedWord = _escapeRegExp(word);
+        Object.keys(terms).forEach((term) => {
+          if (term.match(escapedWord) && !terms[word])
+            arr.push({ files: terms[term], score: Scorer.partialTerm });
+        });
+        Object.keys(titleTerms).forEach((term) => {
+          if (term.match(escapedWord) && !titleTerms[word])
+            arr.push({ files: titleTerms[word], score: Scorer.partialTitle });
+        });
       }
 
       // no match but word was a required one
-      if ($u.every(_o, function(o){return o.files === undefined;})) {
-        break;
-      }
+      if (arr.every((record) => record.files === undefined)) return;
+
       // found search word in contents
-      $u.each(_o, function(o) {
-        var _files = o.files;
-        if (_files === undefined)
-          return
+      arr.forEach((record) => {
+        if (record.files === undefined) return;
 
-        if (_files.length === undefined)
-          _files = [_files];
-        files = files.concat(_files);
+        let recordFiles = record.files;
+        if (recordFiles.length === undefined) recordFiles = [recordFiles];
+        files.push(...recordFiles);
 
-        // set score for the word in each file to Scorer.term
-        for (j = 0; j < _files.length; j++) {
-          file = _files[j];
-          if (!(file in scoreMap))
-            scoreMap[file] = {};
-          scoreMap[file][word] = o.score;
-        }
+        // set score for the word in each file
+        recordFiles.forEach((file) => {
+          if (!scoreMap.has(file)) scoreMap.set(file, {});
+          scoreMap.get(file)[word] = record.score;
+        });
       });
 
       // create the mapping
-      for (j = 0; j < files.length; j++) {
-        file = files[j];
-        if (file in fileMap && fileMap[file].indexOf(word) === -1)
-          fileMap[file].push(word);
-        else
-          fileMap[file] = [word];
-      }
-    }
+      files.forEach((file) => {
+        if (fileMap.has(file) && fileMap.get(file).indexOf(word) === -1)
+          fileMap.get(file).push(word);
+        else fileMap.set(file, [word]);
+      });
+    });
 
     // now check if the files don't contain excluded terms
-    for (file in fileMap) {
-      var valid = true;
-
+    const results = [];
+    for (const [file, wordList] of fileMap) {
       // check if all requirements are matched
-      var filteredTermCount = // as search terms with length < 3 are discarded: ignore
-        searchterms.filter(function(term){return term.length > 2}).length
+
+      // as search terms with length < 3 are discarded
+      const filteredTermCount = [...searchTerms].filter(
+        (term) => term.length > 2
+      ).length;
       if (
-        fileMap[file].length != searchterms.length &&
-        fileMap[file].length != filteredTermCount
-      ) continue;
+        wordList.length !== searchTerms.size &&
+        wordList.length !== filteredTermCount
+      )
+        continue;
 
       // ensure that none of the excluded terms is in the search result
-      for (i = 0; i < excluded.length; i++) {
-        if (terms[excluded[i]] == file ||
-            titleterms[excluded[i]] == file ||
-            $u.contains(terms[excluded[i]] || [], file) ||
-            $u.contains(titleterms[excluded[i]] || [], file)) {
-          valid = false;
-          break;
-        }
-      }
+      if (
+        [...excludedTerms].some(
+          (term) =>
+            terms[term] === file ||
+            titleTerms[term] === file ||
+            (terms[term] || []).includes(file) ||
+            (titleTerms[term] || []).includes(file)
+        )
+      )
+        break;
 
-      // if we have still a valid result we can add it to the result list
-      if (valid) {
-        // select one (max) score for the file.
-        // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
-        var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
-        results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
-      }
+      // select one (max) score for the file.
+      const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w]));
+      // add result to the result list
+      results.push([
+        docNames[file],
+        titles[file],
+        "",
+        null,
+        score,
+        filenames[file],
+      ]);
     }
     return results;
   },
@@ -496,34 +499,33 @@ var Search = {
   /**
    * helper function to return a node containing the
    * search summary for a given text. keywords is a list
-   * of stemmed words, hlwords is the list of normal, unstemmed
+   * of stemmed words, highlightWords is the list of normal, unstemmed
    * words. the first one is used to find the occurrence, the
    * latter for highlighting it.
    */
-  makeSearchSummary : function(htmlText, keywords, hlwords) {
-    var text = Search.htmlToText(htmlText);
-    if (text == "") {
-      return null;
-    }
-    var textLower = text.toLowerCase();
-    var start = 0;
-    $.each(keywords, function() {
-      var i = textLower.indexOf(this.toLowerCase());
-      if (i > -1)
-        start = i;
-    });
-    start = Math.max(start - 120, 0);
-    var excerpt = ((start > 0) ? '...' : '') +
-      $.trim(text.substr(start, 240)) +
-      ((start + 240 - text.length) ? '...' : '');
-    var rv = $('<p class="context"></p>').text(excerpt);
-    $.each(hlwords, function() {
-      rv = rv.highlightText(this, 'highlighted');
-    });
-    return rv;
-  }
+  makeSearchSummary: (htmlText, keywords, highlightWords) => {
+    const text = Search.htmlToText(htmlText).toLowerCase();
+    if (text === "") return null;
+
+    const actualStartPosition = [...keywords]
+      .map((k) => text.indexOf(k.toLowerCase()))
+      .filter((i) => i > -1)
+      .slice(-1)[0];
+    const startWithContext = Math.max(actualStartPosition - 120, 0);
+
+    const top = startWithContext === 0 ? "" : "...";
+    const tail = startWithContext + 240 < text.length ? "..." : "";
+
+    let summary = document.createElement("div");
+    summary.classList.add("context");
+    summary.innerText = top + text.substr(startWithContext, 240).trim() + tail;
+
+    highlightWords.forEach((highlightWord) =>
+      _highlightText(summary, highlightWord, "highlighted")
+    );
+
+    return summary;
+  },
 };
 
-$(document).ready(function() {
-  Search.init();
-});
+_ready(Search.init);
diff --git a/doc/LectureNotes/_build/html/_static/styles/bootstrap.css b/doc/LectureNotes/_build/html/_static/styles/bootstrap.css
new file mode 100644
index 000000000..2476a5e76
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/styles/bootstrap.css
@@ -0,0 +1,6 @@
+/*!
+ * Bootstrap  v5.2.3 (https://getbootstrap.com/)
+ * Copyright 2011-2022 The Bootstrap Authors
+ * Copyright 2011-2022 Twitter, Inc.
+ * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE)
+ */:root{--bs-blue:#0d6efd;--bs-indigo:#6610f2;--bs-purple:#6f42c1;--bs-pink:#d63384;--bs-red:#dc3545;--bs-orange:#fd7e14;--bs-yellow:#ffc107;--bs-green:#198754;--bs-teal:#20c997;--bs-cyan:#0dcaf0;--bs-black:#000;--bs-white:#fff;--bs-gray:#6c757d;--bs-gray-dark:#343a40;--bs-gray-100:#f8f9fa;--bs-gray-200:#e9ecef;--bs-gray-300:#dee2e6;--bs-gray-400:#ced4da;--bs-gray-500:#adb5bd;--bs-gray-600:#6c757d;--bs-gray-700:#495057;--bs-gray-800:#343a40;--bs-gray-900:#212529;--bs-primary:#0d6efd;--bs-secondary:#6c757d;--bs-success:#198754;--bs-info:#0dcaf0;--bs-warning:#ffc107;--bs-danger:#dc3545;--bs-light:#f8f9fa;--bs-dark:#212529;--bs-primary-rgb:13,110,253;--bs-secondary-rgb:108,117,125;--bs-success-rgb:25,135,84;--bs-info-rgb:13,202,240;--bs-warning-rgb:255,193,7;--bs-danger-rgb:220,53,69;--bs-light-rgb:248,249,250;--bs-dark-rgb:33,37,41;--bs-white-rgb:255,255,255;--bs-black-rgb:0,0,0;--bs-body-color-rgb:33,37,41;--bs-body-bg-rgb:255,255,255;--bs-font-sans-serif:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue","Noto Sans","Liberation Sans",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";--bs-font-monospace:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier 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1rem}b,strong{font-weight:bolder}.small,small{font-size:.875em}.mark,mark{background-color:var(--bs-highlight-bg);padding:.1875em}sub,sup{font-size:.75em;line-height:0;position:relative;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:var(--bs-link-color);text-decoration:underline}a:hover{color:var(--bs-link-hover-color)}a:not([href]):not([class]),a:not([href]):not([class]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:var(--bs-font-monospace);font-size:1em}pre{display:block;font-size:.875em;margin-bottom:1rem;margin-top:0;overflow:auto}pre code{color:inherit;font-size:inherit;word-break:normal}code{word-wrap:break-word;color:var(--bs-code-color);font-size:.875em}a>code{color:inherit}kbd{background-color:var(--bs-body-color);border-radius:.25rem;color:var(--bs-body-bg);font-size:.875em;padding:.1875rem .375rem}kbd kbd{font-size:1em;padding:0}figure{margin:0 0 1rem}img,svg{vertical-align:middle}table{border-collapse:collapse;caption-side:bottom}caption{color:#6c757d;padding-bottom:.5rem;padding-top:.5rem;text-align:left}th{text-align:inherit;text-align:-webkit-match-parent}tbody,td,tfoot,th,thead,tr{border:0 solid;border-color:inherit}label{display:inline-block}button{border-radius:0}button:focus:not(:focus-visible){outline:0}button,input,optgroup,select,textarea{font-family:inherit;font-size:inherit;line-height:inherit;margin:0}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}select:disabled{opacity:1}[list]:not([type=date]):not([type=datetime-local]):not([type=month]):not([type=week]):not([type=time])::-webkit-calendar-picker-indicator{display:none!important}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}::-moz-focus-inner{border-style:none;padding:0}textarea{resize:vertical}fieldset{border:0;margin:0;min-width:0;padding:0}legend{float:left;font-size:calc(1.275rem + .3vw);line-height:inherit;margin-bottom:.5rem;padding:0;width:100%}@media(min-width:1200px){legend{font-size:1.5rem}}legend+*{clear:left}::-webkit-datetime-edit-day-field,::-webkit-datetime-edit-fields-wrapper,::-webkit-datetime-edit-hour-field,::-webkit-datetime-edit-minute,::-webkit-datetime-edit-month-field,::-webkit-datetime-edit-text,::-webkit-datetime-edit-year-field{padding:0}::-webkit-inner-spin-button{height:auto}[type=search]{-webkit-appearance:textfield;outline-offset:-2px}::-webkit-search-decoration{-webkit-appearance:none}::-webkit-color-swatch-wrapper{padding:0}::file-selector-button{-webkit-appearance:button;font:inherit}output{display:inline-block}iframe{border:0}summary{cursor:pointer;display:list-item}progress{vertical-align:baseline}[hidden]{display:none!important}.lead{font-size:1.25rem;font-weight:300}.display-1{font-size:calc(1.625rem + 4.5vw);font-weight:300;line-height:1.2}@media(min-width:1200px){.display-1{font-size:5rem}}.display-2{font-size:calc(1.575rem + 3.9vw);font-weight:300;line-height:1.2}@media(min-width:1200px){.display-2{font-size:4.5rem}}.display-3{font-size:calc(1.525rem + 3.3vw);font-weight:300;line-height:1.2}@media(min-width:1200px){.display-3{font-size:4rem}}.display-4{font-size:calc(1.475rem + 2.7vw);font-weight:300;line-height:1.2}@media(min-width:1200px){.display-4{font-size:3.5rem}}.display-5{font-size:calc(1.425rem + 2.1vw);font-weight:300;line-height:1.2}@media(min-width:1200px){.display-5{font-size:3rem}}.display-6{font-size:calc(1.375rem + 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rgba(13,110,253,.25);--bs-pagination-active-color:#fff;--bs-pagination-active-bg:#0d6efd;--bs-pagination-active-border-color:#0d6efd;--bs-pagination-disabled-color:#6c757d;--bs-pagination-disabled-bg:#fff;--bs-pagination-disabled-border-color:#dee2e6;display:flex;list-style:none;padding-left:0}.page-link{background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);color:var(--bs-pagination-color);display:block;font-size:var(--bs-pagination-font-size);padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);position:relative;text-decoration:none;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s 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var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-primary{background-color:#cfe2ff;color:#084298}.list-group-item-primary.list-group-item-action:focus,.list-group-item-primary.list-group-item-action:hover{background-color:#bacbe6;color:#084298}.list-group-item-primary.list-group-item-action.active{background-color:#084298;border-color:#084298;color:#fff}.list-group-item-secondary{background-color:#e2e3e5;color:#41464b}.list-group-item-secondary.list-group-item-action:focus,.list-group-item-secondary.list-group-item-action:hover{background-color:#cbccce;color:#41464b}.list-group-item-secondary.list-group-item-action.active{background-color:#41464b;border-color:#41464b;color:#fff}.list-group-item-success{background-color:#d1e7dd;color:#0f5132}.list-group-item-success.list-group-item-action:focus,.list-group-item-success.list-group-item-action:hover{background-color:#bcd0c7;color:#0f5132}.list-group-item-success.list-group-item-action.active{background-color:#0f5132;border-color:#0f5132;color:#fff}.list-group-item-info{background-color:#cff4fc;color:#055160}.list-group-item-info.list-group-item-action:focus,.list-group-item-info.list-group-item-action:hover{background-color:#badce3;color:#055160}.list-group-item-info.list-group-item-action.active{background-color:#055160;border-color:#055160;color:#fff}.list-group-item-warning{background-color:#fff3cd;color:#664d03}.list-group-item-warning.list-group-item-action:focus,.list-group-item-warning.list-group-item-action:hover{background-color:#e6dbb9;color:#664d03}.list-group-item-warning.list-group-item-action.active{background-color:#664d03;border-color:#664d03;color:#fff}.list-group-item-danger{background-color:#f8d7da;color:#842029}.list-group-item-danger.list-group-item-action:focus,.list-group-item-danger.list-group-item-action:hover{background-color:#dfc2c4;color:#842029}.list-group-item-danger.list-group-item-action.active{background-color:#842029;border-color:#842029;color:#fff}.list-group-item-light{background-color:#fefefe;color:#636464}.list-group-item-light.list-group-item-action:focus,.list-group-item-light.list-group-item-action:hover{background-color:#e5e5e5;color:#636464}.list-group-item-light.list-group-item-action.active{background-color:#636464;border-color:#636464;color:#fff}.list-group-item-dark{background-color:#d3d3d4;color:#141619}.list-group-item-dark.list-group-item-action:focus,.list-group-item-dark.list-group-item-action:hover{background-color:#bebebf;color:#141619}.list-group-item-dark.list-group-item-action.active{background-color:#141619;border-color:#141619;color:#fff}.btn-close{background:transparent url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16'%3E%3Cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3E%3C/svg%3E") 50%/1em auto no-repeat;border:0;border-radius:.375rem;box-sizing:content-box;color:#000;height:1em;opacity:.5;padding:.25em;width:1em}.btn-close:hover{color:#000;opacity:.75;text-decoration:none}.btn-close:focus{box-shadow:0 0 0 .25rem rgba(13,110,253,.25);opacity:1;outline:0}.btn-close.disabled,.btn-close:disabled{opacity:.25;pointer-events:none;user-select:none}.btn-close-white{filter:invert(1) grayscale(100%) brightness(200%)}.toast{--bs-toast-zindex:1090;--bs-toast-padding-x:0.75rem;--bs-toast-padding-y:0.5rem;--bs-toast-spacing:1.5rem;--bs-toast-max-width:350px;--bs-toast-font-size:0.875rem;--bs-toast-color: 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diff --git a/doc/LectureNotes/_build/html/_static/styles/sphinx-book-theme.css b/doc/LectureNotes/_build/html/_static/styles/sphinx-book-theme.css
new file mode 100644
index 000000000..e514f24e3
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/styles/sphinx-book-theme.css
@@ -0,0 +1,8 @@
+/*! sphinx-book-theme CSS
+ * BSD 3-Clause License
+ * Copyright (c) 2020, EBP
+ * All rights reserved.
+ *
+ * This follows the 7-1 pattern described here:
+ * https://sass-guidelin.es/#architecture
+ */html{--pst-font-size-base:none}html[data-theme=light]{--sbt-color-announcement:#616161}html[data-theme=dark],html[data-theme=light]{--pst-color-primary:#579aca}html{scroll-padding-top:4rem}.sbt-scroll-pixel-helper{position:absolute;width:0;height:0;top:0;left:0}.d-n,.onlyprint{display:none}@media print{.onlyprint{display:block!important}}@media print{.noprint{display:none!important}}.bd-article-container h1,.bd-article-container h2,.bd-article-container h3,.bd-article-container h4,.bd-article-container h5,.bd-article-container p.caption{color:var(--pst-color-muted)}.bd-article-container h1,.bd-article-container h2{font-weight:500}a.brackets:before{color:inherit;font-family:inherit;margin-right:0}table{position:relative}@media print{.bd-main .bd-content{margin-left:2rem;height:auto}.bd-main .bd-content #jb-print-docs-body{margin-left:0}.bd-main .bd-content #jb-print-docs-body h1{font-size:3em;text-align:center;margin-bottom:0}.bd-main .bd-content .bd-article{padding-top:0}.bd-main 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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/_static/styles/theme.css b/doc/LectureNotes/_build/html/_static/styles/theme.css
new file mode 100644
index 000000000..4519dd912
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/styles/theme.css
@@ -0,0 +1,2 @@
+/* Provided by Sphinx's 'basic' theme, and included in the final set of assets */
+@import "../basic.css";
diff --git a/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/LICENSE.txt b/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/LICENSE.txt
new file mode 100644
index 000000000..cc557ece4
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/LICENSE.txt
@@ -0,0 +1,165 @@
+Fonticons, Inc. (https://fontawesome.com)
+
+--------------------------------------------------------------------------------
+
+Font Awesome Free License
+
+Font Awesome Free is free, open source, and GPL friendly. You can use it for
+commercial projects, open source projects, or really almost whatever you want.
+Full Font Awesome Free license: https://fontawesome.com/license/free.
+
+--------------------------------------------------------------------------------
+
+# Icons: CC BY 4.0 License (https://creativecommons.org/licenses/by/4.0/)
+
+The Font Awesome Free download is licensed under a Creative Commons
+Attribution 4.0 International License and applies to all icons packaged
+as SVG and JS file types.
+
+--------------------------------------------------------------------------------
+
+# Fonts: SIL OFL 1.1 License
+
+In the Font Awesome Free download, the SIL OFL license applies to all icons
+packaged as web and desktop font files.
+
+Copyright (c) 2022 Fonticons, Inc. (https://fontawesome.com)
+with Reserved Font Name: "Font Awesome".
+
+This Font Software is licensed under the SIL Open Font License, Version 1.1.
+This license is copied below, and is also available with a FAQ at:
+http://scripts.sil.org/OFL
+
+SIL OPEN FONT LICENSE
+Version 1.1 - 26 February 2007
+
+PREAMBLE
+The goals of the Open Font License (OFL) are to stimulate worldwide
+development of collaborative font projects, to support the font creation
+efforts of academic and linguistic communities, and to provide a free and
+open framework in which fonts may be shared and improved in partnership
+with others.
+
+The OFL allows the licensed fonts to be used, studied, modified and
+redistributed freely as long as they are not sold by themselves. The
+fonts, including any derivative works, can be bundled, embedded,
+redistributed and/or sold with any software provided that any reserved
+names are not used by derivative works. The fonts and derivatives,
+however, cannot be released under any other type of license. The
+requirement for fonts to remain under this license does not apply
+to any document created using the fonts or their derivatives.
+
+DEFINITIONS
+"Font Software" refers to the set of files released by the Copyright
+Holder(s) under this license and clearly marked as such. This may
+include source files, build scripts and documentation.
+
+"Reserved Font Name" refers to any names specified as such after the
+copyright statement(s).
+
+"Original Version" refers to the collection of Font Software components as
+distributed by the Copyright Holder(s).
+
+"Modified Version" refers to any derivative made by adding to, deleting,
+or substituting — in part or in whole — any of the components of the
+Original Version, by changing formats or by porting the Font Software to a
+new environment.
+
+"Author" refers to any designer, engineer, programmer, technical
+writer or other person who contributed to the Font Software.
+
+PERMISSION & CONDITIONS
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of the Font Software, to use, study, copy, merge, embed, modify,
+redistribute, and sell modified and unmodified copies of the Font
+Software, subject to the following conditions:
+
+1) Neither the Font Software nor any of its individual components,
+in Original or Modified Versions, may be sold by itself.
+
+2) Original or Modified Versions of the Font Software may be bundled,
+redistributed and/or sold with any software, provided that each copy
+contains the above copyright notice and this license. These can be
+included either as stand-alone text files, human-readable headers or
+in the appropriate machine-readable metadata fields within text or
+binary files as long as those fields can be easily viewed by the user.
+
+3) No Modified Version of the Font Software may use the Reserved Font
+Name(s) unless explicit written permission is granted by the corresponding
+Copyright Holder. This restriction only applies to the primary font name as
+presented to the users.
+
+4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font
+Software shall not be used to promote, endorse or advertise any
+Modified Version, except to acknowledge the contribution(s) of the
+Copyright Holder(s) and the Author(s) or with their explicit written
+permission.
+
+5) The Font Software, modified or unmodified, in part or in whole,
+must be distributed entirely under this license, and must not be
+distributed under any other license. The requirement for fonts to
+remain under this license does not apply to any document created
+using the Font Software.
+
+TERMINATION
+This license becomes null and void if any of the above conditions are
+not met.
+
+DISCLAIMER
+THE FONT SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT
+OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE
+COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL
+DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM
+OTHER DEALINGS IN THE FONT SOFTWARE.
+
+--------------------------------------------------------------------------------
+
+# Code: MIT License (https://opensource.org/licenses/MIT)
+
+In the Font Awesome Free download, the MIT license applies to all non-font and
+non-icon files.
+
+Copyright 2022 Fonticons, Inc.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the "Software"), to deal in the
+Software without restriction, including without limitation the rights to use, copy,
+modify, merge, publish, distribute, sublicense, and/or sell copies of the Software,
+and to permit persons to whom the Software is furnished to do so, subject to the
+following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
+INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
+PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
+OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+--------------------------------------------------------------------------------
+
+# Attribution
+
+Attribution is required by MIT, SIL OFL, and CC BY licenses. Downloaded Font
+Awesome Free files already contain embedded comments with sufficient
+attribution, so you shouldn't need to do anything additional when using these
+files normally.
+
+We've kept attribution comments terse, so we ask that you do not actively work
+to remove them from files, especially code. They're a great way for folks to
+learn about Font Awesome.
+
+--------------------------------------------------------------------------------
+
+# Brand Icons
+
+All brand icons are trademarks of their respective owners. The use of these
+trademarks does not indicate endorsement of the trademark holder by Font
+Awesome, nor vice versa. **Please do not use brand logos for any purpose except
+to represent the company, product, or service to which they refer.**
diff --git a/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/css/all.min.css b/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/css/all.min.css
new file mode 100644
index 000000000..aad4b1d9d
--- /dev/null
+++ b/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/css/all.min.css
@@ -0,0 +1,5 @@
+/*!
+ * Font Awesome Free 6.1.2 by @fontawesome - https://fontawesome.com
+ * License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License)
+ * Copyright 2022 Fonticons, Inc.
+ */.fa{font-family:var(--fa-style-family,"Font Awesome 6 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new file mode 100644
index 000000000..f504685da
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+ * Copyright 2022 Fonticons, Inc.
+ */
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diff --git a/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2 b/doc/LectureNotes/_build/html/_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2
new file mode 100644
index 0000000000000000000000000000000000000000..4a7f96652ca9a7f6c7106cc548515ba3d7281af9
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--- a/doc/LectureNotes/_build/html/_static/webpack-macros.html
+++ b/doc/LectureNotes/_build/html/_static/webpack-macros.html
@@ -1,25 +1,31 @@
-<!-- these macros are generated by "yarn build:production". do not edit by hand. -->
+<!--
+  AUTO-GENERATED from webpack.config.js, do **NOT** edit by hand.
+  These are re-used in layout.html
+-->
+{# Load FontAwesome icons #}
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-  <link rel="stylesheet"
-    href="{{ pathto('_static/vendor/fontawesome/5.13.0/css/all.min.css', 1) }}">
-  <link rel="preload" as="font" type="font/woff2" crossorigin
-    href="{{ pathto('_static/vendor/fontawesome/5.13.0/webfonts/fa-solid-900.woff2', 1) }}">
-  <link rel="preload" as="font" type="font/woff2" crossorigin
-    href="{{ pathto('_static/vendor/fontawesome/5.13.0/webfonts/fa-brands-400.woff2', 1) }}">
+  <link href="{{ pathto('_static/vendor/fontawesome/6.1.2/css/all.min.css', 1) }}?digest=ac02cc09edc035673794" rel="stylesheet" />
+  <link rel="preload" as="font" type="font/woff2" crossorigin href="{{ pathto('_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2', 1) }}" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="{{ pathto('_static/vendor/fontawesome/6.1.2/webfonts/fa-brands-400.woff2', 1) }}" />
+<link rel="preload" as="font" type="font/woff2" crossorigin href="{{ pathto('_static/vendor/fontawesome/6.1.2/webfonts/fa-regular-400.woff2', 1) }}" />
 {% endmacro %}
 
-{% macro head_pre_fonts() %}
-{% endmacro %}
-
-{% macro head_pre_bootstrap() %}
-  <link href="{{ pathto('_static/css/theme.css', 1) }}" rel="stylesheet">
-  <link href="{{ pathto('_static/css/index.ff1ffe594081f20da1ef19478df9384b.css', 1) }}" rel="stylesheet">
+{% macro head_pre_assets() %}
+  <!-- Loaded before other Sphinx assets -->
+  <link href="{{ pathto('_static/styles/theme.css', 1) }}?digest=ac02cc09edc035673794" rel="stylesheet" />
+<link href="{{ pathto('_static/styles/bootstrap.css', 1) }}?digest=ac02cc09edc035673794" rel="stylesheet" />
+<link href="{{ pathto('_static/styles/pydata-sphinx-theme.css', 1) }}?digest=ac02cc09edc035673794" rel="stylesheet" />
 {% endmacro %}
 
 {% macro head_js_preload() %}
-  <link rel="preload" as="script" href="{{ pathto('_static/js/index.be7d3bbb2ef33a8344ce.js', 1) }}">
+  <!-- Pre-loaded scripts that we'll load fully later -->
+  <link rel="preload" as="script" href="{{ pathto('_static/scripts/bootstrap.js', 1) }}?digest=ac02cc09edc035673794" />
+<link rel="preload" as="script" href="{{ pathto('_static/scripts/pydata-sphinx-theme.js', 1) }}?digest=ac02cc09edc035673794" />
+  <script src="{{ pathto('_static/vendor/fontawesome/6.1.2/js/all.min.js', 1) }}?digest=ac02cc09edc035673794"></script>
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 {% macro body_post() %}
-  <script src="{{ pathto('_static/js/index.be7d3bbb2ef33a8344ce.js', 1) }}"></script>
+  <!-- Scripts loaded after <body> so the DOM is not blocked -->
+  <script src="{{ pathto('_static/scripts/bootstrap.js', 1) }}?digest=ac02cc09edc035673794"></script>
+<script src="{{ pathto('_static/scripts/pydata-sphinx-theme.js', 1) }}?digest=ac02cc09edc035673794"></script>
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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/chapter1.html b/doc/LectureNotes/_build/html/chapter1.html
index f7a949576..b9be87a2b 100644
--- a/doc/LectureNotes/_build/html/chapter1.html
+++ b/doc/LectureNotes/_build/html/chapter1.html
@@ -1,50 +1,61 @@
 
+
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-<html>
+
+<html lang="en" >
+
   <head>
     <meta charset="utf-8" />
-    <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+    <meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.18.1: http://docutils.sourceforge.net/" />
+
     <title>3. Linear Regression &#8212; Applied Data Analysis and Machine Learning</title>
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-  <link href="_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
+  
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-    
-  <link rel="stylesheet"
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-  <link rel="preload" as="font" type="font/woff2" crossorigin
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+  
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+  <link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.1.2/webfonts/fa-solid-900.woff2" />
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-    
-  <link rel="preload" as="script" href="_static/js/index.be7d3bbb2ef33a8344ce.js">
+    <link rel="stylesheet" type="text/css" href="_static/design-style.4045f2051d55cab465a707391d5b2007.min.css" />
+  
+  <!-- Pre-loaded scripts that we'll load fully later -->
+  <link rel="preload" as="script" href="_static/scripts/bootstrap.js?digest=ac02cc09edc035673794" />
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+  <script src="_static/vendor/fontawesome/6.1.2/js/all.min.js?digest=ac02cc09edc035673794"></script>
 
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     <script src="_static/jquery.js"></script>
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+    <script src="_static/_sphinx_javascript_frameworks_compat.js"></script>
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-    <script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
-    <script src="_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
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+    <script>DOCUMENTATION_OPTIONS.pagename = 'chapter1';</script>
     <link rel="index" title="Index" href="genindex.html" />
     <link rel="search" title="Search" href="search.html" />
     <link rel="next" title="4. Ridge and Lasso Regression" href="chapter2.html" />
     <link rel="prev" title="2. Linear Algebra, Handling of Arrays and more Python Features" href="linalg.html" />
-    <meta name="viewport" content="width=device-width, initial-scale=1" />
-    <meta name="docsearch:language" content="None">
-    
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-    <!-- Google Analytics -->
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+  <meta name="viewport" content="width=device-width, initial-scale=1"/>
+  <meta name="docsearch:language" content="en"/>
   </head>
-  <body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
-    
-    <div class="container-fluid" id="banner"></div>
+  
+  
+  <body data-bs-spy="scroll" data-bs-target=".bd-toc-nav" data-offset="180" data-bs-root-margin="0px 0px -60%" data-default-mode="">
 
-    
+  
+  
+  <a class="skip-link" href="#main-content">Skip to main content</a>
+  
+  <div id="pst-scroll-pixel-helper"></div>
 
-    <div class="container-xl">
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-          
-<div class="col-12 col-md-3 bd-sidebar site-navigation show" id="site-navigation">
-    
-        <div class="navbar-brand-box">
-    <a class="navbar-brand text-wrap" href="index.html">
+  
+  <button type="button" class="btn rounded-pill" id="pst-back-to-top">
+    <i class="fa-solid fa-arrow-up"></i>
+    Back to top
+  </button>
+
+  
+  <input type="checkbox"
+          class="sidebar-toggle"
+          name="__primary"
+          id="__primary"/>
+  <label class="overlay overlay-primary" for="__primary"></label>
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+          name="__secondary"
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+  <label class="overlay overlay-secondary" for="__secondary"></label>
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+  <div class="search-button__wrapper">
+    <div class="search-button__overlay"></div>
+    <div class="search-button__search-container">
+<form class="bd-search d-flex align-items-center"
+      action="search.html"
+      method="get">
+  <i class="fa-solid fa-magnifying-glass"></i>
+  <input type="search"
+         class="form-control"
+         name="q"
+         id="search-input"
+         placeholder="Search this book..."
+         aria-label="Search this book..."
+         autocomplete="off"
+         autocorrect="off"
+         autocapitalize="off"
+         spellcheck="false"/>
+  <span class="search-button__kbd-shortcut"><kbd class="kbd-shortcut__modifier">Ctrl</kbd>+<kbd>K</kbd></span>
+</form></div>
+  </div>
+  
+    <nav class="bd-header navbar navbar-expand-lg bd-navbar">
+    </nav>
+  
+  <div class="bd-container">
+    <div class="bd-container__inner bd-page-width">
       
-        <!-- `logo` is deprecated in Sphinx 4.0, so remove this when we stop supporting 3 -->
+      <div class="bd-sidebar-primary bd-sidebar">
         
+
+  
+  <div class="sidebar-header-items sidebar-primary__section">
+    
+    
+    
+    
+  </div>
+  
+    <div class="sidebar-primary-items__start sidebar-primary__section">
+        <div class="sidebar-primary-item">
+  
+
+<a class="navbar-brand logo" href="intro.html">
+  
+  
+  
+  
+    
+    
       
-      
-      <img src="_static/logo.png" class="logo" alt="logo">
-      
-      
-      <h1 class="site-logo" id="site-title">Applied Data Analysis and Machine Learning</h1>
-      
-    </a>
-</div><form class="bd-search d-flex align-items-center" action="search.html" method="get">
-  <i class="icon fas fa-search"></i>
-  <input type="search" class="form-control" name="q" id="search-input" placeholder="Search this book..." aria-label="Search this book..." autocomplete="off" >
-</form><nav class="bd-links" id="bd-docs-nav" aria-label="Main">
-    <div class="bd-toc-item active">
-        <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="intro.html">
-   Applied Data Analysis and Machine Learning
-  </a>
- </li>
-</ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  About the course
- </span>
-</p>
+    
+    
+    <img src="_static/logo.png" class="logo__image only-light" alt="Logo image"/>
+    <script>document.write(`<img src="_static/logo.png" class="logo__image only-dark" alt="Logo image"/>`);</script>
+  
+  
+</a></div>
+        <div class="sidebar-primary-item"><nav class="bd-links" id="bd-docs-nav" aria-label="Main">
+    <div class="bd-toc-item navbar-nav active">
+        
+        <ul class="nav bd-sidenav bd-sidenav__home-link">
+            <li class="toctree-l1">
+                <a class="reference internal" href="intro.html">
+                    Applied Data Analysis and Machine Learning
+                </a>
+            </li>
+        </ul>
+        <p aria-level="2" class="caption" role="heading"><span class="caption-text">About the course</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="schedule.html">
-   Teaching schedule with links to material
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="teachers.html">
-   Teachers and Grading
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="textbooks.html">
-   Textbooks
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="schedule.html">Teaching schedule with links to material</a></li>
+<li class="toctree-l1"><a class="reference internal" href="teachers.html">Teachers and Grading</a></li>
+<li class="toctree-l1"><a class="reference internal" href="textbooks.html">Textbooks</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="statistics.html">
-   1. Elements of Probability Theory and Statistical Data Analysis
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="linalg.html">
-   2. Linear Algebra, Handling of Arrays and more Python Features
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
 <ul class="current nav bd-sidenav">
- <li class="toctree-l1 current active">
-  <a class="current reference internal" href="#">
-   3. Linear Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter2.html">
-   4. Ridge and Lasso Regression
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter3.html">
-   5. Resampling Methods
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter4.html">
-   6. Logistic Regression
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapteroptimization.html">
-   7. Optimization, the central part of any Machine Learning algortithm
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
-  </a>
- </li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter6.html">
-   9. Decision trees, overarching aims
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek34.html">
-   Exercises week 34
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week34.html">
-   Week 34: Introduction to the course, Logistics and Practicalities
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek35.html">
-   Exercises week 35
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week35.html">
-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek36.html">
-   Exercises week 36
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week36.html">
-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek37.html">
-   Exercises week 37
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+    <h1>Linear Regression</h1>
+    <!-- Table of contents -->
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-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction">
-   3.1. Introduction
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-machine-learning">
-   3.2. What is Machine Learning?
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">
-     3.2.1. A Frequentist approach to data analysis
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#what-is-a-good-model">
-     3.2.2. What is a good model?
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">
-   3.3. Simple linear regression model using
-   <strong>
-    scikit-learn
-   </strong>
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#organizing-our-data">
-     3.3.1. Organizing our data
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-basic-elements">
-   3.4. Linear Regression, basic elements
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-chi-2-function">
-     3.4.1. The
-     <span class="math notranslate nohighlight">
-      \(\chi^2\)
-     </span>
-     function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">
-     3.4.2. Fitting an Equation of State for Dense Nuclear Matter
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   3.5. Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-boston-housing-data-example">
-   3.6. The Boston housing data example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#housing-data-the-code">
-   3.7. Housing data, the code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">
-   3.8. Reducing the number of degrees of freedom, overarching view
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">
-   3.9. Testing the Means Squared Error as function of Complexity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercises">
-   3.10. Exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">
-   3.11. Exercise 1: Setting up various Python environments
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">
-   3.12. Exercise 2: making your own data and exploring scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-3-normalizing-our-data">
-   3.13. Exercise 3: Normalizing our data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-4-adding-ridge-regression">
-   3.14. Exercise 4: Adding Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-5-analytical-exercises">
-   3.15. Exercise 5: Analytical exercises
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">3.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-machine-learning">3.2. What is Machine Learning?</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">3.2.1. A Frequentist approach to data analysis</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model">3.2.2. What is a good model?</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">3.3. Simple linear regression model using <strong>scikit-learn</strong></a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#organizing-our-data">3.3.1. Organizing our data</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-basic-elements">3.4. Linear Regression, basic elements</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-chi-2-function">3.4.1. The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">3.4.2. Fitting an Equation of State for Dense Nuclear Matter</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">3.5. Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-boston-housing-data-example">3.6. The Boston housing data example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#housing-data-the-code">3.7. Housing data, the code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">3.8. Reducing the number of degrees of freedom, overarching view</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">3.9. Testing the Means Squared Error as function of Complexity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">3.10. Exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">3.11. Exercise 1: Setting up various Python environments</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">3.12. Exercise 2: making your own data and exploring scikit-learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-normalizing-our-data">3.13. Exercise 3: Normalizing our data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-4-adding-ridge-regression">3.14. Exercise 4: Adding Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-5-analytical-exercises">3.15. Exercise 5: Analytical exercises</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Linear Regression</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction">
-   3.1. Introduction
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-machine-learning">
-   3.2. What is Machine Learning?
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">
-     3.2.1. A Frequentist approach to data analysis
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#what-is-a-good-model">
-     3.2.2. What is a good model?
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">
-   3.3. Simple linear regression model using
-   <strong>
-    scikit-learn
-   </strong>
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#organizing-our-data">
-     3.3.1. Organizing our data
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-basic-elements">
-   3.4. Linear Regression, basic elements
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-chi-2-function">
-     3.4.1. The
-     <span class="math notranslate nohighlight">
-      \(\chi^2\)
-     </span>
-     function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">
-     3.4.2. Fitting an Equation of State for Dense Nuclear Matter
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   3.5. Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-boston-housing-data-example">
-   3.6. The Boston housing data example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#housing-data-the-code">
-   3.7. Housing data, the code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">
-   3.8. Reducing the number of degrees of freedom, overarching view
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">
-   3.9. Testing the Means Squared Error as function of Complexity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercises">
-   3.10. Exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">
-   3.11. Exercise 1: Setting up various Python environments
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">
-   3.12. Exercise 2: making your own data and exploring scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-3-normalizing-our-data">
-   3.13. Exercise 3: Normalizing our data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-4-adding-ridge-regression">
-   3.14. Exercise 4: Adding Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-5-analytical-exercises">
-   3.15. Exercise 5: Analytical exercises
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter1.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="linear-regression">
-<h1><span class="section-number">3. </span>Linear Regression<a class="headerlink" href="#linear-regression" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="introduction">
-<h2><span class="section-number">3.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+doconce format html chapter1.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="linear-regression">
+<h1><span class="section-number">3. </span>Linear Regression<a class="headerlink" href="#linear-regression" title="Permalink to this heading">#</a></h1>
+<section id="introduction">
+<h2><span class="section-number">3.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
 <p>Our emphasis throughout this series of lectures is on understanding
 the mathematical aspects of different algorithms used in the fields of
 data analysis and machine learning.</p>
@@ -659,9 +471,9 @@ Learning, Scikit-Learn and Tensorflow (see below for links etc).
 Moreover, the examples we introduce will serve as inputs to many of
 our discussions later, as well as allowing you to set up models and
 produce your own data and get started with programming.</p>
-</div>
-<div class="section" id="what-is-machine-learning">
-<h2><span class="section-number">3.2. </span>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-is-machine-learning">
+<h2><span class="section-number">3.2. </span>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this heading">#</a></h2>
 <p>Statistics, data science and machine learning form important fields of
 research in modern science.  They describe how to learn and make
 predictions from data, as well as allowing us to extract important
@@ -744,8 +556,8 @@ whether we deal with supervised or unsupervised learning.</p>
 <li><p>The last ingredient is a so-called <strong>cost/loss</strong> function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.</p></li>
 </ul>
 <p>At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called <strong>gradient methods</strong>.</p>
-<div class="section" id="a-frequentist-approach-to-data-analysis">
-<h3><span class="section-number">3.2.1. </span>A Frequentist approach to data analysis<a class="headerlink" href="#a-frequentist-approach-to-data-analysis" title="Permalink to this headline">¶</a></h3>
+<section id="a-frequentist-approach-to-data-analysis">
+<h3><span class="section-number">3.2.1. </span>A Frequentist approach to data analysis<a class="headerlink" href="#a-frequentist-approach-to-data-analysis" title="Permalink to this heading">#</a></h3>
 <p>When you hear phrases like <strong>predictions and estimations</strong> and
 <strong>correlations and causations</strong>, what do you think of?  May be you think
 of the difference between classifying new data points and generating
@@ -768,9 +580,9 @@ where the aim is to make predictions and find correlations. We focus
 less on for example extracting a probability distribution function (PDF). The PDF can be
 used in turn to make estimations and find causations such as given <span class="math notranslate nohighlight">\(A\)</span>
 what is the likelihood of finding <span class="math notranslate nohighlight">\(B\)</span>.</p>
-</div>
-<div class="section" id="what-is-a-good-model">
-<h3><span class="section-number">3.2.2. </span>What is a good model?<a class="headerlink" href="#what-is-a-good-model" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="what-is-a-good-model">
+<h3><span class="section-number">3.2.2. </span>What is a good model?<a class="headerlink" href="#what-is-a-good-model" title="Permalink to this heading">#</a></h3>
 <p>In science and engineering we often end up in situations where we want to infer (or learn) a
 quantitative model <span class="math notranslate nohighlight">\(M\)</span> for a given set of sample points <span class="math notranslate nohighlight">\(\boldsymbol{X} \in [x_1, x_2,\dots x_N]\)</span>.</p>
 <p>As we will see repeatedly in these lectures, we could try to fit these data points to a model given by a
@@ -804,10 +616,10 @@ simplest class of models and increase the complexity of the models only when the
 simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
 may first try the simplest class of models, namely linear models, followed obviously by more complex models.</p>
 <p>How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.</p>
-</div>
-</div>
-<div class="section" id="simple-linear-regression-model-using-scikit-learn">
-<h2><span class="section-number">3.3. </span>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="simple-linear-regression-model-using-scikit-learn">
+<h2><span class="section-number">3.3. </span>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>We start with perhaps our simplest possible example, using
 <strong>Scikit-Learn</strong> to perform linear regression analysis on a data set
 produced by us.</p>
@@ -884,7 +696,55 @@ Thereafter we wish to apply it to data which were not included in the training.
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/chapter1_9_0.png" src="_images/chapter1_9_0.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Importing various packages</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
+</div>
 </div>
 </div>
 <p>This example serves several aims. It allows us to demonstrate several
@@ -968,9 +828,6 @@ to be dominated by outliers.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter1_17_0.png" src="_images/chapter1_17_0.png" />
-</div>
 </div>
 <p>Depending on the parameter in front of the normal distribution, we may
 have a small or larger relative error. Try to play around with
@@ -1014,19 +871,6 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha: 
- [1.89563529]
-Coefficient beta : 
- [[5.26512016]]
-Mean squared error: 0.27
-Variance score: 0.87
-Mean squared log error: 0.01
-Mean absolute error: 0.41
-</pre></div>
-</div>
-<img alt="_images/chapter1_19_1.png" src="_images/chapter1_19_1.png" />
-</div>
 </div>
 <p>The function <strong>coef</strong> gives us the parameter <span class="math notranslate nohighlight">\(\beta\)</span> of our fit while <strong>intercept</strong> yields
 <span class="math notranslate nohighlight">\(\alpha\)</span>. Depending on the constant in front of the normal distribution, we get values near or far from <span class="math notranslate nohighlight">\(alpha =2\)</span> and <span class="math notranslate nohighlight">\(\beta =5\)</span>. Try to play around with different parameters in front of the normal distribution. The function <strong>meansquarederror</strong> gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as</p>
@@ -1120,12 +964,6 @@ a linear <span class="math notranslate nohighlight">\(x\)</span>-dependence we s
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter1_33_0.png" src="_images/chapter1_33_0.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0049999999999999845
-</pre></div>
-</div>
-</div>
 </div>
 <p>Let us now dive into  nuclear physics and remind ourselves briefly about some basic features about binding
 energies.  A basic quantity which can be measured for the ground
@@ -1187,8 +1025,8 @@ to the experimental data.</p>
 <p>We could also add a so-called pairing term, which is a correction term that
 arises from the tendency of proton pairs and neutron pairs to
 occur. An even number of particles is more stable than an odd number.</p>
-<div class="section" id="organizing-our-data">
-<h3><span class="section-number">3.3.1. </span>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this headline">¶</a></h3>
+<section id="organizing-our-data">
+<h3><span class="section-number">3.3.1. </span>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this heading">#</a></h3>
 <p>Let us start with reading and organizing our data.
 We start with the compilation of masses and binding energies from 2016.
 After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data.</p>
@@ -1271,11 +1109,6 @@ data) to actually open the file and simply take a look at it!</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;                                                                                                                         \nThis is taken from the data file of the mass 2016 evaluation.                                                               \nAll files are 3436 lines long with 124 character per line.                                                                  \n       Headers are 39 lines long.                                                                                           \n   col 1     :  Fortran character control: 1 = page feed  0 = line feed                                                     \n   format    :  a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5                     \n   These formats are reflected in the pandas widths variable below, see the statement                                       \n   widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),                                                            \n   Pandas has also a variable header, with length 39 in this case.                                                          \n&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>The data we are interested in are in columns 2, 3, 4 and 11, giving us
 the number of neutrons, protons, mass numbers and binding energies,
@@ -1304,40 +1137,6 @@ covert them into the <strong>pandas</strong> DataFrame structure.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">ValueError</span><span class="g g-Whitespace">                                </span>Traceback (most recent call last)
-<span class="nn">Input In [8],</span> in <span class="ni">&lt;cell line: 2&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Read the experimental data with Pandas</span>
-<span class="ne">----&gt; </span><span class="mi">2</span> <span class="n">Masses</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_fwf</span><span class="p">(</span><span class="n">infile</span><span class="p">,</span> <span class="n">usecols</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">11</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span>               <span class="n">names</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;N&#39;</span><span class="p">,</span> <span class="s1">&#39;Z&#39;</span><span class="p">,</span> <span class="s1">&#39;A&#39;</span><span class="p">,</span> <span class="s1">&#39;Element&#39;</span><span class="p">,</span> <span class="s1">&#39;Ebinding&#39;</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span>               <span class="n">widths</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">13</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">12</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">1</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span>               <span class="n">header</span><span class="o">=</span><span class="mi">39</span><span class="p">,</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span>               <span class="n">index_col</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="c1"># Extrapolated values are indicated by &#39;#&#39; in place of the decimal place, so</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="c1"># the Ebinding column won&#39;t be numeric. Coerce to float and drop these entries.</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="n">Masses</span><span class="p">[</span><span class="s1">&#39;Ebinding&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">to_numeric</span><span class="p">(</span><span class="n">Masses</span><span class="p">[</span><span class="s1">&#39;Ebinding&#39;</span><span class="p">],</span> <span class="n">errors</span><span class="o">=</span><span class="s1">&#39;coerce&#39;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/util/_decorators.py:311,</span> in <span class="ni">deprecate_nonkeyword_arguments.&lt;locals&gt;.decorate.&lt;locals&gt;.wrapper</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">    </span><span class="mi">305</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">num_allow_args</span><span class="p">:</span>
-<span class="g g-Whitespace">    </span><span class="mi">306</span>     <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">307</span>         <span class="n">msg</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">arguments</span><span class="o">=</span><span class="n">arguments</span><span class="p">),</span>
-<span class="g g-Whitespace">    </span><span class="mi">308</span>         <span class="ne">FutureWarning</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">309</span>         <span class="n">stacklevel</span><span class="o">=</span><span class="n">stacklevel</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">310</span>     <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">311</span> <span class="k">return</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/io/parsers/readers.py:871,</span> in <span class="ni">read_fwf</span><span class="nt">(filepath_or_buffer, colspecs, widths, infer_nrows, **kwds)</span>
-<span class="g g-Whitespace">    </span><span class="mi">869</span>                     <span class="n">len_index</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">index_col</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">870</span>         <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">names</span><span class="p">)</span> <span class="o">+</span> <span class="n">len_index</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">colspecs</span><span class="p">):</span>
-<span class="ne">--&gt; </span><span class="mi">871</span>             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Length of colspecs must match length of names&quot;</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">873</span> <span class="n">kwds</span><span class="p">[</span><span class="s2">&quot;colspecs&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">colspecs</span>
-<span class="g g-Whitespace">    </span><span class="mi">874</span> <span class="n">kwds</span><span class="p">[</span><span class="s2">&quot;infer_nrows&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">infer_nrows</span>
-
-<span class="ne">ValueError</span>: Length of colspecs must match length of names
-</pre></div>
-</div>
-</div>
 </div>
 <p>We have now read in the data, grouped them according to the variables we are interested in.
 We see how easy it is to reorganize the data using <strong>pandas</strong>. If we
@@ -1497,10 +1296,10 @@ functionality.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="linear-regression-basic-elements">
-<h2><span class="section-number">3.4. </span>Linear Regression, basic elements<a class="headerlink" href="#linear-regression-basic-elements" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="linear-regression-basic-elements">
+<h2><span class="section-number">3.4. </span>Linear Regression, basic elements<a class="headerlink" href="#linear-regression-basic-elements" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/LectureAug27.mp4?vrtx=view-as-webpage">Video of Lecture</a>.</p>
 <p>Fitting a continuous function with linear parameterization in terms of the parameters  <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.</p>
 <ul class="simple">
@@ -1959,8 +1758,8 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 </div>
-<div class="section" id="the-chi-2-function">
-<h3><span class="section-number">3.4.1. </span>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#the-chi-2-function" title="Permalink to this headline">¶</a></h3>
+<section id="the-chi-2-function">
+<h3><span class="section-number">3.4.1. </span>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#the-chi-2-function" title="Permalink to this heading">#</a></h3>
 <p>Normally, the response (dependent or outcome) variable <span class="math notranslate nohighlight">\(y_i\)</span> is the
 outcome of a numerical experiment or another type of experiment and is
 thus only an approximation to the true value. It is then always
@@ -2078,9 +1877,9 @@ often from both being underdetermined and overdetermined in the
 unknown coefficients <span class="math notranslate nohighlight">\(\beta_i\)</span>.  A better approach is to use the
 Singular Value Decomposition (SVD) method discussed below. Or using
 Lasso and Ridge regression. See below.</p>
-</div>
-<div class="section" id="fitting-an-equation-of-state-for-dense-nuclear-matter">
-<h3><span class="section-number">3.4.2. </span>Fitting an Equation of State for Dense Nuclear Matter<a class="headerlink" href="#fitting-an-equation-of-state-for-dense-nuclear-matter" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="fitting-an-equation-of-state-for-dense-nuclear-matter">
+<h3><span class="section-number">3.4.2. </span>Fitting an Equation of State for Dense Nuclear Matter<a class="headerlink" href="#fitting-an-equation-of-state-for-dense-nuclear-matter" title="Permalink to this heading">#</a></h3>
 <p>Before we continue, let us introduce yet another example. We are going to fit the
 nuclear equation of state using results from many-body calculations.
 The equation of state we have made available here, as function of
@@ -2172,10 +1971,10 @@ instead of our own matrix inversion implementation.</p>
 </div>
 <p>The above simple polynomial in density <span class="math notranslate nohighlight">\(\rho\)</span> gives an excellent fit
 to the data.</p>
-</div>
-</div>
-<div class="section" id="splitting-our-data-in-training-and-test-data">
-<h2><span class="section-number">3.5. </span>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="splitting-our-data-in-training-and-test-data">
+<h2><span class="section-number">3.5. </span>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this heading">#</a></h2>
 <p>It is normal in essentially all Machine Learning studies to split the
 data in a training set and a test set (sometimes also an additional
 validation set).  <strong>Scikit-Learn</strong> has an own function for this. There
@@ -2332,9 +2131,9 @@ but now splitting the data into a training set and a test set.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="the-boston-housing-data-example">
-<h2><span class="section-number">3.6. </span>The Boston housing data example<a class="headerlink" href="#the-boston-housing-data-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-boston-housing-data-example">
+<h2><span class="section-number">3.6. </span>The Boston housing data example<a class="headerlink" href="#the-boston-housing-data-example" title="Permalink to this heading">#</a></h2>
 <p>The Boston housing<br />
 data set was originally a part of UCI Machine Learning Repository
 and has been removed now. The data set is now included in <strong>Scikit-Learn</strong>’s
@@ -2342,7 +2141,7 @@ library.  There are 506 samples and 13 feature (predictor) variables
 in this data set. The objective is to predict the value of prices of
 the house using the features (predictors) listed here.</p>
 <p>The features/predictors are</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>CRIM: Per capita crime rate by town</p></li>
 <li><p>ZN: Proportion of residential land zoned for lots over 25000 square feet</p></li>
 <li><p>INDUS: Proportion of non-retail business acres per town</p></li>
@@ -2357,9 +2156,9 @@ the house using the features (predictors) listed here.</p>
 <li><p>LSTAT: Percentage of lower status of the population</p></li>
 <li><p>MEDV: Median value of owner-occupied homes in USD 1000s</p></li>
 </ol>
-</div>
-<div class="section" id="housing-data-the-code">
-<h2><span class="section-number">3.7. </span>Housing data, the code<a class="headerlink" href="#housing-data-the-code" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="housing-data-the-code">
+<h2><span class="section-number">3.7. </span>Housing data, the code<a class="headerlink" href="#housing-data-the-code" title="Permalink to this heading">#</a></h2>
 <p>We start by importing the libraries</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2523,9 +2322,9 @@ the house using the features (predictors) listed here.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="reducing-the-number-of-degrees-of-freedom-overarching-view">
-<h2><span class="section-number">3.8. </span>Reducing the number of degrees of freedom, overarching view<a class="headerlink" href="#reducing-the-number-of-degrees-of-freedom-overarching-view" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reducing-the-number-of-degrees-of-freedom-overarching-view">
+<h2><span class="section-number">3.8. </span>Reducing the number of degrees of freedom, overarching view<a class="headerlink" href="#reducing-the-number-of-degrees-of-freedom-overarching-view" title="Permalink to this heading">#</a></h2>
 <p>Many Machine Learning problems involve thousands or even millions of
 features for each training instance. Not only does this make training
 extremely slow, it can also make it much harder to find a good
@@ -2636,9 +2435,9 @@ transformation</p>
 x_j^{(i)} \rightarrow (b-a)\frac{x_j^{(i)} - \min(x_j)}{\max(x_j) - \min(x_j)} - a
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\min(x_j)\)</span> and <span class="math notranslate nohighlight">\(\max(x_j)\)</span> return the minimum and maximum value of <span class="math notranslate nohighlight">\(x_j\)</span> over the data set, respectively.</p>
-</div>
-<div class="section" id="testing-the-means-squared-error-as-function-of-complexity">
-<h2><span class="section-number">3.9. </span>Testing the Means Squared Error as function of Complexity<a class="headerlink" href="#testing-the-means-squared-error-as-function-of-complexity" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="testing-the-means-squared-error-as-function-of-complexity">
+<h2><span class="section-number">3.9. </span>Testing the Means Squared Error as function of Complexity<a class="headerlink" href="#testing-the-means-squared-error-as-function-of-complexity" title="Permalink to this heading">#</a></h2>
 <p>Before we proceed with a more detailed analysis of the so-called
 Bias-Variance tradeoff, we present here an example of the relation
 between model complexity and the mean squared error for the triaining
@@ -2687,12 +2486,12 @@ ourmodel (here in terms of the polynomial degree of the model).</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="exercises">
-<h2><span class="section-number">3.10. </span>Exercises<a class="headerlink" href="#exercises" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="exercise-1-setting-up-various-python-environments">
-<h2><span class="section-number">3.11. </span>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercises">
+<h2><span class="section-number">3.10. </span>Exercises<a class="headerlink" href="#exercises" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="exercise-1-setting-up-various-python-environments">
+<h2><span class="section-number">3.11. </span>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this heading">#</a></h2>
 <p>The first exercise here is of a mere technical art. We want you to have</p>
 <ul class="simple">
 <li><p>git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo <a class="reference external" href="https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html">GitHub facilities</a>.</p></li>
@@ -2708,7 +2507,7 @@ on Python.</p>
 <p>If you have Python installed (we recommend Python3) and you feel
 pretty familiar with installing different packages, we recommend that
 you install the following Python packages via <strong>pip</strong> as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>pip install numpy scipy matplotlib ipython scikit-learn sympy pandas pillow</p></li>
 </ol>
 <p>For <strong>Tensorflow</strong>, we recommend following the instructions in the text of
@@ -2718,12 +2517,12 @@ you install the following Python packages via <strong>pip</strong> as</p>
 <p>For OSX users we recommend, after having installed Xcode, to
 install <strong>brew</strong>. Brew allows for a seamless installation of additional
 software via for example</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>brew install python3</p></li>
 </ol>
 <p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
 you can use <strong>pip</strong> as well and simply install Python as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>sudo apt-get install python3  (or python for Python2.7)</p></li>
 </ol>
 <p>If you don’t want to perform these operations separately and venture
@@ -2746,9 +2545,9 @@ distribution for scientific and analytic computing distribution and
 analysis environment, available for free and under a commercial
 license.</p>
 <p>We recommend using <strong>Anaconda</strong> if you are not too familiar with setting paths in a terminal environment.</p>
-</div>
-<div class="section" id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
-<h2><span class="section-number">3.12. </span>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
+<h2><span class="section-number">3.12. </span>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>We will generate our own dataset for a function <span class="math notranslate nohighlight">\(y(x)\)</span> where <span class="math notranslate nohighlight">\(x \in [0,1]\)</span> and defined by random numbers computed with the uniform distribution. The function <span class="math notranslate nohighlight">\(y\)</span> is a quadratic polynomial in <span class="math notranslate nohighlight">\(x\)</span> with added stochastic noise according to the normal distribution <span class="math notranslate nohighlight">\(\cal {N}(0,1)\)</span>.
 The following simple Python instructions define our <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> values (with 100 data points).</p>
 <div class="cell docutils container">
@@ -2759,7 +2558,7 @@ The following simple Python instructions define our <span class="math notranslat
 </div>
 </div>
 </div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Write your own code (following the examples under the <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter1.html">regression notes</a>) for computing the parametrization of the data set fitting a second-order polynomial.</p></li>
 <li><p>Use thereafter <strong>scikit-learn</strong> (see again the examples in the regression slides) and compare with your own code.   When compairing with <em>scikit_learn</em>, make sure you set the option for the intercept to <strong>FALSE</strong>, see <a class="reference external" href="https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html">https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html</a>. This feature will be explained in more detail during the lectures of week 35 and week 36. You can find more in <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#more-on-rescaling-data">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#more-on-rescaling-data</a>.</p></li>
 <li><p>Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</p></li>
@@ -2831,9 +2630,9 @@ The code here is an example of where we define our own design matrix and fit par
 </div>
 </div>
 </div>
-<!-- --- end solution of exercise --- --></div>
-<div class="section" id="exercise-3-normalizing-our-data">
-<h2><span class="section-number">3.13. </span>Exercise 3: Normalizing our data<a class="headerlink" href="#exercise-3-normalizing-our-data" title="Permalink to this headline">¶</a></h2>
+<!-- --- end solution of exercise --- --></section>
+<section id="exercise-3-normalizing-our-data">
+<h2><span class="section-number">3.13. </span>Exercise 3: Normalizing our data<a class="headerlink" href="#exercise-3-normalizing-our-data" title="Permalink to this heading">#</a></h2>
 <p>A much used approach before starting to train the data is  to preprocess our
 data. Normally the data may need a rescaling and/or may be sensitive
 to extreme values. Scaling the data renders our inputs much more
@@ -2951,9 +2750,9 @@ Write a first code which sets up a design matrix <span class="math notranslate n
 Perform an ordinary least squares and compute the means squared error and the <span class="math notranslate nohighlight">\(R2\)</span> factor for the training data and the test data, with and without scaling.</p>
 <p><strong>c)</strong>
 Add now a model which allows you to make polynomials up to degree <span class="math notranslate nohighlight">\(15\)</span>.  Perform a standard OLS fitting of the training data and compute the MSE and <span class="math notranslate nohighlight">\(R2\)</span> for the training and test data and plot both test and training data MSE and <span class="math notranslate nohighlight">\(R2\)</span> as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?</p>
-</div>
-<div class="section" id="exercise-4-adding-ridge-regression">
-<h2><span class="section-number">3.14. </span>Exercise 4: Adding Ridge Regression<a class="headerlink" href="#exercise-4-adding-ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-4-adding-ridge-regression">
+<h2><span class="section-number">3.14. </span>Exercise 4: Adding Ridge Regression<a class="headerlink" href="#exercise-4-adding-ridge-regression" title="Permalink to this heading">#</a></h2>
 <p>This exercise is a continuation of exercise 2. We will use the same function to
 generate our data set, still staying with a simple function <span class="math notranslate nohighlight">\(y(x)\)</span>
 which we want to fit using linear regression, but now extending the
@@ -3086,9 +2885,9 @@ parameter <span class="math notranslate nohighlight">\(\lambda\)</span>. This pr
 </div>
 </div>
 </div>
-<!-- --- end solution of exercise --- --></div>
-<div class="section" id="exercise-5-analytical-exercises">
-<h2><span class="section-number">3.15. </span>Exercise 5: Analytical exercises<a class="headerlink" href="#exercise-5-analytical-exercises" title="Permalink to this headline">¶</a></h2>
+<!-- --- end solution of exercise --- --></section>
+<section id="exercise-5-analytical-exercises">
+<h2><span class="section-number">3.15. </span>Exercise 5: Analytical exercises<a class="headerlink" href="#exercise-5-analytical-exercises" title="Permalink to this heading">#</a></h2>
 <p>In this exercise we derive the expressions for various derivatives of
 products of vectors and matrices. Such derivatives are central to the
 optimization of various cost functions. Although we will often use
@@ -3168,8 +2967,8 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
 \frac{\partial (\boldsymbol{a}^T\boldsymbol{f})}{\partial \boldsymbol{a}}=\boldsymbol{a}^T\boldsymbol{A}+\boldsymbol{f}^T=\boldsymbol{a}^T\left(\boldsymbol{A}+\boldsymbol{A}^T\right),
 \]</div>
 <p>since <span class="math notranslate nohighlight">\(f\)</span> depends on <span class="math notranslate nohighlight">\(a\)</span> and we have used the chain rule for derivatives on the derivative of <span class="math notranslate nohighlight">\(f\)</span> with respect to <span class="math notranslate nohighlight">\(a\)</span>.</p>
-<!-- --- end solution of exercise --- --></div>
-</div>
+<!-- --- end solution of exercise --- --></section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -3183,7 +2982,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -3191,44 +2990,126 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">3.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-machine-learning">3.2. What is Machine Learning?</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">3.2.1. A Frequentist approach to data analysis</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model">3.2.2. What is a good model?</a></li>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">3.3. Simple linear regression model using <strong>scikit-learn</strong></a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#organizing-our-data">3.3.1. Organizing our data</a></li>
+</ul>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-basic-elements">3.4. Linear Regression, basic elements</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-chi-2-function">3.4.1. The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">3.4.2. Fitting an Equation of State for Dense Nuclear Matter</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">3.5. Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-boston-housing-data-example">3.6. The Boston housing data example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#housing-data-the-code">3.7. Housing data, the code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">3.8. Reducing the number of degrees of freedom, overarching view</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">3.9. Testing the Means Squared Error as function of Complexity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">3.10. Exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">3.11. Exercise 1: Setting up various Python environments</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">3.12. Exercise 2: making your own data and exploring scikit-learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-normalizing-our-data">3.13. Exercise 3: Normalizing our data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-4-adding-ridge-regression">3.14. Exercise 4: Adding Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-5-analytical-exercises">3.15. Exercise 5: Analytical exercises</a></li>
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-<p aria-level="2" class="caption" role="heading">
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-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
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-   1. Elements of Probability Theory and Statistical Data Analysis
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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-   7. Optimization, the central part of any Machine Learning algortithm
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-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
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+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   13. Neural networks
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-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
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-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">14. Building a Feed Forward Neural Network</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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-            <div class="tocsection onthispage pt-5 pb-3">
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                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#defining-the-cost-function">
-   14.1. Defining the cost function
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#example-binary-classification-problem">
-     14.1.1. Example: binary classification problem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-softmax-function">
-     14.1.2. The Softmax function
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#developing-a-code-for-doing-neural-networks-with-back-propagation">
-   14.2. Developing a code for doing neural networks with back propagation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#collect-and-pre-process-data">
-     14.2.1. Collect and pre-process data
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#train-and-test-datasets">
-     14.2.2. Train and test datasets
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#define-model-and-architecture">
-     14.2.3. Define model and architecture
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#layers">
-     14.2.4. Layers
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#feed-forward-pass">
-     14.2.5. Feed-forward pass
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#choose-cost-function-and-optimizer">
-     14.2.6. Choose cost function and optimizer
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#optimizing-the-cost-function">
-     14.2.7. Optimizing the cost function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#regularization">
-     14.2.8. Regularization
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#matrix-multiplication">
-     14.2.9. Matrix  multiplication
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#improving-performance">
-   14.3. Improving performance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#evaluate-model-performance-on-test-data">
-   14.4. Evaluate model performance on test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adjust-hyperparameters">
-   14.5. Adjust hyperparameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#visualization">
-   14.6. Visualization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#scikit-learn-implementation">
-   14.7. scikit-learn implementation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   14.8. Visualization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#building-neural-networks-in-tensorflow-and-keras">
-   14.9. Building neural networks in Tensorflow and Keras
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-breast-cancer-data-now-with-keras">
-   14.10. The Breast Cancer Data, now with Keras
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fine-tuning-neural-network-hyperparameters">
-   14.11. Fine-tuning neural network hyperparameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#which-activation-function-should-i-use">
-   14.12. Which activation function should I use?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-relu-function-family">
-   14.13. The RELU function family
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#batch-normalization">
-   14.14. Batch Normalization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#dropout">
-   14.15. Dropout
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-clipping">
-   14.16. Gradient Clipping
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-top-down-perspective-on-neural-networks">
-   14.17. A top-down perspective on Neural networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#limitations-of-supervised-learning-with-deep-networks">
-   14.18. Limitations of supervised learning with deep networks
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#defining-the-cost-function">14.1. Defining the cost function</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#example-binary-classification-problem">14.1.1. Example: binary classification problem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-softmax-function">14.1.2. The Softmax function</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#developing-a-code-for-doing-neural-networks-with-back-propagation">14.2. Developing a code for doing neural networks with back propagation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#collect-and-pre-process-data">14.2.1. Collect and pre-process data</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#train-and-test-datasets">14.2.2. Train and test datasets</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#define-model-and-architecture">14.2.3. Define model and architecture</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#layers">14.2.4. Layers</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#feed-forward-pass">14.2.5. Feed-forward pass</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#choose-cost-function-and-optimizer">14.2.6. Choose cost function and optimizer</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-the-cost-function">14.2.7. Optimizing the cost function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#regularization">14.2.8. Regularization</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#matrix-multiplication">14.2.9. Matrix  multiplication</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#improving-performance">14.3. Improving performance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#evaluate-model-performance-on-test-data">14.4. Evaluate model performance on test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adjust-hyperparameters">14.5. Adjust hyperparameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#visualization">14.6. Visualization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#scikit-learn-implementation">14.7. scikit-learn implementation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">14.8. Visualization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#building-neural-networks-in-tensorflow-and-keras">14.9. Building neural networks in Tensorflow and Keras</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-breast-cancer-data-now-with-keras">14.10. The Breast Cancer Data, now with Keras</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fine-tuning-neural-network-hyperparameters">14.11. Fine-tuning neural network hyperparameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#which-activation-function-should-i-use">14.12. Which activation function should I use?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-relu-function-family">14.13. The RELU function family</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#batch-normalization">14.14. Batch Normalization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#dropout">14.15. Dropout</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-clipping">14.16. Gradient Clipping</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-top-down-perspective-on-neural-networks">14.17. A top-down perspective on Neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#limitations-of-supervised-learning-with-deep-networks">14.18. Limitations of supervised learning with deep networks</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Building a Feed Forward Neural Network</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#defining-the-cost-function">
-   14.1. Defining the cost function
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#example-binary-classification-problem">
-     14.1.1. Example: binary classification problem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-softmax-function">
-     14.1.2. The Softmax function
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#developing-a-code-for-doing-neural-networks-with-back-propagation">
-   14.2. Developing a code for doing neural networks with back propagation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#collect-and-pre-process-data">
-     14.2.1. Collect and pre-process data
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#train-and-test-datasets">
-     14.2.2. Train and test datasets
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#define-model-and-architecture">
-     14.2.3. Define model and architecture
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#layers">
-     14.2.4. Layers
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#feed-forward-pass">
-     14.2.5. Feed-forward pass
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#choose-cost-function-and-optimizer">
-     14.2.6. Choose cost function and optimizer
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#optimizing-the-cost-function">
-     14.2.7. Optimizing the cost function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#regularization">
-     14.2.8. Regularization
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#matrix-multiplication">
-     14.2.9. Matrix  multiplication
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#improving-performance">
-   14.3. Improving performance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#evaluate-model-performance-on-test-data">
-   14.4. Evaluate model performance on test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adjust-hyperparameters">
-   14.5. Adjust hyperparameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#visualization">
-   14.6. Visualization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#scikit-learn-implementation">
-   14.7. scikit-learn implementation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   14.8. Visualization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#building-neural-networks-in-tensorflow-and-keras">
-   14.9. Building neural networks in Tensorflow and Keras
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-breast-cancer-data-now-with-keras">
-   14.10. The Breast Cancer Data, now with Keras
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fine-tuning-neural-network-hyperparameters">
-   14.11. Fine-tuning neural network hyperparameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#which-activation-function-should-i-use">
-   14.12. Which activation function should I use?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-relu-function-family">
-   14.13. The RELU function family
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#batch-normalization">
-   14.14. Batch Normalization
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#dropout">
-   14.15. Dropout
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-clipping">
-   14.16. Gradient Clipping
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-top-down-perspective-on-neural-networks">
-   14.17. A top-down perspective on Neural networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#limitations-of-supervised-learning-with-deep-networks">
-   14.18. Limitations of supervised learning with deep networks
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter10.do.txt --no_mako --><div class="tex2jax_ignore mathjax_ignore section" id="building-a-feed-forward-neural-network">
-<h1><span class="section-number">14. </span>Building a Feed Forward Neural Network<a class="headerlink" href="#building-a-feed-forward-neural-network" title="Permalink to this headline">¶</a></h1>
+doconce format html chapter10.do.txt --no_mako --><section class="tex2jax_ignore mathjax_ignore" id="building-a-feed-forward-neural-network">
+<h1><span class="section-number">14. </span>Building a Feed Forward Neural Network<a class="headerlink" href="#building-a-feed-forward-neural-network" title="Permalink to this heading">#</a></h1>
 <p>We are now gong to develop an example based on the MNIST data
 base. This is a classification problem and we need to use our
 cross-entropy function we discussed in connection with logistic
@@ -727,8 +474,8 @@ P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(y \in \{0, 1\}\)</span>  and <span class="math notranslate nohighlight">\(\hat{\theta}\)</span> represents the weights and biases
 of our network.</p>
-<div class="section" id="defining-the-cost-function">
-<h2><span class="section-number">14.1. </span>Defining the cost function<a class="headerlink" href="#defining-the-cost-function" title="Permalink to this headline">¶</a></h2>
+<section id="defining-the-cost-function">
+<h2><span class="section-number">14.1. </span>Defining the cost function<a class="headerlink" href="#defining-the-cost-function" title="Permalink to this heading">#</a></h2>
 <p>Our cost function is given as (see the Logistic regression lectures)</p>
 <div class="math notranslate nohighlight">
 \[
@@ -765,8 +512,8 @@ P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1
 \]</div>
 <p>See the logistic regression lectures for a full definition of the cost function.</p>
 <p>The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!</p>
-<div class="section" id="example-binary-classification-problem">
-<h3><span class="section-number">14.1.1. </span>Example: binary classification problem<a class="headerlink" href="#example-binary-classification-problem" title="Permalink to this headline">¶</a></h3>
+<section id="example-binary-classification-problem">
+<h3><span class="section-number">14.1.1. </span>Example: binary classification problem<a class="headerlink" href="#example-binary-classification-problem" title="Permalink to this heading">#</a></h3>
 <p>As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters <span class="math notranslate nohighlight">\(\beta\)</span> as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -806,9 +553,9 @@ Our cost function at the final layer <span class="math notranslate nohighlight">
 \frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.
 \]</div>
 <p>In case we use another activation function than the logistic one, we need to evaluate other derivatives.</p>
-</div>
-<div class="section" id="the-softmax-function">
-<h3><span class="section-number">14.1.2. </span>The Softmax function<a class="headerlink" href="#the-softmax-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="the-softmax-function">
+<h3><span class="section-number">14.1.2. </span>The Softmax function<a class="headerlink" href="#the-softmax-function" title="Permalink to this heading">#</a></h3>
 <p>In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation <span class="math notranslate nohighlight">\(z_i^l\)</span>, that is we need</p>
 <div class="math notranslate nohighlight">
 \[
@@ -826,12 +573,12 @@ f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.
 \frac{\partial f(z_i^l)}{\partial z_j^l}= f(z_i^l)\left(\delta_{ij}-f(z_j^l)\right),
 \]</div>
 <p>which in case of the simply binary model reduces to  having <span class="math notranslate nohighlight">\(i=j\)</span>.</p>
-</div>
-</div>
-<div class="section" id="developing-a-code-for-doing-neural-networks-with-back-propagation">
-<h2><span class="section-number">14.2. </span>Developing a code for doing neural networks with back propagation<a class="headerlink" href="#developing-a-code-for-doing-neural-networks-with-back-propagation" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="developing-a-code-for-doing-neural-networks-with-back-propagation">
+<h2><span class="section-number">14.2. </span>Developing a code for doing neural networks with back propagation<a class="headerlink" href="#developing-a-code-for-doing-neural-networks-with-back-propagation" title="Permalink to this heading">#</a></h2>
 <p>One can identify a set of key steps when using neural networks to solve supervised learning problems:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Collect and pre-process data</p></li>
 <li><p>Define model and architecture</p></li>
 <li><p>Choose cost function and optimizer</p></li>
@@ -839,8 +586,8 @@ f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.
 <li><p>Evaluate model performance on test data</p></li>
 <li><p>Adjust hyperparameters (if necessary, network architecture)</p></li>
 </ol>
-<div class="section" id="collect-and-pre-process-data">
-<h3><span class="section-number">14.2.1. </span>Collect and pre-process data<a class="headerlink" href="#collect-and-pre-process-data" title="Permalink to this headline">¶</a></h3>
+<section id="collect-and-pre-process-data">
+<h3><span class="section-number">14.2.1. </span>Collect and pre-process data<a class="headerlink" href="#collect-and-pre-process-data" title="Permalink to this heading">#</a></h3>
 <p>Here we will be using the MNIST dataset, which is readily available through the <strong>scikit-learn</strong>
 package. You may also find it for example <a class="reference external" href="http://yann.lecun.com/exdb/mnist/">here</a>.<br />
 The <em>MNIST</em> (Modified National Institute of Standards and Technology) database is a large database
@@ -925,17 +672,60 @@ images.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)
-labels = (n_inputs) = (1797,)
-X = (n_inputs, n_features) = (1797, 64)
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># import necessary packages</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/chapter10_39_1.png" src="_images/chapter10_39_1.png" />
 </div>
 </div>
-</div>
-<div class="section" id="train-and-test-datasets">
-<h3><span class="section-number">14.2.2. </span>Train and test datasets<a class="headerlink" href="#train-and-test-datasets" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="train-and-test-datasets">
+<h3><span class="section-number">14.2.2. </span>Train and test datasets<a class="headerlink" href="#train-and-test-datasets" title="Permalink to this heading">#</a></h3>
 <p>Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.</p>
 <p>We will reserve <span class="math notranslate nohighlight">\(80 \%\)</span> of our dataset for training and <span class="math notranslate nohighlight">\(20 \%\)</span> for testing.</p>
 <p>It is important that the train and test datasets are drawn randomly from our dataset, to ensure
@@ -975,16 +765,10 @@ collected from 12.00 to 24.00.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Number of training images: 1437
-Number of test images: 360
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="define-model-and-architecture">
-<h3><span class="section-number">14.2.3. </span>Define model and architecture<a class="headerlink" href="#define-model-and-architecture" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="define-model-and-architecture">
+<h3><span class="section-number">14.2.3. </span>Define model and architecture<a class="headerlink" href="#define-model-and-architecture" title="Permalink to this heading">#</a></h3>
 <p>Our simple feed-forward neural network will consist of an <em>input</em> layer, a single <em>hidden</em> layer and an <em>output</em> layer. The activation <span class="math notranslate nohighlight">\(y\)</span> of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have</p>
 <div class="math notranslate nohighlight">
 \[ z = \sum_{i=1}^n w_i a_i ,\]</div>
@@ -1012,9 +796,9 @@ We will be using the sigmoid function <span class="math notranslate nohighlight"
 <div class="math notranslate nohighlight">
 \[ f(x) = \sigma(x) = \frac{1}{1 + e^{-x}} ,\]</div>
 <p>which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.</p>
-</div>
-<div class="section" id="layers">
-<h3><span class="section-number">14.2.4. </span>Layers<a class="headerlink" href="#layers" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="layers">
+<h3><span class="section-number">14.2.4. </span>Layers<a class="headerlink" href="#layers" title="Permalink to this heading">#</a></h3>
 <ul class="simple">
 <li><p>Input</p></li>
 </ul>
@@ -1069,9 +853,9 @@ of values. Without it, any input with the value 0 will be mapped to zero (before
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="feed-forward-pass">
-<h3><span class="section-number">14.2.5. </span>Feed-forward pass<a class="headerlink" href="#feed-forward-pass" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="feed-forward-pass">
+<h3><span class="section-number">14.2.5. </span>Feed-forward pass<a class="headerlink" href="#feed-forward-pass" title="Permalink to this heading">#</a></h3>
 <p>Denote <span class="math notranslate nohighlight">\(F\)</span> the number of features, <span class="math notranslate nohighlight">\(H\)</span> the number of hidden neurons and <span class="math notranslate nohighlight">\(C\)</span> the number of categories.<br />
 For each input image we calculate a weighted sum of input features (pixel values) to each neuron <span class="math notranslate nohighlight">\(j\)</span> in the hidden layer <span class="math notranslate nohighlight">\(l\)</span>:</p>
 <div class="math notranslate nohighlight">
@@ -1147,24 +931,10 @@ This is then passed through the activation:</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>probabilities = (n_inputs, n_categories) = (1437, 10)
-probability that image 0 is in category 0,1,2,...,9 = 
-[5.41511965e-04 2.17174962e-03 8.84355903e-03 1.44970586e-03
- 1.10378326e-04 5.08318298e-09 2.03256632e-04 1.92507116e-03
- 9.84443254e-01 3.11507992e-04]
-probabilities sum up to: 1.0
-
-predictions = (n_inputs) = (1437,)
-prediction for image 0: 8
-correct label for image 0: 6
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="choose-cost-function-and-optimizer">
-<h3><span class="section-number">14.2.6. </span>Choose cost function and optimizer<a class="headerlink" href="#choose-cost-function-and-optimizer" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="choose-cost-function-and-optimizer">
+<h3><span class="section-number">14.2.6. </span>Choose cost function and optimizer<a class="headerlink" href="#choose-cost-function-and-optimizer" title="Permalink to this heading">#</a></h3>
 <p>To measure how well our neural network is doing we need to introduce a cost function.<br />
 We will call the function that gives the error of a single sample output the <em>loss</em> function, and the function
 that gives the total error of our network across all samples the <em>cost</em> function.
@@ -1181,9 +951,9 @@ We define the cost function <span class="math notranslate nohighlight">\(\mathca
 probability of the correct category <span class="math notranslate nohighlight">\(c'\)</span><br />
 (i.e. the category <span class="math notranslate nohighlight">\(c'\)</span> such that <span class="math notranslate nohighlight">\(y_{ic'} = 1\)</span>). This means that the cross entropy loss only punishes you for how wrong
 you got the correct label. The probability of category <span class="math notranslate nohighlight">\(c\)</span> is given by the softmax function. The vector <span class="math notranslate nohighlight">\(\hat{\theta}\)</span> represents the parameters of our network, i.e. all the weights and biases.</p>
-</div>
-<div class="section" id="optimizing-the-cost-function">
-<h3><span class="section-number">14.2.7. </span>Optimizing the cost function<a class="headerlink" href="#optimizing-the-cost-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="optimizing-the-cost-function">
+<h3><span class="section-number">14.2.7. </span>Optimizing the cost function<a class="headerlink" href="#optimizing-the-cost-function" title="Permalink to this heading">#</a></h3>
 <p>The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is <em>gradient descent</em> and its generalizations. The idea behind gradient descent
 is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a <em>local</em> minimum of the cost function.<br />
 Each parameter <span class="math notranslate nohighlight">\(\theta\)</span> is iteratively adjusted according to the rule</p>
@@ -1202,14 +972,14 @@ We denote each minibatch <span class="math notranslate nohighlight">\(B_k\)</spa
 \frac{1}{M} \sum_{i \in B_k} \nabla \mathcal{L}_i(\theta) ,\]</div>
 <p>i.e. instead of averaging the loss over the entire dataset, we average over a minibatch.</p>
 <p>This has two important benefits:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Introducing stochasticity decreases the chance that the algorithm becomes stuck in a local minima.</p></li>
 <li><p>It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient.</p></li>
 </ol>
 <p>The various optmization  methods, with codes and algorithms,  are discussed in our lectures on <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html">Gradient descent approaches</a>.</p>
-</div>
-<div class="section" id="regularization">
-<h3><span class="section-number">14.2.8. </span>Regularization<a class="headerlink" href="#regularization" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="regularization">
+<h3><span class="section-number">14.2.8. </span>Regularization<a class="headerlink" href="#regularization" title="Permalink to this heading">#</a></h3>
 <p>It is common to add an extra term to the cost function, proportional
 to the size of the weights.  This is equivalent to constraining the
 size of the weights, so that they do not grow out of control.
@@ -1230,9 +1000,9 @@ layer (<span class="math notranslate nohighlight">\(+1\)</span> for the bias), a
 every parameter.  We use the <em>backpropagation</em> algorithm discussed
 above. This is a clever use of the chain rule that allows us to
 calculate the gradient efficently.</p>
-</div>
-<div class="section" id="matrix-multiplication">
-<h3><span class="section-number">14.2.9. </span>Matrix  multiplication<a class="headerlink" href="#matrix-multiplication" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="matrix-multiplication">
+<h3><span class="section-number">14.2.9. </span>Matrix  multiplication<a class="headerlink" href="#matrix-multiplication" title="Permalink to this heading">#</a></h3>
 <p>To more efficently train our network these equations are implemented using matrix operations.<br />
 The error in the output layer is calculated simply as, with <span class="math notranslate nohighlight">\(\hat{t}\)</span> being our targets,</p>
 <div class="math notranslate nohighlight">
@@ -1329,23 +1099,11 @@ the <em>Hadamard product</em>, meaning element-wise multiplication.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Old accuracy on training data: 0.1440501043841336
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>New accuracy on training data: 0.09951287404314545
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="improving-performance">
-<h2><span class="section-number">14.3. </span>Improving performance<a class="headerlink" href="#improving-performance" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="improving-performance">
+<h2><span class="section-number">14.3. </span>Improving performance<a class="headerlink" href="#improving-performance" title="Permalink to this heading">#</a></h2>
 <p>As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.<br />
 In order to obtain a network that does something useful, we will have to do a bit more work.</p>
 <p>The choice of <em>hyperparameters</em> such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a <em>grid-search</em> is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates <span class="math notranslate nohighlight">\(\eta = 10^{-6}, 10^{-5},...,10^{-1}\)</span> with different regularization parameters <span class="math notranslate nohighlight">\(\lambda = 10^{-6},...,10^{-0}\)</span>.</p>
@@ -1460,9 +1218,9 @@ being realizations of this object with different hyperparameters. An implementat
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="evaluate-model-performance-on-test-data">
-<h2><span class="section-number">14.4. </span>Evaluate model performance on test data<a class="headerlink" href="#evaluate-model-performance-on-test-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="evaluate-model-performance-on-test-data">
+<h2><span class="section-number">14.4. </span>Evaluate model performance on test data<a class="headerlink" href="#evaluate-model-performance-on-test-data" title="Permalink to this heading">#</a></h2>
 <p>To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.<br />
 We measure the performance of the network using the <em>accuracy</em> score.<br />
 The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of <span class="math notranslate nohighlight">\(1\)</span>.</p>
@@ -1490,15 +1248,10 @@ The accuracy is as you would expect just the number of images correctly labeled
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Accuracy score on test set:  0.9444444444444444
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="adjust-hyperparameters">
-<h2><span class="section-number">14.5. </span>Adjust hyperparameters<a class="headerlink" href="#adjust-hyperparameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="adjust-hyperparameters">
+<h2><span class="section-number">14.5. </span>Adjust hyperparameters<a class="headerlink" href="#adjust-hyperparameters" title="Permalink to this heading">#</a></h2>
 <p>We now perform a grid search to find the optimal hyperparameters for the network.<br />
 Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around <span class="math notranslate nohighlight">\(98\%\)</span> (<span class="math notranslate nohighlight">\(2\%\)</span> error rate).</p>
 <div class="cell docutils container">
@@ -1526,393 +1279,10 @@ Note that we are only using 1 layer with 50 neurons, and human performance is es
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1e-05
-Accuracy score on test set:  0.11666666666666667
-</pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.0001
-Accuracy score on test set:  0.20833333333333334
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.001
-Accuracy score on test set:  0.12222222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.01
-Accuracy score on test set:  0.14722222222222223
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.1
-Accuracy score on test set:  0.17777777777777778
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1.0
-Accuracy score on test set:  0.16111111111111112
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  10.0
-Accuracy score on test set:  0.20277777777777778
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1e-05
-Accuracy score on test set:  0.5305555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.0001
-Accuracy score on test set:  0.5944444444444444
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.001
-Accuracy score on test set:  0.5888888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.01
-Accuracy score on test set:  0.6111111111111112
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.1
-Accuracy score on test set:  0.5222222222222223
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1.0
-Accuracy score on test set:  0.5555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  10.0
-Accuracy score on test set:  0.8055555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  1e-05
-Accuracy score on test set:  0.85
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.0001
-Accuracy score on test set:  0.85
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.001
-Accuracy score on test set:  0.875
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.01
-Accuracy score on test set:  0.8666666666666667
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.1
-Accuracy score on test set:  0.8638888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  1.0
-Accuracy score on test set:  0.9555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  10.0
-Accuracy score on test set:  0.925
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  1e-05
-Accuracy score on test set:  0.9472222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.0001
-Accuracy score on test set:  0.9277777777777778
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.001
-Accuracy score on test set:  0.9472222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.01
-Accuracy score on test set:  0.9305555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.1
-Accuracy score on test set:  0.9555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  1.0
-Accuracy score on test set:  0.7694444444444445
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  10.0
-Accuracy score on test set:  0.19166666666666668
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  1e-05
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.0001
-Accuracy score on test set:  0.08611111111111111
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.001
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.01
-Accuracy score on test set:  0.08888888888888889
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.1
-Accuracy score on test set:  0.08611111111111111
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  1.0
-Accuracy score on test set:  0.08888888888888889
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  10.0
-Accuracy score on test set:  0.09166666666666666
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  1e-05
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.0001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.01
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.1
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  1.0
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  10.0
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1e-05
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.0001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.001
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.01
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.1
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1.0
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp
-  exp_term = np.exp(self.z_o)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
-  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  10.0
-Accuracy score on test set:  0.07777777777777778
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="visualization">
-<h2><span class="section-number">14.6. </span>Visualization<a class="headerlink" href="#visualization" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="visualization">
+<h2><span class="section-number">14.6. </span>Visualization<a class="headerlink" href="#visualization" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># visual representation of grid search</span>
@@ -1951,26 +1321,10 @@ Accuracy score on test set:  0.07777777777777778
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp
-  return 1/(1 + np.exp(-x))
-</pre></div>
 </div>
-<img alt="_images/chapter10_59_1.png" src="_images/chapter10_59_1.png" />
-<img alt="_images/chapter10_59_2.png" src="_images/chapter10_59_2.png" />
-</div>
-</div>
-</div>
-<div class="section" id="scikit-learn-implementation">
-<h2><span class="section-number">14.7. </span>scikit-learn implementation<a class="headerlink" href="#scikit-learn-implementation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="scikit-learn-implementation">
+<h2><span class="section-number">14.7. </span>scikit-learn implementation<a class="headerlink" href="#scikit-learn-implementation" title="Permalink to this heading">#</a></h2>
 <p><strong>scikit-learn</strong> focuses more
 on traditional machine learning methods, such as regression,
 clustering, decision trees, etc. As such, it has only two types of
@@ -2002,330 +1356,10 @@ performance overall.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1e-05
-Accuracy score on test set:  0.18333333333333332
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.0001
-Accuracy score on test set:  0.18611111111111112
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.001
-Accuracy score on test set:  0.13055555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.01
-Accuracy score on test set:  0.24444444444444444
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  0.1
-Accuracy score on test set:  0.23333333333333334
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  1.0
-Accuracy score on test set:  0.12777777777777777
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1e-05
-Lambda =  10.0
-Accuracy score on test set:  0.1527777777777778
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1e-05
-Accuracy score on test set:  0.9111111111111111
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.0001
-Accuracy score on test set:  0.8888888888888888
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.001
-Accuracy score on test set:  0.8722222222222222
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.01
-Accuracy score on test set:  0.8305555555555556
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  0.1
-Accuracy score on test set:  0.8888888888888888
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  1.0
-Accuracy score on test set:  0.8805555555555555
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.0001
-Lambda =  10.0
-Accuracy score on test set:  0.8944444444444445
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  1e-05
-Accuracy score on test set:  0.975
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.0001
-Accuracy score on test set:  0.9777777777777777
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.001
-Accuracy score on test set:  0.9805555555555555
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.01
-Accuracy score on test set:  0.9861111111111112
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  0.1
-Accuracy score on test set:  0.9805555555555555
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  1.0
-Accuracy score on test set:  0.9777777777777777
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.001
-Lambda =  10.0
-Accuracy score on test set:  0.9444444444444444
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn&#39;t converged yet.
-  warnings.warn(
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  1e-05
-Accuracy score on test set:  0.9861111111111112
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.0001
-Accuracy score on test set:  0.9888888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.001
-Accuracy score on test set:  0.9888888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.01
-Accuracy score on test set:  0.9861111111111112
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  0.1
-Accuracy score on test set:  0.9888888888888889
-
-Learning rate  =  0.01
-Lambda =  1.0
-Accuracy score on test set:  0.9722222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.01
-Lambda =  10.0
-Accuracy score on test set:  0.9527777777777777
-
-Learning rate  =  0.1
-Lambda =  1e-05
-Accuracy score on test set:  0.9027777777777778
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.0001
-Accuracy score on test set:  0.8583333333333333
-
-Learning rate  =  0.1
-Lambda =  0.001
-Accuracy score on test set:  0.8722222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  0.01
-Accuracy score on test set:  0.9055555555555556
-
-Learning rate  =  0.1
-Lambda =  0.1
-Accuracy score on test set:  0.8805555555555555
-
-Learning rate  =  0.1
-Lambda =  1.0
-Accuracy score on test set:  0.8722222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  0.1
-Lambda =  10.0
-Accuracy score on test set:  0.8666666666666667
-
-Learning rate  =  1.0
-Lambda =  1e-05
-Accuracy score on test set:  0.08611111111111111
-
-Learning rate  =  1.0
-Lambda =  0.0001
-Accuracy score on test set:  0.10555555555555556
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  0.001
-Accuracy score on test set:  0.10555555555555556
-
-Learning rate  =  1.0
-Lambda =  0.01
-Accuracy score on test set:  0.17777777777777778
-
-Learning rate  =  1.0
-Lambda =  0.1
-Accuracy score on test set:  0.08333333333333333
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  1.0
-Lambda =  1.0
-Accuracy score on test set:  0.08888888888888889
-
-Learning rate  =  1.0
-Lambda =  10.0
-Accuracy score on test set:  0.09444444444444444
-
-Learning rate  =  10.0
-Lambda =  1e-05
-Accuracy score on test set:  0.17222222222222222
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  0.0001
-Accuracy score on test set:  0.11666666666666667
-
-Learning rate  =  10.0
-Lambda =  0.001
-Accuracy score on test set:  0.10555555555555556
-
-Learning rate  =  10.0
-Lambda =  0.01
-Accuracy score on test set:  0.1388888888888889
-
-Learning rate  =  10.0
-Lambda =  0.1
-Accuracy score on test set:  0.11388888888888889
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Learning rate  =  10.0
-Lambda =  1.0
-Accuracy score on test set:  0.10555555555555556
-
-Learning rate  =  10.0
-Lambda =  10.0
-Accuracy score on test set:  0.09444444444444444
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="id1">
-<h2><span class="section-number">14.8. </span>Visualization<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2><span class="section-number">14.8. </span>Visualization<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># optional</span>
@@ -2365,14 +1399,10 @@ Accuracy score on test set:  0.09444444444444444
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter10_63_0.png" src="_images/chapter10_63_0.png" />
-<img alt="_images/chapter10_63_1.png" src="_images/chapter10_63_1.png" />
 </div>
-</div>
-</div>
-<div class="section" id="building-neural-networks-in-tensorflow-and-keras">
-<h2><span class="section-number">14.9. </span>Building neural networks in Tensorflow and Keras<a class="headerlink" href="#building-neural-networks-in-tensorflow-and-keras" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="building-neural-networks-in-tensorflow-and-keras">
+<h2><span class="section-number">14.9. </span>Building neural networks in Tensorflow and Keras<a class="headerlink" href="#building-neural-networks-in-tensorflow-and-keras" title="Permalink to this heading">#</a></h2>
 <p>Now we want  to build on the experience gained from our neural network implementation in NumPy and scikit-learn
 and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy
 and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.</p>
@@ -2407,14 +1437,6 @@ and/or if you use <strong>anaconda</strong>, just write (or install from the gra
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span>  <span class="n">Input</span> <span class="n">In</span> <span class="p">[</span><span class="mi">12</span><span class="p">]</span>
-    <span class="n">conda</span> <span class="n">create</span> <span class="o">-</span><span class="n">n</span> <span class="n">tf</span> <span class="n">tensorflow</span>
-          <span class="o">^</span>
-<span class="ne">SyntaxError</span>: invalid syntax
-</pre></div>
-</div>
-</div>
 </div>
 <p>To install the current release of GPU TensorFlow</p>
 <div class="cell docutils container">
@@ -2591,9 +1613,9 @@ If you have Anaconda installed you may run the following command</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="the-breast-cancer-data-now-with-keras">
-<h2><span class="section-number">14.10. </span>The Breast Cancer Data, now with Keras<a class="headerlink" href="#the-breast-cancer-data-now-with-keras" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-breast-cancer-data-now-with-keras">
+<h2><span class="section-number">14.10. </span>The Breast Cancer Data, now with Keras<a class="headerlink" href="#the-breast-cancer-data-now-with-keras" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span>
@@ -2765,9 +1787,9 @@ If you have Anaconda installed you may run the following command</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="fine-tuning-neural-network-hyperparameters">
-<h2><span class="section-number">14.11. </span>Fine-tuning neural network hyperparameters<a class="headerlink" href="#fine-tuning-neural-network-hyperparameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="fine-tuning-neural-network-hyperparameters">
+<h2><span class="section-number">14.11. </span>Fine-tuning neural network hyperparameters<a class="headerlink" href="#fine-tuning-neural-network-hyperparameters" title="Permalink to this heading">#</a></h2>
 <p>The flexibility of neural networks is also one of their main
 drawbacks: there are many hyperparameters to tweak. Not only can you
 use any imaginable network topology (how neurons/nodes are interconnected),
@@ -2796,9 +1818,9 @@ as large image classification or speech recognition, typically require networks
 and they need a huge amount
 of training data. However, you will rarely have to train such networks from scratch: it is much more
 common to reuse parts of a pretrained state-of-the-art network that performs a similar task.</p>
-</div>
-<div class="section" id="which-activation-function-should-i-use">
-<h2><span class="section-number">14.12. </span>Which activation function should I use?<a class="headerlink" href="#which-activation-function-should-i-use" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="which-activation-function-should-i-use">
+<h2><span class="section-number">14.12. </span>Which activation function should I use?<a class="headerlink" href="#which-activation-function-should-i-use" title="Permalink to this heading">#</a></h2>
 <p>The Back propagation algorithm we derived above works by going from
 the output layer to the input layer, propagating the error gradient on
 the way. Once the algorithm has computed the gradient of the cost
@@ -2861,9 +1883,9 @@ that other activation functions behave much better in deep neural
 networks, in particular the ReLU activation function, mostly because
 it does not saturate for positive values (and also because it is quite
 fast to compute).</p>
-</div>
-<div class="section" id="the-relu-function-family">
-<h2><span class="section-number">14.13. </span>The RELU function family<a class="headerlink" href="#the-relu-function-family" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-relu-function-family">
+<h2><span class="section-number">14.13. </span>The RELU function family<a class="headerlink" href="#the-relu-function-family" title="Permalink to this heading">#</a></h2>
 <p>The ReLU activation function suffers from a problem known as the dying
 ReLUs: during training, some neurons effectively die, meaning they
 stop outputting anything other than 0.</p>
@@ -2898,9 +1920,9 @@ bootstrap to evaluate other activation functions.</p>
 <li><p>For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).</p></li>
 <li><p>For regression tasks, you can simply use no activation function at all.</p></li>
 </ul>
-</div>
-<div class="section" id="batch-normalization">
-<h2><span class="section-number">14.14. </span>Batch Normalization<a class="headerlink" href="#batch-normalization" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="batch-normalization">
+<h2><span class="section-number">14.14. </span>Batch Normalization<a class="headerlink" href="#batch-normalization" title="Permalink to this heading">#</a></h2>
 <p>Batch Normalization
 aims to address the vanishing/exploding gradients problems, and more generally the problem that the
 distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.</p>
@@ -2911,27 +1933,27 @@ learn the optimal scale and mean of the inputs for each layer.
 In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and
 standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current
 mini-batch, from this the name batch normalization.</p>
-</div>
-<div class="section" id="dropout">
-<h2><span class="section-number">14.15. </span>Dropout<a class="headerlink" href="#dropout" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="dropout">
+<h2><span class="section-number">14.15. </span>Dropout<a class="headerlink" href="#dropout" title="Permalink to this heading">#</a></h2>
 <p>It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but
 excluding the output neurons) has a probability <span class="math notranslate nohighlight">\(p\)</span> of being temporarily dropped out, meaning it will be
 entirely ignored during this training step, but it may be active during the next step.</p>
 <p>The
 hyperparameter <span class="math notranslate nohighlight">\(p\)</span> is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.
 It is viewed as one of the most popular regularization techniques.</p>
-</div>
-<div class="section" id="gradient-clipping">
-<h2><span class="section-number">14.16. </span>Gradient Clipping<a class="headerlink" href="#gradient-clipping" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-clipping">
+<h2><span class="section-number">14.16. </span>Gradient Clipping<a class="headerlink" href="#gradient-clipping" title="Permalink to this heading">#</a></h2>
 <p>A popular technique to lessen the exploding gradients problem is to simply clip the gradients during
 backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural
 networks).</p>
 <p>This technique is called Gradient Clipping.</p>
 <p>In general however, Batch
 Normalization is preferred.</p>
-</div>
-<div class="section" id="a-top-down-perspective-on-neural-networks">
-<h2><span class="section-number">14.17. </span>A top-down perspective on Neural networks<a class="headerlink" href="#a-top-down-perspective-on-neural-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-top-down-perspective-on-neural-networks">
+<h2><span class="section-number">14.17. </span>A top-down perspective on Neural networks<a class="headerlink" href="#a-top-down-perspective-on-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>The first thing we would like to do is divide the data into two or three
 parts. A training set, a validation or dev (development) set, and a
 test set. The test set is the data on which we want to make
@@ -2963,9 +1985,9 @@ the test data. The difference between the performance of the algorithm
 on these two validation sets quantifies the train-test mismatch. This
 can serve as another important diagnostic when using DNNs for
 supervised learning.</p>
-</div>
-<div class="section" id="limitations-of-supervised-learning-with-deep-networks">
-<h2><span class="section-number">14.18. </span>Limitations of supervised learning with deep networks<a class="headerlink" href="#limitations-of-supervised-learning-with-deep-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="limitations-of-supervised-learning-with-deep-networks">
+<h2><span class="section-number">14.18. </span>Limitations of supervised learning with deep networks<a class="headerlink" href="#limitations-of-supervised-learning-with-deep-networks" title="Permalink to this heading">#</a></h2>
 <p>Like all statistical methods, supervised learning using neural
 networks has important limitations. This is especially important when
 one seeks to apply these methods, especially to physics problems. Like
@@ -2981,8 +2003,8 @@ features).</p>
 <li><p><strong>Many problems are not about prediction.</strong> In natural science we are often interested in learning something about the underlying distribution that generates the data. In this case, it is often difficult to cast these ideas in a supervised learning setting. While the problems are related, it is possible to make good predictions with a <em>wrong</em> model. The model might or might not be useful for understanding the underlying science.</p></li>
 </ul>
 <p>Some of these remarks are particular to DNNs, others are shared by all supervised learning methods. This motivates the use of unsupervised methods which in part circumvent these problems.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2996,7 +2018,7 @@ features).</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -3004,44 +2026,133 @@ features).</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#defining-the-cost-function">14.1. Defining the cost function</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#example-binary-classification-problem">14.1.1. Example: binary classification problem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-softmax-function">14.1.2. The Softmax function</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#developing-a-code-for-doing-neural-networks-with-back-propagation">14.2. Developing a code for doing neural networks with back propagation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#collect-and-pre-process-data">14.2.1. Collect and pre-process data</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#train-and-test-datasets">14.2.2. Train and test datasets</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#define-model-and-architecture">14.2.3. Define model and architecture</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#layers">14.2.4. Layers</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#feed-forward-pass">14.2.5. Feed-forward pass</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#choose-cost-function-and-optimizer">14.2.6. Choose cost function and optimizer</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-the-cost-function">14.2.7. Optimizing the cost function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#regularization">14.2.8. Regularization</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#matrix-multiplication">14.2.9. Matrix  multiplication</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#improving-performance">14.3. Improving performance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#evaluate-model-performance-on-test-data">14.4. Evaluate model performance on test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adjust-hyperparameters">14.5. Adjust hyperparameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#visualization">14.6. Visualization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#scikit-learn-implementation">14.7. scikit-learn implementation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">14.8. Visualization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#building-neural-networks-in-tensorflow-and-keras">14.9. Building neural networks in Tensorflow and Keras</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-breast-cancer-data-now-with-keras">14.10. The Breast Cancer Data, now with Keras</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fine-tuning-neural-network-hyperparameters">14.11. Fine-tuning neural network hyperparameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#which-activation-function-should-i-use">14.12. Which activation function should I use?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-relu-function-family">14.13. The RELU function family</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#batch-normalization">14.14. Batch Normalization</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#dropout">14.15. Dropout</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-clipping">14.16. Gradient Clipping</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-top-down-perspective-on-neural-networks">14.17. A top-down perspective on Neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#limitations-of-supervised-learning-with-deep-networks">14.18. Limitations of supervised learning with deep networks</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
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                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-exponential-decay">
-   15.1. Example: Exponential decay
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reformulating-the-problem">
-   15.2. Reformulating the problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent">
-   15.3. Gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-code-for-solving-the-ode">
-   15.4. The code for solving the ODE
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">
-   15.5. The network with one input layer, specified number of hidden layers, and one output layer
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#example-population-growth">
-     15.5.1. Example: Population growth
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-forward-euler-to-solve-the-ode">
-   15.6. Using forward Euler to solve the ODE
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-the-one-dimensional-poisson-equation">
-   15.7. Solving the one dimensional Poisson equation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#comparing-with-a-numerical-scheme">
-     15.7.1. Comparing with a numerical scheme
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#partial-differential-equations">
-   15.8. Partial Differential Equations
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#type-of-problem">
-     15.8.1. Type of problem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#network-requirements">
-     15.8.2. Network requirements
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-the-diffusion-equation">
-   15.9. Example: The diffusion equation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#setting-up-the-network-using-autograd-the-full-program">
-     15.9.1. Setting up the network using Autograd; The full program
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-the-wave-equation-with-neural-networks">
-   15.10. Solving the wave equation with Neural Networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resources-on-differential-equations-and-deep-learning">
-   15.11. Resources on differential equations and deep learning
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-exponential-decay">15.1. Example: Exponential decay</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reformulating-the-problem">15.2. Reformulating the problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent">15.3. Gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-code-for-solving-the-ode">15.4. The code for solving the ODE</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">15.5. The network with one input layer, specified number of hidden layers, and one output layer</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#example-population-growth">15.5.1. Example: Population growth</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-forward-euler-to-solve-the-ode">15.6. Using forward Euler to solve the ODE</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-one-dimensional-poisson-equation">15.7. Solving the one dimensional Poisson equation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#comparing-with-a-numerical-scheme">15.7.1. Comparing with a numerical scheme</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#partial-differential-equations">15.8. Partial Differential Equations</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#type-of-problem">15.8.1. Type of problem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#network-requirements">15.8.2. Network requirements</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-the-diffusion-equation">15.9. Example: The diffusion equation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#setting-up-the-network-using-autograd-the-full-program">15.9.1. Setting up the network using Autograd; The full program</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-wave-equation-with-neural-networks">15.10. Solving the wave equation with Neural Networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resources-on-differential-equations-and-deep-learning">15.11. Resources on differential equations and deep learning</a></li>
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-                <h1>Solving Differential Equations  with Deep Learning</h1>
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-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-exponential-decay">
-   15.1. Example: Exponential decay
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reformulating-the-problem">
-   15.2. Reformulating the problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent">
-   15.3. Gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-code-for-solving-the-ode">
-   15.4. The code for solving the ODE
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">
-   15.5. The network with one input layer, specified number of hidden layers, and one output layer
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#example-population-growth">
-     15.5.1. Example: Population growth
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-forward-euler-to-solve-the-ode">
-   15.6. Using forward Euler to solve the ODE
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-the-one-dimensional-poisson-equation">
-   15.7. Solving the one dimensional Poisson equation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#comparing-with-a-numerical-scheme">
-     15.7.1. Comparing with a numerical scheme
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#partial-differential-equations">
-   15.8. Partial Differential Equations
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#type-of-problem">
-     15.8.1. Type of problem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#network-requirements">
-     15.8.2. Network requirements
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-the-diffusion-equation">
-   15.9. Example: The diffusion equation
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#setting-up-the-network-using-autograd-the-full-program">
-     15.9.1. Setting up the network using Autograd; The full program
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-the-wave-equation-with-neural-networks">
-   15.10. Solving the wave equation with Neural Networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resources-on-differential-equations-and-deep-learning">
-   15.11. Resources on differential equations and deep learning
-  </a>
- </li>
-</ul>
 
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter11.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="solving-differential-equations-with-deep-learning">
-<h1><span class="section-number">15. </span>Solving Differential Equations  with Deep Learning<a class="headerlink" href="#solving-differential-equations-with-deep-learning" title="Permalink to this headline">¶</a></h1>
+doconce format html chapter11.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="solving-differential-equations-with-deep-learning">
+<h1><span class="section-number">15. </span>Solving Differential Equations  with Deep Learning<a class="headerlink" href="#solving-differential-equations-with-deep-learning" title="Permalink to this heading">#</a></h1>
 <p>The Universal Approximation Theorem states that a neural network can
 approximate any function at a single hidden layer along with one input
 and output layer to any given precision.</p>
@@ -593,10 +453,10 @@ f\left(x, \, g(x), \, g'(x), \, g''(x), \, \dots \, , \, g^{(n)}(x)\right) = 0
 \end{equation}
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(g(x)\)</span> is the function to find, and <span class="math notranslate nohighlight">\(g^{(n)}(x)\)</span> is the <span class="math notranslate nohighlight">\(n\)</span>-th derivative of <span class="math notranslate nohighlight">\(g(x)\)</span>.</p>
-<p>The <span class="math notranslate nohighlight">\(f\left(x, g(x), g'(x), g''(x), \, \dots \, , g^{(n)}(x)\right)\)</span> is just a way to write that there is an expression involving <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(g(x), \ g'(x), \ g''(x), \, \dots \, , \text{ and } g^{(n)}(x)\)</span> on the left side of the equality sign in (<a class="reference external" href="#ode">1</a>).
+<p>The <span class="math notranslate nohighlight">\(f\left(x, g(x), g'(x), g''(x), \, \dots \, , g^{(n)}(x)\right)\)</span> is just a way to write that there is an expression involving <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(g(x), \ g'(x), \ g''(x), \, \dots \, , \text{ and } g^{(n)}(x)\)</span> on the left side of the equality sign in (<span class="xref myst">1</span>).
 The highest order of derivative, that is the value of <span class="math notranslate nohighlight">\(n\)</span>, determines to the order of the equation.
 The equation is referred to as a <span class="math notranslate nohighlight">\(n\)</span>-th order ODE.
-Along with (<a class="reference external" href="#ode">1</a>), some additional conditions of the function <span class="math notranslate nohighlight">\(g(x)\)</span> are typically given
+Along with (<span class="xref myst">1</span>), some additional conditions of the function <span class="math notranslate nohighlight">\(g(x)\)</span> are typically given
 for the solution to be unique.</p>
 <p>Let the trial solution <span class="math notranslate nohighlight">\(g_t(x)\)</span> be</p>
 <!-- Equation labels as ordinary links -->
@@ -619,7 +479,7 @@ the conditions.</p>
 <p>But what about the network <span class="math notranslate nohighlight">\(N(x,P)\)</span>?</p>
 <p>As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation.</p>
 <p>For the minimization to be defined, we need to have a cost function at hand to minimize.</p>
-<p>It is given that <span class="math notranslate nohighlight">\(f\left(x, \, g(x), \, g'(x), \, g''(x), \, \dots \, , \, g^{(n)}(x)\right)\)</span> should be equal to zero in (<a class="reference external" href="#ode">1</a>).
+<p>It is given that <span class="math notranslate nohighlight">\(f\left(x, \, g(x), \, g'(x), \, g''(x), \, \dots \, , \, g^{(n)}(x)\right)\)</span> should be equal to zero in (<span class="xref myst">1</span>).
 We can choose to consider the mean squared error as the cost function for an input <span class="math notranslate nohighlight">\(x\)</span>.
 Since we are looking at one input, the cost function is just <span class="math notranslate nohighlight">\(f\)</span> squared.
 The cost function <span class="math notranslate nohighlight">\(c\left(x, P \right)\)</span> can therefore be expressed as</p>
@@ -638,13 +498,13 @@ the cost function becomes</p>
 \end{equation}
 \]</div>
 <p>The neural net should then find the parameters <span class="math notranslate nohighlight">\(P\)</span> that minimizes the cost function in
-(<a class="reference external" href="#cost">3</a>) for a set of <span class="math notranslate nohighlight">\(N\)</span> training samples <span class="math notranslate nohighlight">\(x_i\)</span>.</p>
+(<span class="xref myst">3</span>) for a set of <span class="math notranslate nohighlight">\(N\)</span> training samples <span class="math notranslate nohighlight">\(x_i\)</span>.</p>
 <p>To perform the minimization using gradient descent, the gradient of <span class="math notranslate nohighlight">\(C\left(\boldsymbol{x}, P\right)\)</span> is needed.
-It might happen so that finding an analytical expression of the gradient of <span class="math notranslate nohighlight">\(C(\boldsymbol{x}, P)\)</span> from (<a class="reference external" href="#cost">3</a>) gets too messy, depending on which cost function one desires to use.</p>
+It might happen so that finding an analytical expression of the gradient of <span class="math notranslate nohighlight">\(C(\boldsymbol{x}, P)\)</span> from (<span class="xref myst">3</span>) gets too messy, depending on which cost function one desires to use.</p>
 <p>Luckily, there exists libraries that makes the job for us through automatic differentiation.
 Automatic differentiation is a method of finding the derivatives numerically with very high precision.</p>
-<div class="section" id="example-exponential-decay">
-<h2><span class="section-number">15.1. </span>Example: Exponential decay<a class="headerlink" href="#example-exponential-decay" title="Permalink to this headline">¶</a></h2>
+<section id="example-exponential-decay">
+<h2><span class="section-number">15.1. </span>Example: Exponential decay<a class="headerlink" href="#example-exponential-decay" title="Permalink to this heading">#</a></h2>
 <p>An exponential decay of a quantity <span class="math notranslate nohighlight">\(g(x)\)</span> is described by the equation</p>
 <!-- Equation labels as ordinary links -->
 <div id="solve_expdec"></div>
@@ -655,7 +515,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
 \end{equation}
 \]</div>
 <p>with <span class="math notranslate nohighlight">\(g(0) = g_0\)</span> for some chosen initial value <span class="math notranslate nohighlight">\(g_0\)</span>.</p>
-<p>The analytical solution of (<a class="reference external" href="#solve_expdec">4</a>) is</p>
+<p>The analytical solution of (<span class="xref myst">4</span>) is</p>
 <!-- Equation labels as ordinary links -->
 <div id="_auto2"></div>
 <div class="math notranslate nohighlight">
@@ -665,7 +525,7 @@ Automatic differentiation is a method of finding the derivatives numerically wit
 \label{_auto2} \tag{5}
 \end{equation}
 \]</div>
-<p>Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of (<a class="reference external" href="#solve_expdec">4</a>).</p>
+<p>Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of (<span class="xref myst">4</span>).</p>
 <p>The program will use a neural network to solve</p>
 <!-- Equation labels as ordinary links -->
 <div id="solveode"></div>
@@ -688,7 +548,7 @@ If there are <span class="math notranslate nohighlight">\(N_{\text{hidden} }\)</
 <p>The first column in <span class="math notranslate nohighlight">\(P_{\text{hidden} }\)</span> represents the bias for each neuron in the hidden layer and the second column represents the weights for each neuron in the hidden layer from the input layer.
 If there are <span class="math notranslate nohighlight">\(N_{\text{output} }\)</span> neurons in the output layer, then <span class="math notranslate nohighlight">\(P_{\text{output}} \)</span> is a <span class="math notranslate nohighlight">\(N_{\text{output} } \times (1 + N_{\text{hidden} })\)</span> matrix.</p>
 <p>Its first column represents the bias of each neuron and the remaining columns represents the weights to each neuron.</p>
-<p>It is given that <span class="math notranslate nohighlight">\(g(0) = g_0\)</span>. The trial solution must fulfill this condition to be a proper solution of (<a class="reference external" href="#solveode">6</a>). A possible way to ensure that <span class="math notranslate nohighlight">\(g_t(0, P) = g_0\)</span>, is to let <span class="math notranslate nohighlight">\(F(N(x,P)) = x \cdot N(x,P)\)</span> and <span class="math notranslate nohighlight">\(A(x) = g_0\)</span>. This gives the following trial solution:</p>
+<p>It is given that <span class="math notranslate nohighlight">\(g(0) = g_0\)</span>. The trial solution must fulfill this condition to be a proper solution of (<span class="xref myst">6</span>). A possible way to ensure that <span class="math notranslate nohighlight">\(g_t(0, P) = g_0\)</span>, is to let <span class="math notranslate nohighlight">\(F(N(x,P)) = x \cdot N(x,P)\)</span> and <span class="math notranslate nohighlight">\(A(x) = g_0\)</span>. This gives the following trial solution:</p>
 <!-- Equation labels as ordinary links -->
 <div id="trial"></div>
 <div class="math notranslate nohighlight">
@@ -697,13 +557,13 @@ If there are <span class="math notranslate nohighlight">\(N_{\text{output} }\)</
 g_t(x, P) = g_0 + x \cdot N(x, P)
 \end{equation}
 \]</div>
-</div>
-<div class="section" id="reformulating-the-problem">
-<h2><span class="section-number">15.2. </span>Reformulating the problem<a class="headerlink" href="#reformulating-the-problem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reformulating-the-problem">
+<h2><span class="section-number">15.2. </span>Reformulating the problem<a class="headerlink" href="#reformulating-the-problem" title="Permalink to this heading">#</a></h2>
 <p>We wish that our neural network manages to minimize a given cost function.</p>
-<p>A reformulation of out equation, (<a class="reference external" href="#solveode">6</a>), must therefore be done,
+<p>A reformulation of out equation, (<span class="xref myst">6</span>), must therefore be done,
 such that it describes the problem a neural network can solve for.</p>
-<p>The neural network must find the set of weights and biases <span class="math notranslate nohighlight">\(P\)</span> such that the trial solution in (<a class="reference external" href="#trial">7</a>) satisfies (<a class="reference external" href="#solveode">6</a>).</p>
+<p>The neural network must find the set of weights and biases <span class="math notranslate nohighlight">\(P\)</span> such that the trial solution in (<span class="xref myst">7</span>) satisfies (<span class="xref myst">6</span>).</p>
 <p>The trial solution</p>
 <div class="math notranslate nohighlight">
 \[
@@ -719,7 +579,7 @@ g_t'(x, P) = - \gamma g_t(x, P)
 \end{equation}
 \]</div>
 <p>is fulfilled as <em>best as possible</em>.</p>
-<p>The left hand side and right hand side of (<a class="reference external" href="#nnmin">8</a>) must be computed separately, and then the neural network must choose weights and biases, contained in <span class="math notranslate nohighlight">\(P\)</span>, such that the sides are equal as best as possible.
+<p>The left hand side and right hand side of (<span class="xref myst">8</span>) must be computed separately, and then the neural network must choose weights and biases, contained in <span class="math notranslate nohighlight">\(P\)</span>, such that the sides are equal as best as possible.
 This means that the absolute or squared difference between the sides must be as close to zero, ideally equal to zero.
 In this case, the difference squared shows to be an appropriate measurement of how erroneous the trial solution is with respect to <span class="math notranslate nohighlight">\(P\)</span> of the neural network.</p>
 <p>This gives the following cost function our neural network must solve for:</p>
@@ -753,7 +613,7 @@ In this case, the difference squared shows to be an appropriate measurement of h
 \[
 \min_{P_{\text{hidden} }, \ P_{\text{output} }} C(\boldsymbol{x}, \{P_{\text{hidden} }, P_{\text{output} }\})
 \]</div>
-<p>For simplicity, it is assumed that the input is an array <span class="math notranslate nohighlight">\(\boldsymbol{x} = (x_1, \dots, x_N)\)</span> with <span class="math notranslate nohighlight">\(N\)</span> elements. It is at these points the neural network should find <span class="math notranslate nohighlight">\(P\)</span> such that it fulfills (<a class="reference external" href="#min">9</a>).</p>
+<p>For simplicity, it is assumed that the input is an array <span class="math notranslate nohighlight">\(\boldsymbol{x} = (x_1, \dots, x_N)\)</span> with <span class="math notranslate nohighlight">\(N\)</span> elements. It is at these points the neural network should find <span class="math notranslate nohighlight">\(P\)</span> such that it fulfills (<span class="xref myst">9</span>).</p>
 <p>First, the neural network must feed forward the inputs.
 This means that <span class="math notranslate nohighlight">\(\boldsymbol{x}s\)</span> must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further.
 The input layer will consist of <span class="math notranslate nohighlight">\(N_{\text{input} }\)</span> neurons, passing its element to each neuron in the hidden layer.  The number of neurons in the hidden layer will be <span class="math notranslate nohighlight">\(N_{\text{hidden} }\)</span>.</p>
@@ -788,7 +648,7 @@ x_1 &amp; x_2 &amp; \dots &amp; x_N
 &amp;= \boldsymbol{p}_{i, \text{hidden}}^T X
 \end{aligned}
 \end{split}\]</div>
-<p>The vector <span class="math notranslate nohighlight">\(\boldsymbol{p}_{i, \text{hidden}}^T\)</span> constitutes each row in <span class="math notranslate nohighlight">\(P_{\text{hidden} }\)</span>, which contains the weights for the neural network to minimize according to (<a class="reference external" href="#min">9</a>).</p>
+<p>The vector <span class="math notranslate nohighlight">\(\boldsymbol{p}_{i, \text{hidden}}^T\)</span> constitutes each row in <span class="math notranslate nohighlight">\(P_{\text{hidden} }\)</span>, which contains the weights for the neural network to minimize according to (<span class="xref myst">9</span>).</p>
 <p>After having found <span class="math notranslate nohighlight">\(\boldsymbol{z}_{i}^{\text{hidden}} \)</span> for every <span class="math notranslate nohighlight">\(i\)</span>-th neuron within the hidden layer, the vector will be sent to an activation function <span class="math notranslate nohighlight">\(a_i(\boldsymbol{z})\)</span>.</p>
 <p>In this example, the sigmoid function has been chosen to be the activation function for each hidden neuron:</p>
 <div class="math notranslate nohighlight">
@@ -842,9 +702,9 @@ C(\boldsymbol{x}, P) = \frac{1}{N} \sum_i  \big(g_t'(x_i, P) - ( -\gamma g_t(x_i
 \]</div>
 <p>In order to minimize the cost function, an optimization method must be chosen.</p>
 <p>Here, gradient descent with a constant step size has been chosen.</p>
-</div>
-<div class="section" id="gradient-descent">
-<h2><span class="section-number">15.3. </span>Gradient descent<a class="headerlink" href="#gradient-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-descent">
+<h2><span class="section-number">15.3. </span>Gradient descent<a class="headerlink" href="#gradient-descent" title="Permalink to this heading">#</a></h2>
 <p>The idea of the gradient descent algorithm is to update parameters in
 a direction where the cost function decreases goes to a minimum.</p>
 <p>In general, the update of some parameters <span class="math notranslate nohighlight">\(\boldsymbol{\omega}\)</span> given a cost
@@ -871,9 +731,9 @@ P_{\text{hidden},\text{new}} &amp;= P_{\text{hidden}} - \lambda \nabla_{P_{\text
 P_{\text{output},\text{new}} &amp;= P_{\text{output}} - \lambda \nabla_{P_{\text{output}}} C(\boldsymbol{x}, P)
 \end{aligned}
 \end{split}\]</div>
-</div>
-<div class="section" id="the-code-for-solving-the-ode">
-<h2><span class="section-number">15.4. </span>The code for solving the ODE<a class="headerlink" href="#the-code-for-solving-the-ode" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-code-for-solving-the-ode">
+<h2><span class="section-number">15.4. </span>The code for solving the ODE<a class="headerlink" href="#the-code-for-solving-the-ode" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
@@ -1026,19 +886,60 @@ P_{\text{output},\text{new}} &amp;= P_{\text{output}} - \lambda \nabla_{P_{\text
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 367.01
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span><span class="p">,</span> <span class="n">elementwise_grad</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.0666807
-Max absolute difference: 0.0437499
-</pre></div>
-</div>
-<img alt="_images/chapter11_50_2.png" src="_images/chapter11_50_2.png" />
 </div>
 </div>
-</div>
-<div class="section" id="the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">
-<h2><span class="section-number">15.5. </span>The network with one input layer, specified number of hidden layers, and one output layer<a class="headerlink" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">
+<h2><span class="section-number">15.5. </span>The network with one input layer, specified number of hidden layers, and one output layer<a class="headerlink" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer" title="Permalink to this heading">#</a></h2>
 <p>It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.</p>
 <p>The number of neurons within each hidden layer are given as a list of integers in the program below.</p>
 <div class="cell docutils container">
@@ -1204,22 +1105,9 @@ Max absolute difference: 0.0437499
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 324.246
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.119936
-</pre></div>
-</div>
-<img alt="_images/chapter11_52_3.png" src="_images/chapter11_52_3.png" />
-</div>
-</div>
-<div class="section" id="example-population-growth">
-<h3><span class="section-number">15.5.1. </span>Example: Population growth<a class="headerlink" href="#example-population-growth" title="Permalink to this headline">¶</a></h3>
+<section id="example-population-growth">
+<h3><span class="section-number">15.5.1. </span>Example: Population growth<a class="headerlink" href="#example-population-growth" title="Permalink to this heading">#</a></h3>
 <p>A logistic model of population growth assumes that a population converges toward an equilibrium.
 The population growth can be modeled by</p>
 <!-- Equation labels as ordinary links -->
@@ -1430,25 +1318,11 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 0.221805
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.000417932
-The max absolute difference between the solutions is: 0.00424909
-</pre></div>
-</div>
-<img alt="_images/chapter11_58_3.png" src="_images/chapter11_58_3.png" />
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="using-forward-euler-to-solve-the-ode">
-<h2><span class="section-number">15.6. </span>Using forward Euler to solve the ODE<a class="headerlink" href="#using-forward-euler-to-solve-the-ode" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="using-forward-euler-to-solve-the-ode">
+<h2><span class="section-number">15.6. </span>Using forward Euler to solve the ODE<a class="headerlink" href="#using-forward-euler-to-solve-the-ode" title="Permalink to this heading">#</a></h2>
 <p>A straightforward way of solving an ODE numerically, is to use Euler’s method.</p>
 <p>Euler’s method uses Taylor series to approximate the value at a function <span class="math notranslate nohighlight">\(f\)</span> at a step <span class="math notranslate nohighlight">\(\Delta x\)</span> from <span class="math notranslate nohighlight">\(x\)</span>:</p>
 <div class="math notranslate nohighlight">
@@ -1489,7 +1363,7 @@ t_i &amp;= i\Delta t \\
 \end{equation} \label{odenum} \tag{12}
 \end{split}\]</div>
 <p>for <span class="math notranslate nohighlight">\(i \geq 1\)</span> and <span class="math notranslate nohighlight">\(g_0 = g(t_0) = g(0) = g_0\)</span>.</p>
-<p>Equation (<a class="reference external" href="#odenum">12</a>) could be implemented in the following way,
+<p>Equation (<span class="xref myst">12</span>) could be implemented in the following way,
 extending the program that uses the network using Autograd:</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1561,27 +1435,10 @@ extending the program that uses the network using Autograd:</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 0.221805
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.000417932
-The max absolute difference between the solutions is: 0.00424909
-Max absolute difference between Euler method and analytical: 0.011225
-Max absolute difference between deep neural network and analytical: 0.00424909
-</pre></div>
-</div>
-<img alt="_images/chapter11_66_3.png" src="_images/chapter11_66_3.png" />
-<img alt="_images/chapter11_66_4.png" src="_images/chapter11_66_4.png" />
-</div>
-</div>
-</div>
-<div class="section" id="solving-the-one-dimensional-poisson-equation">
-<h2><span class="section-number">15.7. </span>Solving the one dimensional Poisson equation<a class="headerlink" href="#solving-the-one-dimensional-poisson-equation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="solving-the-one-dimensional-poisson-equation">
+<h2><span class="section-number">15.7. </span>Solving the one dimensional Poisson equation<a class="headerlink" href="#solving-the-one-dimensional-poisson-equation" title="Permalink to this heading">#</a></h2>
 <p>The Poisson equation for <span class="math notranslate nohighlight">\(g(x)\)</span> in one dimension is</p>
 <!-- Equation labels as ordinary links -->
 <div id="poisson"></div>
@@ -1783,23 +1640,9 @@ g(x) = x(1 - x)\exp(x)
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 457.256
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.00310113
-The max absolute difference between the solutions is: 0.000464088
-</pre></div>
-</div>
-<img alt="_images/chapter11_79_3.png" src="_images/chapter11_79_3.png" />
-</div>
-</div>
-<div class="section" id="comparing-with-a-numerical-scheme">
-<h3><span class="section-number">15.7.1. </span>Comparing with a numerical scheme<a class="headerlink" href="#comparing-with-a-numerical-scheme" title="Permalink to this headline">¶</a></h3>
+<section id="comparing-with-a-numerical-scheme">
+<h3><span class="section-number">15.7.1. </span>Comparing with a numerical scheme<a class="headerlink" href="#comparing-with-a-numerical-scheme" title="Permalink to this heading">#</a></h3>
 <p>The Poisson equation is possible to solve using Taylor series to approximate the second derivative.</p>
 <p>Using Taylor series, the second derivative can be expressed as</p>
 <div class="math notranslate nohighlight">
@@ -1816,7 +1659,7 @@ g''(x) = \frac{g(x + \Delta x) - 2g(x) + g(x-\Delta x)}{\Delta x^2} + E_{\Delta
 g''(x) \approx \frac{g(x + \Delta x) - 2g(x) + g(x-\Delta x)}{\Delta x^2}
 \end{equation}
 \]</div>
-<p>If <span class="math notranslate nohighlight">\(x_i = i \Delta x = x_{i-1} + \Delta x\)</span> and <span class="math notranslate nohighlight">\(g_i = g(x_i)\)</span> for <span class="math notranslate nohighlight">\(i = 1,\dots N_x - 2\)</span> with <span class="math notranslate nohighlight">\(N_x\)</span> being the number of values for <span class="math notranslate nohighlight">\(x\)</span>, (<a class="reference external" href="#approx">15</a>) becomes</p>
+<p>If <span class="math notranslate nohighlight">\(x_i = i \Delta x = x_{i-1} + \Delta x\)</span> and <span class="math notranslate nohighlight">\(g_i = g(x_i)\)</span> for <span class="math notranslate nohighlight">\(i = 1,\dots N_x - 2\)</span> with <span class="math notranslate nohighlight">\(N_x\)</span> being the number of values for <span class="math notranslate nohighlight">\(x\)</span>, (<span class="xref myst">15</span>) becomes</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
 \begin{aligned}
@@ -2073,27 +1916,11 @@ f(x_{N_x - 2})
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost: 457.256
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Final cost: 0.00310113
-The max absolute difference between the analytical solution and DNN Autograd: 0.000464088
-The max absolute difference between the analytical solution and numerical scheme: 0.00266858
-</pre></div>
-</div>
-<img alt="_images/chapter11_91_3.png" src="_images/chapter11_91_3.png" />
-<img alt="_images/chapter11_91_4.png" src="_images/chapter11_91_4.png" />
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="partial-differential-equations">
-<h2><span class="section-number">15.8. </span>Partial Differential Equations<a class="headerlink" href="#partial-differential-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="partial-differential-equations">
+<h2><span class="section-number">15.8. </span>Partial Differential Equations<a class="headerlink" href="#partial-differential-equations" title="Permalink to this heading">#</a></h2>
 <p>A partial differential equation (PDE) has a solution here the function
 is defined by multiple variables.  The equation may involve all kinds
 of combinations of which variables the function is differentiated with
@@ -2108,8 +1935,8 @@ respect to.</p>
 \end{equation}
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(f\)</span> is an expression involving all kinds of possible mixed derivatives of <span class="math notranslate nohighlight">\(g(x_1,\dots,x_N)\)</span> up to an order <span class="math notranslate nohighlight">\(n\)</span>. In order for the solution to be unique, some additional conditions must also be given.</p>
-<div class="section" id="type-of-problem">
-<h3><span class="section-number">15.8.1. </span>Type of problem<a class="headerlink" href="#type-of-problem" title="Permalink to this headline">¶</a></h3>
+<section id="type-of-problem">
+<h3><span class="section-number">15.8.1. </span>Type of problem<a class="headerlink" href="#type-of-problem" title="Permalink to this heading">#</a></h3>
 <p>The problem our network must solve for, is similar to the ODE case.
 We must have a trial solution <span class="math notranslate nohighlight">\(g_t\)</span> at hand.</p>
 <p>For instance, the trial solution could be expressed as</p>
@@ -2122,13 +1949,13 @@ We must have a trial solution <span class="math notranslate nohighlight">\(g_t\)
 <p>where <span class="math notranslate nohighlight">\(h_1(x_1,\dots,x_N)\)</span> is a function that ensures <span class="math notranslate nohighlight">\(g_t(x_1,\dots,x_N)\)</span> satisfies some given conditions.
 The neural network <span class="math notranslate nohighlight">\(N(x_1,\dots,x_N,P)\)</span> has weights and biases described by <span class="math notranslate nohighlight">\(P\)</span> and <span class="math notranslate nohighlight">\(h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P))\)</span> is an expression using the output from the neural network in some way.</p>
 <p>The role of the function <span class="math notranslate nohighlight">\(h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P))\)</span>, is to ensure that the output of <span class="math notranslate nohighlight">\(N(x_1,\dots,x_N,P)\)</span> is zero when <span class="math notranslate nohighlight">\(g_t(x_1,\dots,x_N)\)</span> is evaluated at the values of <span class="math notranslate nohighlight">\(x_1,\dots,x_N\)</span> where the given conditions must be satisfied. The function <span class="math notranslate nohighlight">\(h_1(x_1,\dots,x_N)\)</span> should alone make <span class="math notranslate nohighlight">\(g_t(x_1,\dots,x_N)\)</span> satisfy the conditions.</p>
-</div>
-<div class="section" id="network-requirements">
-<h3><span class="section-number">15.8.2. </span>Network requirements<a class="headerlink" href="#network-requirements" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="network-requirements">
+<h3><span class="section-number">15.8.2. </span>Network requirements<a class="headerlink" href="#network-requirements" title="Permalink to this heading">#</a></h3>
 <p>The network tries then the minimize the cost function following the
 same ideas as described for the ODE case, but now with more than one
 variables to consider.  The concept still remains the same; find a set
-of parameters <span class="math notranslate nohighlight">\(P\)</span> such that the expression <span class="math notranslate nohighlight">\(f\)</span> in (<a class="reference external" href="#PDE">17</a>) is as
+of parameters <span class="math notranslate nohighlight">\(P\)</span> such that the expression <span class="math notranslate nohighlight">\(f\)</span> in (<span class="xref myst">17</span>) is as
 close to zero as possible.</p>
 <p>As for the ODE case, the cost function is the mean squared error that
 the network must try to minimize. The cost function for the network to
@@ -2147,10 +1974,10 @@ C\left(\boldsymbol{x}, P\right) = f\left( \left( \boldsymbol{x}, \frac{\partial
 \[
 C\left(X, P \right) = \sum_{i=1}^M f\left( \left( \boldsymbol{x}_i, \frac{\partial g(\boldsymbol{x}_i) }{\partial x_1}, \dots , \frac{\partial g(\boldsymbol{x}_i) }{\partial x_N}, \frac{\partial g(\boldsymbol{x}_i) }{\partial x_1\partial x_2}, \, \dots \, , \frac{\partial^n g(\boldsymbol{x}_i) }{\partial x_N^n} \right) \right)^2.
 \]</div>
-</div>
-</div>
-<div class="section" id="example-the-diffusion-equation">
-<h2><span class="section-number">15.9. </span>Example: The diffusion equation<a class="headerlink" href="#example-the-diffusion-equation" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="example-the-diffusion-equation">
+<h2><span class="section-number">15.9. </span>Example: The diffusion equation<a class="headerlink" href="#example-the-diffusion-equation" title="Permalink to this heading">#</a></h2>
 <p>In one spatial dimension, the equation reads</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2317,8 +2144,8 @@ mixed derivatives of <span class="math notranslate nohighlight">\(g(x,t)\)</span
 </div>
 </div>
 </div>
-<div class="section" id="setting-up-the-network-using-autograd-the-full-program">
-<h3><span class="section-number">15.9.1. </span>Setting up the network using Autograd; The full program<a class="headerlink" href="#setting-up-the-network-using-autograd-the-full-program" title="Permalink to this headline">¶</a></h3>
+<section id="setting-up-the-network-using-autograd-the-full-program">
+<h3><span class="section-number">15.9.1. </span>Setting up the network using Autograd; The full program<a class="headerlink" href="#setting-up-the-network-using-autograd-the-full-program" title="Permalink to this heading">#</a></h3>
 <p>Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.</p>
 <p>The analytical solution of our problem is</p>
 <div class="math notranslate nohighlight">
@@ -2558,190 +2385,11 @@ Using TensorFlow results in a much better execution time. Try it!</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify &#39;dtype=object&#39; when creating the ndarray.
-  return asarray(a).size
-</pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Initial cost:  41.05505310046363
-</pre></div>
-</div>
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">KeyboardInterrupt</span><span class="g g-Whitespace">                         </span>Traceback (most recent call last)
-<span class="nn">Input In [9],</span> in <span class="ni">&lt;cell line: 129&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">    </span><span class="mi">140</span> <span class="n">num_iter</span> <span class="o">=</span> <span class="mi">250</span>
-<span class="g g-Whitespace">    </span><span class="mi">141</span> <span class="n">lmb</span> <span class="o">=</span> <span class="mf">0.01</span>
-<span class="ne">--&gt; </span><span class="mi">143</span> <span class="n">P</span> <span class="o">=</span> <span class="n">solve_pde_deep_neural_network</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">t</span><span class="p">,</span> <span class="n">num_hidden_neurons</span><span class="p">,</span> <span class="n">num_iter</span><span class="p">,</span> <span class="n">lmb</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">145</span> <span class="c1">## Store the results</span>
-<span class="g g-Whitespace">    </span><span class="mi">146</span> <span class="n">g_dnn_ag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">Nx</span><span class="p">,</span> <span class="n">Nt</span><span class="p">))</span>
-
-<span class="nn">Input In [9],</span> in <span class="ni">solve_pde_deep_neural_network</span><span class="nt">(x, t, num_neurons, num_iter, lmb)</span>
-<span class="g g-Whitespace">    </span><span class="mi">118</span> <span class="c1"># Let the update be done num_iter times</span>
-<span class="g g-Whitespace">    </span><span class="mi">119</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">num_iter</span><span class="p">):</span>
-<span class="ne">--&gt; </span><span class="mi">120</span>     <span class="n">cost_grad</span> <span class="o">=</span>  <span class="n">cost_function_grad</span><span class="p">(</span><span class="n">P</span><span class="p">,</span> <span class="n">x</span> <span class="p">,</span> <span class="n">t</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">122</span>     <span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_hidden</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
-<span class="g g-Whitespace">    </span><span class="mi">123</span>         <span class="n">P</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">=</span> <span class="n">P</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">-</span> <span class="n">lmb</span> <span class="o">*</span> <span class="n">cost_grad</span><span class="p">[</span><span class="n">l</span><span class="p">]</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>     <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="nd">@unary_to_nary</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span> <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>     <span class="sd">&quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span><span class="sd">     Returns a function which computes the gradient of `fun` with respect to</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span><span class="sd">     positional argument number `argnum`. The returned function takes the same</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span><span class="sd">     arguments as `fun`, but returns the gradient instead. The function `fun`</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span><span class="sd">     should be scalar-valued. The gradient has the same type as the argument.&quot;&quot;&quot;</span>
-<span class="ne">---&gt; </span><span class="mi">25</span>     <span class="n">vjp</span><span class="p">,</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">_make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span>     <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span>         <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Grad only applies to real scalar-output functions. &quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span>                         <span class="s2">&quot;Try jacobian, elementwise_grad or holomorphic_grad.&quot;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10,</span> in <span class="ni">make_vjp</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="k">def</span> <span class="nf">make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span>     <span class="n">start_node</span> <span class="o">=</span> <span class="n">VJPNode</span><span class="o">.</span><span class="n">new_root</span><span class="p">()</span>
-<span class="ne">---&gt; </span><span class="mi">10</span>     <span class="n">end_value</span><span class="p">,</span> <span class="n">end_node</span> <span class="o">=</span>  <span class="n">trace</span><span class="p">(</span><span class="n">start_node</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span>     <span class="k">if</span> <span class="n">end_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">12</span>         <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">zeros</span><span class="p">()</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10,</span> in <span class="ni">trace</span><span class="nt">(start_node, fun, x)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="k">with</span> <span class="n">trace_stack</span><span class="o">.</span><span class="n">new_trace</span><span class="p">()</span> <span class="k">as</span> <span class="n">t</span><span class="p">:</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span>     <span class="n">start_box</span> <span class="o">=</span> <span class="n">new_box</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">start_node</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">10</span>     <span class="n">end_box</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="n">start_box</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span>     <span class="k">if</span> <span class="n">isbox</span><span class="p">(</span><span class="n">end_box</span><span class="p">)</span> <span class="ow">and</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_trace</span> <span class="o">==</span> <span class="n">start_box</span><span class="o">.</span><span class="n">_trace</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">12</span>         <span class="k">return</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_value</span><span class="p">,</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_node</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f.&lt;locals&gt;.unary_f</span><span class="nt">(x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">13</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">14</span>     <span class="n">subargs</span> <span class="o">=</span> <span class="n">subvals</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">argnum</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
-<span class="ne">---&gt; </span><span class="mi">15</span> <span class="k">return</span> <span class="n">fun</span><span class="p">(</span><span class="o">*</span><span class="n">subargs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">Input In [9],</span> in <span class="ni">cost_function</span><span class="nt">(P, x, t)</span>
-<span class="g g-Whitespace">     </span><span class="mi">78</span> <span class="n">g_t</span> <span class="o">=</span> <span class="n">g_trial</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">79</span> <span class="n">g_t_jacobian</span> <span class="o">=</span> <span class="n">g_t_jacobian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">80</span> <span class="n">g_t_hessian</span> <span class="o">=</span> <span class="n">g_t_hessian_func</span><span class="p">(</span><span class="n">point</span><span class="p">,</span><span class="n">P</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">82</span> <span class="n">g_t_dt</span> <span class="o">=</span> <span class="n">g_t_jacobian</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
-<span class="g g-Whitespace">     </span><span class="mi">83</span> <span class="n">g_t_d2x</span> <span class="o">=</span> <span class="n">g_t_hessian</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>     <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:78,</span> in <span class="ni">hessian</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">75</span> <span class="nd">@unary_to_nary</span>
-<span class="g g-Whitespace">     </span><span class="mi">76</span> <span class="k">def</span> <span class="nf">hessian</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">77</span>     <span class="s2">&quot;Returns a function that computes the exact Hessian.&quot;</span>
-<span class="ne">---&gt; </span><span class="mi">78</span>     <span class="k">return</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">fun</span><span class="p">))(</span><span class="n">x</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>     <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:61,</span> in <span class="ni">jacobian</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">59</span> <span class="n">jacobian_shape</span> <span class="o">=</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
-<span class="g g-Whitespace">     </span><span class="mi">60</span> <span class="n">grads</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">vjp</span><span class="p">,</span> <span class="n">ans_vspace</span><span class="o">.</span><span class="n">standard_basis</span><span class="p">())</span>
-<span class="ne">---&gt; </span><span class="mi">61</span> <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">(</span><span class="n">grads</span><span class="p">),</span> <span class="n">jacobian_shape</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni">stack</span><span class="nt">(arrays, axis)</span>
-<span class="g g-Whitespace">     </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">84</span>     <span class="c1"># this code is basically copied from numpy/core/shape_base.py&#39;s stack</span>
-<span class="g g-Whitespace">     </span><span class="mi">85</span>     <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
-<span class="g g-Whitespace">     </span><span class="mi">86</span>     <span class="c1"># primitives defined in this file</span>
-<span class="ne">---&gt; </span><span class="mi">88</span>     <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
-<span class="g g-Whitespace">     </span><span class="mi">89</span>     <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">90</span>         <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;need at least one array to stack&#39;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88,</span> in <span class="ni">&lt;listcomp&gt;</span><span class="nt">(.0)</span>
-<span class="g g-Whitespace">     </span><span class="mi">83</span> <span class="k">def</span> <span class="nf">stack</span><span class="p">(</span><span class="n">arrays</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">84</span>     <span class="c1"># this code is basically copied from numpy/core/shape_base.py&#39;s stack</span>
-<span class="g g-Whitespace">     </span><span class="mi">85</span>     <span class="c1"># we need it here because we want to re-implement stack in terms of the</span>
-<span class="g g-Whitespace">     </span><span class="mi">86</span>     <span class="c1"># primitives defined in this file</span>
-<span class="ne">---&gt; </span><span class="mi">88</span>     <span class="n">arrays</span> <span class="o">=</span> <span class="p">[</span><span class="n">array</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span> <span class="k">for</span> <span class="n">arr</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">]</span>
-<span class="g g-Whitespace">     </span><span class="mi">89</span>     <span class="k">if</span> <span class="ow">not</span> <span class="n">arrays</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">90</span>         <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s1">&#39;need at least one array to stack&#39;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14,</span> in <span class="ni">make_vjp.&lt;locals&gt;.vjp</span><span class="nt">(g)</span>
-<span class="ne">---&gt; </span><span class="mi">14</span> <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">backward_pass</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">end_node</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21,</span> in <span class="ni">backward_pass</span><span class="nt">(g, end_node)</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span> <span class="k">for</span> <span class="n">node</span> <span class="ow">in</span> <span class="n">toposort</span><span class="p">(</span><span class="n">end_node</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>     <span class="n">outgrad</span> <span class="o">=</span> <span class="n">outgrads</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">21</span>     <span class="n">ingrads</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">vjp</span><span class="p">(</span><span class="n">outgrad</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span>     <span class="k">for</span> <span class="n">parent</span><span class="p">,</span> <span class="n">ingrad</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">parents</span><span class="p">,</span> <span class="n">ingrads</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span>         <span class="n">outgrads</span><span class="p">[</span><span class="n">parent</span><span class="p">]</span> <span class="o">=</span> <span class="n">add_outgrads</span><span class="p">(</span><span class="n">outgrads</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">parent</span><span class="p">),</span> <span class="n">ingrad</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67,</span> in <span class="ni">defvjp.&lt;locals&gt;.vjp_argnums.&lt;locals&gt;.&lt;lambda&gt;</span><span class="nt">(g)</span>
-<span class="g g-Whitespace">     </span><span class="mi">64</span>         <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">65</span>             <span class="s2">&quot;VJP of </span><span class="si">{}</span><span class="s2"> wrt argnum 0 not defined&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun</span><span class="o">.</span><span class="vm">__name__</span><span class="p">))</span>
-<span class="g g-Whitespace">     </span><span class="mi">66</span>     <span class="n">vjp</span> <span class="o">=</span> <span class="n">vjpfun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">67</span>     <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="p">(</span><span class="n">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">),)</span>
-<span class="g g-Whitespace">     </span><span class="mi">68</span> <span class="k">elif</span> <span class="n">L</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">69</span>     <span class="n">argnum_0</span><span class="p">,</span> <span class="n">argnum_1</span> <span class="o">=</span> <span class="n">argnums</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423,</span> in <span class="ni">matmul_vjp_1.&lt;locals&gt;.&lt;lambda&gt;</span><span class="nt">(g)</span>
-<span class="g g-Whitespace">    </span><span class="mi">421</span> <span class="n">A_ndim</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">422</span> <span class="n">B_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">423</span> <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">matmul_adjoint_1</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">A_ndim</span><span class="p">,</span> <span class="n">B_meta</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:410,</span> in <span class="ni">matmul_adjoint_1</span><span class="nt">(A, G, A_ndim, B_meta)</span>
-<span class="g g-Whitespace">    </span><span class="mi">408</span> <span class="k">else</span><span class="p">:</span>  <span class="c1"># We need to swap the last two axes of A</span>
-<span class="g g-Whitespace">    </span><span class="mi">409</span>     <span class="n">A</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">swapaxes</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">A_ndim</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">A_ndim</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">410</span> <span class="n">result</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">G</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">411</span> <span class="k">if</span> <span class="n">B_is_vec</span><span class="p">:</span>
-<span class="g g-Whitespace">    </span><span class="mi">412</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">result</span><span class="p">,</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">G</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45,</span> in <span class="ni">primitive.&lt;locals&gt;.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">43</span>     <span class="n">argnums</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">argnum</span>    <span class="k">for</span> <span class="n">argnum</span><span class="p">,</span> <span class="n">_</span>   <span class="ow">in</span> <span class="n">boxed_args</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">44</span>     <span class="n">ans</span> <span class="o">=</span> <span class="n">f_wrapped</span><span class="p">(</span><span class="o">*</span><span class="n">argvals</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">45</span>     <span class="n">node</span> <span class="o">=</span> <span class="n">node_constructor</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">f_wrapped</span><span class="p">,</span> <span class="n">argvals</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">,</span> <span class="n">argnums</span><span class="p">,</span> <span class="n">parents</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">46</span>     <span class="k">return</span> <span class="n">new_box</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">trace</span><span class="p">,</span> <span class="n">node</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">47</span> <span class="k">else</span><span class="p">:</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36,</span> in <span class="ni">VJPNode.__init__</span><span class="nt">(self, value, fun, args, kwargs, parent_argnums, parents)</span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span>     <span class="n">fun_name</span> <span class="o">=</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="s1">&#39;__name__&#39;</span><span class="p">,</span> <span class="n">fun</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">34</span>     <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span><span class="s2">&quot;VJP of </span><span class="si">{}</span><span class="s2"> wrt argnums </span><span class="si">{}</span><span class="s2"> not defined&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span>                               <span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun_name</span><span class="p">,</span> <span class="n">parent_argnums</span><span class="p">))</span>
-<span class="ne">---&gt; </span><span class="mi">36</span> <span class="bp">self</span><span class="o">.</span><span class="n">vjp</span> <span class="o">=</span> <span class="n">vjpmaker</span><span class="p">(</span><span class="n">parent_argnums</span><span class="p">,</span> <span class="n">value</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:77,</span> in <span class="ni">defvjp.&lt;locals&gt;.vjp_argnums</span><span class="nt">(argnums, ans, args, kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">74</span>         <span class="k">raise</span> <span class="ne">NotImplementedError</span><span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">75</span>             <span class="s2">&quot;VJP of </span><span class="si">{}</span><span class="s2"> wrt argnums 0, 1 not defined&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">fun</span><span class="o">.</span><span class="vm">__name__</span><span class="p">))</span>
-<span class="g g-Whitespace">     </span><span class="mi">76</span>     <span class="n">vjp_0</span> <span class="o">=</span> <span class="n">vjp_0_fun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">77</span>     <span class="n">vjp_1</span> <span class="o">=</span> <span class="n">vjp_1_fun</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">78</span>     <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="p">(</span><span class="n">vjp_0</span><span class="p">(</span><span class="n">g</span><span class="p">),</span> <span class="n">vjp_1</span><span class="p">(</span><span class="n">g</span><span class="p">))</span>
-<span class="g g-Whitespace">     </span><span class="mi">79</span> <span class="k">else</span><span class="p">:</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:422,</span> in <span class="ni">matmul_vjp_1</span><span class="nt">(ans, A, B)</span>
-<span class="g g-Whitespace">    </span><span class="mi">420</span> <span class="k">def</span> <span class="nf">matmul_vjp_1</span><span class="p">(</span><span class="n">ans</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">):</span>
-<span class="g g-Whitespace">    </span><span class="mi">421</span>     <span class="n">A_ndim</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">422</span>     <span class="n">B_meta</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">metadata</span><span class="p">(</span><span class="n">B</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">423</span>     <span class="k">return</span> <span class="k">lambda</span> <span class="n">g</span><span class="p">:</span> <span class="n">matmul_adjoint_1</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">g</span><span class="p">,</span> <span class="n">A_ndim</span><span class="p">,</span> <span class="n">B_meta</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:61,</span> in <span class="ni">notrace_primitive.&lt;locals&gt;.f_wrapped</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">58</span> <span class="nd">@wraps</span><span class="p">(</span><span class="n">f_raw</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">59</span> <span class="k">def</span> <span class="nf">f_wrapped</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">60</span>     <span class="n">argvals</span> <span class="o">=</span> <span class="nb">map</span><span class="p">(</span><span class="n">getval</span><span class="p">,</span> <span class="n">args</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">61</span>     <span class="k">return</span> <span class="n">f_raw</span><span class="p">(</span><span class="o">*</span><span class="n">argvals</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:148,</span> in <span class="ni">metadata</span><span class="nt">(A)</span>
-<span class="g g-Whitespace">    </span><span class="mi">146</span> <span class="nd">@notrace_primitive</span>
-<span class="g g-Whitespace">    </span><span class="mi">147</span> <span class="k">def</span> <span class="nf">metadata</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
-<span class="ne">--&gt; </span><span class="mi">148</span>     <span class="k">return</span> <span class="n">_np</span><span class="o">.</span><span class="n">shape</span><span class="p">(</span><span class="n">A</span><span class="p">),</span> <span class="n">_np</span><span class="o">.</span><span class="n">ndim</span><span class="p">(</span><span class="n">A</span><span class="p">),</span> <span class="n">_np</span><span class="o">.</span><span class="n">result_type</span><span class="p">(</span><span class="n">A</span><span class="p">),</span> <span class="n">_np</span><span class="o">.</span><span class="n">iscomplexobj</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
-
-<span class="ne">KeyboardInterrupt</span>: 
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="solving-the-wave-equation-with-neural-networks">
-<h2><span class="section-number">15.10. </span>Solving the wave equation with Neural Networks<a class="headerlink" href="#solving-the-wave-equation-with-neural-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="solving-the-wave-equation-with-neural-networks">
+<h2><span class="section-number">15.10. </span>Solving the wave equation with Neural Networks<a class="headerlink" href="#solving-the-wave-equation-with-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>The wave equation is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2783,7 +2431,7 @@ g(x,0) &amp;= u(x), &amp;x\in[0,1] \\
 \end{split}\]</div>
 <p>In this example, let <span class="math notranslate nohighlight">\(c = 1\)</span> and <span class="math notranslate nohighlight">\(u(x) = \sin(\pi x)\)</span> and <span class="math notranslate nohighlight">\(v(x) = -\pi\sin(\pi x)\)</span>.</p>
 <p>Setting up the network is done in similar matter as for the example of solving the diffusion equation.
-The only things we have to change, is the trial solution such that it satisfies the conditions from (<a class="reference external" href="#condwave">20</a>) and the cost function.</p>
+The only things we have to change, is the trial solution such that it satisfies the conditions from (<span class="xref myst">20</span>) and the cost function.</p>
 <p>The trial solution becomes slightly different since we have other conditions than in the example of solving the diffusion equation. Here, a possible trial solution <span class="math notranslate nohighlight">\(g_t(x,t)\)</span> is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3026,17 +2674,17 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="resources-on-differential-equations-and-deep-learning">
-<h2><span class="section-number">15.11. </span>Resources on differential equations and deep learning<a class="headerlink" href="#resources-on-differential-equations-and-deep-learning" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="resources-on-differential-equations-and-deep-learning">
+<h2><span class="section-number">15.11. </span>Resources on differential equations and deep learning<a class="headerlink" href="#resources-on-differential-equations-and-deep-learning" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p><a class="reference external" href="https://pdfs.semanticscholar.org/d061/df393e0e8fbfd0ea24976458b7d42419040d.pdf">Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al</a></p></li>
 <li><p><a class="reference external" href="https://becominghuman.ai/neural-networks-for-solving-differential-equations-fa230ac5e04c">Neural networks for solving differential equations by A. Honchar</a></p></li>
 <li><p><a class="reference external" href="http://cs229.stanford.edu/proj2013/ChiaramonteKiener-SolvingDifferentialEquationsUsingNeuralNetworks.pdf">Solving differential equations using neural networks by M.M Chiaramonte and M. Kiener</a></p></li>
 <li><p><a class="reference external" href="https://www.springer.com/us/book/9783540225515">Introduction to Partial Differential Equations by A. Tveito, R. Winther</a></p></li>
 </ol>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -3050,7 +2698,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -3058,44 +2706,124 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <i class="fa-solid fa-list"></i> Contents
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+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-exponential-decay">15.1. Example: Exponential decay</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reformulating-the-problem">15.2. Reformulating the problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent">15.3. Gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-code-for-solving-the-ode">15.4. The code for solving the ODE</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer">15.5. The network with one input layer, specified number of hidden layers, and one output layer</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#example-population-growth">15.5.1. Example: Population growth</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-forward-euler-to-solve-the-ode">15.6. Using forward Euler to solve the ODE</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-one-dimensional-poisson-equation">15.7. Solving the one dimensional Poisson equation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#comparing-with-a-numerical-scheme">15.7.1. Comparing with a numerical scheme</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#partial-differential-equations">15.8. Partial Differential Equations</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#type-of-problem">15.8.1. Type of problem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#network-requirements">15.8.2. Network requirements</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-the-diffusion-equation">15.9. Example: The diffusion equation</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#setting-up-the-network-using-autograd-the-full-program">15.9.1. Setting up the network using Autograd; The full program</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-the-wave-equation-with-neural-networks">15.10. Solving the wave equation with Neural Networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resources-on-differential-equations-and-deep-learning">15.11. Resources on differential equations and deep learning</a></li>
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-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
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-  Decision Trees, Ensemble Methods and Boosting
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#neural-networks-vs-cnns">
-   16.1. Neural Networks vs CNNs
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#layers-used-to-build-cnns">
-   16.2. Layers used to build CNNs
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-cnns">
-   16.3. Mathematics of CNNs
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">
-     16.3.1. Convolution Examples: Polynomial multiplication
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">
-     16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#two-dimensional-objects">
-   16.4. Two-dimensional Objects
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-dimensionalities">
-   16.5. More on Dimensionalities
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-dimensionality-remarks">
-   16.6. Further Dimensionality Remarks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">
-   16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-mnist-dataset-again">
-     16.7.1. The MNIST dataset again
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#systematic-reduction">
-     16.7.2. Systematic reduction
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#prerequisites-collect-and-pre-process-data">
-     16.7.3. Prerequisites: Collect and pre-process data
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cifar01-data-set">
-   16.8. The CIFAR01 data set
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#neural-networks-vs-cnns">16.1. Neural Networks vs CNNs</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#layers-used-to-build-cnns">16.2. Layers used to build CNNs</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-cnns">16.3. Mathematics of CNNs</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">16.3.1. Convolution Examples: Polynomial multiplication</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#two-dimensional-objects">16.4. Two-dimensional Objects</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-dimensionalities">16.5. More on Dimensionalities</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-dimensionality-remarks">16.6. Further Dimensionality Remarks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-mnist-dataset-again">16.7.1. The MNIST dataset again</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#systematic-reduction">16.7.2. Systematic reduction</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites-collect-and-pre-process-data">16.7.3. Prerequisites: Collect and pre-process data</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cifar01-data-set">16.8. The CIFAR01 data set</a></li>
 </ul>
-
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-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Convolutional Neural Networks</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#neural-networks-vs-cnns">
-   16.1. Neural Networks vs CNNs
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#layers-used-to-build-cnns">
-   16.2. Layers used to build CNNs
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-cnns">
-   16.3. Mathematics of CNNs
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">
-     16.3.1. Convolution Examples: Polynomial multiplication
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">
-     16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#two-dimensional-objects">
-   16.4. Two-dimensional Objects
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-dimensionalities">
-   16.5. More on Dimensionalities
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-dimensionality-remarks">
-   16.6. Further Dimensionality Remarks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">
-   16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-mnist-dataset-again">
-     16.7.1. The MNIST dataset again
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#systematic-reduction">
-     16.7.2. Systematic reduction
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#prerequisites-collect-and-pre-process-data">
-     16.7.3. Prerequisites: Collect and pre-process data
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cifar01-data-set">
-   16.8. The CIFAR01 data set
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter12.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="convolutional-neural-networks">
-<h1><span class="section-number">16. </span>Convolutional Neural Networks<a class="headerlink" href="#convolutional-neural-networks" title="Permalink to this headline">¶</a></h1>
+doconce format html chapter12.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="convolutional-neural-networks">
+<h1><span class="section-number">16. </span>Convolutional Neural Networks<a class="headerlink" href="#convolutional-neural-networks" title="Permalink to this heading">#</a></h1>
 <p>Convolutional neural networks (CNNs) were developed during the last
 decade of the previous century, with a focus on character recognition
 tasks. Nowadays, CNNs are a central element in the spectacular success
@@ -565,8 +456,8 @@ the network.</strong></p>
 <a class="reference external" href="https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html">IN5400 – Machine Learning for Image Analysis</a>
 and the slides of <a class="reference external" href="http://cs231n.github.io/convolutional-networks/">CS231</a>.</p>
 <p>Another good read is the article here <a class="reference external" href="https://arxiv.org/pdf/1603.07285.pdf">https://arxiv.org/pdf/1603.07285.pdf</a>.</p>
-<div class="section" id="neural-networks-vs-cnns">
-<h2><span class="section-number">16.1. </span>Neural Networks vs CNNs<a class="headerlink" href="#neural-networks-vs-cnns" title="Permalink to this headline">¶</a></h2>
+<section id="neural-networks-vs-cnns">
+<h2><span class="section-number">16.1. </span>Neural Networks vs CNNs<a class="headerlink" href="#neural-networks-vs-cnns" title="Permalink to this heading">#</a></h2>
 <p>Neural networks are defined as <strong>affine transformations</strong>, that is
 a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an
 output (to which a bias vector is usually added before passing the result
@@ -630,9 +521,9 @@ dimension.</p>
 <!-- dom:FIGURE: [figslides/cnn.jpeg, width=500 frac=0.6]  A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels). -->
 <!-- begin figure -->
 <p><img src="figslides/cnn.jpeg" width="500"><p style="font-size: 0.9em"><i>Figure 1: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).</i></p></p>
-<!-- end figure --></div>
-<div class="section" id="layers-used-to-build-cnns">
-<h2><span class="section-number">16.2. </span>Layers used to build CNNs<a class="headerlink" href="#layers-used-to-build-cnns" title="Permalink to this headline">¶</a></h2>
+<!-- end figure --></section>
+<section id="layers-used-to-build-cnns">
+<h2><span class="section-number">16.2. </span>Layers used to build CNNs<a class="headerlink" href="#layers-used-to-build-cnns" title="Permalink to this heading">#</a></h2>
 <p>A simple CNN is a sequence of layers, and every layer of a CNN
 transforms one volume of activations to another through a
 differentiable function. We use three main types of layers to build
@@ -669,9 +560,9 @@ are consistent with the labels in the training set for each image.</p>
 <p>The key idea in CNNs for say imaging is that in images neighbor pixels tend to be related! So we connect
 only neighboring neurons in the input instead of connecting all with the first hidden layer.</p>
 <p>We say we perform a filtering (convolution is the mathematical operation).</p>
-</div>
-<div class="section" id="mathematics-of-cnns">
-<h2><span class="section-number">16.3. </span>Mathematics of CNNs<a class="headerlink" href="#mathematics-of-cnns" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="mathematics-of-cnns">
+<h2><span class="section-number">16.3. </span>Mathematics of CNNs<a class="headerlink" href="#mathematics-of-cnns" title="Permalink to this heading">#</a></h2>
 <p>The mathematics of CNNs is based on the mathematical operation of
 <strong>convolution</strong>.  In mathematics (in particular in functional analysis),
 convolution is represented by matheematical operation (integration,
@@ -697,8 +588,8 @@ y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a).
 \]</div>
 <p>Computing the inverse of the above convolution operations is known as deconvolution.</p>
 <p>How can we use this? And what does it mean? Let us study some familiar examples first.</p>
-<div class="section" id="convolution-examples-polynomial-multiplication">
-<h3><span class="section-number">16.3.1. </span>Convolution Examples: Polynomial multiplication<a class="headerlink" href="#convolution-examples-polynomial-multiplication" title="Permalink to this headline">¶</a></h3>
+<section id="convolution-examples-polynomial-multiplication">
+<h3><span class="section-number">16.3.1. </span>Convolution Examples: Polynomial multiplication<a class="headerlink" href="#convolution-examples-polynomial-multiplication" title="Permalink to this heading">#</a></h3>
 <p>We have already met such an example in project 1 when we tried to set
 up the design matrix for a two-dimensional function. This was an
 example of polynomial multiplication.  Let us recast such a problem in terms of the convolution operation.
@@ -771,9 +662,9 @@ In this case we have</p>
 When implementing the above equation we do not encode (and allocate memory) the matrices explicitely.
 We rather code the convolutions in the minimal memory footprint that they require.</p>
 <p>Does the number of floating point operations change here when we use the commutative property?</p>
-</div>
-<div class="section" id="convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">
-<h3><span class="section-number">16.3.2. </span>Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)<a class="headerlink" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">
+<h3><span class="section-number">16.3.2. </span>Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)<a class="headerlink" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms" title="Permalink to this heading">#</a></h3>
 <p>For problems with so-called harmonic oscillations, given by for example the following differential equation</p>
 <div class="math notranslate nohighlight">
 \[
@@ -837,7 +728,55 @@ driven by purely sinusoidal sources.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/chapter12_35_0.png" src="_images/chapter12_35_0.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">math</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
+</div>
 </div>
 </div>
 <p>For the sinusoidal example the
@@ -900,9 +839,9 @@ g_n&amp;=&amp;\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau).
 \end{eqnarray}
 \end{split}\]</div>
 <p>To check the consistency of these expressions and to verify
-Eq. (<a class="reference external" href="#eq:fourierdef2">4</a>), one can insert the expansion of <span class="math notranslate nohighlight">\(F(t)\)</span> in
-Eq. (<a class="reference external" href="#eq:fourierdef1">3</a>) into the expression for the coefficients in
-Eq. (<a class="reference external" href="#eq:fourierdef2">4</a>) and see whether</p>
+Eq. (<span class="xref myst">4</span>), one can insert the expansion of <span class="math notranslate nohighlight">\(F(t)\)</span> in
+Eq. (<span class="xref myst">3</span>) into the expression for the coefficients in
+Eq. (<span class="xref myst">4</span>) and see whether</p>
 <div class="math notranslate nohighlight">
 \[
 \begin{eqnarray}
@@ -979,14 +918,11 @@ square wave signal.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter12_51_0.png" src="_images/chapter12_51_0.png" />
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="two-dimensional-objects">
-<h2><span class="section-number">16.4. </span>Two-dimensional Objects<a class="headerlink" href="#two-dimensional-objects" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="two-dimensional-objects">
+<h2><span class="section-number">16.4. </span>Two-dimensional Objects<a class="headerlink" href="#two-dimensional-objects" title="Permalink to this heading">#</a></h2>
 <p>We often use convolutions over more than one dimension at a time. If
 we have a two-dimensional image <span class="math notranslate nohighlight">\(I\)</span> as input, we can have a <strong>filter</strong>
 defined by a two-dimensional <strong>kernel</strong> <span class="math notranslate nohighlight">\(K\)</span>. This leads to an output <span class="math notranslate nohighlight">\(S\)</span></p>
@@ -1005,9 +941,9 @@ S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i-m,j-n)K(m,n).
 \[
 S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i+m,j-+)K(m,n).
 \]</div>
-</div>
-<div class="section" id="more-on-dimensionalities">
-<h2><span class="section-number">16.5. </span>More on Dimensionalities<a class="headerlink" href="#more-on-dimensionalities" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-on-dimensionalities">
+<h2><span class="section-number">16.5. </span>More on Dimensionalities<a class="headerlink" href="#more-on-dimensionalities" title="Permalink to this heading">#</a></h2>
 <p>In fields like signal processing (and imaging as well), one designs
 so-called filters. These filters are defined by the convolutions and
 are often hand-crafted. One may specify filters for smoothing, edge
@@ -1027,9 +963,9 @@ It means that we have only one output node. But since this output node connects
 \mathrm{NumberParameters}=10^{10}+10^4+10^4+1 \approx 10^{10},
 \]</div>
 <p>that is ten billion parameters to determine.</p>
-</div>
-<div class="section" id="further-dimensionality-remarks">
-<h2><span class="section-number">16.6. </span>Further Dimensionality Remarks<a class="headerlink" href="#further-dimensionality-remarks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="further-dimensionality-remarks">
+<h2><span class="section-number">16.6. </span>Further Dimensionality Remarks<a class="headerlink" href="#further-dimensionality-remarks" title="Permalink to this heading">#</a></h2>
 <p>In today’s architecture one can train such neural networks, however
 this is a huge number of parameters for the task at hand. In general,
 it is a very wasteful and inefficient use of dense matrices as
@@ -1044,9 +980,9 @@ other than those that are very far away. Similarly, sounds are
 repeated in multiple times in the signal. While slightly simplistic,
 reasoning about such a sound example demonstrates this. The same
 principles then apply to images and other similar data.</p>
-</div>
-<div class="section" id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">
-<h2><span class="section-number">16.7. </span>CNNs in more detail, building convolutional neural networks in Tensorflow and Keras<a class="headerlink" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">
+<h2><span class="section-number">16.7. </span>CNNs in more detail, building convolutional neural networks in Tensorflow and Keras<a class="headerlink" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras" title="Permalink to this heading">#</a></h2>
 <p>As discussed above, CNNs are neural networks built from the assumption that the inputs
 to the network are 2D images. This is important because the number of features or pixels in images
 grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.</p>
@@ -1060,8 +996,8 @@ dataset of images, we require a 4D matrix or <strong>tensor</strong>. This tenso
 \[
 (n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) .
 \]</div>
-<div class="section" id="the-mnist-dataset-again">
-<h3><span class="section-number">16.7.1. </span>The MNIST dataset again<a class="headerlink" href="#the-mnist-dataset-again" title="Permalink to this headline">¶</a></h3>
+<section id="the-mnist-dataset-again">
+<h3><span class="section-number">16.7.1. </span>The MNIST dataset again<a class="headerlink" href="#the-mnist-dataset-again" title="Permalink to this heading">#</a></h3>
 <p>The MNIST dataset consists of grayscale images with a pixel size of
 <span class="math notranslate nohighlight">\(28\times 28\)</span>, meaning we require <span class="math notranslate nohighlight">\(28 \times 28 = 724\)</span> weights to each
 neuron in the first hidden layer.</p>
@@ -1093,9 +1029,9 @@ further passed through a <strong>pooling layer</strong>, which reduces the size
 convolutional layer, e.g. by taking the maximum or average across some
 small regions, and this serves as input to the next convolutional
 layer.</p>
-</div>
-<div class="section" id="systematic-reduction">
-<h3><span class="section-number">16.7.2. </span>Systematic reduction<a class="headerlink" href="#systematic-reduction" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="systematic-reduction">
+<h3><span class="section-number">16.7.2. </span>Systematic reduction<a class="headerlink" href="#systematic-reduction" title="Permalink to this heading">#</a></h3>
 <p>By systematically reducing the size of the input volume, through
 convolution and pooling, the network should create representations of
 small parts of the input, and then from them assemble representations
@@ -1104,9 +1040,9 @@ input to a hidden layer, such that each neuron in the final pooling
 layer is connected to every single neuron in the hidden layer. This
 then serves as input to the output layer, e.g. a softmax output for
 classification.</p>
-</div>
-<div class="section" id="prerequisites-collect-and-pre-process-data">
-<h3><span class="section-number">16.7.3. </span>Prerequisites: Collect and pre-process data<a class="headerlink" href="#prerequisites-collect-and-pre-process-data" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="prerequisites-collect-and-pre-process-data">
+<h3><span class="section-number">16.7.3. </span>Prerequisites: Collect and pre-process data<a class="headerlink" href="#prerequisites-collect-and-pre-process-data" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># import necessary packages</span>
@@ -1152,13 +1088,6 @@ classification.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>inputs = (n_inputs, pixel_width, pixel_height, depth) = (1797, 8, 8, 1)
-labels = (n_inputs) = (1797,)
-</pre></div>
-</div>
-<img alt="_images/chapter12_67_1.png" src="_images/chapter12_67_1.png" />
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1187,217 +1116,6 @@ labels = (n_inputs) = (1797,)
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.
-  warnings.warn(&quot;JAX on Mac ARM machines is experimental and minimally tested. &quot;
-</pre></div>
-</div>
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">AttributeError</span><span class="g g-Whitespace">                            </span>Traceback (most recent call last)
-<span class="nn">Input In [4],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
-<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">tensorflow.keras</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">models</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.layers</span> <span class="kn">import</span> <span class="n">Input</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.models</span> <span class="kn">import</span> <span class="n">Sequential</span>      <span class="c1">#This allows appending layers to existing models</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">51</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">data</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
-<span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">30</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">data</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
-<span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">47</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">layers</span>
-<span class="g g-Whitespace">     </span><span class="mi">46</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">linalg</span>
-<span class="ne">---&gt; </span><span class="mi">47</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">logging</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lookup</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">9</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">constants</span>
-<span class="ne">----&gt; </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">experimental</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">Interpreter</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpHint</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">authoring</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.analyzer</span> <span class="kn">import</span> <span class="n">ModelAnalyzer</span> <span class="k">as</span> <span class="n">Analyzer</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpResolverType</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental.authoring namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.authoring.authoring</span> <span class="kn">import</span> <span class="n">compatible</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="n">authoring</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">43</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">import</span> <span class="nn">functools</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="ne">---&gt; </span><span class="mi">43</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">convert</span>
-<span class="g g-Whitespace">     </span><span class="mi">44</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.metrics</span> <span class="kn">import</span> <span class="n">converter_error_data_pb2</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">convert</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">29</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span> <span class="kn">import</span> <span class="nn">six</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite_constants</span>
-<span class="ne">---&gt; </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">util</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">wrap_toco</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.convert_phase</span> <span class="kn">import</span> <span class="n">Component</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">util</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">47</span> <span class="c1"># Jax functions used by TFLite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="c1"># pylint: disable=unused-import</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="k">try</span><span class="p">:</span>
-<span class="ne">---&gt; </span><span class="mi">51</span>   <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">_xla_computation</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span>   <span class="n">_xla_computation</span> <span class="o">=</span> <span class="kc">None</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">116</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="kn">from</span> <span class="nn">._src.config</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">41</span>   <span class="n">config</span> <span class="k">as</span> <span class="n">config</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span>   <span class="n">enable_checks</span> <span class="k">as</span> <span class="n">enable_checks</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">51</span>   <span class="n">numpy_rank_promotion</span> <span class="k">as</span> <span class="n">numpy_rank_promotion</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._src.api</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">54</span>   <span class="n">ad</span><span class="p">,</span>  <span class="c1"># TODO(phawkins): update users to avoid this.</span>
-<span class="g g-Whitespace">     </span><span class="mi">55</span>   <span class="n">checkpoint</span> <span class="k">as</span> <span class="n">checkpoint</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">114</span>   <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">xla_computation</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">115</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">116</span> <span class="kn">from</span> <span class="nn">.experimental.maps</span> <span class="kn">import</span> <span class="n">soft_pmap</span> <span class="k">as</span> <span class="n">soft_pmap</span>
-<span class="g g-Whitespace">    </span><span class="mi">117</span> <span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">__version__</span> <span class="k">as</span> <span class="n">__version__</span>
-<span class="g g-Whitespace">    </span><span class="mi">119</span> <span class="c1"># These submodules are separate because they are in an import cycle with</span>
-<span class="g g-Whitespace">    </span><span class="mi">120</span> <span class="c1"># jax and rely on the names imported above.</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">maps</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">26</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span> <span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">wraps</span><span class="p">,</span> <span class="n">partial</span><span class="p">,</span> <span class="n">partialmethod</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span> <span class="kn">from</span> <span class="nn">enum</span> <span class="kn">import</span> <span class="n">Enum</span>
-<span class="ne">---&gt; </span><span class="mi">26</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">numpy</span> <span class="k">as</span> <span class="n">jnp</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">core</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">linear_util</span> <span class="k">as</span> <span class="n">lu</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2018 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> 
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">linalg</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span> <span class="kn">from</span> <span class="nn">jax.interpreters.xla</span> <span class="kn">import</span> <span class="n">DeviceArray</span> <span class="k">as</span> <span class="n">DeviceArray</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">17</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2020 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">14</span> 
-<span class="g g-Whitespace">     </span><span class="mi">15</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">17</span> <span class="kn">from</span> <span class="nn">jax._src.numpy.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span>   <span class="n">ifft</span> <span class="k">as</span> <span class="n">ifft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>   <span class="n">ifft2</span> <span class="k">as</span> <span class="n">ifft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>   <span class="n">ifftn</span> <span class="k">as</span> <span class="n">ifftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span>   <span class="n">ifftshift</span> <span class="k">as</span> <span class="n">ifftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span>   <span class="n">ihfft</span> <span class="k">as</span> <span class="n">ihfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span>   <span class="n">irfft</span> <span class="k">as</span> <span class="n">irfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span>   <span class="n">irfft2</span> <span class="k">as</span> <span class="n">irfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">25</span>   <span class="n">irfftn</span> <span class="k">as</span> <span class="n">irfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span>   <span class="n">fft2</span> <span class="k">as</span> <span class="n">fft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span>   <span class="n">fftfreq</span> <span class="k">as</span> <span class="n">fftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span>   <span class="n">fftn</span> <span class="k">as</span> <span class="n">fftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span>   <span class="n">fftshift</span> <span class="k">as</span> <span class="n">fftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span>   <span class="n">hfft</span> <span class="k">as</span> <span class="n">hfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span>   <span class="n">rfft</span> <span class="k">as</span> <span class="n">rfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span>   <span class="n">rfft2</span> <span class="k">as</span> <span class="n">rfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">34</span>   <span class="n">rfftfreq</span> <span class="k">as</span> <span class="n">rfftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span>   <span class="n">rfftn</span> <span class="k">as</span> <span class="n">rfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">36</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="c1"># Module initialization is encapsulated in a function to avoid accidental</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="c1"># namespace pollution.</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="n">_NOT_IMPLEMENTED</span> <span class="o">=</span> <span class="p">[]</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">16</span> <span class="kn">import</span> <span class="nn">operator</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">lax</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">jax._src.lib</span> <span class="kn">import</span> <span class="n">xla_client</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span> <span class="kn">from</span> <span class="nn">jax._src.util</span> <span class="kn">import</span> <span class="n">safe_zip</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">332</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">299</span> <span class="kn">from</span> <span class="nn">jax._src.lax.lax</span> <span class="kn">import</span> <span class="p">(</span><span class="n">_reduce_sum</span><span class="p">,</span> <span class="n">_reduce_max</span><span class="p">,</span> <span class="n">_reduce_min</span><span class="p">,</span> <span class="n">_reduce_or</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">300</span>                   <span class="n">_reduce_and</span><span class="p">,</span> <span class="n">_reduce_window_sum</span><span class="p">,</span> <span class="n">_reduce_window_max</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">301</span>                   <span class="n">_reduce_window_min</span><span class="p">,</span> <span class="n">_reduce_window_prod</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">306</span>                   <span class="n">_upcast_fp16_for_computation</span><span class="p">,</span> <span class="n">_broadcasting_shape_rule</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">307</span>                   <span class="n">_eye</span><span class="p">,</span> <span class="n">_tri</span><span class="p">,</span> <span class="n">_delta</span><span class="p">,</span> <span class="n">_ones</span><span class="p">,</span> <span class="n">_zeros</span><span class="p">,</span> <span class="n">_dilate_shape</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">308</span> <span class="kn">from</span> <span class="nn">jax._src.lax.control_flow</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">309</span>   <span class="n">associative_scan</span> <span class="k">as</span> <span class="n">associative_scan</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">310</span>   <span class="n">cond</span> <span class="k">as</span> <span class="n">cond</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">330</span>   <span class="n">while_p</span> <span class="k">as</span> <span class="n">while_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">331</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">332</span> <span class="kn">from</span> <span class="nn">jax._src.lax.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">333</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">334</span>   <span class="n">fft_p</span> <span class="k">as</span> <span class="n">fft_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">335</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">336</span> <span class="kn">from</span> <span class="nn">jax._src.lax.parallel</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">337</span>   <span class="n">all_gather</span> <span class="k">as</span> <span class="n">all_gather</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">338</span>   <span class="n">all_to_all</span> <span class="k">as</span> <span class="n">all_to_all</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">355</span>   <span class="n">xeinsum</span> <span class="k">as</span> <span class="n">xeinsum</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">356</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">357</span> <span class="kn">from</span> <span class="nn">jax._src.lax.other</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">358</span>   <span class="n">conv_general_dilated_patches</span> <span class="k">as</span> <span class="n">conv_general_dilated_patches</span>
-<span class="g g-Whitespace">    </span><span class="mi">359</span> <span class="p">)</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">145</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">143</span> <span class="n">batching</span><span class="o">.</span><span class="n">primitive_batchers</span><span class="p">[</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">fft_batching_rule</span>
-<span class="g g-Whitespace">    </span><span class="mi">144</span> <span class="k">if</span> <span class="n">pocketfft</span><span class="p">:</span>
-<span class="ne">--&gt; </span><span class="mi">145</span>   <span class="n">xla</span><span class="o">.</span><span class="n">backend_specific_translations</span><span class="p">[</span><span class="s1">&#39;cpu&#39;</span><span class="p">][</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">pocketfft</span><span class="o">.</span><span class="n">pocketfft</span>
-
-<span class="ne">AttributeError</span>: module &#39;jaxlib.pocketfft&#39; has no attribute &#39;pocketfft&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1489,10 +1207,10 @@ labels = (n_inputs) = (1797,)
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="the-cifar01-data-set">
-<h2><span class="section-number">16.8. </span>The CIFAR01 data set<a class="headerlink" href="#the-cifar01-data-set" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="the-cifar01-data-set">
+<h2><span class="section-number">16.8. </span>The CIFAR01 data set<a class="headerlink" href="#the-cifar01-data-set" title="Permalink to this heading">#</a></h2>
 <p>The CIFAR10 dataset contains 60,000 color images in 10 classes, with
 6,000 images in each class. The dataset is divided into 50,000
 training images and 10,000 testing images. The classes are mutually
@@ -1601,8 +1319,8 @@ history = model.fit(train_images, train_labels, epochs=10,
 </div>
 </div>
 </div>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1616,7 +1334,7 @@ history = model.fit(train_images, train_labels, epochs=10,
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1624,44 +1342,117 @@ history = model.fit(train_images, train_labels, epochs=10,
     </script>
     <script>kernelName = 'python3'</script>
 
-              </div>
+                </article>
               
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-            <p class="prev-next-subtitle">previous</p>
-            <p class="prev-next-title"><span class="section-number">15. </span>Solving Differential Equations  with Deep Learning</p>
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-    
-      By Morten Hjorth-Jensen<br/>
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+            
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+                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
 
+  <div class="sidebar-secondary-item">
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+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#neural-networks-vs-cnns">16.1. Neural Networks vs CNNs</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#layers-used-to-build-cnns">16.2. Layers used to build CNNs</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-cnns">16.3. Mathematics of CNNs</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#convolution-examples-polynomial-multiplication">16.3.1. Convolution Examples: Polynomial multiplication</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms">16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#two-dimensional-objects">16.4. Two-dimensional Objects</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-dimensionalities">16.5. More on Dimensionalities</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-dimensionality-remarks">16.6. Further Dimensionality Remarks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras">16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-mnist-dataset-again">16.7.1. The MNIST dataset again</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#systematic-reduction">16.7.2. Systematic reduction</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites-collect-and-pre-process-data">16.7.3. Prerequisites: Collect and pre-process data</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cifar01-data-set">16.8. The CIFAR01 data set</a></li>
+</ul>
+  </nav></div>
 
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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html
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-<p aria-level="2" class="caption" role="heading">
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-  From Regression to Support Vector Machines
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Decision Trees, Ensemble Methods and Boosting
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Dimensionality Reduction
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Deep Learning Methods
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-   16. Convolutional Neural Networks
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">17. Recurrent neural networks: Overarching view</a></li>
+
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+    <h1>Recurrent neural networks: Overarching view</h1>
+    <!-- Table of contents -->
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-            <div class="tocsection onthispage pt-5 pb-3">
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-            <nav id="bd-toc-nav" aria-label="Page">
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                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h1 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#">
-   17. Recurrent neural networks: Overarching view
-  </a>
-  <ul class="visible nav section-nav flex-column">
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-simple-example">
-     17.1. A simple example
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#an-extrapolation-example">
-     17.2. An extrapolation example
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#predicting-new-points-with-a-trained-recurrent-neural-network">
-     17.3. Predicting New Points With A Trained Recurrent Neural Network
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#other-types-of-recurrent-neural-networks">
-     17.4. Other Types of Recurrent Neural Networks
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h1 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#generative-models">
-   18. Generative Models
-  </a>
-  <ul class="visible nav section-nav flex-column">
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#generative-adversarial-networks">
-     18.1. Generative Adversarial Networks
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#writing-our-first-generative-adversarial-network">
-     18.2. Writing Our First Generative Adversarial Network
-    </a>
-    <ul class="nav section-nav flex-column">
-     <li class="toc-h3 nav-item toc-entry">
-      <a class="reference internal nav-link" href="#mnist-and-gans">
-       18.2.1. MNIST and GANs
-      </a>
-     </li>
-    </ul>
-   </li>
-  </ul>
- </li>
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#">17. Recurrent neural networks: Overarching view</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-simple-example">17.1. A simple example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-extrapolation-example">17.2. An extrapolation example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#predicting-new-points-with-a-trained-recurrent-neural-network">17.3. Predicting New Points With A Trained Recurrent Neural Network</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-types-of-recurrent-neural-networks">17.4. Other Types of Recurrent Neural Networks</a></li>
+</ul>
+</li>
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#generative-models">18. Generative Models</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#generative-adversarial-networks">18.1. Generative Adversarial Networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-our-first-generative-adversarial-network">18.2. Writing Our First Generative Adversarial Network</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#mnist-and-gans">18.2.1. MNIST and GANs</a></li>
+</ul>
+</li>
+</ul>
+</li>
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-   17. Recurrent neural networks: Overarching view
-  </a>
-  <ul class="visible nav section-nav flex-column">
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-simple-example">
-     17.1. A simple example
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#an-extrapolation-example">
-     17.2. An extrapolation example
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#predicting-new-points-with-a-trained-recurrent-neural-network">
-     17.3. Predicting New Points With A Trained Recurrent Neural Network
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#other-types-of-recurrent-neural-networks">
-     17.4. Other Types of Recurrent Neural Networks
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h1 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#generative-models">
-   18. Generative Models
-  </a>
-  <ul class="visible nav section-nav flex-column">
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#generative-adversarial-networks">
-     18.1. Generative Adversarial Networks
-    </a>
-   </li>
-   <li class="toc-h2 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#writing-our-first-generative-adversarial-network">
-     18.2. Writing Our First Generative Adversarial Network
-    </a>
-    <ul class="nav section-nav flex-column">
-     <li class="toc-h3 nav-item toc-entry">
-      <a class="reference internal nav-link" href="#mnist-and-gans">
-       18.2.1. MNIST and GANs
-      </a>
-     </li>
-    </ul>
-   </li>
-  </ul>
- </li>
-</ul>
 
-                        </nav>
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+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter13.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="recurrent-neural-networks-overarching-view">
-<h1><span class="section-number">17. </span>Recurrent neural networks: Overarching view<a class="headerlink" href="#recurrent-neural-networks-overarching-view" title="Permalink to this headline">¶</a></h1>
+doconce format html chapter13.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="recurrent-neural-networks-overarching-view">
+<h1><span class="section-number">17. </span>Recurrent neural networks: Overarching view<a class="headerlink" href="#recurrent-neural-networks-overarching-view" title="Permalink to this heading">#</a></h1>
 <p>Till now our focus has been, including convolutional neural networks
 as well, on feedforward neural networks. The output or the activations
 flow only in one direction, from the input layer to the output layer.</p>
@@ -520,8 +446,8 @@ example, they can take sentences, documents, or audio samples as
 input, making them extremely useful for natural language processing
 systems such as automatic translation and speech-to-text.</p>
 <p>More to text to be added</p>
-<div class="section" id="a-simple-example">
-<h2><span class="section-number">17.1. </span>A simple example<a class="headerlink" href="#a-simple-example" title="Permalink to this headline">¶</a></h2>
+<section id="a-simple-example">
+<h2><span class="section-number">17.1. </span>A simple example<a class="headerlink" href="#a-simple-example" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
@@ -598,222 +524,60 @@ systems such as automatic translation and speech-to-text.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.
-  warnings.warn(&quot;JAX on Mac ARM machines is experimental and minimally tested. &quot;
-</pre></div>
-</div>
 <div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">AttributeError</span><span class="g g-Whitespace">                            </span>Traceback (most recent call last)
-<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 7&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
-<span class="ne">----&gt; </span><span class="mi">7</span> <span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">tensorflow.keras</span> <span class="kn">import</span> <span class="n">datasets</span><span class="p">,</span> <span class="n">layers</span><span class="p">,</span> <span class="n">models</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">tensorflow.keras.layers</span> <span class="kn">import</span> <span class="n">Input</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Start importing packages</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">51</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">data</span>
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
 <span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">30</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">data</span>
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
-<span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">47</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">layers</span>
-<span class="g g-Whitespace">     </span><span class="mi">46</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">linalg</span>
-<span class="ne">---&gt; </span><span class="mi">47</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">logging</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lookup</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">9</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">constants</span>
-<span class="ne">----&gt; </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">experimental</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">Interpreter</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpHint</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">authoring</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.analyzer</span> <span class="kn">import</span> <span class="n">ModelAnalyzer</span> <span class="k">as</span> <span class="n">Analyzer</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpResolverType</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental.authoring namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.authoring.authoring</span> <span class="kn">import</span> <span class="n">compatible</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="n">authoring</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">43</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">import</span> <span class="nn">functools</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="ne">---&gt; </span><span class="mi">43</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">convert</span>
-<span class="g g-Whitespace">     </span><span class="mi">44</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.metrics</span> <span class="kn">import</span> <span class="n">converter_error_data_pb2</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">convert</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">29</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span> <span class="kn">import</span> <span class="nn">six</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite_constants</span>
-<span class="ne">---&gt; </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">util</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">wrap_toco</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.convert_phase</span> <span class="kn">import</span> <span class="n">Component</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">util</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">47</span> <span class="c1"># Jax functions used by TFLite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="c1"># pylint: disable=unused-import</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="k">try</span><span class="p">:</span>
-<span class="ne">---&gt; </span><span class="mi">51</span>   <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">_xla_computation</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span>   <span class="n">_xla_computation</span> <span class="o">=</span> <span class="kc">None</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">116</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="kn">from</span> <span class="nn">._src.config</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">41</span>   <span class="n">config</span> <span class="k">as</span> <span class="n">config</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span>   <span class="n">enable_checks</span> <span class="k">as</span> <span class="n">enable_checks</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">51</span>   <span class="n">numpy_rank_promotion</span> <span class="k">as</span> <span class="n">numpy_rank_promotion</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._src.api</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">54</span>   <span class="n">ad</span><span class="p">,</span>  <span class="c1"># TODO(phawkins): update users to avoid this.</span>
-<span class="g g-Whitespace">     </span><span class="mi">55</span>   <span class="n">checkpoint</span> <span class="k">as</span> <span class="n">checkpoint</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">114</span>   <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">xla_computation</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">115</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">116</span> <span class="kn">from</span> <span class="nn">.experimental.maps</span> <span class="kn">import</span> <span class="n">soft_pmap</span> <span class="k">as</span> <span class="n">soft_pmap</span>
-<span class="g g-Whitespace">    </span><span class="mi">117</span> <span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">__version__</span> <span class="k">as</span> <span class="n">__version__</span>
-<span class="g g-Whitespace">    </span><span class="mi">119</span> <span class="c1"># These submodules are separate because they are in an import cycle with</span>
-<span class="g g-Whitespace">    </span><span class="mi">120</span> <span class="c1"># jax and rely on the names imported above.</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">maps</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">26</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span> <span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">wraps</span><span class="p">,</span> <span class="n">partial</span><span class="p">,</span> <span class="n">partialmethod</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span> <span class="kn">from</span> <span class="nn">enum</span> <span class="kn">import</span> <span class="n">Enum</span>
-<span class="ne">---&gt; </span><span class="mi">26</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">numpy</span> <span class="k">as</span> <span class="n">jnp</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">core</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">linear_util</span> <span class="k">as</span> <span class="n">lu</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2018 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> 
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">linalg</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span> <span class="kn">from</span> <span class="nn">jax.interpreters.xla</span> <span class="kn">import</span> <span class="n">DeviceArray</span> <span class="k">as</span> <span class="n">DeviceArray</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">17</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2020 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">14</span> 
-<span class="g g-Whitespace">     </span><span class="mi">15</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">17</span> <span class="kn">from</span> <span class="nn">jax._src.numpy.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span>   <span class="n">ifft</span> <span class="k">as</span> <span class="n">ifft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>   <span class="n">ifft2</span> <span class="k">as</span> <span class="n">ifft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>   <span class="n">ifftn</span> <span class="k">as</span> <span class="n">ifftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span>   <span class="n">ifftshift</span> <span class="k">as</span> <span class="n">ifftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span>   <span class="n">ihfft</span> <span class="k">as</span> <span class="n">ihfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span>   <span class="n">irfft</span> <span class="k">as</span> <span class="n">irfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span>   <span class="n">irfft2</span> <span class="k">as</span> <span class="n">irfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">25</span>   <span class="n">irfftn</span> <span class="k">as</span> <span class="n">irfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span>   <span class="n">fft2</span> <span class="k">as</span> <span class="n">fft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span>   <span class="n">fftfreq</span> <span class="k">as</span> <span class="n">fftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span>   <span class="n">fftn</span> <span class="k">as</span> <span class="n">fftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span>   <span class="n">fftshift</span> <span class="k">as</span> <span class="n">fftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span>   <span class="n">hfft</span> <span class="k">as</span> <span class="n">hfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span>   <span class="n">rfft</span> <span class="k">as</span> <span class="n">rfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span>   <span class="n">rfft2</span> <span class="k">as</span> <span class="n">rfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">34</span>   <span class="n">rfftfreq</span> <span class="k">as</span> <span class="n">rfftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span>   <span class="n">rfftn</span> <span class="k">as</span> <span class="n">rfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">36</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="c1"># Module initialization is encapsulated in a function to avoid accidental</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="c1"># namespace pollution.</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="n">_NOT_IMPLEMENTED</span> <span class="o">=</span> <span class="p">[]</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">16</span> <span class="kn">import</span> <span class="nn">operator</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">lax</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">jax._src.lib</span> <span class="kn">import</span> <span class="n">xla_client</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span> <span class="kn">from</span> <span class="nn">jax._src.util</span> <span class="kn">import</span> <span class="n">safe_zip</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">332</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">299</span> <span class="kn">from</span> <span class="nn">jax._src.lax.lax</span> <span class="kn">import</span> <span class="p">(</span><span class="n">_reduce_sum</span><span class="p">,</span> <span class="n">_reduce_max</span><span class="p">,</span> <span class="n">_reduce_min</span><span class="p">,</span> <span class="n">_reduce_or</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">300</span>                   <span class="n">_reduce_and</span><span class="p">,</span> <span class="n">_reduce_window_sum</span><span class="p">,</span> <span class="n">_reduce_window_max</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">301</span>                   <span class="n">_reduce_window_min</span><span class="p">,</span> <span class="n">_reduce_window_prod</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">306</span>                   <span class="n">_upcast_fp16_for_computation</span><span class="p">,</span> <span class="n">_broadcasting_shape_rule</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">307</span>                   <span class="n">_eye</span><span class="p">,</span> <span class="n">_tri</span><span class="p">,</span> <span class="n">_delta</span><span class="p">,</span> <span class="n">_ones</span><span class="p">,</span> <span class="n">_zeros</span><span class="p">,</span> <span class="n">_dilate_shape</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">308</span> <span class="kn">from</span> <span class="nn">jax._src.lax.control_flow</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">309</span>   <span class="n">associative_scan</span> <span class="k">as</span> <span class="n">associative_scan</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">310</span>   <span class="n">cond</span> <span class="k">as</span> <span class="n">cond</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">330</span>   <span class="n">while_p</span> <span class="k">as</span> <span class="n">while_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">331</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">332</span> <span class="kn">from</span> <span class="nn">jax._src.lax.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">333</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">334</span>   <span class="n">fft_p</span> <span class="k">as</span> <span class="n">fft_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">335</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">336</span> <span class="kn">from</span> <span class="nn">jax._src.lax.parallel</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">337</span>   <span class="n">all_gather</span> <span class="k">as</span> <span class="n">all_gather</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">338</span>   <span class="n">all_to_all</span> <span class="k">as</span> <span class="n">all_to_all</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">355</span>   <span class="n">xeinsum</span> <span class="k">as</span> <span class="n">xeinsum</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">356</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">357</span> <span class="kn">from</span> <span class="nn">jax._src.lax.other</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">358</span>   <span class="n">conv_general_dilated_patches</span> <span class="k">as</span> <span class="n">conv_general_dilated_patches</span>
-<span class="g g-Whitespace">    </span><span class="mi">359</span> <span class="p">)</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">145</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">143</span> <span class="n">batching</span><span class="o">.</span><span class="n">primitive_batchers</span><span class="p">[</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">fft_batching_rule</span>
-<span class="g g-Whitespace">    </span><span class="mi">144</span> <span class="k">if</span> <span class="n">pocketfft</span><span class="p">:</span>
-<span class="ne">--&gt; </span><span class="mi">145</span>   <span class="n">xla</span><span class="o">.</span><span class="n">backend_specific_translations</span><span class="p">[</span><span class="s1">&#39;cpu&#39;</span><span class="p">][</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">pocketfft</span><span class="o">.</span><span class="n">pocketfft</span>
-
-<span class="ne">AttributeError</span>: module &#39;jaxlib.pocketfft&#39; has no attribute &#39;pocketfft&#39;
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="an-extrapolation-example">
-<h2><span class="section-number">17.2. </span>An extrapolation example<a class="headerlink" href="#an-extrapolation-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="an-extrapolation-example">
+<h2><span class="section-number">17.2. </span>An extrapolation example<a class="headerlink" href="#an-extrapolation-example" title="Permalink to this heading">#</a></h2>
 <p>The following code provides an example of how recurrent neural
 networks can be used to extrapolate to unknown values of physics data
 sets.  Specifically, the data sets used in this program come from
@@ -879,7 +643,7 @@ y values far removed from the training data set.</p>
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># FORMAT_DATA</span>
 <span class="k">def</span> <span class="nf">format_data</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">length_of_sequence</span> <span class="o">=</span> <span class="mi">2</span><span class="p">):</span>  
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            data(a numpy array): the data that will be the inputs to the recurrent neural</span>
 <span class="sd">                network</span>
@@ -914,7 +678,7 @@ y values far removed from the training data set.</p>
 <span class="c1"># The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.</span>
 
 <span class="k">def</span> <span class="nf">rnn</span><span class="p">(</span><span class="n">length_of_sequences</span><span class="p">,</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">stateful</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            length_of_sequences (an int): the number of y values in &quot;x data&quot;.  This is determined</span>
 <span class="sd">                when the data is formatted</span>
@@ -953,13 +717,13 @@ y values far removed from the training data set.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="predicting-new-points-with-a-trained-recurrent-neural-network">
-<h2><span class="section-number">17.3. </span>Predicting New Points With A Trained Recurrent Neural Network<a class="headerlink" href="#predicting-new-points-with-a-trained-recurrent-neural-network" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="predicting-new-points-with-a-trained-recurrent-neural-network">
+<h2><span class="section-number">17.3. </span>Predicting New Points With A Trained Recurrent Neural Network<a class="headerlink" href="#predicting-new-points-with-a-trained-recurrent-neural-network" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">test_rnn</span> <span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">y_test</span><span class="p">,</span> <span class="n">plot_min</span><span class="p">,</span> <span class="n">plot_max</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            x1 (a list or numpy array): The complete x component of the data set</span>
 <span class="sd">            y_test (a list or numpy array): The complete y component of the data set</span>
@@ -1066,7 +830,7 @@ network.  For some ideas on how to improve the performance of a
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">rnn_2layers</span><span class="p">(</span><span class="n">length_of_sequences</span><span class="p">,</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">stateful</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            length_of_sequences (an int): the number of y values in &quot;x data&quot;.  This is determined</span>
 <span class="sd">                when the data is formatted</span>
@@ -1155,9 +919,9 @@ network.  For some ideas on how to improve the performance of a
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="other-types-of-recurrent-neural-networks">
-<h2><span class="section-number">17.4. </span>Other Types of Recurrent Neural Networks<a class="headerlink" href="#other-types-of-recurrent-neural-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-types-of-recurrent-neural-networks">
+<h2><span class="section-number">17.4. </span>Other Types of Recurrent Neural Networks<a class="headerlink" href="#other-types-of-recurrent-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>Besides a simple recurrent neural network layer, there are two other
 commonly used types of recurrent neural network layers: Long Short
 Term Memory (LSTM) and Gated Recurrent Unit (GRU).  For a short
@@ -1174,7 +938,7 @@ of recurrent neural networks (see the link above and also
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">lstm_2layers</span><span class="p">(</span><span class="n">length_of_sequences</span><span class="p">,</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">stateful</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            length_of_sequences (an int): the number of y values in &quot;x data&quot;.  This is determined</span>
 <span class="sd">                when the data is formatted</span>
@@ -1211,7 +975,7 @@ of recurrent neural networks (see the link above and also
     <span class="k">return</span> <span class="n">model</span>
 
 <span class="k">def</span> <span class="nf">dnn2_gru2</span><span class="p">(</span><span class="n">length_of_sequences</span><span class="p">,</span> <span class="n">batch_size</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="n">stateful</span> <span class="o">=</span> <span class="kc">False</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">        Inputs:</span>
 <span class="sd">            length_of_sequences (an int): the number of y values in &quot;x data&quot;.  This is determined</span>
 <span class="sd">                when the data is formatted</span>
@@ -1367,10 +1131,10 @@ of recurrent neural networks (see the link above and also
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="tex2jax_ignore mathjax_ignore section" id="generative-models">
-<h1><span class="section-number">18. </span>Generative Models<a class="headerlink" href="#generative-models" title="Permalink to this headline">¶</a></h1>
+</section>
+</section>
+<section class="tex2jax_ignore mathjax_ignore" id="generative-models">
+<h1><span class="section-number">18. </span>Generative Models<a class="headerlink" href="#generative-models" title="Permalink to this heading">#</a></h1>
 <p><strong>Generative models</strong> describe a class of statistical models that are a contrast
 to <strong>discriminative models</strong>. Informally we say that generative models can
 generate new data instances while discriminative models discriminate between
@@ -1383,8 +1147,8 @@ conditional probability <span class="math notranslate nohighlight">\(p(y | x)\)<
 boundaries in the data space (often high dimensional), while generative models
 try to model how data is placed throughout the space.</p>
 <p><strong>Note</strong>: this material is thanks to Linus Ekstrøm.</p>
-<div class="section" id="generative-adversarial-networks">
-<h2><span class="section-number">18.1. </span>Generative Adversarial Networks<a class="headerlink" href="#generative-adversarial-networks" title="Permalink to this headline">¶</a></h2>
+<section id="generative-adversarial-networks">
+<h2><span class="section-number">18.1. </span>Generative Adversarial Networks<a class="headerlink" href="#generative-adversarial-networks" title="Permalink to this heading">#</a></h2>
 <p><strong>Generative Adversarial Networks</strong> are a type of unsupervised machine learning
 algorithm proposed by <a class="reference external" href="https://arxiv.org/pdf/1406.2661.pdf">Goodfellow et. al</a>
 in 2014 (short and good article).</p>
@@ -1505,9 +1269,9 @@ Direct quote: “In this best-performing formulation, the generator aims to
 increase the log probability that the discriminator makes a mistake, rather than
 aiming to decrease the log probability that the discriminator makes the correct
 prediction.” <a class="reference external" href="https://arxiv.org/abs/1701.00160">Another interesting read</a></p>
-</div>
-<div class="section" id="writing-our-first-generative-adversarial-network">
-<h2><span class="section-number">18.2. </span>Writing Our First Generative Adversarial Network<a class="headerlink" href="#writing-our-first-generative-adversarial-network" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="writing-our-first-generative-adversarial-network">
+<h2><span class="section-number">18.2. </span>Writing Our First Generative Adversarial Network<a class="headerlink" href="#writing-our-first-generative-adversarial-network" title="Permalink to this heading">#</a></h2>
 <p>Let us now move on to actually implementing a GAN in tensorflow. We will study
 the performance of our GAN on the MNIST dataset. This code is based on and
 adapted from the
@@ -1548,8 +1312,8 @@ adapted from the
 </div>
 </div>
 </div>
-<div class="section" id="mnist-and-gans">
-<h3><span class="section-number">18.2.1. </span>MNIST and GANs<a class="headerlink" href="#mnist-and-gans" title="Permalink to this headline">¶</a></h3>
+<section id="mnist-and-gans">
+<h3><span class="section-number">18.2.1. </span>MNIST and GANs<a class="headerlink" href="#mnist-and-gans" title="Permalink to this heading">#</a></h3>
 <p>Let’s have a quick look</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1570,7 +1334,7 @@ our case we are trying to predict MNIST images (<span class="math notranslate no
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">generator_model</span><span class="p">():</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to</span>
 <span class="sd">    produce an image from a random seed. We start with a Dense layer taking this</span>
 <span class="sd">    random sample as an input and subsequently upsample through multiple</span>
@@ -1636,7 +1400,7 @@ classifier.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">discriminator_model</span><span class="p">():</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    The discriminator is a convolutional neural network based image classifier</span>
 <span class="sd">    &quot;&quot;&quot;</span>
 
@@ -1825,7 +1589,7 @@ training.</p>
         <span class="k">if</span> <span class="p">(</span><span class="n">epoch</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="mi">15</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
             <span class="n">checkpoint</span><span class="o">.</span><span class="n">save</span><span class="p">(</span><span class="n">file_prefix</span><span class="o">=</span><span class="n">checkpoint_prefix</span><span class="p">)</span>
 
-        <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Time for epoch </span><span class="si">{</span><span class="n">epoch</span><span class="si">}</span><span class="s1"> is </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
+        <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Time for epoch </span><span class="si">{</span><span class="n">epoch</span><span class="si">}</span><span class="s1"> is </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
 
     <span class="c1">#generate_and_save_images(generator, epochs, seed_images)</span>
 
@@ -1999,9 +1763,9 @@ latent space.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2015,7 +1779,7 @@ latent space.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -2023,44 +1787,116 @@ latent space.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
-              </div>
+                </article>
               
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+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#">17. Recurrent neural networks: Overarching view</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-simple-example">17.1. A simple example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-extrapolation-example">17.2. An extrapolation example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#predicting-new-points-with-a-trained-recurrent-neural-network">17.3. Predicting New Points With A Trained Recurrent Neural Network</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-types-of-recurrent-neural-networks">17.4. Other Types of Recurrent Neural Networks</a></li>
+</ul>
+</li>
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#generative-models">18. Generative Models</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#generative-adversarial-networks">18.1. Generative Adversarial Networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-our-first-generative-adversarial-network">18.2. Writing Our First Generative Adversarial Network</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#mnist-and-gans">18.2.1. MNIST and GANs</a></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
 
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
 <ul class="nav bd-sidenav">
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
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+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="nav bd-sidenav">
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+    <h1>Ridge and Lasso Regression</h1>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">
-   4.1. Mathematical Interpretation of Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-singular-value-decomposition">
-   4.2. The singular value decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basic-math-of-the-svd">
-   4.3. Basic math of the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#codes-for-the-svd">
-   4.4. Codes for the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">
-   4.5. Code for SVD and Inversion of Matrices
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">
-   4.6. Mathematics of the SVD and implications
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">
-   4.7. Further properties (important for our analyses later)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-covariance-matrix">
-   4.8. Meet the Covariance Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-with-the-svd">
-   4.9. Linking with the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   4.10. Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   4.11. Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   4.12. Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   4.13. Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-bayes-theorem-with-ridge-and-lasso-regression">
-   4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">4.1. Mathematical Interpretation of Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-singular-value-decomposition">4.2. The singular value decomposition</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-math-of-the-svd">4.3. Basic math of the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#codes-for-the-svd">4.4. Codes for the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">4.5. Code for SVD and Inversion of Matrices</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">4.6. Mathematics of the SVD and implications</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">4.7. Further properties (important for our analyses later)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance-matrix">4.8. Meet the Covariance Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-with-the-svd">4.9. Linking with the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">4.10. Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">4.11. Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">4.12. Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">4.13. Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-bayes-theorem-with-ridge-and-lasso-regression">4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression</a></li>
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-                <h1>Ridge and Lasso Regression</h1>
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-                            <h2> Contents </h2>
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-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">
-   4.1. Mathematical Interpretation of Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-singular-value-decomposition">
-   4.2. The singular value decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basic-math-of-the-svd">
-   4.3. Basic math of the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#codes-for-the-svd">
-   4.4. Codes for the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">
-   4.5. Code for SVD and Inversion of Matrices
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">
-   4.6. Mathematics of the SVD and implications
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">
-   4.7. Further properties (important for our analyses later)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-covariance-matrix">
-   4.8. Meet the Covariance Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-with-the-svd">
-   4.9. Linking with the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   4.10. Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   4.11. Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   4.12. Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   4.13. Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-bayes-theorem-with-ridge-and-lasso-regression">
-   4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression
-  </a>
- </li>
-</ul>
 
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+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter2.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="ridge-and-lasso-regression">
-<h1><span class="section-number">4. </span>Ridge and Lasso Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="mathematical-interpretation-of-ordinary-least-squares">
-<h2><span class="section-number">4.1. </span>Mathematical Interpretation of Ordinary Least Squares<a class="headerlink" href="#mathematical-interpretation-of-ordinary-least-squares" title="Permalink to this headline">¶</a></h2>
+doconce format html chapter2.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="ridge-and-lasso-regression">
+<h1><span class="section-number">4. </span>Ridge and Lasso Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this heading">#</a></h1>
+<section id="mathematical-interpretation-of-ordinary-least-squares">
+<h2><span class="section-number">4.1. </span>Mathematical Interpretation of Ordinary Least Squares<a class="headerlink" href="#mathematical-interpretation-of-ordinary-least-squares" title="Permalink to this heading">#</a></h2>
 <p>What is presented here is a mathematical analysis of various regression algorithms (ordinary least  squares, Ridge and Lasso Regression). The analysis is based on an important algorithm in linear algebra, the so-called Singular Value Decomposition (SVD).</p>
 <p>We have shown that in ordinary least squares (OLS) the optimal parameters <span class="math notranslate nohighlight">\(\beta\)</span> are given by</p>
 <div class="math notranslate nohighlight">
@@ -591,9 +477,9 @@ We can then interpret our optimal model <span class="math notranslate nohighligh
 \boldsymbol{\epsilon}=\boldsymbol{y}-\tilde{\boldsymbol{y}}=0.
 \]</div>
 <p>This serves also as a useful test of our codes.</p>
-</div>
-<div class="section" id="the-singular-value-decomposition">
-<h2><span class="section-number">4.2. </span>The singular value decomposition<a class="headerlink" href="#the-singular-value-decomposition" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-singular-value-decomposition">
+<h2><span class="section-number">4.2. </span>The singular value decomposition<a class="headerlink" href="#the-singular-value-decomposition" title="Permalink to this heading">#</a></h2>
 <p>The examples we have looked at so far are cases where we normally can
 invert the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>. Using a polynomial expansion where we fit of various functions leads to
 row vectors of the design matrix which are essentially orthogonal due
@@ -681,9 +567,9 @@ the regression parameters <span class="math notranslate nohighlight">\(\beta_i\)
 \boldsymbol{X}^{T} \boldsymbol{X} \rightarrow \boldsymbol{X}^{T} \boldsymbol{X}+\lambda \boldsymbol{I},
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> is the identity matrix.  When we discuss <strong>Ridge</strong> regression this is actually what we end up evaluating. The parameter <span class="math notranslate nohighlight">\(\lambda\)</span> is called a hyperparameter. More about this later.</p>
-</div>
-<div class="section" id="basic-math-of-the-svd">
-<h2><span class="section-number">4.3. </span>Basic math of the SVD<a class="headerlink" href="#basic-math-of-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="basic-math-of-the-svd">
+<h2><span class="section-number">4.3. </span>Basic math of the SVD<a class="headerlink" href="#basic-math-of-the-svd" title="Permalink to this heading">#</a></h2>
 <p>From standard linear algebra we know that a square matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> can be diagonalized if and only if it is
 a so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Normal_matrix">normal matrix</a>, that is if <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times n}\)</span>
 we have <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}\)</span> or if <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{C}}^{n\times n}\)</span> we have <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^{\dagger}=\boldsymbol{X}^{\dagger}\boldsymbol{X}\)</span>.
@@ -762,15 +648,15 @@ the decomposition.</p>
 If <span class="math notranslate nohighlight">\(p &gt; n\)</span>, then only the first <span class="math notranslate nohighlight">\(n\)</span> columns of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span> are computed and <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> has dimension <span class="math notranslate nohighlight">\(n\times n\)</span>.
 The <span class="math notranslate nohighlight">\(n=p\)</span> case is obvious, we retain the full SVD.
 In general the economy-size SVD leads to less FLOPS and still conserving the desired accuracy.</p>
-</div>
-<div class="section" id="codes-for-the-svd">
-<h2><span class="section-number">4.4. </span>Codes for the SVD<a class="headerlink" href="#codes-for-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="codes-for-the-svd">
+<h2><span class="section-number">4.4. </span>Codes for the SVD<a class="headerlink" href="#codes-for-the-svd" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="c1"># SVD inversion</span>
 <span class="k">def</span> <span class="nf">SVD</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
+<span class="w">    </span><span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
 <span class="sd">    SVD is numerically more stable than the inversion algorithms provided by</span>
 <span class="sd">    numpy and scipy.linalg at the cost of being slower.</span>
 <span class="sd">    &#39;&#39;&#39;</span>
@@ -837,9 +723,9 @@ matrix.</p>
 <p>If you wish to include the zero singular values, you will need to
 resize the matrices and set up a diagonal matrix as done in the above
 example</p>
-</div>
-<div class="section" id="code-for-svd-and-inversion-of-matrices">
-<h2><span class="section-number">4.5. </span>Code for SVD and Inversion of Matrices<a class="headerlink" href="#code-for-svd-and-inversion-of-matrices" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="code-for-svd-and-inversion-of-matrices">
+<h2><span class="section-number">4.5. </span>Code for SVD and Inversion of Matrices<a class="headerlink" href="#code-for-svd-and-inversion-of-matrices" title="Permalink to this heading">#</a></h2>
 <p>How do we use the SVD to invert a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> which is singular or near singular?
 The simple answer is to use the linear algebra function for the pseudoinverse, that is</p>
 <div class="cell docutils container">
@@ -855,7 +741,7 @@ The simple answer is to use the linear algebra function for the pseudoinverse, t
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="c1"># SVD inversion</span>
 <span class="k">def</span> <span class="nf">SVDinv</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
+<span class="w">    </span><span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
 <span class="sd">    SVD is numerically more stable than the inversion algorithms provided by</span>
 <span class="sd">    numpy and scipy.linalg at the cost of being slower.</span>
 <span class="sd">    &#39;&#39;&#39;</span>
@@ -888,13 +774,13 @@ The simple answer is to use the linear algebra function for the pseudoinverse, t
  [2 4 5]
  [3 5 6]]
 test U
-[[-2.22044605e-16 -7.49932427e-16 -8.23408962e-16]
- [-7.49932427e-16  0.00000000e+00  4.77954956e-17]
- [-8.23408962e-16  4.77954956e-17  2.22044605e-16]]
+[[ 4.44089210e-16 -4.69484813e-16 -6.67314874e-16]
+ [-4.69484813e-16 -4.44089210e-16 -1.54041041e-16]
+ [-6.67314874e-16 -1.54041041e-16  1.11022302e-16]]
 test VT
-[[ 3.33066907e-16 -7.32066545e-17  3.32714903e-16]
- [-7.32066545e-17  0.00000000e+00 -1.82997013e-16]
- [ 3.32714903e-16 -1.82997013e-16 -3.33066907e-16]]
+[[ 2.22044605e-16  3.78156479e-17  1.85278920e-16]
+ [ 3.78156479e-17  0.00000000e+00 -6.33166055e-17]
+ [ 1.85278920e-16 -6.33166055e-17 -1.11022302e-16]]
 [[0. 0. 0.]
  [0. 0. 0.]
  [0. 0. 0.]]
@@ -955,9 +841,9 @@ It is used for the calculation of the inverse for singular or near singular matr
 </div>
 </div>
 <p>As you can see from these examples, our own decomposition based on the SVD agrees the pseudoinverse algorithm provided by <strong>Numpy</strong>.</p>
-</div>
-<div class="section" id="mathematics-of-the-svd-and-implications">
-<h2><span class="section-number">4.6. </span>Mathematics of the SVD and implications<a class="headerlink" href="#mathematics-of-the-svd-and-implications" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="mathematics-of-the-svd-and-implications">
+<h2><span class="section-number">4.6. </span>Mathematics of the SVD and implications<a class="headerlink" href="#mathematics-of-the-svd-and-implications" title="Permalink to this heading">#</a></h2>
 <p>Let us take a closer look at the mathematics of the SVD and the various implications for machine learning studies.</p>
 <p>Our starting point is our design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> of dimension <span class="math notranslate nohighlight">\(n\times p\)</span></p>
 <div class="math notranslate nohighlight">
@@ -1061,9 +947,9 @@ decomposition of the design matrix.</p>
 \tilde{y}_{\mathrm{OLS}}=\boldsymbol{U}\boldsymbol{U}^T\boldsymbol{y}=\sum_{i=0}^{p-1}\boldsymbol{u}_i\boldsymbol{u}^T_i\boldsymbol{y},
 \]</div>
 <p>It means that the ordinary least square model (with the optimal parameters) <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\)</span>, corresponds to an orthogonal transformation of the output (or target) vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> by the vectors of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span>.</p>
-</div>
-<div class="section" id="further-properties-important-for-our-analyses-later">
-<h2><span class="section-number">4.7. </span>Further properties (important for our analyses later)<a class="headerlink" href="#further-properties-important-for-our-analyses-later" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="further-properties-important-for-our-analyses-later">
+<h2><span class="section-number">4.7. </span>Further properties (important for our analyses later)<a class="headerlink" href="#further-properties-important-for-our-analyses-later" title="Permalink to this heading">#</a></h2>
 <p>Let us study again <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> in terms of our SVD,</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1104,9 +990,9 @@ always refer to the number of features in our data set, while the
 number of rows represents the number of data inputs. Note that in
 other texts you may find the opposite notation. This has consequences
 for the definition of for example the covariance matrix and its relation to the SVD.</p>
-</div>
-<div class="section" id="meet-the-covariance-matrix">
-<h2><span class="section-number">4.8. </span>Meet the Covariance Matrix<a class="headerlink" href="#meet-the-covariance-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="meet-the-covariance-matrix">
+<h2><span class="section-number">4.8. </span>Meet the Covariance Matrix<a class="headerlink" href="#meet-the-covariance-matrix" title="Permalink to this heading">#</a></h2>
 <p>Before we move on to a discussion of Ridge and Lasso regression, we want to show an important example of the above.</p>
 <p>We have already noted that the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> in ordinary
 least squares is proportional to the second derivative of the cost
@@ -1265,10 +1151,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.003788445263115483
-3.859628021353642
-[[0.93725291 2.8143782 ]
- [2.8143782  9.64008343]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.015836015068980684
+4.146630977737321
+[[0.88786042 2.4773343 ]
+ [2.4773343  7.74767365]]
 </pre></div>
 </div>
 </div>
@@ -1305,10 +1191,10 @@ a more brute force way. Here we scale the mean values for each column of the des
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07783152589039466
-2.06282378894371
-[[1.         0.66124684]
- [0.66124684 1.        ]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07636331150360104
+1.4231233000637726
+[[1.         0.68477696]
+ [0.68477696 1.        ]]
 </pre></div>
 </div>
 </div>
@@ -1338,30 +1224,15 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.15499979 -0.6924788 ]
- [-0.50456256 -2.98248681]
- [ 1.97264311  4.4533029 ]
- [ 0.03286166 -0.27108228]
- [-0.97421755 -3.08891672]
- [-0.3744637   0.62223681]
- [ 1.18655084  4.67392051]
- [-0.51719273 -1.14648903]
- [-0.51793145 -1.51975002]
- [-0.14868784 -0.04825655]]
-          0         1
-0 -0.155000 -0.692479
-1 -0.504563 -2.982487
-2  1.972643  4.453303
-3  0.032862 -0.271082
-4 -0.974218 -3.088917
-5 -0.374464  0.622237
-6  1.186551  4.673921
-7 -0.517193 -1.146489
-8 -0.517931 -1.519750
-9 -0.148688 -0.048257
-          0         1
-0  1.000000  0.929612
-1  0.929612  1.000000
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">7</span><span class="p">],</span> <span class="n">line</span> <span class="mi">2</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="ne">----&gt; </span><span class="mi">2</span> <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="n">n</span> <span class="o">=</span> <span class="mi">10</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;pandas&#39;
 </pre></div>
 </div>
 </div>
@@ -1415,43 +1286,6 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>     0         1         2         3         4         5         6         7   \
-0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.079729  0.074983  0.077280  0.078995  0.080168  0.068546  0.070577   
-2   0.0  0.074983  0.071314  0.073127  0.075035  0.076519  0.065106  0.067183   
-3   0.0  0.077280  0.073127  0.080979  0.082487  0.083517  0.075422  0.077387   
-4   0.0  0.078995  0.075035  0.082487  0.084199  0.085447  0.076612  0.078725   
-5   0.0  0.080168  0.076519  0.083517  0.085447  0.086942  0.077411  0.079671   
-6   0.0  0.068546  0.065106  0.075422  0.076612  0.077411  0.072522  0.074203   
-7   0.0  0.070577  0.067183  0.077387  0.078725  0.079671  0.074203  0.076007   
-8   0.0  0.072638  0.069315  0.079368  0.080867  0.081977  0.075887  0.077825   
-9   0.0  0.074671  0.071455  0.081315  0.082991  0.084282  0.077536  0.079615   
-10  0.0  0.060425  0.057463  0.068676  0.069583  0.070161  0.067515  0.068912   
-11  0.0  0.062197  0.059245  0.070486  0.071501  0.072183  0.069129  0.070625   
-12  0.0  0.064048  0.061113  0.072365  0.073497  0.074293  0.070797  0.072398   
-13  0.0  0.065974  0.063066  0.074310  0.075569  0.076491  0.072515  0.074230   
-14  0.0  0.067967  0.065101  0.076313  0.077711  0.078771  0.074276  0.076112   
-
-          8         9         10        11        12        13        14  
-0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.072638  0.074671  0.060425  0.062197  0.064048  0.065974  0.067967  
-2   0.069315  0.071455  0.057463  0.059245  0.061113  0.063066  0.065101  
-3   0.079368  0.081315  0.068676  0.070486  0.072365  0.074310  0.076313  
-4   0.080867  0.082991  0.069583  0.071501  0.073497  0.075569  0.077711  
-5   0.081977  0.084282  0.070161  0.072183  0.074293  0.076491  0.078771  
-6   0.075887  0.077536  0.067515  0.069129  0.070797  0.072515  0.074276  
-7   0.077825  0.079615  0.068912  0.070625  0.072398  0.074230  0.076112  
-8   0.079786  0.081728  0.070305  0.072122  0.074007  0.075958  0.077970  
-9   0.081728  0.083834  0.071659  0.073585  0.075587  0.077666  0.079814  
-10  0.070305  0.071659  0.063876  0.065268  0.066700  0.068170  0.069669  
-11  0.072122  0.073585  0.065268  0.066742  0.068261  0.069823  0.071420  
-12  0.074007  0.075587  0.066700  0.068261  0.069873  0.071534  0.073236  
-13  0.075958  0.077666  0.068170  0.069823  0.071534  0.073300  0.075115  
-14  0.077970  0.079814  0.069669  0.071420  0.073236  0.075115  0.077050  
-</pre></div>
-</div>
-</div>
 </div>
 <p>We note here that the covariance is zero for the first rows and
 columns since all matrix elements in the design matrix were set to one
@@ -1494,9 +1328,9 @@ x_{01}x_{00}+x_{11}x_{10} &amp; x_{01}^2+x_{11}^2\\
 that this is the covariance of the vectors <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> of the
 design/feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
 <p>It is easy to generalize this to a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\)</span>.</p>
-</div>
-<div class="section" id="linking-with-the-svd">
-<h2><span class="section-number">4.9. </span>Linking with the SVD<a class="headerlink" href="#linking-with-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linking-with-the-svd">
+<h2><span class="section-number">4.9. </span>Linking with the SVD<a class="headerlink" href="#linking-with-the-svd" title="Permalink to this heading">#</a></h2>
 <p>We saw earlier that</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1582,9 +1416,9 @@ measure how much correlations are contained in the rows of <span class="math not
 <p>Since we will mainly be interested in the correlations among the features
 of our data (the columns of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>, the quantity of interest for us are the non-zero singular
 values and the column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>.</p>
-</div>
-<div class="section" id="id1">
-<h2><span class="section-number">4.10. </span>Ridge and Lasso Regression<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2><span class="section-number">4.10. </span>Ridge and Lasso Regression<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>Let us remind ourselves about the expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is
 our optimization problem is</p>
 <div class="math notranslate nohighlight">
@@ -1841,7 +1675,7 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 \frac{\partial C(\boldsymbol{\beta})}{\partial \beta_1}=-2(2-\beta_1)+\lambda\mathrm{sgn}(\beta_1)=0.
 \]</div>
 <p>We have now four cases to solve besides the trivial cases <span class="math notranslate nohighlight">\(\beta_0\)</span> and/or <span class="math notranslate nohighlight">\(\beta_1\)</span> are zero, namely</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &gt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &gt; 0\)</span>,</p></li>
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &gt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &lt; 0\)</span>,</p></li>
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &lt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &gt; 0\)</span>,</p></li>
@@ -1927,14 +1761,6 @@ We select values of the hyperparameter <span class="math notranslate nohighlight
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[2. 2.]
-Training MSE for OLS
-3.0
-</pre></div>
-</div>
-<img alt="_images/chapter2_252_1.png" src="_images/chapter2_252_1.png" />
-</div>
 </div>
 <p>We see here that we reach a plateau for the Ridge results. Writing out the coefficients <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>, we observe that they are getting smaller and smaller and our error stabilizes since the predicted values of <span class="math notranslate nohighlight">\(\tilde{\boldsymbol{y}}\)</span> approach zero.</p>
 <p>This happens also for Lasso regression, as seen from the next code
@@ -2003,214 +1829,6 @@ shows the best performance of the three regression methods.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[2. 2.]
-Training MSE for OLS
-3.0
-[1.99995    1.99980002]
-[ 0.50001525 -0.99953475]
-[1.99993978 1.99975913]
-[ 0.50001525 -0.99944272]
-[1.99992746 1.99970988]
-[ 0.50001525 -0.99933188]
-[1.99991263 1.99965056]
-[ 0.50001525 -0.99919837]
-[1.99989476 1.99957911]
-[ 0.50001524 -0.99903755]
-[1.99987324 1.99949306]
-[ 0.50001524 -0.99884384]
-[1.99984732 1.99938942]
-[ 0.50001524 -0.99861053]
-[1.9998161  1.99926459]
-[ 0.50001523 -0.9983295 ]
-[1.99977849 1.99911427]
-[ 0.50001523 -0.99799099]
-[1.9997332  1.99893323]
-[ 0.50001522 -0.99758326]
-[1.99967865 1.99871521]
-[ 0.50001521 -0.99709215]
-[1.99961294 1.99845267]
-[ 0.50001521 -0.99650061]
-[1.99953381 1.99813653]
-[ 0.50001519 -0.99578809]
-[1.9994385  1.99775587]
-[ 0.50001518 -0.99492986]
-[1.9993237  1.99729756]
-[ 0.50001517 -0.99389612]
-[1.99918546 1.9967458 ]
-[ 0.50001515 -0.99265097]
-[1.99901896 1.99608161]
-[ 0.50001512 -0.99115119]
-[1.99881845 1.99528218]
-[ 0.5000151 -0.9893447]
-[1.998577  1.9943201]
-[ 0.50001506 -0.98716878]
-[1.99828624 1.99316252]
-[ 0.50001502 -0.98454786]
-[1.99793613 1.99176998]
-[ 0.50001498 -0.98139097]
-[1.99751458 1.99009525]
-[ 0.50001492 -0.97758848]
-[1.99700706 1.98808176]
-[ 0.50001485 -0.97300836]
-[1.9963961  1.98566191]
-[ 0.50001476 -0.9674916 ]
-[1.99566069 1.98275501]
-[ 0.50001466 -0.96084663]
-[1.9947756  1.97926491]
-[ 0.50001454 -0.95284275]
-[1.99371056 1.97507735]
-[ 0.50001439 -0.94320205]
-[1.99242921 1.97005689]
-[ 0.50001422 -0.93158979]
-[1.99088801 1.9640435 ]
-[ 0.500014   -0.91760278]
-[1.9890348  1.95684892]
-[ 0.50001374 -0.90075537]
-[1.98680716 1.9482527 ]
-[ 0.50001343 -0.88046261]
-[1.98413059 1.93799826]
-[ 0.50001306 -0.85601992]
-[1.98091621 1.92578916]
-[ 0.50001261 -0.8265786 ]
-[1.97705827 1.91128596]
-[ 0.50001207 -0.79111643]
-[1.97243128 1.89410423]
-[ 0.50001142 -0.74840212]
-[1.96688672 1.87381451]
-[ 0.50001063 -0.69695259]
-[1.96024953 1.84994524]
-[ 0.50000969 -0.63498144]
-[1.95231424 1.82198978]
-[ 0.50000855 -0.56033697]
-[1.94284104 1.78941903]
-[ 0.50000718 -0.47042744]
-[1.93155188 1.75170092]
-[ 0.50000553 -0.3621311 ]
-[1.91812702 1.70832814]
-[ 0.50001414 -0.23167717]
-[1.90220243 1.65885453]
-[ 0.50000455 -0.07456491]
-[1.88336879 1.60293962]
-[ 0.47132891 -0.        ]
-[1.86117291 1.54039921]
-[ 0.41433969 -0.        ]
-[1.83512277 1.47125748]
-[ 0.34569596 -0.        ]
-[1.80469739 1.39579407]
-[ 0.26301436 -0.        ]
-[1.76936315 1.31457796]
-[ 0.16342407 -0.        ]
-[1.72859758 1.22847924]
-[ 0.04346721 -0.        ]
-[1.68192193 1.13865173]
-[ 0. -0.]
-[1.62894215 1.04648335]
-[ 0. -0.]
-[1.56939714 0.95351665]
-[ 0. -0.]
-[1.50321091 0.86134827]
-[ 0. -0.]
-[1.43054282 0.77152076]
-[ 0. -0.]
-[1.35182854 0.68542204]
-[ 0. -0.]
-[1.26780278 0.60420593]
-[ 0. -0.]
-[1.17949575 0.52874252]
-[ 0. -0.]
-[1.0881981  0.45960079]
-[ 0. -0.]
-[0.99539415 0.39706038]
-[ 0. -0.]
-[0.90266948 0.34114547]
-[ 0. -0.]
-[0.81160425 0.29167186]
-[ 0. -0.]
-[0.7236674  0.24829908]
-[ 0. -0.]
-[0.64012627 0.21058097]
-[ 0. -0.]
-[0.56198284 0.17801022]
-[ 0. -0.]
-[0.48994188 0.15005476]
-[ 0. -0.]
-[0.42441033 0.12618549]
-[ 0. -0.]
-[0.3655222  0.10589577]
-[ 0. -0.]
-[0.31318084 0.08871404]
-[ 0. -0.]
-[0.26710969 0.07421084]
-[ 0. -0.]
-[0.22690428 0.06200174]
-[ 0. -0.]
-[0.19207979 0.0517473 ]
-[ 0. -0.]
-[0.16211139 0.04315108]
-[ 0. -0.]
-[0.13646574 0.0359565 ]
-[ 0. -0.]
-[0.11462415 0.02994311]
-[ 0. -0.]
-[0.09609807 0.02492265]
-[ 0. -0.]
-[0.08043851 0.02073509]
-[ 0. -0.]
-[0.06724062 0.01724499]
-[ 0. -0.]
-[0.05614483 0.01433809]
-[ 0. -0.]
-[0.04683565 0.01191824]
-[ 0. -0.]
-[0.039039   0.00990475]
-[ 0. -0.]
-[0.03251863 0.00823002]
-[ 0. -0.]
-[0.02707227 0.00683748]
-[ 0. -0.]
-[0.02252765 0.0056799 ]
-[ 0. -0.]
-[0.01873869 0.00471782]
-[ 0. -0.]
-[0.01558197 0.00391839]
-[ 0. -0.]
-[0.01295356 0.0032542 ]
-[ 0. -0.]
-[0.01076611 0.00270244]
-[ 0. -0.]
-[0.00894639 0.00224413]
-[ 0. -0.]
-[0.0074331  0.00186347]
-[ 0. -0.]
-[0.00617499 0.00154733]
-[ 0. -0.]
-[0.00512927 0.00128479]
-[ 0. -0.]
-[0.00426027 0.00106677]
-[ 0. -0.]
-[0.00353823 0.00088573]
-[ 0. -0.]
-[0.00293838 0.00073541]
-[ 0. -0.]
-[0.0024401  0.00061058]
-[ 0. -0.]
-[0.00202624 0.00050694]
-[ 0. -0.]
-[0.00168251 0.00042089]
-[ 0. -0.]
-[0.00139705 0.00034944]
-[ 0. -0.]
-[0.00115999 0.00029012]
-[ 0. -0.]
-[0.00096314 0.00024087]
-[ 0. -0.]
-[0.00079968 0.00019998]
-[ 0. -0.]
-</pre></div>
-</div>
-<img alt="_images/chapter2_254_1.png" src="_images/chapter2_254_1.png" />
-</div>
 </div>
 <p>We bring then back our exponential function example and study all
 three regression methods.  Depending on the level of noise, we note
@@ -2304,25 +1922,15 @@ set of <span class="math notranslate nohighlight">\(\lambda\)</span> values.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 2.03099776 -0.17917768  5.18029127]
-Training MSE for OLS
-0.009163470508352218
-Test MSE OLS
-0.008675369724975977
-</pre></div>
-</div>
-<img alt="_images/chapter2_256_1.png" src="_images/chapter2_256_1.png" />
-</div>
 </div>
 <p>Both these example send a clear message. The addition of a
 shrinkage/regularization term implies that we need to perform a search
 for the optimal values of <span class="math notranslate nohighlight">\(\lambda\)</span>. We will see this throughout these
 series of lectures.</p>
 <p>As a small addendum, we note that you can also solve this problem using the convex optimization package <a class="reference external" href="https://cvxopt.org/examples/mlbook/l1regls.html">CVXOPT</a>. This requires, in addition to having installed <strong>CVXOPT</strong>, you need to download the file <em><a class="reference external" href="http://l1regl.py">l1regl.py</a></em>.</p>
-</div>
-<div class="section" id="linking-the-regression-analysis-with-a-statistical-interpretation">
-<h2><span class="section-number">4.11. </span>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linking-the-regression-analysis-with-a-statistical-interpretation">
+<h2><span class="section-number">4.11. </span>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this heading">#</a></h2>
 <p>We will now couple the discussions of ordinary least squares, Ridge
 and Lasso regression with a statistical interpretation, that is we
 move from a linear algebra analysis to a statistical analysis. In
@@ -2459,9 +2067,9 @@ when we employ Ridge regression, allowing us again to define a confidence interv
 <p>The difference is non-negative definite since each component of the
 matrix product is non-negative definite.
 This means the variance we obtain with the standard OLS will always for <span class="math notranslate nohighlight">\(\lambda &gt; 0\)</span> be larger than the variance of <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.</p>
-</div>
-<div class="section" id="deriving-ols-from-a-probability-distribution">
-<h2><span class="section-number">4.12. </span>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-ols-from-a-probability-distribution">
+<h2><span class="section-number">4.12. </span>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this heading">#</a></h2>
 <p>Our basic assumption when we derived the OLS equations was to assume
 that our output is determined by a given continuous function
 <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and a random noise <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> given by the normal
@@ -2648,9 +2256,9 @@ p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y=
 \end{equation}
 \]</div>
 <p>That is, in case of a positive test, there is only a <span class="math notranslate nohighlight">\(3\%\)</span> chance of having breast cancer!</p>
-</div>
-<div class="section" id="bayes-theorem-and-ridge-and-lasso-regression">
-<h2><span class="section-number">4.13. </span>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bayes-theorem-and-ridge-and-lasso-regression">
+<h2><span class="section-number">4.13. </span>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Hitherto we have discussed Ridge and Lasso regression in terms of a
 linear analysis. This may to many of you feel rather technical and
 perhaps not that intuitive. The question is whether we can develop a
@@ -2733,14 +2341,6 @@ order to another one.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.0169643   0.27924636 -1.4087793   1.03308408  0.        ]
-Test MSE OLS
-0.9582286166520774
-</pre></div>
-</div>
-<img alt="_images/chapter2_322_1.png" src="_images/chapter2_322_1.png" />
-</div>
 </div>
 <p>How can we understand this?</p>
 <p>Let us write out the values of the coefficients <span class="math notranslate nohighlight">\(\beta_i\)</span> as functions
@@ -2802,228 +2402,6 @@ large variance (normally for higher orders in the polynomial).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>beta</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.986699</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>-0.606760</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>1.280573</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.850164</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.000000</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>beta</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.978553</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>-0.511888</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>1.051418</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.701370</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.000000</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>beta</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.946957</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>-0.162246</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>0.221921</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.167787</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.000000</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>beta</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.906747</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.017665</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>-0.029483</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.053849</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.000000</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>beta</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.718165</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.156956</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>0.040102</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.001880</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.000000</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>As an exercise, repeat these calculations with ordinary least squares
 only with and without noise. Calculate thereafter the variance of the
@@ -3032,9 +2410,9 @@ noise. Here we recommend to use <span class="math notranslate nohighlight">\(\si
 added noise (which follows a normal distribution with mean value zero).
 Comment your results. If you have a large noise term, do the parameters <span class="math notranslate nohighlight">\(\beta_j\)</span> vary more as function
 of model complexity? And what about their variance?</p>
-</div>
-<div class="section" id="linking-bayes-theorem-with-ridge-and-lasso-regression">
-<h2><span class="section-number">4.14. </span>Linking Bayes’ Theorem with Ridge and Lasso Regression<a class="headerlink" href="#linking-bayes-theorem-with-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linking-bayes-theorem-with-ridge-and-lasso-regression">
+<h2><span class="section-number">4.14. </span>Linking Bayes’ Theorem with Ridge and Lasso Regression<a class="headerlink" href="#linking-bayes-theorem-with-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>We have seen that Ridge regression suppresses those features which
 have a small singular value. This corresponds to a feature which exhibits
 a large variance in the parameters <span class="math notranslate nohighlight">\(\beta_j\)</span>.
@@ -3120,8 +2498,8 @@ C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol
 <span class="math notranslate nohighlight">\(\sigma^2=1/(2\lambda)\)</span>. Thus, increasing the variance means
 decreasing <span class="math notranslate nohighlight">\(\lambda\)</span> and shrinking the variance means increasing
 <span class="math notranslate nohighlight">\(\lambda\)</span>. When we increase <span class="math notranslate nohighlight">\(\lambda\)</span>, this corresponds to shrinking the role of less important features (small singular values).</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -3135,7 +2513,7 @@ decreasing <span class="math notranslate nohighlight">\(\lambda\)</span> and shr
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -3143,44 +2521,114 @@ decreasing <span class="math notranslate nohighlight">\(\lambda\)</span> and shr
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <i class="fa-solid fa-list"></i> Contents
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+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">4.1. Mathematical Interpretation of Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-singular-value-decomposition">4.2. The singular value decomposition</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-math-of-the-svd">4.3. Basic math of the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#codes-for-the-svd">4.4. Codes for the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">4.5. Code for SVD and Inversion of Matrices</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">4.6. Mathematics of the SVD and implications</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">4.7. Further properties (important for our analyses later)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance-matrix">4.8. Meet the Covariance Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-with-the-svd">4.9. Linking with the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">4.10. Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">4.11. Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">4.12. Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">4.13. Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-bayes-theorem-with-ridge-and-lasso-regression">4.14. Linking Bayes’ Theorem with Ridge and Lasso Regression</a></li>
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diff --git a/doc/LectureNotes/_build/html/chapter3.html b/doc/LectureNotes/_build/html/chapter3.html
index 2194b7987..9a6d63e7f 100644
--- a/doc/LectureNotes/_build/html/chapter3.html
+++ b/doc/LectureNotes/_build/html/chapter3.html
@@ -1,50 +1,61 @@
 
+
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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-<p aria-level="2" class="caption" role="heading">
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-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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 </ul>
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 </ul>
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+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+    <h1>Resampling Methods</h1>
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-            <div class="tocsection onthispage pt-5 pb-3">
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                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction">
-   5.1. Introduction
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reminder-on-statistics">
-   5.2. Reminder on Statistics
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   5.3. Resampling methods
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#bootstrap">
-     5.3.1. Bootstrap
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-bias-variance-tradeoff">
-   5.4. The bias-variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation">
-   5.5. Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-rescaling-data">
-   5.6. More on Rescaling data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-complicated-example-the-ising-model">
-   5.7. More complicated Example: The Ising model
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercises-and-projects">
-   5.8. Exercises and Projects
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-ordinary-least-square-ols-on-the-franke-function">
-     5.8.1. Exercise: Ordinary Least Square (OLS) on the Franke function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-bias-variance-trade-off-and-resampling-techniques">
-     5.8.2. Exercise: Bias-variance trade-off and resampling techniques
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity">
-     5.8.3. Exercise:  Cross-validation as resampling techniques, adding more complexity
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-ridge-regression-on-the-franke-function-with-resampling">
-     5.8.4. Exercise: Ridge Regression on the Franke function  with resampling
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-lasso-regression-on-the-franke-function-with-resampling">
-     5.8.5. Exercise: Lasso Regression on the Franke function  with resampling
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-analysis-of-real-data">
-     5.8.6. Exercise: Analysis of real data
-    </a>
-   </li>
-  </ul>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">5.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reminder-on-statistics">5.2. Reminder on Statistics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">5.3. Resampling methods</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#bootstrap">5.3.1. Bootstrap</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-bias-variance-tradeoff">5.4. The bias-variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation">5.5. Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-rescaling-data">5.6. More on Rescaling data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-complicated-example-the-ising-model">5.7. More complicated Example: The Ising model</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises-and-projects">5.8. Exercises and Projects</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-ordinary-least-square-ols-on-the-franke-function">5.8.1. Exercise: Ordinary Least Square (OLS) on the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-bias-variance-trade-off-and-resampling-techniques">5.8.2. Exercise: Bias-variance trade-off and resampling techniques</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity">5.8.3. Exercise:  Cross-validation as resampling techniques, adding more complexity</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-ridge-regression-on-the-franke-function-with-resampling">5.8.4. Exercise: Ridge Regression on the Franke function  with resampling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-lasso-regression-on-the-franke-function-with-resampling">5.8.5. Exercise: Lasso Regression on the Franke function  with resampling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-analysis-of-real-data">5.8.6. Exercise: Analysis of real data</a></li>
+</ul>
+</li>
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-   5.2. Reminder on Statistics
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-  <a class="reference internal nav-link" href="#the-bias-variance-tradeoff">
-   5.4. The bias-variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation">
-   5.5. Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-rescaling-data">
-   5.6. More on Rescaling data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-complicated-example-the-ising-model">
-   5.7. More complicated Example: The Ising model
-  </a>
- </li>
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-    <a class="reference internal nav-link" href="#exercise-ordinary-least-square-ols-on-the-franke-function">
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-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-bias-variance-trade-off-and-resampling-techniques">
-     5.8.2. Exercise: Bias-variance trade-off and resampling techniques
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity">
-     5.8.3. Exercise:  Cross-validation as resampling techniques, adding more complexity
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-ridge-regression-on-the-franke-function-with-resampling">
-     5.8.4. Exercise: Ridge Regression on the Franke function  with resampling
-    </a>
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-lasso-regression-on-the-franke-function-with-resampling">
-     5.8.5. Exercise: Lasso Regression on the Franke function  with resampling
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#exercise-analysis-of-real-data">
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-    </a>
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+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter3.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="resampling-methods">
-<h1><span class="section-number">5. </span>Resampling Methods<a class="headerlink" href="#resampling-methods" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="introduction">
-<h2><span class="section-number">5.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+doconce format html chapter3.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="resampling-methods">
+<h1><span class="section-number">5. </span>Resampling Methods<a class="headerlink" href="#resampling-methods" title="Permalink to this heading">#</a></h1>
+<section id="introduction">
+<h2><span class="section-number">5.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
 <p>Resampling methods are an indispensable tool in modern
 statistics. They involve repeatedly drawing samples from a training
 set and refitting a model of interest on each sample in order to
@@ -574,7 +447,7 @@ the resulting fits differ. Such an approach may allow us to obtain
 information that would not be available from fitting the model only
 once using the original training sample.</p>
 <p>Two resampling methods are often used in Machine Learning analyses,</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>The <strong>bootstrap method</strong></p></li>
 <li><p>and <strong>Cross-Validation</strong></p></li>
 </ol>
@@ -600,9 +473,9 @@ bootstrap is widely used.</p>
 <li><p>The results can be analysed with the same statistical tools as we would use analysing experimental data.</p></li>
 <li><p>As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.</p></li>
 </ul>
-</div>
-<div class="section" id="reminder-on-statistics">
-<h2><span class="section-number">5.2. </span>Reminder on Statistics<a class="headerlink" href="#reminder-on-statistics" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reminder-on-statistics">
+<h2><span class="section-number">5.2. </span>Reminder on Statistics<a class="headerlink" href="#reminder-on-statistics" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>As in other experiments, many numerical  experiments have two classes of errors:</p>
 <ul>
@@ -743,9 +616,9 @@ when we employ Ridge regression, allowing us again to define a confidence interv
 <p>The difference is non-negative definite since each component of the
 matrix product is non-negative definite.
 This means the variance we obtain with the standard OLS will always for <span class="math notranslate nohighlight">\(\lambda &gt; 0\)</span> be larger than the variance of <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.</p>
-</div>
-<div class="section" id="id1">
-<h2><span class="section-number">5.3. </span>Resampling methods<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2><span class="section-number">5.3. </span>Resampling methods<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>With all these analytical equations for both the OLS and Ridge
 regression, we will now outline how to assess a given model. This will
 lead us to a discussion of the so-called bias-variance tradeoff (see
@@ -755,7 +628,7 @@ the mean-squared error (MSE), mainly used for fitting of continuous
 functions. Another choice is the absolute error.</p>
 <p>In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,
 we discuss the</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>prediction error or simply the <strong>test error</strong> <span class="math notranslate nohighlight">\(\mathrm{Err_{Test}}\)</span>, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the</p></li>
 <li><p>training error <span class="math notranslate nohighlight">\(\mathrm{Err_{Train}}\)</span>, which is the average loss over the training data.</p></li>
 </ol>
@@ -819,21 +692,21 @@ number <span class="math notranslate nohighlight">\(i\)</span> is left out. Usin
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.101292 sec
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Runtime: 0.085891 sec
 Jackknife Statistics :
 original           bias      std. error
- 99.9618        99.9518        0.148771
+ 99.8321        99.8221         0.15031
 </pre></div>
 </div>
 </div>
 </div>
-<div class="section" id="bootstrap">
-<h3><span class="section-number">5.3.1. </span>Bootstrap<a class="headerlink" href="#bootstrap" title="Permalink to this headline">¶</a></h3>
+<section id="bootstrap">
+<h3><span class="section-number">5.3.1. </span>Bootstrap<a class="headerlink" href="#bootstrap" title="Permalink to this heading">#</a></h3>
 <p>Bootstrapping is a nonparametric approach to statistical inference
 that substitutes computation for more traditional distributional
 assumptions and asymptotic results. Bootstrapping offers a number of
 advantages:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>The bootstrap is quite general, although there are some cases in which it fails.</p></li>
 <li><p>Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.</p></li>
 <li><p>It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically.</p></li>
@@ -853,7 +726,7 @@ more than one component, and the components are independent, we use the
 same estimator on each component separately.  If the probability
 density function of <span class="math notranslate nohighlight">\(X_i\)</span>, <span class="math notranslate nohighlight">\(p(x)\)</span>, had been known, then it would have
 been straight forward to do this by:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Drawing lots of numbers from <span class="math notranslate nohighlight">\(p(x)\)</span>, suppose we call one such set of numbers <span class="math notranslate nohighlight">\((X_1^*, X_2^*, \cdots, X_n^*)\)</span>.</p></li>
 <li><p>Then using these numbers, we could compute a replica of <span class="math notranslate nohighlight">\(\widehat{\beta}\)</span> called <span class="math notranslate nohighlight">\(\widehat{\beta}^*\)</span>.</p></li>
 </ol>
@@ -874,7 +747,7 @@ frequency of the observation <span class="math notranslate nohighlight">\(X_i\)<
 <span class="math notranslate nohighlight">\((X_1^*,X_2^*,\cdots,X_n^*)\)</span> with replacement from the vector
 <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
 <p>The independent bootstrap works like this:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Draw with replacement <span class="math notranslate nohighlight">\(n\)</span> numbers for the observed variables <span class="math notranslate nohighlight">\(\boldsymbol{x} = (x_1,x_2,\cdots,x_n)\)</span>.</p></li>
 <li><p>Define a vector <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span> containing the values which were drawn from <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span>.</p></li>
 <li><p>Using the vector <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span> compute <span class="math notranslate nohighlight">\(\widehat{\beta}^*\)</span> by evaluating <span class="math notranslate nohighlight">\(\widehat \beta\)</span> under the observations <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span>.</p></li>
@@ -1039,9 +912,53 @@ theorem.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
-original           bias      std. error
- 99.9169   14.873        99.9169        0.147934
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
 </div>
@@ -1062,14 +979,11 @@ original           bias      std. error
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter3_51_0.png" src="_images/chapter3_51_0.png" />
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="the-bias-variance-tradeoff">
-<h2><span class="section-number">5.4. </span>The bias-variance tradeoff<a class="headerlink" href="#the-bias-variance-tradeoff" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="the-bias-variance-tradeoff">
+<h2><span class="section-number">5.4. </span>The bias-variance tradeoff<a class="headerlink" href="#the-bias-variance-tradeoff" title="Permalink to this heading">#</a></h2>
 <p>We will discuss the bias-variance tradeoff in the context of
 continuous predictions such as regression. However, many of the
 intuitions and ideas discussed here also carry over to classification
@@ -1176,15 +1090,6 @@ We use a more compact notation in terms of the expectation value</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Error: 0.013121574062587286
-Bias^2: 0.012073649469946107
-Var: 0.0010479245926411787
-0.013121574062587286 &gt;= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286
-</pre></div>
-</div>
-<img alt="_images/chapter3_65_1.png" src="_images/chapter3_65_1.png" />
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1237,85 +1142,6 @@ Var: 0.0010479245926411787
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 0
-Error: 0.32149601703519115
-Bias^2: 0.3123314713548606
-Var: 0.009164545680330616
-0.32149601703519115 &gt;= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912
-Polynomial degree: 1
-Error: 0.08426840630693412
-Bias^2: 0.0796891867672603
-Var: 0.004579219539673834
-0.08426840630693412 &gt;= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
-Polynomial degree: 2
-Error: 0.10398646080125037
-Bias^2: 0.10077114273548984
-Var: 0.0032153180657605116
-0.10398646080125037 &gt;= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036
-Polynomial degree: 3
-Error: 0.06547790180152352
-Bias^2: 0.062082386342319454
-Var: 0.0033955154592040923
-0.06547790180152352 &gt;= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355
-Polynomial degree: 4
-Error: 0.06844519414009445
-Bias^2: 0.06453579006728322
-Var: 0.003909404072811221
-0.06844519414009445 &gt;= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 5
-Error: 0.05227921801205679
-Bias^2: 0.04818727730430286
-Var: 0.004091940707753925
-0.05227921801205679 &gt;= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679
-Polynomial degree: 6
-Error: 0.03781367141738902
-Bias^2: 0.03365768507152769
-Var: 0.0041559863458613296
-0.03781367141738902 &gt;= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902
-Polynomial degree: 7
-Error: 0.027609773491022394
-Bias^2: 0.022999498260366198
-Var: 0.004610275230656182
-0.027609773491022394 &gt;= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238
-Polynomial degree: 8
-Error: 0.017355848195593312
-Bias^2: 0.010331721306655165
-Var: 0.007024126888938144
-0.017355848195593312 &gt;= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331
-Polynomial degree: 9
-Error: 0.026605727637184558
-Bias^2: 0.010018312644139219
-Var: 0.016587414993045335
-0.026605727637184558 &gt;= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554
-Polynomial degree: 10
-Error: 0.021592704588021178
-Bias^2: 0.010516485576646504
-Var: 0.01107621901137467
-0.021592704588021178 &gt;= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174
-Polynomial degree: 11
-Error: 0.07160048164232538
-Bias^2: 0.014436800088896381
-Var: 0.05716368155342902
-0.07160048164232538 &gt;= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254
-Polynomial degree: 12
-Error: 0.11547777218876518
-Bias^2: 0.016285782696017142
-Var: 0.09919198949274803
-0.11547777218876518 &gt;= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 13
-Error: 0.2284246870217162
-Bias^2: 0.01975416527168255
-Var: 0.20867052175003364
-0.2284246870217162 &gt;= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162
-</pre></div>
-</div>
-<img alt="_images/chapter3_66_3.png" src="_images/chapter3_66_3.png" />
-</div>
 </div>
 <p>The bias-variance tradeoff summarizes the fundamental tension in
 machine learning, particularly supervised learning, between the
@@ -1417,30 +1243,6 @@ flexible statistical methods have higher variance.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>============================
-Underfitting vs. Overfitting
-============================
-
-This example demonstrates the problems of underfitting and overfitting and
-how we can use linear regression with polynomial features to approximate
-nonlinear functions. The plot shows the function that we want to approximate,
-which is a part of the cosine function. In addition, the samples from the
-real function and the approximations of different models are displayed. The
-models have polynomial features of different degrees. We can see that a
-linear function (polynomial with degree 1) is not sufficient to fit the
-training samples. This is called **underfitting**. A polynomial of degree 4
-approximates the true function almost perfectly. However, for higher degrees
-the model will **overfit** the training data, i.e. it learns the noise of the
-training data.
-We evaluate quantitatively **overfitting** / **underfitting** by using
-cross-validation. We calculate the mean squared error (MSE) on the validation
-set, the higher, the less likely the model generalizes correctly from the
-training data.
-</pre></div>
-</div>
-<img alt="_images/chapter3_68_1.png" src="_images/chapter3_68_1.png" />
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1525,116 +1327,10 @@ training data.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:   1
-Mean squared error on training data: 439230.69504801
-Mean squared error on test data: 481979.17861098
-Degree of polynomial:   2
-Mean squared error on training data: 115822.95008046
-Mean squared error on test data: 123711.53703498
-Degree of polynomial:   3
-Mean squared error on training data: 9011.85263220
-Mean squared error on test data: 10913.84780262
-Degree of polynomial:   4
-Mean squared error on training data: 303.47610036
-Mean squared error on test data: 426.30787294
-Degree of polynomial:   5
-Mean squared error on training data: 3.80354994
-Mean squared error on test data: 5.98822371
-Degree of polynomial:   6
-Mean squared error on training data: 3.66204648
-Mean squared error on test data: 8.14812206
-Degree of polynomial:   7
-Mean squared error on training data: 0.47075725
-Mean squared error on test data: 2.00607783
-</pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:   8
-Mean squared error on training data: 0.04912436
-Mean squared error on test data: 0.21596432
-Degree of polynomial:   9
-Mean squared error on training data: 0.02522069
-Mean squared error on test data: 0.08576932
-Degree of polynomial:  10
-Mean squared error on training data: 0.02511518
-Mean squared error on test data: 1.20015436
-Degree of polynomial:  11
-Mean squared error on training data: 0.01640891
-Mean squared error on test data: 1.35533773
-Degree of polynomial:  12
-Mean squared error on training data: 0.00813803
-Mean squared error on test data: 0.17446471
-Degree of polynomial:  13
-Mean squared error on training data: 0.00759119
-Mean squared error on test data: 1.08131003
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  14
-Mean squared error on training data: 0.00472199
-Mean squared error on test data: 0.81333804
-Degree of polynomial:  15
-Mean squared error on training data: 0.00410478
-Mean squared error on test data: 92.09172409
-Degree of polynomial:  16
-Mean squared error on training data: 0.00315593
-Mean squared error on test data: 234.38533185
-Degree of polynomial:  17
-Mean squared error on training data: 0.00242999
-Mean squared error on test data: 1271.35771826
-Degree of polynomial:  18
-Mean squared error on training data: 0.00228742
-Mean squared error on test data: 108.27092910
-Degree of polynomial:  19
-Mean squared error on training data: 0.00156376
-Mean squared error on test data: 1371.99051150
-Degree of polynomial:  20
-Mean squared error on training data: 0.00137818
-Mean squared error on test data: 1887.86252988
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  21
-Mean squared error on training data: 0.00118508
-Mean squared error on test data: 14859.69908626
-Degree of polynomial:  22
-Mean squared error on training data: 0.00092647
-Mean squared error on test data: 876.51191552
-Degree of polynomial:  23
-Mean squared error on training data: 0.00085889
-Mean squared error on test data: 5594.60815105
-Degree of polynomial:  24
-Mean squared error on training data: 0.00084705
-Mean squared error on test data: 1277.61702282
-Degree of polynomial:  25
-Mean squared error on training data: 0.00079129
-Mean squared error on test data: 128664.31650694
-Degree of polynomial:  26
-Mean squared error on training data: 0.00076905
-Mean squared error on test data: 19003.94822514
-Degree of polynomial:  27
-Mean squared error on training data: 0.00068946
-Mean squared error on test data: 2379.66219404
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  28
-Mean squared error on training data: 0.00062595
-Mean squared error on test data: 4082.19983530
-Degree of polynomial:  29
-Mean squared error on training data: 0.00060705
-Mean squared error on test data: 3250.17647619
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(trainingerror), label=&#39;Training Error&#39;)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
-</pre></div>
-</div>
-<img alt="_images/chapter3_69_6.png" src="_images/chapter3_69_6.png" />
-</div>
-</div>
-</div>
-<div class="section" id="cross-validation">
-<h2><span class="section-number">5.5. </span>Cross-validation<a class="headerlink" href="#cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="cross-validation">
+<h2><span class="section-number">5.5. </span>Cross-validation<a class="headerlink" href="#cross-validation" title="Permalink to this heading">#</a></h2>
 <p>When the repetitive splitting of the data set is done randomly,
 samples may accidently end up in a fast majority of the splits in
 either training or test set. Such samples may have an unbalanced
@@ -1674,7 +1370,7 @@ cross-validation (LOOCV).</p>
 \end{align*}
 \]</div>
 <p>For the various values of <span class="math notranslate nohighlight">\(k\)</span></p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>shuffle the dataset randomly.</p></li>
 <li><p>Split the dataset into <span class="math notranslate nohighlight">\(k\)</span> groups.</p></li>
 <li><p>For each unique group:</p></li>
@@ -1683,7 +1379,7 @@ cross-validation (LOOCV).</p>
 <p>b. Take the remaining groups as a training data set</p>
 <p>c. Fit a model on the training set and evaluate it on the test set</p>
 <p>d. Retain the evaluation score and discard the model</p>
-<ol class="simple">
+<ol class="arabic simple" start="5">
 <li><p>Summarize the model using the sample of model evaluation scores</p></li>
 </ol>
 <p>The code here uses Ridge regression with cross-validation (CV)  resampling and <span class="math notranslate nohighlight">\(k\)</span>-fold CV in order to fit a specific polynomial.</p>
@@ -1781,9 +1477,6 @@ cross-validation (LOOCV).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter3_75_0.png" src="_images/chapter3_75_0.png" />
-</div>
 </div>
 <p>More examples of the application of cross-validation follow here.</p>
 <div class="cell docutils container">
@@ -1858,18 +1551,11 @@ cross-validation (LOOCV).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label=&#39;Test Error&#39;)
-</pre></div>
-</div>
-<img alt="_images/chapter3_77_1.png" src="_images/chapter3_77_1.png" />
-</div>
 </div>
 <p>Note that we have kept the intercept in the first column of design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>. When we call the corresponding <strong>Scikit-Learn</strong> function we need thus to set the intercept to <strong>False</strong>. Libraries like <strong>Scikit-Learn</strong> normally scale the design matrix and do not fit intercept. See the discussions below.</p>
-</div>
-<div class="section" id="more-on-rescaling-data">
-<h2><span class="section-number">5.6. </span>More on Rescaling data<a class="headerlink" href="#more-on-rescaling-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-on-rescaling-data">
+<h2><span class="section-number">5.6. </span>More on Rescaling data<a class="headerlink" href="#more-on-rescaling-data" title="Permalink to this heading">#</a></h2>
 <p>We end this chapter by adding some words on scaling and how to deal with the intercept for regression cases.</p>
 <p>When you are comparing your own code with for example <strong>Scikit-Learn</strong>’s
 library, there are some technicalities to keep in mind.  The examples
@@ -1930,11 +1616,6 @@ on your eventual new data set  before making a prediction. If we translate this
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;\n#Model training, we compute the mean value of y and X\ny_train_mean = np.mean(y_train)\nX_train_mean = np.mean(X_train,axis=0)\nX_train = X_train - X_train_mean\ny_train = y_train - y_train_mean\n\n# The we fit our model with the training data\ntrained_model = some_model.fit(X_train,y_train)\n\n\n#Model prediction, we need also to transform our data set used for the prediction.\nX_test = X_test - X_train_mean #Use mean from training data\ny_pred = trained_model(X_test)\ny_pred = y_pred + y_train_mean\n&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>Let us try to understand what this may imply mathematically when we
 subtract the mean values, also known as <em>zero centering</em>. For
@@ -2118,26 +1799,6 @@ Note also that we do not split the data into training and test.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True beta: [2, 0.5, 3.7]
-Fitted beta: [2.08376632 0.19569961 3.97898392]
-Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]
-MSE with intercept column
-0.004113634617443139
-MSE with intercept column from SKL
-0.004113634617443147
-Manual intercept: 2.083766322923899
-Fitted beta (wiothout intercept): [0.19569961 3.97898392]
-Sklearn intercept: 2.0837663229239043
-Sklearn fitted beta (without intercept): [0.19569961 3.97898392]
-MSE with Manual intercept
-0.00411363461744314
-MSE with Sklearn intercept
-0.004113634617443131
-</pre></div>
-</div>
-<img alt="_images/chapter3_112_1.png" src="_images/chapter3_112_1.png" />
-</div>
 </div>
 <p>The intercept is the value of our output/target variable
 when all our features are zero and our function crosses the <span class="math notranslate nohighlight">\(y\)</span>-axis (for a one-dimensional case).</p>
@@ -2240,99 +1901,6 @@ intercept.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Beta values for own Ridge implementation
-[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02
-  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02
- -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02
- -9.80609616e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02
-  2.64742912e-02  1.63249532e-02 -5.01831251e-05 -2.15098090e-02]
-Beta values for Scikit-Learn Ridge implementation
-[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02
-  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02
- -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02
- -9.80609615e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02
-  2.64742912e-02  1.63249532e-02 -5.01831207e-05 -2.15098090e-02]
-MSE values for own Ridge implementation
-4.3632959215700067e-07
-MSE values for Scikit-Learn Ridge implementation
-4.363295916323784e-07
-Beta values for own Ridge implementation
-[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471
-  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093
- -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565
-  0.02976145  0.04543942]
-Beta values for Scikit-Learn Ridge implementation
-[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471
-  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093
- -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565
-  0.02976145  0.04543942]
-MSE values for own Ridge implementation
-5.194042827197027e-06
-MSE values for Scikit-Learn Ridge implementation
-5.1940428268204826e-06
-Beta values for own Ridge implementation
-[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007
-  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499
-  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318
- -0.01708852 -0.01708781]
-Beta values for Scikit-Learn Ridge implementation
-[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007
-  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499
-  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318
- -0.01708852 -0.01708781]
-MSE values for own Ridge implementation
-2.0940821989643363e-05
-MSE values for Scikit-Learn Ridge implementation
-2.094082198961999e-05
-Beta values for own Ridge implementation
-[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361
-  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985
-  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387
-  0.00249435  0.00105081]
-Beta values for Scikit-Learn Ridge implementation
-[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361
-  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985
-  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387
-  0.00249435  0.00105081]
-MSE values for own Ridge implementation
-0.0003153514830957865
-MSE values for Scikit-Learn Ridge implementation
-0.00031535148309580783
-Beta values for own Ridge implementation
-[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02
- -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02
- -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03
- -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04
-  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]
-Beta values for Scikit-Learn Ridge implementation
-[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02
- -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02
- -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03
- -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04
-  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]
-MSE values for own Ridge implementation
-0.015072388895177157
-MSE values for Scikit-Learn Ridge implementation
-0.0150723888951771
-Beta values for own Ridge implementation
-[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427
- 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728
- 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987
- 0.0036237  0.003301  ]
-Beta values for Scikit-Learn Ridge implementation
-[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427
- 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728
- 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987
- 0.0036237  0.003301  ]
-MSE values for own Ridge implementation
-0.26409315307910036
-MSE values for Scikit-Learn Ridge implementation
-0.26409315307910025
-</pre></div>
-</div>
-<img alt="_images/chapter3_120_1.png" src="_images/chapter3_120_1.png" />
-</div>
 </div>
 <p>The results here agree when we force <strong>Scikit-Learn</strong>’s Ridge function to include the first column in our design matrix.
 We see that the results agree very well. Here we have thus explicitely included the intercept column in the design matrix.
@@ -2421,121 +1989,6 @@ Let us see how we can change this code by zero centering.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Beta values for own Ridge implementation
-[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01
-  2.18613217e-01  1.02054837e-01 -4.25617658e-04 -5.90475506e-02
- -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02
-  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02
-  2.02198703e-02 -3.46383925e-03 -3.63025821e-02]
-Beta values for Scikit-Learn Ridge implementation
-[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01
-  2.18613217e-01  1.02054837e-01 -4.25617654e-04 -5.90475506e-02
- -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02
-  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02
-  2.02198702e-02 -3.46383925e-03 -3.63025821e-02]
-Intercept from own implementation:
-1.0330308045188872
-Intercept from Scikit-Learn Ridge implementation
-1.0330308045183219
-MSE values for own Ridge implementation
-3.1392559591206444e-06
-MSE values for Scikit-Learn Ridge implementation
-3.1392559585048734e-06
-Beta values for own Ridge implementation
-[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649
-  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964
- -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906
-  0.04423486]
-Beta values for Scikit-Learn Ridge implementation
-[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649
-  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964
- -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906
-  0.04423486]
-Intercept from own implementation:
-1.041148729430595
-Intercept from Scikit-Learn Ridge implementation
-1.041148729430523
-MSE values for own Ridge implementation
-1.96013048502692e-05
-MSE values for Scikit-Learn Ridge implementation
-1.960130485007504e-05
-Beta values for own Ridge implementation
-[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251
-  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499
- -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528
- -0.01290947]
-Beta values for Scikit-Learn Ridge implementation
-[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251
-  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499
- -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528
- -0.01290947]
-Intercept from own implementation:
-1.0495569966278295
-Intercept from Scikit-Learn Ridge implementation
-1.0495569966278269
-MSE values for own Ridge implementation
-5.4959161509377256e-05
-MSE values for Scikit-Learn Ridge implementation
-5.495916150936645e-05
-Beta values for own Ridge implementation
-[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529
-  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792
-  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387
- -0.00905423]
-Beta values for Scikit-Learn Ridge implementation
-[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529
-  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792
-  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387
- -0.00905423]
-Intercept from own implementation:
-1.0399676689527966
-Intercept from Scikit-Learn Ridge implementation
-1.0399676689527975
-MSE values for own Ridge implementation
-7.571105947979352e-05
-MSE values for Scikit-Learn Ridge implementation
-7.571105947979394e-05
-Beta values for own Ridge implementation
-[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114
- -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018
-  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011
-  0.00683964]
-Beta values for Scikit-Learn Ridge implementation
-[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114
- -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018
-  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011
-  0.00683964]
-Intercept from own implementation:
-0.999955585168597
-Intercept from Scikit-Learn Ridge implementation
-0.999955585168597
-MSE values for own Ridge implementation
-0.0007698473260556344
-MSE values for Scikit-Learn Ridge implementation
-0.0007698473260556325
-Beta values for own Ridge implementation
-[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335
- -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117
- -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668
- -0.00058016]
-Beta values for Scikit-Learn Ridge implementation
-[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335
- -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117
- -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668
- -0.00058016]
-Intercept from own implementation:
-0.9637117593816477
-Intercept from Scikit-Learn Ridge implementation
-0.9637117593816477
-MSE values for own Ridge implementation
-0.0023813163025848865
-MSE values for Scikit-Learn Ridge implementation
-0.002381316302584886
-</pre></div>
-</div>
-<img alt="_images/chapter3_122_1.png" src="_images/chapter3_122_1.png" />
-</div>
 </div>
 <p>We see here, when compared to the code which includes explicitely the
 intercept column, that our MSE value is actually smaller. This is
@@ -2546,9 +1999,9 @@ centered matrix and/or vector that enter the fitting procedure. Note
 also that the problem with the intercept occurs mainly in these type
 of polynomial fitting problem.</p>
 <p>The next example is indeed an example where all these discussions about the role of intercept are not present.</p>
-</div>
-<div class="section" id="more-complicated-example-the-ising-model">
-<h2><span class="section-number">5.7. </span>More complicated Example: The Ising model<a class="headerlink" href="#more-complicated-example-the-ising-model" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-complicated-example-the-ising-model">
+<h2><span class="section-number">5.7. </span>More complicated Example: The Ising model<a class="headerlink" href="#more-complicated-example-the-ising-model" title="Permalink to this heading">#</a></h2>
 <p>The one-dimensional Ising model with nearest neighbor interaction, no
 external field and a constant coupling constant <span class="math notranslate nohighlight">\(J\)</span> is given by</p>
 <!-- Equation labels as ordinary links -->
@@ -2747,15 +2200,6 @@ linear system as an equation would reduce this down to
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
-  cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
-  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
-</pre></div>
-</div>
-<img alt="_images/chapter3_154_1.png" src="_images/chapter3_154_1.png" />
-</div>
 </div>
 <p>It is interesting to note that OLS
 considers both <span class="math notranslate nohighlight">\(J_{j, j + 1} = -0.5\)</span> and <span class="math notranslate nohighlight">\(J_{j, j - 1} = -0.5\)</span> as
@@ -2893,15 +2337,6 @@ with the form utilized in linear regression, viz.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
-  cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator
-  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
-</pre></div>
-</div>
-<img alt="_images/chapter3_172_1.png" src="_images/chapter3_172_1.png" />
-</div>
 </div>
 <p>The results agree perfectly with our previous discussion where we used our own code.</p>
 <p>Having explored the ordinary least squares we move on to ridge
@@ -2935,15 +2370,6 @@ cost function is given by</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
-  cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator
-  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
-</pre></div>
-</div>
-<img alt="_images/chapter3_175_1.png" src="_images/chapter3_175_1.png" />
-</div>
 </div>
 <p>In the <strong>Least Absolute Shrinkage and Selection Operator</strong> (LASSO)-method we get a third cost function.</p>
 <!-- Equation labels as ordinary links -->
@@ -2972,15 +2398,6 @@ cost function is given by</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
-  cb = fig.colorbar(im)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator
-  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)
-</pre></div>
-</div>
-<img alt="_images/chapter3_179_1.png" src="_images/chapter3_179_1.png" />
-</div>
 </div>
 <p>It is quite striking how LASSO breaks the symmetry of the coupling
 constant as opposed to ridge and OLS. We get a sparse solution with
@@ -3027,51 +2444,6 @@ constant as opposed to ridge and OLS. We get a sparse solution with
 </pre></div>
 </div>
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-  model = cd_fast.enet_coordinate_descent(
-
- 10%|██████████▌                                                                                              | 1/10 [00:00&lt;00:05,  1.54it/s]
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-</pre></div>
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-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:02&lt;00:00,  7.60it/s]
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>100%|████████████████████████████████████████████████████████████████████████████████████████████████████████| 10/10 [00:02&lt;00:00,  4.93it/s]
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>
-</pre></div>
-</div>
-<img alt="_images/chapter3_181_13.png" src="_images/chapter3_181_13.png" />
-</div>
 </div>
 <p>We see that LASSO reaches a good solution for low
 values of <span class="math notranslate nohighlight">\(\lambda\)</span>, but will “wither” when we increase <span class="math notranslate nohighlight">\(\lambda\)</span> too
@@ -3118,16 +2490,13 @@ testing set that is close to the accuracy of the training set.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter3_183_0.png" src="_images/chapter3_183_0.png" />
-</div>
 </div>
 <p>From the above figure we can see that LASSO with <span class="math notranslate nohighlight">\(\lambda = 10^{-2}\)</span>
 achieves a very good accuracy on the test set. This by far surpasses the
 other models for all values of <span class="math notranslate nohighlight">\(\lambda\)</span>.</p>
-</div>
-<div class="section" id="exercises-and-projects">
-<h2><span class="section-number">5.8. </span>Exercises and Projects<a class="headerlink" href="#exercises-and-projects" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercises-and-projects">
+<h2><span class="section-number">5.8. </span>Exercises and Projects<a class="headerlink" href="#exercises-and-projects" title="Permalink to this heading">#</a></h2>
 <p>The main aim of this project is to study in more detail various
 regression methods, including the Ordinary Least Squares (OLS) method,
 The total score is <strong>100</strong> points. Each subtask has its own final score.</p>
@@ -3210,18 +2579,9 @@ which polynomial fits the data best.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
-  ax = fig.gca(projection=&#39;3d&#39;)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.
-  fig.colorbar(surf, shrink=0.5, aspect=5)
-</pre></div>
 </div>
-<img alt="_images/chapter3_188_1.png" src="_images/chapter3_188_1.png" />
-</div>
-</div>
-<div class="section" id="exercise-ordinary-least-square-ols-on-the-franke-function">
-<h3><span class="section-number">5.8.1. </span>Exercise: Ordinary Least Square (OLS) on the Franke function<a class="headerlink" href="#exercise-ordinary-least-square-ols-on-the-franke-function" title="Permalink to this headline">¶</a></h3>
+<section id="exercise-ordinary-least-square-ols-on-the-franke-function">
+<h3><span class="section-number">5.8.1. </span>Exercise: Ordinary Least Square (OLS) on the Franke function<a class="headerlink" href="#exercise-ordinary-least-square-ols-on-the-franke-function" title="Permalink to this heading">#</a></h3>
 <p>We will generate our own dataset for a function
 <span class="math notranslate nohighlight">\(\mathrm{FrankeFunction}(x,y)\)</span> with <span class="math notranslate nohighlight">\(x,y \in [0,1]\)</span>. The function
 <span class="math notranslate nohighlight">\(f(x,y)\)</span> is the Franke function. You should explore also the addition
@@ -3264,9 +2624,9 @@ is no explicit recipe for how much data should be included as training
 data and say test data.  An accepted rule of thumb is to use
 approximately <span class="math notranslate nohighlight">\(2/3\)</span> to <span class="math notranslate nohighlight">\(4/5\)</span> of the data as training data.</p>
 <p>You can easily reuse the solutions to your exercises from week 35 and week 36.</p>
-</div>
-<div class="section" id="exercise-bias-variance-trade-off-and-resampling-techniques">
-<h3><span class="section-number">5.8.2. </span>Exercise: Bias-variance trade-off and resampling techniques<a class="headerlink" href="#exercise-bias-variance-trade-off-and-resampling-techniques" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="exercise-bias-variance-trade-off-and-resampling-techniques">
+<h3><span class="section-number">5.8.2. </span>Exercise: Bias-variance trade-off and resampling techniques<a class="headerlink" href="#exercise-bias-variance-trade-off-and-resampling-techniques" title="Permalink to this heading">#</a></h3>
 <p>Our aim here is to study the bias-variance trade-off by implementing the <strong>bootstrap</strong> resampling technique.</p>
 <p>With a code which does OLS and includes resampling techniques,
 we will now discuss the bias-variance trade-off in the context of
@@ -3313,9 +2673,9 @@ studying the MSE value as function of the complexity of your model.</p>
 of your model complexity (the degree of the polynomial) and the number
 of data points, and possibly also your training and test data using the <strong>bootstrap</strong> resampling method.</p>
 <p>Note also that when you calculate the bias, in all applications you don’t know the function values <span class="math notranslate nohighlight">\(f_i\)</span>. You would hence replace them with the actual data points <span class="math notranslate nohighlight">\(y_i\)</span>.</p>
-</div>
-<div class="section" id="exercise-cross-validation-as-resampling-techniques-adding-more-complexity">
-<h3><span class="section-number">5.8.3. </span>Exercise:  Cross-validation as resampling techniques, adding more complexity<a class="headerlink" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="exercise-cross-validation-as-resampling-techniques-adding-more-complexity">
+<h3><span class="section-number">5.8.3. </span>Exercise:  Cross-validation as resampling techniques, adding more complexity<a class="headerlink" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity" title="Permalink to this heading">#</a></h3>
 <p>The aim here is to write your own code for another widely popular
 resampling technique, the so-called cross-validation method.  Again,
 before you start with cross-validation approach, you should scale your
@@ -3328,9 +2688,9 @@ from the test folds. You can compare your own code with that from
 you got from your <strong>bootstrap</strong> code. Comment your results. Try <span class="math notranslate nohighlight">\(5-10\)</span>
 folds.  You can also compare your own cross-validation code with the
 one provided by <strong>Scikit-Learn</strong>.</p>
-</div>
-<div class="section" id="exercise-ridge-regression-on-the-franke-function-with-resampling">
-<h3><span class="section-number">5.8.4. </span>Exercise: Ridge Regression on the Franke function  with resampling<a class="headerlink" href="#exercise-ridge-regression-on-the-franke-function-with-resampling" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="exercise-ridge-regression-on-the-franke-function-with-resampling">
+<h3><span class="section-number">5.8.4. </span>Exercise: Ridge Regression on the Franke function  with resampling<a class="headerlink" href="#exercise-ridge-regression-on-the-franke-function-with-resampling" title="Permalink to this heading">#</a></h3>
 <p>Write your own code for the Ridge method, either using matrix
 inversion or the singular value decomposition as done in the previous
 exercise. Perform the same bootstrap analysis as in the
@@ -3339,25 +2699,25 @@ analyze your results with those obtained in exercises 1-3. Study the
 dependence on <span class="math notranslate nohighlight">\(\lambda\)</span>.</p>
 <p>Study also the bias-variance trade-off as function of various values of
 the parameter <span class="math notranslate nohighlight">\(\lambda\)</span>. For the bias-variance trade-off, use the <strong>bootstrap</strong> resampling method. Comment your results.</p>
-</div>
-<div class="section" id="exercise-lasso-regression-on-the-franke-function-with-resampling">
-<h3><span class="section-number">5.8.5. </span>Exercise: Lasso Regression on the Franke function  with resampling<a class="headerlink" href="#exercise-lasso-regression-on-the-franke-function-with-resampling" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="exercise-lasso-regression-on-the-franke-function-with-resampling">
+<h3><span class="section-number">5.8.5. </span>Exercise: Lasso Regression on the Franke function  with resampling<a class="headerlink" href="#exercise-lasso-regression-on-the-franke-function-with-resampling" title="Permalink to this heading">#</a></h3>
 <p>This exercise is essentially a repeat of the previous two ones, but now
 with Lasso regression. Write either your own code (difficult and optional) or, in this case,
 you can also use the functionalities of <strong>Scikit-Learn</strong> (recommended).
 Give a
 critical discussion of the three methods and a judgement of which
 model fits the data best.  Perform here as well an analysis of the bias-variance trade-off using the <strong>bootstrap</strong> resampling technique and an analysis of the mean squared error using cross-validation.</p>
-</div>
-<div class="section" id="exercise-analysis-of-real-data">
-<h3><span class="section-number">5.8.6. </span>Exercise: Analysis of real data<a class="headerlink" href="#exercise-analysis-of-real-data" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="exercise-analysis-of-real-data">
+<h3><span class="section-number">5.8.6. </span>Exercise: Analysis of real data<a class="headerlink" href="#exercise-analysis-of-real-data" title="Permalink to this heading">#</a></h3>
 <p>With our codes functioning and having been tested properly on a
 simpler function we are now ready to look at real data. We will
 essentially repeat in this exercise what was done in exercises 1-5. However, we
 need first to download the data and prepare properly the inputs to our
 codes.  We are going to download digital terrain data from the website
 <a class="reference external" href="https://earthexplorer.usgs.gov/">https://earthexplorer.usgs.gov/</a>,</p>
-<p>Or, if you prefer, we have placed selected datafiles at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles">https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles</a></p>
+<p>Or, if you prefer, we have placed selected datafiles at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2021/Project1/DataFiles">CompPhysics/MachineLearning</a></p>
 <p>In order to obtain data for a specific region, you need to register as
 a user (free) at this website and then decide upon which area you want
 to fetch the digital terrain data from.  In order to be able to read
@@ -3371,16 +2731,6 @@ Python program using</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [31],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
-<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">scipy</span><span class="o">.</span><span class="n">misc</span><span class="o">.</span><span class="n">imread</span>
-
-<span class="ne">NameError</span>: name &#39;scipy&#39; is not defined
-</pre></div>
-</div>
-</div>
 </div>
 <p>Here is a simple part of a Python code which reads and plots the data
 from such files</p>
@@ -3420,9 +2770,9 @@ model fits the data best.</p>
 <p>At the end, you should present a critical evaluation of your results
 and discuss the applicability of these regression methods to the type
 of data presented here (either the terrain data we propose or other data sets).</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -3436,7 +2786,7 @@ of data presented here (either the terrain data we propose or other data sets).<
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -3444,44 +2794,119 @@ of data presented here (either the terrain data we propose or other data sets).<
     </script>
     <script>kernelName = 'python3'</script>
 
-              </div>
+                </article>
               
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-            <p class="prev-next-title"><span class="section-number">4. </span>Ridge and Lasso Regression</p>
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+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">5.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reminder-on-statistics">5.2. Reminder on Statistics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">5.3. Resampling methods</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#bootstrap">5.3.1. Bootstrap</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-bias-variance-tradeoff">5.4. The bias-variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation">5.5. Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-rescaling-data">5.6. More on Rescaling data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-complicated-example-the-ising-model">5.7. More complicated Example: The Ising model</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises-and-projects">5.8. Exercises and Projects</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-ordinary-least-square-ols-on-the-franke-function">5.8.1. Exercise: Ordinary Least Square (OLS) on the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-bias-variance-trade-off-and-resampling-techniques">5.8.2. Exercise: Bias-variance trade-off and resampling techniques</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-cross-validation-as-resampling-techniques-adding-more-complexity">5.8.3. Exercise:  Cross-validation as resampling techniques, adding more complexity</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-ridge-regression-on-the-franke-function-with-resampling">5.8.4. Exercise: Ridge Regression on the Franke function  with resampling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-lasso-regression-on-the-franke-function-with-resampling">5.8.5. Exercise: Lasso Regression on the Franke function  with resampling</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-analysis-of-real-data">5.8.6. Exercise: Analysis of real data</a></li>
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-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+    <h1>Logistic Regression</h1>
+    <!-- Table of contents -->
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-            <div class="tocsection onthispage pt-5 pb-3">
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+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   6.1. Logistic Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basics">
-   6.2. Basics
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-logistic-function">
-   6.3. The logistic function
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-  <a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">
-   6.4. Examples of likelihood functions used in logistic regression and neural networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wisconsin-cancer-data">
-   6.5. Wisconsin Cancer Data
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">6.1. Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics">6.2. Basics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-logistic-function">6.3. The logistic function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">6.4. Examples of likelihood functions used in logistic regression and neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wisconsin-cancer-data">6.5. Wisconsin Cancer Data</a></li>
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-  </a>
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-   6.2. Basics
-  </a>
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-  <a class="reference internal nav-link" href="#the-logistic-function">
-   6.3. The logistic function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">
-   6.4. Examples of likelihood functions used in logistic regression and neural networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wisconsin-cancer-data">
-   6.5. Wisconsin Cancer Data
-  </a>
- </li>
-</ul>
 
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+              
                 
+<div id="searchbox"></div>
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+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapter4.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="logistic-regression">
-<h1><span class="section-number">6. </span>Logistic Regression<a class="headerlink" href="#logistic-regression" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="id1">
-<h2><span class="section-number">6.1. </span>Logistic Regression<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+doconce format html chapter4.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="logistic-regression">
+<h1><span class="section-number">6. </span>Logistic Regression<a class="headerlink" href="#logistic-regression" title="Permalink to this heading">#</a></h1>
+<section id="id1">
+<h2><span class="section-number">6.1. </span>Logistic Regression<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>In linear regression our main interest was centered on learning the
 coefficients of a functional fit (say a polynomial) in order to be
 able to predict the response of a continuous variable on some unseen
@@ -492,9 +459,9 @@ of basically all modern machine learning algorithms.</p>
 <p>We note also that many of the topics discussed here on logistic
 regression are also commonly used in modern supervised Deep Learning
 models, as we will see later.</p>
-</div>
-<div class="section" id="basics">
-<h2><span class="section-number">6.2. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="basics">
+<h2><span class="section-number">6.2. </span>Basics<a class="headerlink" href="#basics" title="Permalink to this heading">#</a></h2>
 <p>We consider the case where the dependent variables, also called the
 responses or the outcomes, <span class="math notranslate nohighlight">\(y_i\)</span> are discrete and only take values
 from <span class="math notranslate nohighlight">\(k=0,\dots,K-1\)</span> (i.e. <span class="math notranslate nohighlight">\(K\)</span> classes).</p>
@@ -602,112 +569,55 @@ the probability of a given category. This leads us to the logistic function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Common imports</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">os</span>
 
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
 
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>ID</th>
-      <th>Age</th>
-      <th>Agegroup</th>
-      <th>CHD</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>1</td>
-      <td>21</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>2</td>
-      <td>23</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>3</td>
-      <td>25</td>
-      <td>1</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>4</td>
-      <td>29</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>5</td>
-      <td>21</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>...</th>
-      <td>...</td>
-      <td>...</td>
-      <td>...</td>
-      <td>...</td>
-    </tr>
-    <tr>
-      <th>95</th>
-      <td>96</td>
-      <td>61</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>96</th>
-      <td>97</td>
-      <td>69</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>97</th>
-      <td>98</td>
-      <td>65</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>98</th>
-      <td>99</td>
-      <td>64</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>99</th>
-      <td>100</td>
-      <td>63</td>
-      <td>8</td>
-      <td>0</td>
-    </tr>
-  </tbody>
-</table>
-<p>100 rows × 4 columns</p>
-</div></div><img alt="_images/chapter4_8_1.png" src="_images/chapter4_8_1.png" />
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
+</div>
 </div>
 </div>
 <p>What we could attempt however is to plot the mean value for each group.</p>
@@ -724,9 +634,6 @@ the probability of a given category. This leads us to the logistic function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter4_10_0.png" src="_images/chapter4_10_0.png" />
-</div>
 </div>
 <p>We are now trying to find a function <span class="math notranslate nohighlight">\(f(y\vert x)\)</span>, that is a function which gives us an expected value for the output <span class="math notranslate nohighlight">\(y\)</span> with a given input <span class="math notranslate nohighlight">\(x\)</span>.
 In standard linear regression with a linear dependence on <span class="math notranslate nohighlight">\(x\)</span>, we would write this in terms of our model</p>
@@ -744,9 +651,9 @@ us to a very popular model for the function <span class="math notranslate nohigh
 Sigmoid function or logistic model. We will consider this function as
 representing the probability for finding a value of <span class="math notranslate nohighlight">\(y_i\)</span> with a given
 <span class="math notranslate nohighlight">\(x_i\)</span>.</p>
-</div>
-<div class="section" id="the-logistic-function">
-<h2><span class="section-number">6.3. </span>The logistic function<a class="headerlink" href="#the-logistic-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-logistic-function">
+<h2><span class="section-number">6.3. </span>The logistic function<a class="headerlink" href="#the-logistic-function" title="Permalink to this heading">#</a></h2>
 <p>Another widely studied model, is the so-called
 perceptron model, which is an example of a “hard classification” model. We
 will encounter this model when we discuss neural networks as
@@ -763,9 +670,9 @@ belongs to a category <span class="math notranslate nohighlight">\(y_i=\{0,1\}\)
 p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
 \]</div>
 <p>Note that <span class="math notranslate nohighlight">\(1-p(t)= p(-t)\)</span>.</p>
-</div>
-<div class="section" id="examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">
-<h2><span class="section-number">6.4. </span>Examples of likelihood functions used in logistic regression and neural networks<a class="headerlink" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">
+<h2><span class="section-number">6.4. </span>Examples of likelihood functions used in logistic regression and neural networks<a class="headerlink" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>The following code plots the logistic function, the step function and other functions we will encounter from here and on.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -826,11 +733,6 @@ p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter4_18_0.png" src="_images/chapter4_18_0.png" />
-<img alt="_images/chapter4_18_1.png" src="_images/chapter4_18_1.png" />
-<img alt="_images/chapter4_18_2.png" src="_images/chapter4_18_2.png" />
-</div>
 </div>
 <p>We assume now that we have two classes with <span class="math notranslate nohighlight">\(y_i\)</span> either <span class="math notranslate nohighlight">\(0\)</span> or <span class="math notranslate nohighlight">\(1\)</span>. Furthermore we assume also that we have only two parameters <span class="math notranslate nohighlight">\(\beta\)</span> in our fitting of the Sigmoid function, that is we define probabilities</p>
 <div class="math notranslate nohighlight">
@@ -959,9 +861,9 @@ what we derived earlier is compatible with these equations.</p>
 descent method.  Newton’s method and gradient descent methods are
 discussed in the material on <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html">optimization
 methods</a>.</p>
-</div>
-<div class="section" id="wisconsin-cancer-data">
-<h2><span class="section-number">6.5. </span>Wisconsin Cancer Data<a class="headerlink" href="#wisconsin-cancer-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="wisconsin-cancer-data">
+<h2><span class="section-number">6.5. </span>Wisconsin Cancer Data<a class="headerlink" href="#wisconsin-cancer-data" title="Permalink to this heading">#</a></h2>
 <p>We show here how we can use a simple regression case on the breast
 cancer data using Logistic regression as our algorithm for
 classification.</p>
@@ -995,24 +897,6 @@ classification.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
-(143, 30)
-Test set accuracy with Logistic Regression: 0.94
-Test set accuracy Logistic Regression with scaled data: 0.96
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-</pre></div>
-</div>
-</div>
 </div>
 <p>In addition to the above scores, we could also study the covariance (and the correlation matrix).
 We use <strong>Pandas</strong> to compute the correlation matrix.</p>
@@ -1055,10 +939,6 @@ We use <strong>Pandas</strong> to compute the correlation matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter4_57_0.png" src="_images/chapter4_57_0.png" />
-<img alt="_images/chapter4_57_1.png" src="_images/chapter4_57_1.png" />
-</div>
 </div>
 <p>In the above example we note two things. In the first plot we display
 the overlap of benign and malignant tumors as functions of the various
@@ -1092,7 +972,7 @@ the classical Principal Component Analysis (PCA) theorem with
 applications. This will be discussed later this semester (<a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html">week 43</a>).</p>
 <p>Here we present a further way to present our results in terms of a so-called <strong>confusion matrix</strong>, the cumulative gain and the <strong>ROC</strong> curve.
 This way of displaying our data are based upon different ways to classify our possible outcomes. Before we proceed we need some definitions.</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p><strong>TP</strong>: true positive or in other words, something equivalent with a proper classification</p></li>
 <li><p><strong>TN</strong>: true negative, which is equivalent with a correct rejection</p></li>
 <li><p><strong>FP</strong>: false positive, or in simpler words something that is equivalent with a false alarm</p></li>
@@ -1153,33 +1033,9 @@ Based on this we can then define the accuracy score as the sum of correctly pred
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
-(143, 30)
-Test set accuracy with Logistic Regression: 0.94
-Test set accuracy Logistic Regression with scaled data: 0.96
-[1.         1.         1.         1.         1.         1.
- 1.         1.         0.92857143 0.92857143]
-Test set accuracy with Logistic Regression  and scaled data: 0.96
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-</pre></div>
-</div>
-<img alt="_images/chapter4_64_2.png" src="_images/chapter4_64_2.png" />
-<img alt="_images/chapter4_64_3.png" src="_images/chapter4_64_3.png" />
-<img alt="_images/chapter4_64_4.png" src="_images/chapter4_64_4.png" />
-</div>
-</div>
-</div>
 </div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1193,7 +1049,7 @@ Please also refer to the documentation for alternative solver options:
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1201,44 +1057,105 @@ Please also refer to the documentation for alternative solver options:
     </script>
     <script>kernelName = 'python3'</script>
 
-              </div>
+                </article>
               
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+            
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+                <div class="bd-sidebar-secondary bd-toc"><div class="sidebar-secondary-items sidebar-secondary__inner">
 
+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
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+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">6.1. Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics">6.2. Basics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-logistic-function">6.3. The logistic function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks">6.4. Examples of likelihood functions used in logistic regression and neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wisconsin-cancer-data">6.5. Wisconsin Cancer Data</a></li>
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+
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-<p aria-level="2" class="caption" role="heading">
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+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#hyperplanes-and-all-that">
-   8.1. Hyperplanes and all that
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-two-dimensional-case">
-     8.1.1. The two-dimensional case
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-better-approach">
-     8.1.2. A better approach
-    </a>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-quick-reminder-on-lagrangian-multipliers">
-   8.2. A quick Reminder on Lagrangian Multipliers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-soft-classifier">
-   8.3. A soft classifier
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#kernels-and-non-linearity">
-   8.4. Kernels and non-linearity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#different-kernels-and-mercer-s-theorem">
-   8.5. Different kernels and Mercer’s theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-moons-example">
-   8.6. The moons example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-optimization-of-convex-functions">
-   8.7. Mathematical optimization of convex functions
-  </a>
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-</ul>
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+              
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+<div id="jb-print-docs-body" class="onlyprint">
+    <h1>Support Vector Machines, overarching aims</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
+            
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#hyperplanes-and-all-that">8.1. Hyperplanes and all that</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-two-dimensional-case">8.1.1. The two-dimensional case</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#a-better-approach">8.1.2. A better approach</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-quick-reminder-on-lagrangian-multipliers">8.2. A quick Reminder on Lagrangian Multipliers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-soft-classifier">8.3. A soft classifier</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#kernels-and-non-linearity">8.4. Kernels and non-linearity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#different-kernels-and-mercer-s-theorem">8.5. Different kernels and Mercer’s theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-moons-example">8.6. The moons example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-optimization-of-convex-functions">8.7. Mathematical optimization of convex functions</a></li>
+</ul>
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-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Support Vector Machines, overarching aims</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
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-                        
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-                            <h2> Contents </h2>
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-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#hyperplanes-and-all-that">
-   8.1. Hyperplanes and all that
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-two-dimensional-case">
-     8.1.1. The two-dimensional case
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#a-better-approach">
-     8.1.2. A better approach
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-quick-reminder-on-lagrangian-multipliers">
-   8.2. A quick Reminder on Lagrangian Multipliers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-soft-classifier">
-   8.3. A soft classifier
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#kernels-and-non-linearity">
-   8.4. Kernels and non-linearity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#different-kernels-and-mercer-s-theorem">
-   8.5. Different kernels and Mercer’s theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-moons-example">
-   8.6. The moons example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-optimization-of-convex-functions">
-   8.7. Mathematical optimization of convex functions
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="support-vector-machines-overarching-aims">
-<h1><span class="section-number">8. </span>Support Vector Machines, overarching aims<a class="headerlink" href="#support-vector-machines-overarching-aims" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="support-vector-machines-overarching-aims">
+<h1><span class="section-number">8. </span>Support Vector Machines, overarching aims<a class="headerlink" href="#support-vector-machines-overarching-aims" title="Permalink to this heading">#</a></h1>
 <p>A Support Vector Machine (SVM) is a very powerful and versatile
 Machine Learning method, capable of performing linear or nonlinear
 classification, regression, and even outlier detection. It is one of
@@ -516,8 +445,8 @@ latter introduces a so-called softening parameter to be discussed
 below.  We distinguish also between linear and non-linear
 approaches. The latter are the most frequent ones since it is rather
 unlikely that we can separate classes easily by say straight lines.</p>
-<div class="section" id="hyperplanes-and-all-that">
-<h2><span class="section-number">8.1. </span>Hyperplanes and all that<a class="headerlink" href="#hyperplanes-and-all-that" title="Permalink to this headline">¶</a></h2>
+<section id="hyperplanes-and-all-that">
+<h2><span class="section-number">8.1. </span>Hyperplanes and all that<a class="headerlink" href="#hyperplanes-and-all-that" title="Permalink to this heading">#</a></h2>
 <p>The theory behind support vector machines (SVM hereafter) is based on
 the mathematical description of so-called hyperplanes. Let us start
 with a two-dimensional case. This will also allow us to introduce our
@@ -601,12 +530,55 @@ circles.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>LinearSVC:                    [0.28475098] [[1.05364854 1.09903804]]
-SVC:                          [0.31896852] [[1.1203284  1.02625193]]
-SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">datasets</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">from</span> <span class="nn">sklearn.svm</span> <span class="kn">import</span> <span class="n">SVC</span><span class="p">,</span> <span class="n">LinearSVC</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/chapter5_1_1.png" src="_images/chapter5_1_1.png" />
 </div>
 </div>
 <p>The aim of the SVM algorithm is to find a hyperplane in a
@@ -660,8 +632,8 @@ then <span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> lies
 y_i\left(b+w_1x_{i1}+w_2x_{i2}+\dots +w_px_{ip}\right) &gt; 0.
 \]</div>
 <p>When we try to separate hyperplanes, if it exists, we can use it to construct a natural classifier: a test observation is assigned a given class depending on which side of the hyperplane it is located.</p>
-<div class="section" id="the-two-dimensional-case">
-<h3><span class="section-number">8.1.1. </span>The two-dimensional case<a class="headerlink" href="#the-two-dimensional-case" title="Permalink to this headline">¶</a></h3>
+<section id="the-two-dimensional-case">
+<h3><span class="section-number">8.1.1. </span>The two-dimensional case<a class="headerlink" href="#the-two-dimensional-case" title="Permalink to this heading">#</a></h3>
 <p>Let us try to develop our intuition about SVMs by limiting ourselves to a two-dimensional
 plane.  To separate the two classes of data points, there are many
 possible lines (hyperplanes if you prefer a more strict naming)<br />
@@ -728,9 +700,9 @@ gaps between the entries, we may also end up needing many iterations
 before the solutions converge and if the data cannot be separated
 properly into two distinct classes, we may not experience a converge
 at all.</p>
-</div>
-<div class="section" id="a-better-approach">
-<h3><span class="section-number">8.1.2. </span>A better approach<a class="headerlink" href="#a-better-approach" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="a-better-approach">
+<h3><span class="section-number">8.1.2. </span>A better approach<a class="headerlink" href="#a-better-approach" title="Permalink to this heading">#</a></h3>
 <p>A better approach is rather to try to define a large margin between
 the two classes (if they are well separated from the beginning).</p>
 <p>Thus, we wish to find a margin <span class="math notranslate nohighlight">\(M\)</span> with <span class="math notranslate nohighlight">\(\boldsymbol{w}\)</span> normalized to
@@ -760,10 +732,10 @@ y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
 <span class="math notranslate nohighlight">\(\boldsymbol{w}\)</span>. We want to minimize the norm in order to have a as large as
 possible margin <span class="math notranslate nohighlight">\(M\)</span>. Before we proceed, we need to remind ourselves
 about Lagrangian multipliers.</p>
-</div>
-</div>
-<div class="section" id="a-quick-reminder-on-lagrangian-multipliers">
-<h2><span class="section-number">8.2. </span>A quick Reminder on Lagrangian Multipliers<a class="headerlink" href="#a-quick-reminder-on-lagrangian-multipliers" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="a-quick-reminder-on-lagrangian-multipliers">
+<h2><span class="section-number">8.2. </span>A quick Reminder on Lagrangian Multipliers<a class="headerlink" href="#a-quick-reminder-on-lagrangian-multipliers" title="Permalink to this heading">#</a></h2>
 <p>Consider a function of three independent variables <span class="math notranslate nohighlight">\(f(x,y,z)\)</span> . For the function <span class="math notranslate nohighlight">\(f\)</span> to be an
 extreme we have</p>
 <div class="math notranslate nohighlight">
@@ -868,7 +840,7 @@ We must in addition satisfy the <a class="reference external" href="https://en.w
 \[
 \lambda_i\left[y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
 \]</div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>If <span class="math notranslate nohighlight">\(\lambda_i &gt; 0\)</span>, then <span class="math notranslate nohighlight">\(y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1\)</span> and we say that <span class="math notranslate nohighlight">\(x_i\)</span> is on the boundary.</p></li>
 <li><p>If <span class="math notranslate nohighlight">\(y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)&gt; 1\)</span>, we say <span class="math notranslate nohighlight">\(x_i\)</span> is not on the boundary and we set <span class="math notranslate nohighlight">\(\lambda_i=0\)</span>.</p></li>
 </ol>
@@ -917,9 +889,9 @@ b = \frac{1}{N_s}\sum_{j\in N_s}\left(y_j-\sum_{i=1}^n\lambda_iy_i\boldsymbol{x}
 y_i = \mathrm{sign}(\boldsymbol{w}^T\boldsymbol{x}_i+b).
 \]</div>
 <p>Below we discuss how to find the optimal values of <span class="math notranslate nohighlight">\(\lambda_i\)</span>. Before we proceed however, we discuss now the so-called soft classifier.</p>
-</div>
-<div class="section" id="a-soft-classifier">
-<h2><span class="section-number">8.3. </span>A soft classifier<a class="headerlink" href="#a-soft-classifier" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-soft-classifier">
+<h2><span class="section-number">8.3. </span>A soft classifier<a class="headerlink" href="#a-soft-classifier" title="Permalink to this heading">#</a></h2>
 <p>Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.</p>
 <p>Suppose now that classes overlap in feature space, as shown in the
 figure here. One way to deal with this problem before we define the
@@ -1001,9 +973,9 @@ K</p>
 \[
 y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 \]</div>
-</div>
-<div class="section" id="kernels-and-non-linearity">
-<h2><span class="section-number">8.4. </span>Kernels and non-linearity<a class="headerlink" href="#kernels-and-non-linearity" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="kernels-and-non-linearity">
+<h2><span class="section-number">8.4. </span>Kernels and non-linearity<a class="headerlink" href="#kernels-and-non-linearity" title="Permalink to this heading">#</a></h2>
 <p>The cases we have studied till now, were all characterized by two classes
 with a close to linear separability. The classifiers we have described
 so far find linear boundaries in our input feature space. It is
@@ -1067,9 +1039,6 @@ we need to introduce for example a polynomial transformation to a two-dimensiona
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter5_109_0.png" src="_images/chapter5_109_0.png" />
-</div>
 </div>
 <p>Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with <span class="math notranslate nohighlight">\(x_i\)</span> and <span class="math notranslate nohighlight">\(y_i\)</span> as variables)</p>
 <div class="math notranslate nohighlight">
@@ -1134,11 +1103,11 @@ If we add the slack constants this leads to the additional constraint <span clas
 <p>Below we discuss how to solve these equations. Here we note that the matrix <span class="math notranslate nohighlight">\(\boldsymbol{P}\)</span> has matrix elements <span class="math notranslate nohighlight">\(p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j)\)</span>.
 Given a kernel <span class="math notranslate nohighlight">\(K\)</span> and the targets <span class="math notranslate nohighlight">\(y_i\)</span> this matrix is easy to set up. The constraint <span class="math notranslate nohighlight">\(\boldsymbol{y}^T\boldsymbol{\lambda}=0\)</span> leads to <span class="math notranslate nohighlight">\(f=0\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{A}=\boldsymbol{y}\)</span>. How to set up the matrix <span class="math notranslate nohighlight">\(\boldsymbol{G}\)</span> is discussed later. Here note that the inequalities <span class="math notranslate nohighlight">\(0\leq \lambda_i \leq C\)</span> can be split up into
 <span class="math notranslate nohighlight">\(0\leq \lambda_i\)</span> and <span class="math notranslate nohighlight">\(\lambda_i \leq C\)</span>. These two inequalities define then the matrix <span class="math notranslate nohighlight">\(\boldsymbol{G}\)</span> and the vector <span class="math notranslate nohighlight">\(\boldsymbol{h}\)</span>.</p>
-</div>
-<div class="section" id="different-kernels-and-mercer-s-theorem">
-<h2><span class="section-number">8.5. </span>Different kernels and Mercer’s theorem<a class="headerlink" href="#different-kernels-and-mercer-s-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="different-kernels-and-mercer-s-theorem">
+<h2><span class="section-number">8.5. </span>Different kernels and Mercer’s theorem<a class="headerlink" href="#different-kernels-and-mercer-s-theorem" title="Permalink to this heading">#</a></h2>
 <p>There are several popular kernels being used. These are</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Linear: <span class="math notranslate nohighlight">\(K(\boldsymbol{x},\boldsymbol{y})=\boldsymbol{x}^T\boldsymbol{y}\)</span>,</p></li>
 <li><p>Polynomial: <span class="math notranslate nohighlight">\(K(\boldsymbol{x},\boldsymbol{y})=(\boldsymbol{x}^T\boldsymbol{y}+\gamma)^d\)</span>,</p></li>
 <li><p>Gaussian Radial Basis Function: <span class="math notranslate nohighlight">\(K(\boldsymbol{x},\boldsymbol{y})=\exp{\left(-\gamma\vert\vert\boldsymbol{x}-\boldsymbol{y}\vert\vert^2\right)}\)</span>,</p></li>
@@ -1160,9 +1129,9 @@ you don’t know what <span class="math notranslate nohighlight">\(\phi\)</span>
 <p>Note that some frequently used kernels (such as the Sigmoid kernel)
 don’t respect all of Mercer’s conditions, yet they generally work well
 in practice.</p>
-</div>
-<div class="section" id="the-moons-example">
-<h2><span class="section-number">8.6. </span>The moons example<a class="headerlink" href="#the-moons-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-moons-example">
+<h2><span class="section-number">8.6. </span>The moons example<a class="headerlink" href="#the-moons-example" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span><span class="p">,</span> <span class="n">unicode_literals</span>
@@ -1356,25 +1325,10 @@ in practice.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapter5_129_0.png" src="_images/chapter5_129_0.png" />
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_base.py:1206: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
-  warnings.warn(
-</pre></div>
 </div>
-<img alt="_images/chapter5_129_2.png" src="_images/chapter5_129_2.png" />
-<img alt="_images/chapter5_129_3.png" src="_images/chapter5_129_3.png" />
-<img alt="_images/chapter5_129_4.png" src="_images/chapter5_129_4.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Phi(-1.0, -2) = [0.74081822]
-Phi(-1.0, 1) = [0.30119421]
-</pre></div>
-</div>
-<img alt="_images/chapter5_129_6.png" src="_images/chapter5_129_6.png" />
-</div>
-</div>
-</div>
-<div class="section" id="mathematical-optimization-of-convex-functions">
-<h2><span class="section-number">8.7. </span>Mathematical optimization of convex functions<a class="headerlink" href="#mathematical-optimization-of-convex-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="mathematical-optimization-of-convex-functions">
+<h2><span class="section-number">8.7. </span>Mathematical optimization of convex functions<a class="headerlink" href="#mathematical-optimization-of-convex-functions" title="Permalink to this heading">#</a></h2>
 <p>A mathematical (quadratic) optimization problem, or just optimization problem, has the form</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -1467,14 +1421,6 @@ sol[’primal objective’]
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span>  Input In [5]
-    P = matrix(numpy.diag([1,0]), tc=’d’)
-                                     ^
-SyntaxError: invalid character &#39;’&#39; (U+2019)
-</pre></div>
-</div>
-</div>
 </div>
 <p>We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the <strong>slack</strong> parameter <span class="math notranslate nohighlight">\(C\)</span> we have</p>
 <div class="math notranslate nohighlight">
@@ -1490,8 +1436,8 @@ y_ny_1K(\boldsymbol{x}_n,\boldsymbol{x}_1) &amp; y_ny_2K(\boldsymbol{x}_n\boldsy
 <span class="math notranslate nohighlight">\(\boldsymbol{y}=[y_1,y_2,\dots,y_n]\)</span>.
 With  the slack constants this leads to the additional constraint <span class="math notranslate nohighlight">\(0\leq \lambda_i \leq C\)</span>.</p>
 <p><strong>code will be added</strong></p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1505,7 +1451,7 @@ With  the slack constants this leads to the additional constraint <span class="m
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1513,44 +1459,111 @@ With  the slack constants this leads to the additional constraint <span class="m
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#hyperplanes-and-all-that">8.1. Hyperplanes and all that</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-two-dimensional-case">8.1.1. The two-dimensional case</a></li>
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+</ul>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-quick-reminder-on-lagrangian-multipliers">8.2. A quick Reminder on Lagrangian Multipliers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-soft-classifier">8.3. A soft classifier</a></li>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-optimization-of-convex-functions">8.7. Mathematical optimization of convex functions</a></li>
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 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="statistics.html">
-   1. Elements of Probability Theory and Statistical Data Analysis
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="linalg.html">
-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter1.html">
-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-  <a class="reference internal" href="chapter3.html">
-   5. Resampling Methods
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-   6. Logistic Regression
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-   7. Optimization, the central part of any Machine Learning algortithm
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-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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-   12. Clustering and Unsupervised Learning
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+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   15. Solving Differential Equations  with Deep Learning
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="nav bd-sidenav">
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+`);
+</script>
+<label class="sidebar-toggle secondary-toggle btn btn-sm" for="__secondary"title="Toggle secondary sidebar" data-bs-placement="bottom" data-bs-toggle="tooltip">
+    <span class="fa-solid fa-list"></span>
+</label>
+</div></div>
+      
+    </div>
+  
+</div>
+</div>
+              
+              
+
+<div id="jb-print-docs-body" class="onlyprint">
+    <h1>Decision trees, overarching aims</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
             
-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basics-of-a-tree">
-   9.1. Basics of a tree
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#general-features">
-   9.2. General Features
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#building-a-tree-regression">
-   9.3. Building a tree, regression
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#making-a-tree">
-     9.3.1. Making a tree
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#schematic-regression-procedure">
-     9.3.2. Schematic Regression Procedure
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-classification-tree">
-   9.4. A Classification Tree
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#visualizing-the-tree-classification">
-     9.4.1. Visualizing the Tree, Classification
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#other-ways-of-visualizing-the-trees">
-     9.4.2. Other ways of visualizing the trees
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#algorithms-for-setting-up-decision-trees">
-   9.5. Algorithms for Setting up Decision Trees
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-cart-algorithm-for-classification">
-     9.5.1. The CART algorithm for Classification
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-cart-algorithm-for-regression">
-     9.5.2. The CART algorithm for Regression
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#computing-the-gini-index">
-     9.5.3. Computing the Gini index
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#simple-python-code-to-read-in-data-and-perform-classification">
-     9.5.4. Simple Python Code to read in Data and perform Classification
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#entropy-and-the-id3-algorithm">
-   9.6. Entropy and the ID3 algorithm
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#cancer-data-again-now-with-decision-trees-and-other-methods">
-     9.6.1. Cancer Data again now with Decision Trees and other Methods
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#another-example-the-moons-again">
-     9.6.2. Another example, the moons again
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#pros-and-cons-of-trees-pros">
-   9.7. Pros and cons of trees, pros
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#disadvantages">
-     9.7.1. Disadvantages
-    </a>
-   </li>
-  </ul>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics-of-a-tree">9.1. Basics of a tree</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#general-features">9.2. General Features</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#building-a-tree-regression">9.3. Building a tree, regression</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#making-a-tree">9.3.1. Making a tree</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#schematic-regression-procedure">9.3.2. Schematic Regression Procedure</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-classification-tree">9.4. A Classification Tree</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#visualizing-the-tree-classification">9.4.1. Visualizing the Tree, Classification</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#other-ways-of-visualizing-the-trees">9.4.2. Other ways of visualizing the trees</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#algorithms-for-setting-up-decision-trees">9.5. Algorithms for Setting up Decision Trees</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cart-algorithm-for-classification">9.5.1. The CART algorithm for Classification</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cart-algorithm-for-regression">9.5.2. The CART algorithm for Regression</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#computing-the-gini-index">9.5.3. Computing the Gini index</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-python-code-to-read-in-data-and-perform-classification">9.5.4. Simple Python Code to read in Data and perform Classification</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#entropy-and-the-id3-algorithm">9.6. Entropy and the ID3 algorithm</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#cancer-data-again-now-with-decision-trees-and-other-methods">9.6.1. Cancer Data again now with Decision Trees and other Methods</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-the-moons-again">9.6.2. Another example, the moons again</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pros-and-cons-of-trees-pros">9.7. Pros and cons of trees, pros</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#disadvantages">9.7.1. Disadvantages</a></li>
+</ul>
+</li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Decision trees, overarching aims</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basics-of-a-tree">
-   9.1. Basics of a tree
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#general-features">
-   9.2. General Features
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#building-a-tree-regression">
-   9.3. Building a tree, regression
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#making-a-tree">
-     9.3.1. Making a tree
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#schematic-regression-procedure">
-     9.3.2. Schematic Regression Procedure
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-classification-tree">
-   9.4. A Classification Tree
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#visualizing-the-tree-classification">
-     9.4.1. Visualizing the Tree, Classification
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#other-ways-of-visualizing-the-trees">
-     9.4.2. Other ways of visualizing the trees
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#algorithms-for-setting-up-decision-trees">
-   9.5. Algorithms for Setting up Decision Trees
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-cart-algorithm-for-classification">
-     9.5.1. The CART algorithm for Classification
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-cart-algorithm-for-regression">
-     9.5.2. The CART algorithm for Regression
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#computing-the-gini-index">
-     9.5.3. Computing the Gini index
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#simple-python-code-to-read-in-data-and-perform-classification">
-     9.5.4. Simple Python Code to read in Data and perform Classification
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#entropy-and-the-id3-algorithm">
-   9.6. Entropy and the ID3 algorithm
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#cancer-data-again-now-with-decision-trees-and-other-methods">
-     9.6.1. Cancer Data again now with Decision Trees and other Methods
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#another-example-the-moons-again">
-     9.6.2. Another example, the moons again
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#pros-and-cons-of-trees-pros">
-   9.7. Pros and cons of trees, pros
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#disadvantages">
-     9.7.1. Disadvantages
-    </a>
-   </li>
-  </ul>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="decision-trees-overarching-aims">
-<h1><span class="section-number">9. </span>Decision trees, overarching aims<a class="headerlink" href="#decision-trees-overarching-aims" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="decision-trees-overarching-aims">
+<h1><span class="section-number">9. </span>Decision trees, overarching aims<a class="headerlink" href="#decision-trees-overarching-aims" title="Permalink to this heading">#</a></h1>
 <p>We start here with the most basic algorithm, the so-called decision
 tree. With this basic algorithm we can in turn build more complex
 networks, spanning from homogeneous and heterogenous forests (bagging,
@@ -619,8 +459,8 @@ for the resulting underlying datasets are as pure as possible.</p>
 to be the most informative ones. The process of finding the <strong>most
 informative</strong> feature is done until we accomplish a stopping criteria
 where we then finally end up in so called <strong>leaf nodes</strong>.</p>
-<div class="section" id="basics-of-a-tree">
-<h2><span class="section-number">9.1. </span>Basics of a tree<a class="headerlink" href="#basics-of-a-tree" title="Permalink to this headline">¶</a></h2>
+<section id="basics-of-a-tree">
+<h2><span class="section-number">9.1. </span>Basics of a tree<a class="headerlink" href="#basics-of-a-tree" title="Permalink to this heading">#</a></h2>
 <p>A decision tree is typically divided into a <strong>root node</strong>, the <strong>interior nodes</strong>,
 and the final <strong>leaf nodes</strong> or just <strong>leaves</strong>. These entities are then connected by so-called <strong>branches</strong>.</p>
 <p>The leaf nodes
@@ -629,9 +469,9 @@ to our trained model. This is possible since the model has
 learned the underlying structure of the training data and hence can,
 given some assumptions, make predictions about the target feature value
 (class) of unseen query instances.</p>
-</div>
-<div class="section" id="general-features">
-<h2><span class="section-number">9.2. </span>General Features<a class="headerlink" href="#general-features" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="general-features">
+<h2><span class="section-number">9.2. </span>General Features<a class="headerlink" href="#general-features" title="Permalink to this heading">#</a></h2>
 <p>The overarching approach to decision trees is a top-down approach.</p>
 <ul class="simple">
 <li><p>A leaf provides the classification of a given instance.</p></li>
@@ -643,7 +483,7 @@ given some assumptions, make predictions about the target feature value
 node.</p>
 <p>In simplified terms, the process of training a decision tree and
 predicting the target features of query instances is as follows:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature</p></li>
 <li><p>Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process</p></li>
 <li><p>Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the <em>predictions</em> we want to make for new query instances</p></li>
@@ -746,21 +586,62 @@ predicting the target features of query instances is as follows:</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2nd degree coefficients:
-zero power:  4.0618352118150005
-first power:  0.004339135748752641
-second power:  1.9543538503067644e-05
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/chapter6_1_1.png" src="_images/chapter6_1_1.png" />
-<img alt="_images/chapter6_1_2.png" src="_images/chapter6_1_2.png" />
 </div>
 </div>
-</div>
-<div class="section" id="building-a-tree-regression">
-<h2><span class="section-number">9.3. </span>Building a tree, regression<a class="headerlink" href="#building-a-tree-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="building-a-tree-regression">
+<h2><span class="section-number">9.3. </span>Building a tree, regression<a class="headerlink" href="#building-a-tree-regression" title="Permalink to this heading">#</a></h2>
 <p>There are mainly two steps</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>We split the predictor space (the set of possible values <span class="math notranslate nohighlight">\(x_1,x_2,\dots, x_p\)</span>) into <span class="math notranslate nohighlight">\(J\)</span> distinct and non-non-overlapping regions, <span class="math notranslate nohighlight">\(R_1,R_2,\dots,R_J\)</span>.</p></li>
 <li><p>For every observation that falls into the region <span class="math notranslate nohighlight">\(R_j\)</span> , we make the same prediction, which is simply the mean of the response values for the training observations in <span class="math notranslate nohighlight">\(R_j\)</span>.</p></li>
 </ol>
@@ -786,8 +667,8 @@ further down on the tree. It is greedy because at each step of the
 tree-building process, the best split is made at that particular step,
 rather than looking ahead and picking a split that will lead to a
 better tree in some future step.</p>
-<div class="section" id="making-a-tree">
-<h3><span class="section-number">9.3.1. </span>Making a tree<a class="headerlink" href="#making-a-tree" title="Permalink to this headline">¶</a></h3>
+<section id="making-a-tree">
+<h3><span class="section-number">9.3.1. </span>Making a tree<a class="headerlink" href="#making-a-tree" title="Permalink to this heading">#</a></h3>
 <p>In order to implement the recursive binary splitting we start by selecting
 the predictor <span class="math notranslate nohighlight">\(x_j\)</span> and a cutpoint <span class="math notranslate nohighlight">\(s\)</span> that splits the predictor space into two regions <span class="math notranslate nohighlight">\(R_1\)</span> and <span class="math notranslate nohighlight">\(R_2\)</span></p>
 <div class="math notranslate nohighlight">
@@ -858,11 +739,11 @@ so obtaining the whole sequence of subtrees as a function of <span class="math n
 easy. We can select a value of <span class="math notranslate nohighlight">\(\alpha\)</span> using a validation set or using
 cross-validation. We then return to the full data set and obtain the
 subtree corresponding to <span class="math notranslate nohighlight">\(\alpha\)</span>.</p>
-</div>
-<div class="section" id="schematic-regression-procedure">
-<h3><span class="section-number">9.3.2. </span>Schematic Regression Procedure<a class="headerlink" href="#schematic-regression-procedure" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="schematic-regression-procedure">
+<h3><span class="section-number">9.3.2. </span>Schematic Regression Procedure<a class="headerlink" href="#schematic-regression-procedure" title="Permalink to this heading">#</a></h3>
 <p>Building a Regression Tree</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.</p></li>
 <li><p>Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of <span class="math notranslate nohighlight">\(\alpha\)</span>.</p></li>
 <li><p>Use for example <span class="math notranslate nohighlight">\(K\)</span>-fold cross-validation to choose <span class="math notranslate nohighlight">\(\alpha\)</span>. Divide the training observations into <span class="math notranslate nohighlight">\(K\)</span> folds. For each <span class="math notranslate nohighlight">\(k=1,2,\dots,K\)</span> we:</p></li>
@@ -872,14 +753,14 @@ subtree corresponding to <span class="math notranslate nohighlight">\(\alpha\)</
 <li><p>Then we valuate the mean squared prediction error on the data in the left-out <span class="math notranslate nohighlight">\(k\)</span>-th fold, as a function of <span class="math notranslate nohighlight">\(\alpha\)</span>.</p></li>
 <li><p>Finally  we average the results for each value of <span class="math notranslate nohighlight">\(\alpha\)</span>, and pick <span class="math notranslate nohighlight">\(\alpha\)</span> to minimize the average error.</p></li>
 </ul>
-<ol class="simple">
+<ol class="arabic simple" start="4">
 <li><p>Return the subtree from Step 2 that corresponds to the chosen value of <span class="math notranslate nohighlight">\(\alpha\)</span>.</p></li>
 </ol>
 <p>!eblock</p>
-</div>
-</div>
-<div class="section" id="a-classification-tree">
-<h2><span class="section-number">9.4. </span>A Classification Tree<a class="headerlink" href="#a-classification-tree" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="a-classification-tree">
+<h2><span class="section-number">9.4. </span>A Classification Tree<a class="headerlink" href="#a-classification-tree" title="Permalink to this heading">#</a></h2>
 <p>A classification tree is very similar to a regression tree, except
 that it is used to predict a qualitative response rather than a
 quantitative one. Recall that for a regression tree, the predicted
@@ -941,8 +822,8 @@ g = \sum_{k=1}^K p_{mk}(1-p_{mk}).
 \[
 s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 \]</div>
-<div class="section" id="visualizing-the-tree-classification">
-<h3><span class="section-number">9.4.1. </span>Visualizing the Tree, Classification<a class="headerlink" href="#visualizing-the-tree-classification" title="Permalink to this headline">¶</a></h3>
+<section id="visualizing-the-tree-classification">
+<h3><span class="section-number">9.4.1. </span>Visualizing the Tree, Classification<a class="headerlink" href="#visualizing-the-tree-classification" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">os</span>
@@ -981,106 +862,6 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \
-0          17.99         10.38          122.80     1001.0          0.11840   
-1          20.57         17.77          132.90     1326.0          0.08474   
-2          19.69         21.25          130.00     1203.0          0.10960   
-3          11.42         20.38           77.58      386.1          0.14250   
-4          20.29         14.34          135.10     1297.0          0.10030   
-..           ...           ...             ...        ...              ...   
-564        21.56         22.39          142.00     1479.0          0.11100   
-565        20.13         28.25          131.20     1261.0          0.09780   
-566        16.60         28.08          108.30      858.1          0.08455   
-567        20.60         29.33          140.10     1265.0          0.11780   
-568         7.76         24.54           47.92      181.0          0.05263   
-
-     mean compactness  mean concavity  mean concave points  mean symmetry  \
-0             0.27760         0.30010              0.14710         0.2419   
-1             0.07864         0.08690              0.07017         0.1812   
-2             0.15990         0.19740              0.12790         0.2069   
-3             0.28390         0.24140              0.10520         0.2597   
-4             0.13280         0.19800              0.10430         0.1809   
-..                ...             ...                  ...            ...   
-564           0.11590         0.24390              0.13890         0.1726   
-565           0.10340         0.14400              0.09791         0.1752   
-566           0.10230         0.09251              0.05302         0.1590   
-567           0.27700         0.35140              0.15200         0.2397   
-568           0.04362         0.00000              0.00000         0.1587   
-
-     mean fractal dimension  ...  worst radius  worst texture  \
-0                   0.07871  ...        25.380          17.33   
-1                   0.05667  ...        24.990          23.41   
-2                   0.05999  ...        23.570          25.53   
-3                   0.09744  ...        14.910          26.50   
-4                   0.05883  ...        22.540          16.67   
-..                      ...  ...           ...            ...   
-564                 0.05623  ...        25.450          26.40   
-565                 0.05533  ...        23.690          38.25   
-566                 0.05648  ...        18.980          34.12   
-567                 0.07016  ...        25.740          39.42   
-568                 0.05884  ...         9.456          30.37   
-
-     worst perimeter  worst area  worst smoothness  worst compactness  \
-0             184.60      2019.0           0.16220            0.66560   
-1             158.80      1956.0           0.12380            0.18660   
-2             152.50      1709.0           0.14440            0.42450   
-3              98.87       567.7           0.20980            0.86630   
-4             152.20      1575.0           0.13740            0.20500   
-..               ...         ...               ...                ...   
-564           166.10      2027.0           0.14100            0.21130   
-565           155.00      1731.0           0.11660            0.19220   
-566           126.70      1124.0           0.11390            0.30940   
-567           184.60      1821.0           0.16500            0.86810   
-568            59.16       268.6           0.08996            0.06444   
-
-     worst concavity  worst concave points  worst symmetry  \
-0             0.7119                0.2654          0.4601   
-1             0.2416                0.1860          0.2750   
-2             0.4504                0.2430          0.3613   
-3             0.6869                0.2575          0.6638   
-4             0.4000                0.1625          0.2364   
-..               ...                   ...             ...   
-564           0.4107                0.2216          0.2060   
-565           0.3215                0.1628          0.2572   
-566           0.3403                0.1418          0.2218   
-567           0.9387                0.2650          0.4087   
-568           0.0000                0.0000          0.2871   
-
-     worst fractal dimension  
-0                    0.11890  
-1                    0.08902  
-2                    0.08758  
-3                    0.17300  
-4                    0.07678  
-..                       ...  
-564                  0.07115  
-565                  0.06637  
-566                  0.07820  
-567                  0.12400  
-568                  0.07039  
-
-[569 rows x 30 columns]
-     malignant  benign
-0            1       0
-1            1       0
-2            1       0
-3            1       0
-4            1       0
-..         ...     ...
-564          1       0
-565          1       0
-566          1       0
-567          1       0
-568          0       1
-
-[569 rows x 2 columns]
-</pre></div>
-</div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1111,15 +892,10 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="other-ways-of-visualizing-the-trees">
-<h3><span class="section-number">9.4.2. </span>Other ways of visualizing the trees<a class="headerlink" href="#other-ways-of-visualizing-the-trees" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="other-ways-of-visualizing-the-trees">
+<h3><span class="section-number">9.4.2. </span>Other ways of visualizing the trees<a class="headerlink" href="#other-ways-of-visualizing-the-trees" title="Permalink to this heading">#</a></h3>
 <p><strong>Scikit-Learn</strong> has also another way to visualize the trees which is very useful, here with the Iris data.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1133,28 +909,6 @@ s = -\sum_{k=1}^K p_{mk}\log{p_{mk}}.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[Text(0.5, 0.9166666666666666, &#39;X[2] &lt;= 2.45\ngini = 0.667\nsamples = 150\nvalue = [50, 50, 50]&#39;),
- Text(0.4230769230769231, 0.75, &#39;gini = 0.0\nsamples = 50\nvalue = [50, 0, 0]&#39;),
- Text(0.5769230769230769, 0.75, &#39;X[3] &lt;= 1.75\ngini = 0.5\nsamples = 100\nvalue = [0, 50, 50]&#39;),
- Text(0.3076923076923077, 0.5833333333333334, &#39;X[2] &lt;= 4.95\ngini = 0.168\nsamples = 54\nvalue = [0, 49, 5]&#39;),
- Text(0.15384615384615385, 0.4166666666666667, &#39;X[3] &lt;= 1.65\ngini = 0.041\nsamples = 48\nvalue = [0, 47, 1]&#39;),
- Text(0.07692307692307693, 0.25, &#39;gini = 0.0\nsamples = 47\nvalue = [0, 47, 0]&#39;),
- Text(0.23076923076923078, 0.25, &#39;gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]&#39;),
- Text(0.46153846153846156, 0.4166666666666667, &#39;X[3] &lt;= 1.55\ngini = 0.444\nsamples = 6\nvalue = [0, 2, 4]&#39;),
- Text(0.38461538461538464, 0.25, &#39;gini = 0.0\nsamples = 3\nvalue = [0, 0, 3]&#39;),
- Text(0.5384615384615384, 0.25, &#39;X[2] &lt;= 5.45\ngini = 0.444\nsamples = 3\nvalue = [0, 2, 1]&#39;),
- Text(0.46153846153846156, 0.08333333333333333, &#39;gini = 0.0\nsamples = 2\nvalue = [0, 2, 0]&#39;),
- Text(0.6153846153846154, 0.08333333333333333, &#39;gini = 0.0\nsamples = 1\nvalue = [0, 0, 1]&#39;),
- Text(0.8461538461538461, 0.5833333333333334, &#39;X[2] &lt;= 4.85\ngini = 0.043\nsamples = 46\nvalue = [0, 1, 45]&#39;),
- Text(0.7692307692307693, 0.4166666666666667, &#39;X[1] &lt;= 3.1\ngini = 0.444\nsamples = 3\nvalue = [0, 1, 2]&#39;),
- Text(0.6923076923076923, 0.25, &#39;gini = 0.0\nsamples = 2\nvalue = [0, 0, 2]&#39;),
- Text(0.8461538461538461, 0.25, &#39;gini = 0.0\nsamples = 1\nvalue = [0, 1, 0]&#39;),
- Text(0.9230769230769231, 0.4166666666666667, &#39;gini = 0.0\nsamples = 43\nvalue = [0, 0, 43]&#39;)]
-</pre></div>
-</div>
-<img alt="_images/chapter6_24_1.png" src="_images/chapter6_24_1.png" />
-</div>
 </div>
 <p>Alternatively, the tree can also be exported in textual format with the function exporttext.
 This method doesn’t require the installation of external libraries and is more compact:</p>
@@ -1171,24 +925,13 @@ This method doesn’t require the installation of external libraries and is more
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>|--- petal width (cm) &lt;= 0.80
-|   |--- class: 0
-|--- petal width (cm) &gt;  0.80
-|   |--- petal width (cm) &lt;= 1.75
-|   |   |--- class: 1
-|   |--- petal width (cm) &gt;  1.75
-|   |   |--- class: 2
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="algorithms-for-setting-up-decision-trees">
-<h2><span class="section-number">9.5. </span>Algorithms for Setting up Decision Trees<a class="headerlink" href="#algorithms-for-setting-up-decision-trees" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="algorithms-for-setting-up-decision-trees">
+<h2><span class="section-number">9.5. </span>Algorithms for Setting up Decision Trees<a class="headerlink" href="#algorithms-for-setting-up-decision-trees" title="Permalink to this heading">#</a></h2>
 <p>Two algorithms stand out in the set up of decision trees:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>The CART (Classification And Regression Tree) algorithm for both classification and regression</p></li>
 <li><p>The ID3 algorithm based on the computation of the information gain for classification</p></li>
 </ol>
@@ -1196,8 +939,8 @@ This method doesn’t require the installation of external libraries and is more
 <strong>Scikit-Learn</strong> uses the CART algorithm. For classification problems
 you can use either the <strong>gini</strong> index or the <strong>entropy</strong> to split a tree
 in two branches.</p>
-<div class="section" id="the-cart-algorithm-for-classification">
-<h3><span class="section-number">9.5.1. </span>The CART algorithm for Classification<a class="headerlink" href="#the-cart-algorithm-for-classification" title="Permalink to this headline">¶</a></h3>
+<section id="the-cart-algorithm-for-classification">
+<h3><span class="section-number">9.5.1. </span>The CART algorithm for Classification<a class="headerlink" href="#the-cart-algorithm-for-classification" title="Permalink to this heading">#</a></h3>
 <p>For classification, the CART algorithm splits the data set in two subsets using a single feature <span class="math notranslate nohighlight">\(k\)</span> and a threshold <span class="math notranslate nohighlight">\(t_k\)</span>.
 This could be for example a threshold set by a number below a certain circumference of a malign tumor.</p>
 <p>How do we find these two quantities?
@@ -1214,9 +957,9 @@ and so on, recursively. It stops recursing once it reaches the maximum depth (de
 <span class="math notranslate nohighlight">\(max\_depth\)</span> hyperparameter), or if it cannot find a split that will reduce impurity. A few other
 hyperparameters control additional stopping conditions such as the <span class="math notranslate nohighlight">\(min\_samples\_split\)</span>,
 <span class="math notranslate nohighlight">\(min\_samples\_leaf\)</span>, <span class="math notranslate nohighlight">\(min\_weight\_fraction\_leaf\)</span>, and <span class="math notranslate nohighlight">\(max\_leaf\_nodes\)</span>.</p>
-</div>
-<div class="section" id="the-cart-algorithm-for-regression">
-<h3><span class="section-number">9.5.2. </span>The CART algorithm for Regression<a class="headerlink" href="#the-cart-algorithm-for-regression" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="the-cart-algorithm-for-regression">
+<h3><span class="section-number">9.5.2. </span>The CART algorithm for Regression<a class="headerlink" href="#the-cart-algorithm-for-regression" title="Permalink to this heading">#</a></h3>
 <p>The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the
 training set in a way that minimizes say the <strong>gini</strong> or <strong>entropy</strong> impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now</p>
 <div class="math notranslate nohighlight">
@@ -1236,9 +979,9 @@ C(k,t_k) = \frac{m_{\mathrm{left}}}{m}\mathrm{MSE}_{\mathrm{left}}+ \frac{m_{\ma
 <p>the mean value of all observations in a specific node.</p>
 <p>Without any regularization, the regression task for decision trees,
 just like for classification tasks, is  prone to overfitting.</p>
-</div>
-<div class="section" id="computing-the-gini-index">
-<h3><span class="section-number">9.5.3. </span>Computing the Gini index<a class="headerlink" href="#computing-the-gini-index" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="computing-the-gini-index">
+<h3><span class="section-number">9.5.3. </span>Computing the Gini index<a class="headerlink" href="#computing-the-gini-index" title="Permalink to this heading">#</a></h3>
 <p>The example we will look at is a classical one in many Machine
 Learning applications. Based on various meteorological features, we
 have several so-called attributes which decide whether we at the end
@@ -1271,9 +1014,9 @@ humidity and weak and strong for wind.</p>
 <tr><td align="center">   14     </td> <td align="center">   Rain        </td> <td align="center">   Mild           </td> <td align="center">   High        </td> <td align="center">   Strong    </td> <td align="center">   0       </td> </tr>
 </tbody>
 </table>
-</div>
-<div class="section" id="simple-python-code-to-read-in-data-and-perform-classification">
-<h3><span class="section-number">9.5.4. </span>Simple Python Code to read in Data and perform Classification<a class="headerlink" href="#simple-python-code-to-read-in-data-and-perform-classification" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="simple-python-code-to-read-in-data-and-perform-classification">
+<h3><span class="section-number">9.5.4. </span>Simple Python Code to read in Data and perform Classification<a class="headerlink" href="#simple-python-code-to-read-in-data-and-perform-classification" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Common imports</span>
@@ -1346,20 +1089,6 @@ humidity and weak and strong for wind.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">FileNotFoundError</span><span class="g g-Whitespace">                         </span>Traceback (most recent call last)
-<span class="nn">Input In [6],</span> in <span class="ni">&lt;cell line: 37&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">     </span><span class="mi">34</span> <span class="k">def</span> <span class="nf">save_fig</span><span class="p">(</span><span class="n">fig_id</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span>     <span class="n">plt</span><span class="o">.</span><span class="n">savefig</span><span class="p">(</span><span class="n">image_path</span><span class="p">(</span><span class="n">fig_id</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot;.png&quot;</span><span class="p">,</span> <span class="nb">format</span><span class="o">=</span><span class="s1">&#39;png&#39;</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="n">infile</span> <span class="o">=</span> <span class="nb">open</span><span class="p">(</span><span class="n">data_path</span><span class="p">(</span><span class="s2">&quot;rideclass.csv&quot;</span><span class="p">),</span><span class="s1">&#39;r&#39;</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="c1"># Read the experimental data with Pandas</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span>
-
-<span class="ne">FileNotFoundError</span>: [Errno 2] No such file or directory: &#39;DataFiles/rideclass.csv&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>The above functions (gini, entropy and misclassification error) are
 important components of the so-called CART algorithm. We will discuss
@@ -1432,13 +1161,13 @@ algorithm ID3.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="entropy-and-the-id3-algorithm">
-<h2><span class="section-number">9.6. </span>Entropy and the ID3 algorithm<a class="headerlink" href="#entropy-and-the-id3-algorithm" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="entropy-and-the-id3-algorithm">
+<h2><span class="section-number">9.6. </span>Entropy and the ID3 algorithm<a class="headerlink" href="#entropy-and-the-id3-algorithm" title="Permalink to this heading">#</a></h2>
 <p>The ID3 algorithm  learns decision trees by constructing
 them in a top down way, beginning with the question <strong>which attribute should be tested at the root of the tree</strong>?</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.</p></li>
 <li><p>The best attribute is selected and used as the test at the root node of the tree.</p></li>
 <li><p>A descendant of the root node is then created for each possible value of this attribute.</p></li>
@@ -1455,8 +1184,8 @@ examples.</p>
 training examples according to their target classification.</p>
 <p>The ID3 algorithm uses this information gain measure to select among the candidate
 attributes at each step while growing the tree.</p>
-<div class="section" id="cancer-data-again-now-with-decision-trees-and-other-methods">
-<h3><span class="section-number">9.6.1. </span>Cancer Data again now with Decision Trees and other Methods<a class="headerlink" href="#cancer-data-again-now-with-decision-trees-and-other-methods" title="Permalink to this headline">¶</a></h3>
+<section id="cancer-data-again-now-with-decision-trees-and-other-methods">
+<h3><span class="section-number">9.6.1. </span>Cancer Data again now with Decision Trees and other Methods<a class="headerlink" href="#cancer-data-again-now-with-decision-trees-and-other-methods" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1504,9 +1233,9 @@ attributes at each step while growing the tree.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="another-example-the-moons-again">
-<h3><span class="section-number">9.6.2. </span>Another example, the moons again<a class="headerlink" href="#another-example-the-moons-again" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="another-example-the-moons-again">
+<h3><span class="section-number">9.6.2. </span>Another example, the moons again<a class="headerlink" href="#another-example-the-moons-again" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">__future__</span> <span class="kn">import</span> <span class="n">division</span><span class="p">,</span> <span class="n">print_function</span><span class="p">,</span> <span class="n">unicode_literals</span>
@@ -1703,10 +1432,10 @@ attributes at each step while growing the tree.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="pros-and-cons-of-trees-pros">
-<h2><span class="section-number">9.7. </span>Pros and cons of trees, pros<a class="headerlink" href="#pros-and-cons-of-trees-pros" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="pros-and-cons-of-trees-pros">
+<h2><span class="section-number">9.7. </span>Pros and cons of trees, pros<a class="headerlink" href="#pros-and-cons-of-trees-pros" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)</p></li>
 <li><p>Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!</p></li>
@@ -1716,8 +1445,8 @@ attributes at each step while growing the tree.</p>
 <li><p>Can model interactions between the different descriptive features</p></li>
 <li><p>Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)</p></li>
 </ul>
-<div class="section" id="disadvantages">
-<h3><span class="section-number">9.7.1. </span>Disadvantages<a class="headerlink" href="#disadvantages" title="Permalink to this headline">¶</a></h3>
+<section id="disadvantages">
+<h3><span class="section-number">9.7.1. </span>Disadvantages<a class="headerlink" href="#disadvantages" title="Permalink to this heading">#</a></h3>
 <ul class="simple">
 <li><p>Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches</p></li>
 <li><p>If continuous features are used the tree may become quite large and hence less interpretable</p></li>
@@ -1730,9 +1459,9 @@ attributes at each step while growing the tree.</p>
 <p>However, by aggregating many decision trees, using methods like
 bagging, random forests, and boosting, the predictive performance of
 trees can be substantially improved.</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1746,7 +1475,7 @@ trees can be substantially improved.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1754,44 +1483,128 @@ trees can be substantially improved.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <i class="fa-solid fa-list"></i> Contents
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+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics-of-a-tree">9.1. Basics of a tree</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#general-features">9.2. General Features</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#building-a-tree-regression">9.3. Building a tree, regression</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#making-a-tree">9.3.1. Making a tree</a></li>
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+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-classification-tree">9.4. A Classification Tree</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#visualizing-the-tree-classification">9.4.1. Visualizing the Tree, Classification</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#other-ways-of-visualizing-the-trees">9.4.2. Other ways of visualizing the trees</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#algorithms-for-setting-up-decision-trees">9.5. Algorithms for Setting up Decision Trees</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cart-algorithm-for-classification">9.5.1. The CART algorithm for Classification</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cart-algorithm-for-regression">9.5.2. The CART algorithm for Regression</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#computing-the-gini-index">9.5.3. Computing the Gini index</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-python-code-to-read-in-data-and-perform-classification">9.5.4. Simple Python Code to read in Data and perform Classification</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#entropy-and-the-id3-algorithm">9.6. Entropy and the ID3 algorithm</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#cancer-data-again-now-with-decision-trees-and-other-methods">9.6.1. Cancer Data again now with Decision Trees and other Methods</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-the-moons-again">9.6.2. Another example, the moons again</a></li>
+</ul>
+</li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#disadvantages">9.7.1. Disadvantages</a></li>
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-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
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-  Decision Trees, Ensemble Methods and Boosting
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">
-   10.1. An Overview of Ensemble Methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bagging">
-   10.2. Bagging
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bagging-examples">
-   10.3. Bagging Examples
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
-     10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#random-forests">
-   10.4. Random forests
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#compare-bagging-on-trees-with-random-forests">
-     10.4.1. Compare  Bagging on Trees with Random Forests
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#boosting-a-bird-s-eye-view">
-   10.5. Boosting, a Bird’s Eye View
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">
-     10.5.1. Iterative Fitting, Regression and Squared-error Cost Function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">
-     10.5.2. Iterative Fitting, Classification and AdaBoost
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">
-     10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
-   10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">
-   10.7. Gradient Boosting, Examples of Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-classification-example">
-   10.8. Gradient Boosting, Classification Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">
-   10.9. XGBoost: Extreme Gradient Boosting
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-case">
-   10.10. Regression Case
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">10.1. An Overview of Ensemble Methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bagging">10.2. Bagging</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bagging-examples">10.3. Bagging Examples</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree">10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#random-forests">10.4. Random forests</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#compare-bagging-on-trees-with-random-forests">10.4.1. Compare  Bagging on Trees with Random Forests</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#boosting-a-bird-s-eye-view">10.5. Boosting, a Bird’s Eye View</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">10.5.1. Iterative Fitting, Regression and Squared-error Cost Function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">10.5.2. Iterative Fitting, Classification and AdaBoost</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">10.7. Gradient Boosting, Examples of Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-classification-example">10.8. Gradient Boosting, Classification Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">10.9. XGBoost: Extreme Gradient Boosting</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-case">10.10. Regression Case</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">
-   10.1. An Overview of Ensemble Methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bagging">
-   10.2. Bagging
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bagging-examples">
-   10.3. Bagging Examples
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
-     10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#random-forests">
-   10.4. Random forests
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#compare-bagging-on-trees-with-random-forests">
-     10.4.1. Compare  Bagging on Trees with Random Forests
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#boosting-a-bird-s-eye-view">
-   10.5. Boosting, a Bird’s Eye View
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">
-     10.5.1. Iterative Fitting, Regression and Squared-error Cost Function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">
-     10.5.2. Iterative Fitting, Classification and AdaBoost
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">
-     10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
-   10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">
-   10.7. Gradient Boosting, Examples of Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-boosting-classification-example">
-   10.8. Gradient Boosting, Classification Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">
-   10.9. XGBoost: Extreme Gradient Boosting
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-case">
-   10.10. Regression Case
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods">
-<h1><span class="section-number">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods<a class="headerlink" href="#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods">
+<h1><span class="section-number">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods<a class="headerlink" href="#ensemble-methods-from-a-single-tree-to-many-trees-and-extreme-boosting-meet-the-jungle-of-methods" title="Permalink to this heading">#</a></h1>
 <p>As stated previously and seen in many of the examples discussed in the previous chapter about
 a single decision tree, we often end up overfitting our training
 data. This normally means that we have a high variance. Can we reduce
@@ -573,19 +444,19 @@ machine learning algorithms or just use one of them to construct
 forests and jungles of trees, homogeneous ones or heterogenous
 ones. These methods are recognized by different names which we will
 try to explain here. These are</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Voting classifiers</p></li>
 <li><p>Bagging and Pasting</p></li>
 <li><p>Random forests</p></li>
 <li><p>Boosting methods, from adaptive to Extreme Gradient Boosting (XGBoost)</p></li>
 </ol>
 <p>We discuss these methods here.</p>
-<div class="section" id="an-overview-of-ensemble-methods">
-<h2><span class="section-number">10.1. </span>An Overview of Ensemble Methods<a class="headerlink" href="#an-overview-of-ensemble-methods" title="Permalink to this headline">¶</a></h2>
+<section id="an-overview-of-ensemble-methods">
+<h2><span class="section-number">10.1. </span>An Overview of Ensemble Methods<a class="headerlink" href="#an-overview-of-ensemble-methods" title="Permalink to this heading">#</a></h2>
 <!-- FIGURE: [DataFiles/ensembleoverview.png, width=600 frac=0.8] -->
-</div>
-<div class="section" id="bagging">
-<h2><span class="section-number">10.2. </span>Bagging<a class="headerlink" href="#bagging" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bagging">
+<h2><span class="section-number">10.2. </span>Bagging<a class="headerlink" href="#bagging" title="Permalink to this heading">#</a></h2>
 <p>The <strong>plain</strong> decision trees suffer from high
 variance. This means that if we split the training data into two parts
 at random, and fit a decision tree to both halves, the results that we
@@ -637,7 +508,7 @@ predictor, averaged over all <span class="math notranslate nohighlight">\(B\)</s
 <div class="cell_output docutils container">
 <div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
 <span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 2&gt;</span><span class="nt">()</span>
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">2</span>
 <span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="n">heads_proba</span> <span class="o">=</span> <span class="mf">0.51</span>
 <span class="ne">----&gt; </span><span class="mi">2</span> <span class="n">coin_tosses</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">10000</span><span class="p">,</span> <span class="mi">10</span><span class="p">)</span> <span class="o">&lt;</span> <span class="n">heads_proba</span><span class="p">)</span><span class="o">.</span><span class="n">astype</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">int32</span><span class="p">)</span>
 <span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="n">cumulative_heads_ratio</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">coin_tosses</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10001</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
@@ -759,9 +630,9 @@ predictor, averaged over all <span class="math notranslate nohighlight">\(B\)</s
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="bagging-examples">
-<h2><span class="section-number">10.3. </span>Bagging Examples<a class="headerlink" href="#bagging-examples" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bagging-examples">
+<h2><span class="section-number">10.3. </span>Bagging Examples<a class="headerlink" href="#bagging-examples" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <span class="n">BaggingClassifier</span>
@@ -829,8 +700,8 @@ predictor, averaged over all <span class="math notranslate nohighlight">\(B\)</s
 </div>
 </div>
 </div>
-<div class="section" id="making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
-<h3><span class="section-number">10.3.1. </span>Making your own Bootstrap: Changing the Level of the Decision Tree<a class="headerlink" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" title="Permalink to this headline">¶</a></h3>
+<section id="making-your-own-bootstrap-changing-the-level-of-the-decision-tree">
+<h3><span class="section-number">10.3.1. </span>Making your own Bootstrap: Changing the Level of the Decision Tree<a class="headerlink" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree" title="Permalink to this heading">#</a></h3>
 <p>Let us bring up our good old boostrap example from the linear regression lectures. We change the linerar regression algorithm with
 a decision tree wth different depths and perform a bootstrap aggregate (in this case we perform as many bootstraps as data points <span class="math notranslate nohighlight">\(n\)</span>).</p>
 <div class="cell docutils container">
@@ -896,10 +767,10 @@ a decision tree wth different depths and perform a bootstrap aggregate (in this
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="random-forests">
-<h2><span class="section-number">10.4. </span>Random forests<a class="headerlink" href="#random-forests" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="random-forests">
+<h2><span class="section-number">10.4. </span>Random forests<a class="headerlink" href="#random-forests" title="Permalink to this heading">#</a></h2>
 <p>Random forests provide an improvement over bagged trees by way of a
 small tweak that decorrelates the trees.</p>
 <p>As in bagging, we build a
@@ -931,14 +802,14 @@ not lead to a substantial reduction in variance over a single tree in
 this setting.</p>
 <p>The algorithm described here can be applied to both classification and regression problems.</p>
 <p>We will grow of forest of say <span class="math notranslate nohighlight">\(B\)</span> trees.</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>For <span class="math notranslate nohighlight">\(b=1:B\)</span></p></li>
 </ol>
 <ul class="simple">
 <li><p>Draw a bootstrap sample from the training data organized in our <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> matrix.</p></li>
 <li><p>We grow then a random forest tree <span class="math notranslate nohighlight">\(T_b\)</span> based on the bootstrapped data by repeating the steps outlined till we reach the maximum node size is reached</p></li>
 </ul>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>we select <span class="math notranslate nohighlight">\(m \le p\)</span> variables at random from the <span class="math notranslate nohighlight">\(p\)</span> predictors/features</p></li>
 <li><p>pick the best split point among the <span class="math notranslate nohighlight">\(m\)</span> features using for example the CART algorithm and create a new node</p></li>
 <li><p>split the node into daughter nodes</p></li>
@@ -1022,8 +893,8 @@ percentage of the total number of cases.</p>
 <p>Similarly, the receiver operating characteristic curve, or ROC curve,
 displays the diagnostic ability of a binary classifier system as its
 discrimination threshold is varied. It plots the true positive rate against the false positive rate.</p>
-<div class="section" id="compare-bagging-on-trees-with-random-forests">
-<h3><span class="section-number">10.4.1. </span>Compare  Bagging on Trees with Random Forests<a class="headerlink" href="#compare-bagging-on-trees-with-random-forests" title="Permalink to this headline">¶</a></h3>
+<section id="compare-bagging-on-trees-with-random-forests">
+<h3><span class="section-number">10.4.1. </span>Compare  Bagging on Trees with Random Forests<a class="headerlink" href="#compare-bagging-on-trees-with-random-forests" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">bag_clf</span> <span class="o">=</span> <span class="n">BaggingClassifier</span><span class="p">(</span>
@@ -1046,10 +917,10 @@ discrimination threshold is varied. It plots the true positive rate against the
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="boosting-a-bird-s-eye-view">
-<h2><span class="section-number">10.5. </span>Boosting, a Bird’s Eye View<a class="headerlink" href="#boosting-a-bird-s-eye-view" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="boosting-a-bird-s-eye-view">
+<h2><span class="section-number">10.5. </span>Boosting, a Bird’s Eye View<a class="headerlink" href="#boosting-a-bird-s-eye-view" title="Permalink to this heading">#</a></h2>
 <p>The basic idea is to combine weak classifiers in order to create a good
 classifier. With a weak classifier we often intend a classifier which
 produces results which are only slightly better than we would get by
@@ -1093,10 +964,10 @@ simply invert a matrix and obtain the parameters <span class="math notranslate n
 \boldsymbol{\beta}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
 \]</div>
 <p>In iterative fitting or additive modeling, we minimize the cost function with respect to the parameters <span class="math notranslate nohighlight">\(\beta_m\)</span> and <span class="math notranslate nohighlight">\(\gamma_m\)</span>.</p>
-<div class="section" id="iterative-fitting-regression-and-squared-error-cost-function">
-<h3><span class="section-number">10.5.1. </span>Iterative Fitting, Regression and Squared-error Cost Function<a class="headerlink" href="#iterative-fitting-regression-and-squared-error-cost-function" title="Permalink to this headline">¶</a></h3>
+<section id="iterative-fitting-regression-and-squared-error-cost-function">
+<h3><span class="section-number">10.5.1. </span>Iterative Fitting, Regression and Squared-error Cost Function<a class="headerlink" href="#iterative-fitting-regression-and-squared-error-cost-function" title="Permalink to this heading">#</a></h3>
 <p>The way we proceed is as follows (here we specialize to the squared-error cost function)</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Establish a cost function, here <span class="math notranslate nohighlight">\(\cal{C}(\boldsymbol{y},\boldsymbol{f}) = \frac{1}{n} \sum_{i=0}^{n-1}(y_i-f_M(x_i))^2\)</span> with <span class="math notranslate nohighlight">\(f_M(x) = \sum_{i=1}^M \beta_m b(x;\gamma_m)\)</span>.</p></li>
 <li><p>Initialize with a guess <span class="math notranslate nohighlight">\(f_0(x)\)</span>. It could be one or even zero or some random numbers.</p></li>
 <li><p>For <span class="math notranslate nohighlight">\(m=1:M\)</span></p></li>
@@ -1139,9 +1010,9 @@ Taking the derivatives  with respect to <span class="math notranslate nohighligh
 for <span class="math notranslate nohighlight">\(\beta\)</span> gives us an equation for <span class="math notranslate nohighlight">\(\gamma\)</span>. This is a non-linear equation in the unknown <span class="math notranslate nohighlight">\(\gamma\)</span> and has to be solved numerically.</p>
 <p>The solution to these two equations gives us in turn <span class="math notranslate nohighlight">\(\beta_1\)</span> and <span class="math notranslate nohighlight">\(\gamma_1\)</span> leading to the new expression for <span class="math notranslate nohighlight">\(f_1(x)\)</span> as
 <span class="math notranslate nohighlight">\(f_1(x) = \beta_1(1+\gamma_1x)\)</span>. Doing this <span class="math notranslate nohighlight">\(M\)</span> times results in our final estimate for the function <span class="math notranslate nohighlight">\(f\)</span>.</p>
-</div>
-<div class="section" id="iterative-fitting-classification-and-adaboost">
-<h3><span class="section-number">10.5.2. </span>Iterative Fitting, Classification and AdaBoost<a class="headerlink" href="#iterative-fitting-classification-and-adaboost" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="iterative-fitting-classification-and-adaboost">
+<h3><span class="section-number">10.5.2. </span>Iterative Fitting, Classification and AdaBoost<a class="headerlink" href="#iterative-fitting-classification-and-adaboost" title="Permalink to this heading">#</a></h3>
 <p>Let us consider a binary classification problem with two outcomes <span class="math notranslate nohighlight">\(y_i \in \{-1,1\}\)</span> and <span class="math notranslate nohighlight">\(i=0,1,2,\dots,n-1\)</span> as our set of
 observations. We define a classification function <span class="math notranslate nohighlight">\(G(x)\)</span> which produces a prediction taking one or the other of the two values
 <span class="math notranslate nohighlight">\(\{-1,1\}\)</span>.</p>
@@ -1219,9 +1090,9 @@ f_m(x) = f_{m-1}(x) +\beta_m G_m(x).
 \[
 w_i^{m+1} = w_i^m \exp{(-y_i\beta_m G_m(x_i))}
 \]</div>
-</div>
-<div class="section" id="adaptive-boosting-adaboost-basic-algorithm">
-<h3><span class="section-number">10.5.3. </span>Adaptive boosting: AdaBoost, Basic Algorithm<a class="headerlink" href="#adaptive-boosting-adaboost-basic-algorithm" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="adaptive-boosting-adaboost-basic-algorithm">
+<h3><span class="section-number">10.5.3. </span>Adaptive boosting: AdaBoost, Basic Algorithm<a class="headerlink" href="#adaptive-boosting-adaboost-basic-algorithm" title="Permalink to this heading">#</a></h3>
 <p>The algorithm here is rather straightforward. Assume that our weak
 classifier is a decision tree and we consider a binary set of outputs
 with <span class="math notranslate nohighlight">\(y_i \in \{-1,1\}\)</span> and <span class="math notranslate nohighlight">\(i=0,1,2,\dots,n-1\)</span> as our set of
@@ -1237,7 +1108,7 @@ classifier determined by our data via a function <span class="math notranslate n
 <p>where the function <span class="math notranslate nohighlight">\(I()\)</span> is one if we misclassify and zero if we classify correctly.</p>
 <p>With the above definitions we are now ready to set up the algorithm for AdaBoost.
 The basic idea is to set up weights which will be used to scale the correctly classified and the misclassified cases.</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>We start by initializing all weights to <span class="math notranslate nohighlight">\(w_i = 1/n\)</span>, with <span class="math notranslate nohighlight">\(i=0,1,2,\dots n-1\)</span>. It is easy to see that we must have <span class="math notranslate nohighlight">\(\sum_{i=0}^{n-1}w_i = 1\)</span>.</p></li>
 <li><p>We rewrite the misclassification error as</p></li>
 </ol>
@@ -1245,14 +1116,14 @@ The basic idea is to set up weights which will be used to scale the correctly cl
 \[
 \mathrm{\overline{err}}_m=\frac{\sum_{i=0}^{n-1}w_i^m I(y_i\ne G(x_i))}{\sum_{i=0}^{n-1}w_i},
 \]</div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Then we start looping over all attempts at classifying, namely we start an iterative process for <span class="math notranslate nohighlight">\(m=1:M\)</span>, where <span class="math notranslate nohighlight">\(M\)</span> is the final number of classifications. Our given classifier could for example be a plain decision tree.</p></li>
 </ol>
 <p>a. Fit then a given classifier to the training set using the weights <span class="math notranslate nohighlight">\(w_i\)</span>.</p>
 <p>b. Compute then <span class="math notranslate nohighlight">\(\mathrm{err}\)</span> and figure out which events are classified properly and which are classified wrongly.</p>
 <p>c. Define a quantity <span class="math notranslate nohighlight">\(\alpha_{m} = \log{(1-\mathrm{\overline{err}}_m)/\mathrm{\overline{err}}_m}\)</span></p>
 <p>d. Set the new weights to <span class="math notranslate nohighlight">\(w_i = w_i\times \exp{(\alpha_m I(y_i\ne G(x_i)}\)</span>.</p>
-<ol class="simple">
+<ol class="arabic simple" start="5">
 <li><p>Compute the new classifier <span class="math notranslate nohighlight">\(G(x)= \sum_{i=0}^{n-1}\alpha_m I(y_i\ne G(x_i)\)</span>.</p></li>
 </ol>
 <p>For the iterations with <span class="math notranslate nohighlight">\(m \le 2\)</span> the weights are modified
@@ -1290,10 +1161,10 @@ observations that are missed in the previous iterations.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
-<h2><span class="section-number">10.6. </span>Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent<a class="headerlink" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">
+<h2><span class="section-number">10.6. </span>Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent<a class="headerlink" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent" title="Permalink to this heading">#</a></h2>
 <p>Gradient boosting is again a similar technique to Adaptive boosting,
 it combines so-called weak classifiers or regressors into a strong
 method via a series of iterations.</p>
@@ -1343,19 +1214,19 @@ fitting a weak learner to approximate the negative gradient signal.</p>
 C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
 \]</div>
 <p>The way we proceed in an iterative fashion is to</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Initialize our estimate <span class="math notranslate nohighlight">\(f_0(x)\)</span>.</p></li>
 <li><p>For <span class="math notranslate nohighlight">\(m=1:M\)</span>, we</p></li>
 </ol>
 <p>a. compute the negative gradient vector <span class="math notranslate nohighlight">\(\boldsymbol{u}_m = -\partial C(\boldsymbol{y},\boldsymbol{f})/\partial \boldsymbol{f}(x)\)</span> at <span class="math notranslate nohighlight">\(f(x) = f_{m-1}(x)\)</span>;</p>
 <p>b. fit the so-called base-learner to the negative gradient <span class="math notranslate nohighlight">\(h_m(u_m,x)\)</span>;</p>
 <p>c. update the estimate <span class="math notranslate nohighlight">\(f_m(x) = f_{m-1}(x)+h_m(u_m,x)\)</span>;</p>
-<ol class="simple">
+<ol class="arabic simple" start="4">
 <li><p>The final estimate is then <span class="math notranslate nohighlight">\(f_M(x) = \sum_{m=1}^M h_m(u_m,x)\)</span>.</p></li>
 </ol>
-</div>
-<div class="section" id="gradient-boosting-examples-of-regression">
-<h2><span class="section-number">10.7. </span>Gradient Boosting, Examples of Regression<a class="headerlink" href="#gradient-boosting-examples-of-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-boosting-examples-of-regression">
+<h2><span class="section-number">10.7. </span>Gradient Boosting, Examples of Regression<a class="headerlink" href="#gradient-boosting-examples-of-regression" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1408,9 +1279,9 @@ C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="gradient-boosting-classification-example">
-<h2><span class="section-number">10.8. </span>Gradient Boosting, Classification Example<a class="headerlink" href="#gradient-boosting-classification-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-boosting-classification-example">
+<h2><span class="section-number">10.8. </span>Gradient Boosting, Classification Example<a class="headerlink" href="#gradient-boosting-classification-example" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1457,9 +1328,9 @@ C(\boldsymbol{y},\boldsymbol{f})=\sum_{i=0}^{n-1}(y_i-f(x_i))^2.
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="xgboost-extreme-gradient-boosting">
-<h2><span class="section-number">10.9. </span>XGBoost: Extreme Gradient Boosting<a class="headerlink" href="#xgboost-extreme-gradient-boosting" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="xgboost-extreme-gradient-boosting">
+<h2><span class="section-number">10.9. </span>XGBoost: Extreme Gradient Boosting<a class="headerlink" href="#xgboost-extreme-gradient-boosting" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="https://github.com/dmlc/xgboost">XGBoost</a> or Extreme Gradient
 Boosting, is an optimized distributed gradient boosting library
 designed to be highly efficient, flexible and portable. It implements
@@ -1470,9 +1341,9 @@ data science problems in a fast and accurate way. See the <a class="reference ex
 boosting system. It has  a theoretically justified weighted quantile
 sketch for efficient proposal calculation. It introduces a novel sparsity-aware algorithm for parallel tree learning and an effective cache-aware block structure for out-of-core tree learning.</p>
 <p>It is now the algorithm which wins essentially all ML competitions!!!</p>
-</div>
-<div class="section" id="regression-case">
-<h2><span class="section-number">10.10. </span>Regression Case<a class="headerlink" href="#regression-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="regression-case">
+<h2><span class="section-number">10.10. </span>Regression Case<a class="headerlink" href="#regression-case" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1583,8 +1454,8 @@ sketch for efficient proposal calculation. It introduces a novel sparsity-aware
 </div>
 </div>
 </div>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1598,7 +1469,7 @@ sketch for efficient proposal calculation. It introduces a novel sparsity-aware
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1606,44 +1477,121 @@ sketch for efficient proposal calculation. It introduces a novel sparsity-aware
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-overview-of-ensemble-methods">10.1. An Overview of Ensemble Methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bagging">10.2. Bagging</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bagging-examples">10.3. Bagging Examples</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#making-your-own-bootstrap-changing-the-level-of-the-decision-tree">10.3.1. Making your own Bootstrap: Changing the Level of the Decision Tree</a></li>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#boosting-a-bird-s-eye-view">10.5. Boosting, a Bird’s Eye View</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#iterative-fitting-regression-and-squared-error-cost-function">10.5.1. Iterative Fitting, Regression and Squared-error Cost Function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#iterative-fitting-classification-and-adaboost">10.5.2. Iterative Fitting, Classification and AdaBoost</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#adaptive-boosting-adaboost-basic-algorithm">10.5.3. Adaptive boosting: AdaBoost, Basic Algorithm</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-basics-with-steepest-descent-functional-gradient-descent">10.6. Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-examples-of-regression">10.7. Gradient Boosting, Examples of Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-boosting-classification-example">10.8. Gradient Boosting, Classification Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#xgboost-extreme-gradient-boosting">10.9. XGBoost: Extreme Gradient Boosting</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-case">10.10. Regression Case</a></li>
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 </ul>
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 </ul>
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+
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+<div id="jb-print-docs-body" class="onlyprint">
+    <h1>Basic ideas of the Principal Component Analysis (PCA)</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
             
-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
-   11.1. Introducing the Covariance and Correlation functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix">
-   11.2. Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#towards-the-pca-theorem">
-   11.3. Towards the PCA theorem
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-algorithm-before-theorem">
-     11.3.1. The Algorithm before theorem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#writing-our-own-pca-code">
-     11.3.2. Writing our own PCA code
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
-     11.3.3. Diagonalize the sample covariance matrix to obtain the principal components
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#classical-pca-theorem">
-   11.4. Classical PCA Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#geometric-interpretation-and-link-with-singular-value-decomposition">
-   11.5. Geometric Interpretation and link with Singular Value Decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#pca-and-scikit-learn">
-   11.6. PCA and scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#back-to-the-cancer-data">
-   11.7. Back to the Cancer Data
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#incremental-pca">
-     11.7.1. Incremental PCA
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#randomized-pca">
-     11.7.2. Randomized PCA
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#kernel-pca">
-     11.7.3. Kernel PCA
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-techniques">
-   11.8. Other techniques
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">11.1. Introducing the Covariance and Correlation functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix">11.2. Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#towards-the-pca-theorem">11.3. Towards the PCA theorem</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-algorithm-before-theorem">11.3.1. The Algorithm before theorem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-our-own-pca-code">11.3.2. Writing our own PCA code</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">11.3.3. Diagonalize the sample covariance matrix to obtain the principal components</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#classical-pca-theorem">11.4. Classical PCA Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#geometric-interpretation-and-link-with-singular-value-decomposition">11.5. Geometric Interpretation and link with Singular Value Decomposition</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#pca-and-scikit-learn">11.6. PCA and scikit-learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#back-to-the-cancer-data">11.7. Back to the Cancer Data</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#incremental-pca">11.7.1. Incremental PCA</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#randomized-pca">11.7.2. Randomized PCA</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#kernel-pca">11.7.3. Kernel PCA</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-techniques">11.8. Other techniques</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Basic ideas of the Principal Component Analysis (PCA)</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
-   11.1. Introducing the Covariance and Correlation functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix">
-   11.2. Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#towards-the-pca-theorem">
-   11.3. Towards the PCA theorem
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#the-algorithm-before-theorem">
-     11.3.1. The Algorithm before theorem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#writing-our-own-pca-code">
-     11.3.2. Writing our own PCA code
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
-     11.3.3. Diagonalize the sample covariance matrix to obtain the principal components
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#classical-pca-theorem">
-   11.4. Classical PCA Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#geometric-interpretation-and-link-with-singular-value-decomposition">
-   11.5. Geometric Interpretation and link with Singular Value Decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#pca-and-scikit-learn">
-   11.6. PCA and scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#back-to-the-cancer-data">
-   11.7. Back to the Cancer Data
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#incremental-pca">
-     11.7.1. Incremental PCA
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#randomized-pca">
-     11.7.2. Randomized PCA
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#kernel-pca">
-     11.7.3. Kernel PCA
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-techniques">
-   11.8. Other techniques
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="basic-ideas-of-the-principal-component-analysis-pca">
-<h1><span class="section-number">11. </span>Basic ideas of the Principal Component Analysis (PCA)<a class="headerlink" href="#basic-ideas-of-the-principal-component-analysis-pca" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="basic-ideas-of-the-principal-component-analysis-pca">
+<h1><span class="section-number">11. </span>Basic ideas of the Principal Component Analysis (PCA)<a class="headerlink" href="#basic-ideas-of-the-principal-component-analysis-pca" title="Permalink to this heading">#</a></h1>
 <p>The principal component analysis deals with the problem of fitting a
 low-dimensional affine subspace <span class="math notranslate nohighlight">\(S\)</span> of dimension <span class="math notranslate nohighlight">\(d\)</span> much smaller than
 the total dimension <span class="math notranslate nohighlight">\(D\)</span> of the problem at hand (our data
@@ -564,8 +446,8 @@ Historically, the PCA was first formulated in a statistical setting in order to
 <li><p>If so, these intrinsic variables may tell us something important and finding these intrinsic variables is what dimension reduction methods do.</p></li>
 </ul>
 <p>A good read is for example <a class="reference external" href="https://www.springer.com/gp/book/9780387878102">Vidal, Ma and Sastry</a>.</p>
-<div class="section" id="introducing-the-covariance-and-correlation-functions">
-<h2><span class="section-number">11.1. </span>Introducing the Covariance and Correlation functions<a class="headerlink" href="#introducing-the-covariance-and-correlation-functions" title="Permalink to this headline">¶</a></h2>
+<section id="introducing-the-covariance-and-correlation-functions">
+<h2><span class="section-number">11.1. </span>Introducing the Covariance and Correlation functions<a class="headerlink" href="#introducing-the-covariance-and-correlation-functions" title="Permalink to this heading">#</a></h2>
 <p>Before we discuss the PCA theorem, we need to remind ourselves about
 the definition of the covariance and the correlation function. These are quantities</p>
 <p>Suppose we have defined two vectors
@@ -701,17 +583,17 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.03822007730337899
-3.989393825676568
-[[0.90044211 2.80659468]
- [2.80659468 9.73667253]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.08860271693417623
+3.7557911271214808
+[[ 1.08361608  3.3060763 ]
+ [ 3.3060763  10.96612219]]
 </pre></div>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="correlation-matrix">
-<h2><span class="section-number">11.2. </span>Correlation Matrix<a class="headerlink" href="#correlation-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="correlation-matrix">
+<h2><span class="section-number">11.2. </span>Correlation Matrix<a class="headerlink" href="#correlation-matrix" title="Permalink to this heading">#</a></h2>
 <p>The previous example can be converted into the correlation matrix by
 simply scaling the matrix elements with the variances.  We should also
 subtract the mean values for each column. This leads to the following
@@ -744,10 +626,10 @@ a more brute force way. Here we scale the mean values for each column of the des
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07864140367329474
-2.0511284278960114
-[[1.         0.68282072]
- [0.68282072 1.        ]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.07620892676178488
+1.732950730376058
+[[1.         0.64673189]
+ [0.64673189 1.        ]]
 </pre></div>
 </div>
 </div>
@@ -776,30 +658,15 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0.21424133 -1.00310568]
- [ 1.84955363  5.92472578]
- [ 0.43773101  1.60738434]
- [ 0.94910711  2.53617977]
- [-1.00106025 -3.87889126]
- [-0.2544356  -0.48005485]
- [-0.72117282 -1.4229538 ]
- [-0.48783291  0.5970842 ]
- [-0.17565241 -0.84643086]
- [-0.8104791  -3.03393764]]
-          0         1
-0  0.214241 -1.003106
-1  1.849554  5.924726
-2  0.437731  1.607384
-3  0.949107  2.536180
-4 -1.001060 -3.878891
-5 -0.254436 -0.480055
-6 -0.721173 -1.422954
-7 -0.487833  0.597084
-8 -0.175652 -0.846431
-9 -0.810479 -3.033938
-         0        1
-0  1.00000  0.93503
-1  0.93503  1.00000
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="n">line</span> <span class="mi">2</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="ne">----&gt; </span><span class="mi">2</span> <span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="n">n</span> <span class="o">=</span> <span class="mi">10</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;pandas&#39;
 </pre></div>
 </div>
 </div>
@@ -853,43 +720,6 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>     0         1         2         3         4         5         6         7   \
-0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.082232  0.082339  0.080863  0.080028  0.078987  0.072334  0.071321   
-2   0.0  0.082339  0.085298  0.084636  0.085154  0.085104  0.077849  0.077521   
-3   0.0  0.080863  0.084636  0.085290  0.086290  0.086690  0.079860  0.079858   
-4   0.0  0.080028  0.085154  0.086290  0.088026  0.088995  0.081970  0.082385   
-5   0.0  0.078987  0.085104  0.086690  0.088995  0.090424  0.083319  0.084079   
-6   0.0  0.072334  0.077849  0.079860  0.081970  0.083319  0.077182  0.077910   
-7   0.0  0.071321  0.077521  0.079858  0.082385  0.084079  0.077910  0.078901   
-8   0.0  0.070302  0.077012  0.079649  0.082509  0.084487  0.078333  0.079546   
-9   0.0  0.069312  0.076408  0.079319  0.082449  0.084666  0.078555  0.079958   
-10  0.0  0.063977  0.070119  0.072959  0.075620  0.077491  0.072176  0.073337   
-11  0.0  0.063115  0.069617  0.072682  0.075590  0.077676  0.072384  0.073717   
-12  0.0  0.062295  0.069072  0.072344  0.075455  0.077724  0.072474  0.073955   
-13  0.0  0.061529  0.068521  0.071982  0.075263  0.077690  0.072492  0.074102   
-14  0.0  0.060822  0.067984  0.071619  0.075045  0.077611  0.072468  0.074193   
-
-          8         9         10        11        12        13        14  
-0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.070302  0.069312  0.063977  0.063115  0.062295  0.061529  0.060822  
-2   0.077012  0.076408  0.070119  0.069617  0.069072  0.068521  0.067984  
-3   0.079649  0.079319  0.072959  0.072682  0.072344  0.071982  0.071619  
-4   0.082509  0.082449  0.075620  0.075590  0.075455  0.075263  0.075045  
-5   0.084487  0.084666  0.077491  0.077676  0.077724  0.077690  0.077611  
-6   0.078333  0.078555  0.072176  0.072384  0.072474  0.072492  0.072468  
-7   0.079546  0.079958  0.073337  0.073717  0.073955  0.074102  0.074193  
-8   0.080384  0.080965  0.074161  0.074692  0.075064  0.075330  0.075529  
-9   0.080965  0.081699  0.074752  0.075418  0.075911  0.076288  0.076588  
-10  0.074161  0.074752  0.068701  0.069233  0.069621  0.069911  0.070139  
-11  0.074692  0.075418  0.069233  0.069886  0.070381  0.070769  0.071086  
-12  0.075064  0.075911  0.069621  0.070381  0.070975  0.071453  0.071853  
-13  0.075330  0.076288  0.069911  0.070769  0.071453  0.072016  0.072493  
-14  0.075529  0.076588  0.070139  0.071086  0.071853  0.072493  0.073045  
-</pre></div>
-</div>
-</div>
 </div>
 <p>We note here that the covariance is zero for the first rows and
 columns since all matrix elements in the design matrix were set to one
@@ -929,9 +759,9 @@ x_{10}x_{00}+x_{11}x_{01} &amp; x_{10}^2+x_{11}^2\\
 \end{split}\]</div>
 <p>where we wrote $<span class="math notranslate nohighlight">\(\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]\)</span><span class="math notranslate nohighlight">\( to indicate that this the covariance of the vectors \)</span>\boldsymbol{x}<span class="math notranslate nohighlight">\( of the design/feature matrix \)</span>\boldsymbol{X}$.</p>
 <p>It is easy to generalize this to a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\)</span>.</p>
-</div>
-<div class="section" id="towards-the-pca-theorem">
-<h2><span class="section-number">11.3. </span>Towards the PCA theorem<a class="headerlink" href="#towards-the-pca-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="towards-the-pca-theorem">
+<h2><span class="section-number">11.3. </span>Towards the PCA theorem<a class="headerlink" href="#towards-the-pca-theorem" title="Permalink to this heading">#</a></h2>
 <p>We have that the covariance matrix (the correlation matrix involves a simple rescaling) is given as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -968,8 +798,8 @@ these specific directions. Hopefully then we could leave it out
 dimensions where the eigenvalues are very small. If <span class="math notranslate nohighlight">\(p\)</span> is very large,
 we could then aim at reducing <span class="math notranslate nohighlight">\(p\)</span> to <span class="math notranslate nohighlight">\(l &lt;&lt; p\)</span> and handle only <span class="math notranslate nohighlight">\(l\)</span>
 features/predictors.</p>
-<div class="section" id="the-algorithm-before-theorem">
-<h3><span class="section-number">11.3.1. </span>The Algorithm before theorem<a class="headerlink" href="#the-algorithm-before-theorem" title="Permalink to this headline">¶</a></h3>
+<section id="the-algorithm-before-theorem">
+<h3><span class="section-number">11.3.1. </span>The Algorithm before theorem<a class="headerlink" href="#the-algorithm-before-theorem" title="Permalink to this heading">#</a></h3>
 <p>Here’s how we would proceed in setting up the algorithm for the PCA, see also discussion below here.</p>
 <ul class="simple">
 <li><p>Set up the datapoints for the design/feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> with <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\)</span>, with the predictors/features <span class="math notranslate nohighlight">\(p\)</span>  referring to the column numbers and the entries <span class="math notranslate nohighlight">\(n\)</span> being the row elements.</p></li>
@@ -992,9 +822,9 @@ x_{n-1,0} &amp; x_{n-1,1} &amp; x_{n-1,2}&amp; \dots &amp; \dots x_{n-1,p-1}\\
 <li><p>Order the eigenvalue (and the eigenvectors accordingly) in order of decreasing eigenvalues.</p></li>
 <li><p>Keep only those <span class="math notranslate nohighlight">\(l\)</span> eigenvalues larger than a selected threshold value, discarding thus <span class="math notranslate nohighlight">\(p-l\)</span> features since we expect small variations in the data here.</p></li>
 </ul>
-</div>
-<div class="section" id="writing-our-own-pca-code">
-<h3><span class="section-number">11.3.2. </span>Writing our own PCA code<a class="headerlink" href="#writing-our-own-pca-code" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="writing-our-own-pca-code">
+<h3><span class="section-number">11.3.2. </span>Writing our own PCA code<a class="headerlink" href="#writing-our-own-pca-code" title="Permalink to this heading">#</a></h3>
 <p>We will use a simple example first with two-dimensional data
 drawn from a multivariate normal distribution with the following mean and covariance matrix (we have fixed these quantities but will play around with them below):</p>
 <div class="math notranslate nohighlight">
@@ -1073,15 +903,6 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>          0         1
-0  3.965838  1.971865
-1  1.971865  1.997830
-[[3.96583833 1.97186457]
- [1.97186457 1.99783004]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>Note that the way we define the covariance matrix here has a factor <span class="math notranslate nohighlight">\(n-1\)</span> instead of <span class="math notranslate nohighlight">\(n\)</span>. This is included in the <strong>cov()</strong> function by <strong>numpy</strong> and <strong>pandas</strong>.
 Our own code here is not very elegant and asks for obvious improvements. It is tailored to this specific <span class="math notranslate nohighlight">\(2\times 2\)</span> covariance matrix.</p>
@@ -1103,20 +924,12 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
-[[3.96583833 1.97186457]
- [1.97186457 1.99783004]]
-</pre></div>
-</div>
-<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
-</div>
 </div>
 <p>Depending on the number of points <span class="math notranslate nohighlight">\(n\)</span>, we will get results that are close to the covariance values defined above.
 The plot shows how the data are clustered around a line with slope close to one. Is this expected?  Try to change the covariance and the mean values. For example, try to make the variance of the first element much larger than that of the second diagonal element. Try also to shrink the covariance  (the non-diagonal elements) and see how the data points are distributed.</p>
-</div>
-<div class="section" id="diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
-<h3><span class="section-number">11.3.3. </span>Diagonalize the sample covariance matrix to obtain the principal components<a class="headerlink" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
+<h3><span class="section-number">11.3.3. </span>Diagonalize the sample covariance matrix to obtain the principal components<a class="headerlink" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components" title="Permalink to this heading">#</a></h3>
 <p>Now we are ready to solve for the principal components! To do so we
 diagonalize the sample covariance matrix <span class="math notranslate nohighlight">\(\Sigma\)</span>. We can use the
 function <strong>np.linalg.eig</strong> to do so. It will return the eigenvalues and
@@ -1164,27 +977,12 @@ questions.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
-5.185584177293881
-0.7780841853755783
-First eigenvector
-[0.85044503 0.52606392]
-Second eigenvector
-[-0.52606392  0.85044503]
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
-[0.85044503 0.52606392]
-</pre></div>
-</div>
-</div>
 </div>
 <p>This code does not contain all the above elements, but it shows how we can use <strong>Scikit-Learn</strong> to extract the eigenvector which corresponds to the largest eigenvalue. Try to address the questions we pose before the above code.  Try also to change the values of the covariance matrix by making one of the diagonal elements much larger than the other. What do you observe then?</p>
-</div>
-</div>
-<div class="section" id="classical-pca-theorem">
-<h2><span class="section-number">11.4. </span>Classical PCA Theorem<a class="headerlink" href="#classical-pca-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="classical-pca-theorem">
+<h2><span class="section-number">11.4. </span>Classical PCA Theorem<a class="headerlink" href="#classical-pca-theorem" title="Permalink to this heading">#</a></h2>
 <p>We assume now that we have a design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> which has been
 centered as discussed above. For the sake of simplicity we skip the
 overline symbol. The matrix is defined in terms of the various column
@@ -1242,9 +1040,9 @@ discussion in chapter 12.2 of Murphy’s text has also a nice link with
 the Singular Value Decomposition theorem. For categorical data, see
 chapter 12.4 and discussion therein.</p>
 <p>For more details, see for example <a class="reference external" href="https://www.springer.com/gp/book/9780387878102">Vidal, Ma and Sastry, chapter 2</a>.</p>
-</div>
-<div class="section" id="geometric-interpretation-and-link-with-singular-value-decomposition">
-<h2><span class="section-number">11.5. </span>Geometric Interpretation and link with Singular Value Decomposition<a class="headerlink" href="#geometric-interpretation-and-link-with-singular-value-decomposition" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="geometric-interpretation-and-link-with-singular-value-decomposition">
+<h2><span class="section-number">11.5. </span>Geometric Interpretation and link with Singular Value Decomposition<a class="headerlink" href="#geometric-interpretation-and-link-with-singular-value-decomposition" title="Permalink to this heading">#</a></h2>
 <p>For a detailed demonstration of the geometric interpretation, see <a class="reference external" href="https://www.springer.com/gp/book/9780387878102">Vidal, Ma and Sastry, section 2.1.2</a>.</p>
 <p>Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
 First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.</p>
@@ -1279,139 +1077,6 @@ training set, then extracts the first two principal components. First we center
 </pre></div>
 </div>
 </div>
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-      <td>0.689519</td>
-      <td>0.137652</td>
-      <td>-1.025709</td>
-      <td>0.210340</td>
-      <td>-0.076938</td>
-    </tr>
-    <tr>
-      <th>2</th>
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-      <td>0.351636</td>
-      <td>-0.539261</td>
-      <td>1.216683</td>
-      <td>0.340782</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>0.070889</td>
-      <td>-0.614808</td>
-      <td>1.074067</td>
-      <td>-0.038300</td>
-      <td>-1.450257</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>1.794282</td>
-      <td>1.458078</td>
-      <td>-0.207545</td>
-      <td>-0.442600</td>
-      <td>-0.147420</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>1.112383</td>
-      <td>0.647473</td>
-      <td>1.405890</td>
-      <td>0.073598</td>
-      <td>-0.276263</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.397700</td>
-      <td>-1.526744</td>
-      <td>-0.712018</td>
-      <td>1.216290</td>
-      <td>0.418506</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>-0.280647</td>
-      <td>1.106095</td>
-      <td>-1.646283</td>
-      <td>-0.956563</td>
-      <td>-1.564374</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>-0.369139</td>
-      <td>-0.751699</td>
-      <td>0.051649</td>
-      <td>-0.213103</td>
-      <td>0.967809</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>-1.557795</td>
-      <td>-1.066837</td>
-      <td>0.401842</td>
-      <td>-1.213743</td>
-      <td>1.138775</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>     0    1    2    3    4
-0  0.0  0.0  0.0  0.0  0.0
-1  0.0  0.0  0.0  0.0  0.0
-2  0.0  0.0  0.0  0.0  0.0
-3  0.0  0.0  0.0  0.0  0.0
-4  0.0  0.0  0.0  0.0  0.0
-5  0.0  0.0  0.0  0.0  0.0
-6  0.0  0.0  0.0  0.0  0.0
-7  0.0  0.0  0.0  0.0  0.0
-8  0.0  0.0  0.0  0.0  0.0
-9  0.0  0.0  0.0  0.0  0.0
-[[-1.5378811   0.94639099]
- [ 0.86145244 -0.89288636]
- [-0.00445655 -0.81633628]
- [ 0.07145103  1.00433417]
- [ 2.03707133  0.48476997]
- [ 0.72174172  1.4557763 ]
- [-0.55854694 -1.60673226]
- [ 1.6999536  -0.43766686]
- [-1.10405456 -0.31718909]
- [-2.18673098  0.17953942]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering
 the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t
@@ -1427,9 +1092,9 @@ Selecting this hyperplane ensures that the projection will preserve as much vari
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="pca-and-scikit-learn">
-<h2><span class="section-number">11.6. </span>PCA and scikit-learn<a class="headerlink" href="#pca-and-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="pca-and-scikit-learn">
+<h2><span class="section-number">11.6. </span>PCA and scikit-learn<a class="headerlink" href="#pca-and-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
 following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note
 that it automatically takes care of centering the data):</p>
@@ -1443,20 +1108,6 @@ that it automatically takes care of centering the data):</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1.5378811  -0.94639099]
- [-0.86145244  0.89288636]
- [ 0.00445655  0.81633628]
- [-0.07145103 -1.00433417]
- [-2.03707133 -0.48476997]
- [-0.72174172 -1.4557763 ]
- [ 0.55854694  1.60673226]
- [-1.6999536   0.43766686]
- [ 1.10405456  0.31718909]
- [ 2.18673098 -0.17953942]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>After fitting the PCA transformer to the dataset, you can access the principal components using the
 components variable (note that it contains the PCs as horizontal vectors, so, for example, the first
@@ -1467,18 +1118,13 @@ principal component is equal to</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>array([-0.62373464, -0.5303329 ,  0.317367  ,  0.01873344,  0.47815203])
-</pre></div>
-</div>
-</div>
 </div>
 <p>Another very useful piece of information is the explained variance ratio of each principal component,
 available via the <span class="math notranslate nohighlight">\(explained\_variance\_ratio\)</span> variable. It indicates the proportion of the dataset’s
 variance that lies along the axis of each principal component.</p>
-</div>
-<div class="section" id="back-to-the-cancer-data">
-<h2><span class="section-number">11.7. </span>Back to the Cancer Data<a class="headerlink" href="#back-to-the-cancer-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="back-to-the-cancer-data">
+<h2><span class="section-number">11.7. </span>Back to the Cancer Data<a class="headerlink" href="#back-to-the-cancer-data" title="Permalink to this heading">#</a></h2>
 <p>We can now repeat the above but applied to real data, in this case our breast cancer data.
 Here we compute performance scores on the training data using logistic regression.</p>
 <div class="cell docutils container">
@@ -1514,23 +1160,6 @@ Here we compute performance scores on the training data using logistic regressio
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Train set accuracy from Logistic Regression: 0.95
-Train set accuracy scaled data: 0.99
-Train set accuracy scaled and PCA data: 0.96
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-</pre></div>
-</div>
-</div>
 </div>
 <p>We see that our training data after the PCA decomposition has a performance similar to the non-scaled data.</p>
 <p>Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -1560,23 +1189,23 @@ a float between 0.0 and 1.0, indicating the ratio of variance you wish to preser
 </div>
 </div>
 </div>
-<div class="section" id="incremental-pca">
-<h3><span class="section-number">11.7.1. </span>Incremental PCA<a class="headerlink" href="#incremental-pca" title="Permalink to this headline">¶</a></h3>
+<section id="incremental-pca">
+<h3><span class="section-number">11.7.1. </span>Incremental PCA<a class="headerlink" href="#incremental-pca" title="Permalink to this heading">#</a></h3>
 <p>One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
 memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
 been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
 at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
 instances arrive).</p>
-</div>
-<div class="section" id="randomized-pca">
-<h3><span class="section-number">11.7.2. </span>Randomized PCA<a class="headerlink" href="#randomized-pca" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="randomized-pca">
+<h3><span class="section-number">11.7.2. </span>Randomized PCA<a class="headerlink" href="#randomized-pca" title="Permalink to this heading">#</a></h3>
 <p>Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
 algorithm that quickly finds an approximation of the first d principal components. Its computational
 complexity is <span class="math notranslate nohighlight">\(O(m \times d^2)+O(d^3)\)</span>, instead of <span class="math notranslate nohighlight">\(O(m \times n^2) + O(n^3)\)</span>, so it is dramatically faster than the
 previous algorithms when <span class="math notranslate nohighlight">\(d\)</span> is much smaller than <span class="math notranslate nohighlight">\(n\)</span>.</p>
-</div>
-<div class="section" id="kernel-pca">
-<h3><span class="section-number">11.7.3. </span>Kernel PCA<a class="headerlink" href="#kernel-pca" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="kernel-pca">
+<h3><span class="section-number">11.7.3. </span>Kernel PCA<a class="headerlink" href="#kernel-pca" title="Permalink to this heading">#</a></h3>
 <p>The kernel trick is a mathematical technique that implicitly maps instances into a
 very high-dimensional space (called the feature space), enabling nonlinear classification and regression
 with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature
@@ -1595,10 +1224,10 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="other-techniques">
-<h2><span class="section-number">11.8. </span>Other techniques<a class="headerlink" href="#other-techniques" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="other-techniques">
+<h2><span class="section-number">11.8. </span>Other techniques<a class="headerlink" href="#other-techniques" title="Permalink to this heading">#</a></h2>
 <p>There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.</p>
 <p>Here are some of the most popular:</p>
 <ul class="simple">
@@ -1607,8 +1236,8 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
 <li><p><strong>t-Distributed Stochastic Neighbor Embedding</strong> (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).</p></li>
 <li><p>Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures.</p></li>
 </ul>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1622,7 +1251,7 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1630,44 +1259,118 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
     </script>
     <script>kernelName = 'python3'</script>
 
-              </div>
+                </article>
               
-            
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix">11.2. Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#towards-the-pca-theorem">11.3. Towards the PCA theorem</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#the-algorithm-before-theorem">11.3.1. The Algorithm before theorem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-our-own-pca-code">11.3.2. Writing our own PCA code</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">11.3.3. Diagonalize the sample covariance matrix to obtain the principal components</a></li>
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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+    <h1>Neural networks</h1>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#feed-forward-neural-networks">
-   13.1. Feed-forward neural networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convolutional-neural-network">
-   13.2. Convolutional Neural Network
-  </a>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#recurrent-neural-networks">
-   13.3. Recurrent neural networks
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-  <a class="reference internal nav-link" href="#other-types-of-networks">
-   13.4. Other types of networks
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#multilayer-perceptrons">
-   13.5. Multilayer perceptrons
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#matrix-vector-notation-and-activation">
-     13.5.1. Matrix-vector notation  and activation
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#activation-functions">
-     13.5.2. Activation functions
-    </a>
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- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-multilayer-perceptron-mlp">
-   13.6. The multilayer  perceptron (MLP)
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#from-one-to-many-layers-the-universal-approximation-theorem">
-     13.6.1. From one to many layers, the universal approximation theorem
-    </a>
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- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model">
-   13.7. Deriving the back propagation code for a multilayer perceptron model
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#derivatives-and-the-chain-rule">
-     13.7.1. Derivatives and the chain rule
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#bringing-it-together-first-back-propagation-equation">
-     13.7.2. Bringing it together, first back propagation equation
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#final-back-propagating-equation">
-     13.7.3. Final back propagating equation
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#setting-up-the-back-propagation-algorithm">
-     13.7.4. Setting up the Back propagation algorithm
-    </a>
-   </li>
-  </ul>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#feed-forward-neural-networks">13.1. Feed-forward neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convolutional-neural-network">13.2. Convolutional Neural Network</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#recurrent-neural-networks">13.3. Recurrent neural networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-types-of-networks">13.4. Other types of networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#multilayer-perceptrons">13.5. Multilayer perceptrons</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#matrix-vector-notation-and-activation">13.5.1. Matrix-vector notation  and activation</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#activation-functions">13.5.2. Activation functions</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-multilayer-perceptron-mlp">13.6. The multilayer  perceptron (MLP)</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#from-one-to-many-layers-the-universal-approximation-theorem">13.6.1. From one to many layers, the universal approximation theorem</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model">13.7. Deriving the back propagation code for a multilayer perceptron model</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#derivatives-and-the-chain-rule">13.7.1. Derivatives and the chain rule</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#bringing-it-together-first-back-propagation-equation">13.7.2. Bringing it together, first back propagation equation</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#final-back-propagating-equation">13.7.3. Final back propagating equation</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#setting-up-the-back-propagation-algorithm">13.7.4. Setting up the Back propagation algorithm</a></li>
+</ul>
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-   13.2. Convolutional Neural Network
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-   13.4. Other types of networks
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-   13.5. Multilayer perceptrons
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#matrix-vector-notation-and-activation">
-     13.5.1. Matrix-vector notation  and activation
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#activation-functions">
-     13.5.2. Activation functions
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-multilayer-perceptron-mlp">
-   13.6. The multilayer  perceptron (MLP)
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#from-one-to-many-layers-the-universal-approximation-theorem">
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-  <a class="reference internal nav-link" href="#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model">
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#derivatives-and-the-chain-rule">
-     13.7.1. Derivatives and the chain rule
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#bringing-it-together-first-back-propagation-equation">
-     13.7.2. Bringing it together, first back propagation equation
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#final-back-propagating-equation">
-     13.7.3. Final back propagating equation
-    </a>
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#setting-up-the-back-propagation-algorithm">
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-<h1><span class="section-number">13. </span>Neural networks<a class="headerlink" href="#neural-networks" title="Permalink to this headline">¶</a></h1>
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+  <section class="tex2jax_ignore mathjax_ignore" id="neural-networks">
+<h1><span class="section-number">13. </span>Neural networks<a class="headerlink" href="#neural-networks" title="Permalink to this heading">#</a></h1>
 <p>Artificial neural networks are computational systems that can learn to
 perform tasks by considering examples, generally without being
 programmed with any task-specific rules. It is supposed to mimic a
@@ -586,7 +466,7 @@ i.e. has zero output.</p>
 a weighted sum of signals <span class="math notranslate nohighlight">\(x_i, \dots ,x_n\)</span> received by <span class="math notranslate nohighlight">\(n\)</span> other neurons.</p>
 <p>Conceptually, it is helpful to divide neural networks into four
 categories:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>general purpose neural networks for supervised learning,</p></li>
 <li><p>neural networks designed specifically for image processing, the most prominent example of this class being Convolutional Neural Networks (CNNs),</p></li>
 <li><p>neural networks for sequential data such as Recurrent Neural Networks (RNNs), and</p></li>
@@ -624,8 +504,8 @@ nonlinear models for supervised learning.  As we will see, neural nets
 can be viewed as natural, more powerful extensions of supervised
 learning methods such as linear and logistic regression and soft-max
 methods we discussed earlier.</p>
-<div class="section" id="feed-forward-neural-networks">
-<h2><span class="section-number">13.1. </span>Feed-forward neural networks<a class="headerlink" href="#feed-forward-neural-networks" title="Permalink to this headline">¶</a></h2>
+<section id="feed-forward-neural-networks">
+<h2><span class="section-number">13.1. </span>Feed-forward neural networks<a class="headerlink" href="#feed-forward-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>The feed-forward neural network (FFNN) was the first and simplest type
 of ANNs that were devised. In this network, the information moves in
 only one direction: forward through the layers.</p>
@@ -635,9 +515,9 @@ flow. Additionally, each arrow corresponds to a weight variable
 (figure to come).  We observe that each node in a layer is connected
 to <em>all</em> nodes in the subsequent layer, making this a so-called
 <em>fully-connected</em> FFNN.</p>
-</div>
-<div class="section" id="convolutional-neural-network">
-<h2><span class="section-number">13.2. </span>Convolutional Neural Network<a class="headerlink" href="#convolutional-neural-network" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="convolutional-neural-network">
+<h2><span class="section-number">13.2. </span>Convolutional Neural Network<a class="headerlink" href="#convolutional-neural-network" title="Permalink to this heading">#</a></h2>
 <p>A different variant of FFNNs are <em>convolutional neural networks</em>
 (CNNs), which have a connectivity pattern inspired by the animal
 visual cortex. Individual neurons in the visual cortex only respond to
@@ -655,9 +535,9 @@ convolutional layers that learn local features of the input, with a
 fully-connected layer at the end, which gathers all the local data and
 produces the outputs. They have wide applications in image and video
 recognition.</p>
-</div>
-<div class="section" id="recurrent-neural-networks">
-<h2><span class="section-number">13.3. </span>Recurrent neural networks<a class="headerlink" href="#recurrent-neural-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="recurrent-neural-networks">
+<h2><span class="section-number">13.3. </span>Recurrent neural networks<a class="headerlink" href="#recurrent-neural-networks" title="Permalink to this heading">#</a></h2>
 <p>So far we have only mentioned ANNs where information flows in one
 direction: forward. <em>Recurrent neural networks</em> on the other hand,
 have connections between nodes that form directed <em>cycles</em>. This
@@ -668,9 +548,9 @@ sequential information by performing the same task for every element
 in a sequence, where each element depends on previous elements. An
 example of such information is sentences, making recurrent NNs
 especially well-suited for handwriting and speech recognition.</p>
-</div>
-<div class="section" id="other-types-of-networks">
-<h2><span class="section-number">13.4. </span>Other types of networks<a class="headerlink" href="#other-types-of-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-types-of-networks">
+<h2><span class="section-number">13.4. </span>Other types of networks<a class="headerlink" href="#other-types-of-networks" title="Permalink to this heading">#</a></h2>
 <p>There are many other kinds of ANNs that have been developed. One type
 that is specifically designed for interpolation in multidimensional
 space is the radial basis function (RBF) network. RBFs are typically
@@ -681,9 +561,9 @@ linear activation function). The layers are normally fully-connected
 and there are no cycles, thus RBFs can be viewed as a type of
 fully-connected FFNN. They are however usually treated as a separate
 type of NN due the unusual activation functions.</p>
-</div>
-<div class="section" id="multilayer-perceptrons">
-<h2><span class="section-number">13.5. </span>Multilayer perceptrons<a class="headerlink" href="#multilayer-perceptrons" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="multilayer-perceptrons">
+<h2><span class="section-number">13.5. </span>Multilayer perceptrons<a class="headerlink" href="#multilayer-perceptrons" title="Permalink to this heading">#</a></h2>
 <p>One uses often so-called fully-connected feed-forward neural networks
 with three or more layers (an input layer, one or more hidden layers
 and an output layer) consisting of neurons that have non-linear
@@ -852,8 +732,8 @@ the equation for the activations of hidden layer 2 (assuming three nodes for sim
 \label{_auto6} \tag{11}
 \end{equation}
 \end{split}\]</div>
-<div class="section" id="matrix-vector-notation-and-activation">
-<h3><span class="section-number">13.5.1. </span>Matrix-vector notation  and activation<a class="headerlink" href="#matrix-vector-notation-and-activation" title="Permalink to this headline">¶</a></h3>
+<section id="matrix-vector-notation-and-activation">
+<h3><span class="section-number">13.5.1. </span>Matrix-vector notation  and activation<a class="headerlink" href="#matrix-vector-notation-and-activation" title="Permalink to this heading">#</a></h3>
 <p>The activation of node <span class="math notranslate nohighlight">\(i\)</span> in layer 2 is</p>
 <!-- Equation labels as ordinary links -->
 <div id="_auto7"></div>
@@ -870,9 +750,9 @@ and intuitive way to think about MLPs: The output is calculated by a
 series of matrix-vector multiplications and vector additions that are
 used as input to the activation functions. For each operation
 <span class="math notranslate nohighlight">\(\mathrm{W}_l \hat{y}_{l-1}\)</span> we move forward one layer.</p>
-</div>
-<div class="section" id="activation-functions">
-<h3><span class="section-number">13.5.2. </span>Activation functions<a class="headerlink" href="#activation-functions" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="activation-functions">
+<h3><span class="section-number">13.5.2. </span>Activation functions<a class="headerlink" href="#activation-functions" title="Permalink to this heading">#</a></h3>
 <p>A property that characterizes a neural network, other than its
 connectivity, is the choice of activation function(s).  As described
 in, the following restrictions are imposed on an activation function
@@ -983,18 +863,66 @@ become the most popular for <em>deep neural networks</em></p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/chapter9_29_0.png" src="_images/chapter9_29_0.png" />
-<img alt="_images/chapter9_29_1.png" src="_images/chapter9_29_1.png" />
-<img alt="_images/chapter9_29_2.png" src="_images/chapter9_29_2.png" />
-<img alt="_images/chapter9_29_3.png" src="_images/chapter9_29_3.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;The sigmoid function (or the logistic curve) is a </span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> function that takes any real number, z, and outputs a number (0,1).</span>
+<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> It is useful in neural networks for assigning weights on a relative scale.</span>
+<span class="g g-Whitespace">      </span><span class="mi">6</span><span class="sd"> The value z is the weighted sum of parameters involved in the learning algorithm.&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">import</span> <span class="nn">numpy</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="the-multilayer-perceptron-mlp">
-<h2><span class="section-number">13.6. </span>The multilayer  perceptron (MLP)<a class="headerlink" href="#the-multilayer-perceptron-mlp" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="the-multilayer-perceptron-mlp">
+<h2><span class="section-number">13.6. </span>The multilayer  perceptron (MLP)<a class="headerlink" href="#the-multilayer-perceptron-mlp" title="Permalink to this heading">#</a></h2>
 <p>The multilayer perceptron is a very popular, and easy to implement approach, to deep learning. It consists of</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>A neural network with one or more layers of nodes between the input and the output nodes.</p></li>
 <li><p>The multilayer network structure, or architecture, or topology, consists of an input layer, one or more hidden layers, and one output layer.</p></li>
 <li><p>The input nodes pass values to the first hidden layer, its nodes pass the information on to the second and so on till we reach the output layer.</p></li>
@@ -1016,8 +944,8 @@ basis functions (which will correspond to the weights in the network)
 are learned from data. This results in  an important difference between
 neural networks and deep learning approaches on one side and methods
 like logistic regression or linear regression and their modifications on the other side.</p>
-<div class="section" id="from-one-to-many-layers-the-universal-approximation-theorem">
-<h3><span class="section-number">13.6.1. </span>From one to many layers, the universal approximation theorem<a class="headerlink" href="#from-one-to-many-layers-the-universal-approximation-theorem" title="Permalink to this headline">¶</a></h3>
+<section id="from-one-to-many-layers-the-universal-approximation-theorem">
+<h3><span class="section-number">13.6.1. </span>From one to many layers, the universal approximation theorem<a class="headerlink" href="#from-one-to-many-layers-the-universal-approximation-theorem" title="Permalink to this heading">#</a></h3>
 <p>A neural network with only one layer, what we called the simple
 perceptron, is best suited if we have a standard binary model with
 clear (linear) boundaries between the outcomes. As such it could
@@ -1035,10 +963,10 @@ states that simple neural networks can represent a wide variety of
 interesting functions when given appropriate parameters. It is the
 multilayer feedforward architecture itself which gives neural networks
 the potential of being universal approximators.</p>
-</div>
-</div>
-<div class="section" id="deriving-the-back-propagation-code-for-a-multilayer-perceptron-model">
-<h2><span class="section-number">13.7. </span>Deriving the back propagation code for a multilayer perceptron model<a class="headerlink" href="#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="deriving-the-back-propagation-code-for-a-multilayer-perceptron-model">
+<h2><span class="section-number">13.7. </span>Deriving the back propagation code for a multilayer perceptron model<a class="headerlink" href="#deriving-the-back-propagation-code-for-a-multilayer-perceptron-model" title="Permalink to this heading">#</a></h2>
 <p>As we have seen now in a feed forward network, we can express the final output of our network in terms of basic matrix-vector multiplications.
 The unknowwn quantities are our weights <span class="math notranslate nohighlight">\(w_{ij}\)</span> and we need to find an algorithm for changing them so that our errors are as small as possible.
 This leads us to the famous <a class="reference external" href="https://www.nature.com/articles/323533a0">back propagation algorithm</a>.</p>
@@ -1084,8 +1012,8 @@ and their nodes.  It means we have</p>
 \[
 a_j^l = f(z_j^l) = \frac{1}{1+\exp{-(z_j^l)}}.
 \]</div>
-<div class="section" id="derivatives-and-the-chain-rule">
-<h3><span class="section-number">13.7.1. </span>Derivatives and the chain rule<a class="headerlink" href="#derivatives-and-the-chain-rule" title="Permalink to this headline">¶</a></h3>
+<section id="derivatives-and-the-chain-rule">
+<h3><span class="section-number">13.7.1. </span>Derivatives and the chain rule<a class="headerlink" href="#derivatives-and-the-chain-rule" title="Permalink to this heading">#</a></h3>
 <p>From the definition of the activation <span class="math notranslate nohighlight">\(z_j^l\)</span> we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1117,9 +1045,9 @@ a_j^l = f(z_j^l) = \frac{1}{1+\exp{-(z_j^l)}}.
 \[
 \frac{\partial a_j^L}{\partial w_{jk}^{L}} = \frac{\partial a_j^L}{\partial z_{j}^{L}}\frac{\partial z_j^L}{\partial w_{jk}^{L}}=a_j^L(1-a_j^L)a_k^{L-1},
 \]</div>
-</div>
-<div class="section" id="bringing-it-together-first-back-propagation-equation">
-<h3><span class="section-number">13.7.2. </span>Bringing it together, first back propagation equation<a class="headerlink" href="#bringing-it-together-first-back-propagation-equation" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="bringing-it-together-first-back-propagation-equation">
+<h3><span class="section-number">13.7.2. </span>Bringing it together, first back propagation equation<a class="headerlink" href="#bringing-it-together-first-back-propagation-equation" title="Permalink to this heading">#</a></h3>
 <p>We have thus</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1216,9 +1144,9 @@ network learns slowly again.</p>
 backwards in order to the determine the weights and biases. In order
 to do so we need to represent the error in the layer before the final
 one <span class="math notranslate nohighlight">\(L-1\)</span> in terms of the errors in the final output layer.</p>
-</div>
-<div class="section" id="final-back-propagating-equation">
-<h3><span class="section-number">13.7.3. </span>Final back propagating equation<a class="headerlink" href="#final-back-propagating-equation" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="final-back-propagating-equation">
+<h3><span class="section-number">13.7.3. </span>Final back propagating equation<a class="headerlink" href="#final-back-propagating-equation" title="Permalink to this heading">#</a></h3>
 <p>We have that (replacing <span class="math notranslate nohighlight">\(L\)</span> with a general layer <span class="math notranslate nohighlight">\(l\)</span>)</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1241,9 +1169,9 @@ z_j^{l+1} = \sum_{i=1}^{M_{l}}w_{ij}^{l+1}a_i^{l}+b_j^{l+1},
 \]</div>
 <p>This is our final equation.</p>
 <p>We are now ready to set up the algorithm for back propagation and learning the weights and biases.</p>
-</div>
-<div class="section" id="setting-up-the-back-propagation-algorithm">
-<h3><span class="section-number">13.7.4. </span>Setting up the Back propagation algorithm<a class="headerlink" href="#setting-up-the-back-propagation-algorithm" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="setting-up-the-back-propagation-algorithm">
+<h3><span class="section-number">13.7.4. </span>Setting up the Back propagation algorithm<a class="headerlink" href="#setting-up-the-back-propagation-algorithm" title="Permalink to this heading">#</a></h3>
 <p>The four equations  provide us with a way of computing the gradient of the cost function. Let us write this out in the form of an algorithm.</p>
 <p>First, we set up the input data <span class="math notranslate nohighlight">\(\hat{x}\)</span> and the activations
 <span class="math notranslate nohighlight">\(\hat{z}_1\)</span> of the input layer and compute the activation function and
@@ -1273,9 +1201,9 @@ b_j^l \leftarrow b_j^l-\eta \frac{\partial {\cal C}}{\partial b_j^l}=b_j^l-\eta
 \]</div>
 <p>The parameter <span class="math notranslate nohighlight">\(\eta\)</span> is the learning parameter discussed in connection with the gradient descent methods.
 Here it is convenient to use stochastic gradient descent (see the examples below) with mini-batches with an outer loop that steps through multiple epochs of training.</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1289,7 +1217,7 @@ Here it is convenient to use stochastic gradient descent (see the examples below
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1297,44 +1225,120 @@ Here it is convenient to use stochastic gradient descent (see the examples below
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#from-one-to-many-layers-the-universal-approximation-theorem">13.6.1. From one to many layers, the universal approximation theorem</a></li>
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter6.html">
-   9. Decision trees, overarching aims
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
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-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
-  </a>
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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- <li class="toctree-l1">
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-   Exercises week 37
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+    <h1>Optimization, the central part of any Machine Learning algortithm</h1>
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-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
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+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#steepest-descent">
-   7.1. Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-functions">
-   7.2. Convex functions
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#some-simple-problems">
-     7.2.1. Some simple problems
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#standard-steepest-descent">
-   7.3. Standard steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conjugate-gradient-method">
-   7.4. Conjugate gradient method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-linear-regression-solvers">
-   7.5. Revisiting our Linear Regression Solvers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">
-   7.6. Using gradient descent methods, limitations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">
-   7.7. Stochastic Gradient Descent (SGD)
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#program-for-stochastic-gradient">
-     7.7.1. Program for stochastic gradient
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#momentum-based-gd">
-   7.8. Momentum based GD
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#rms-prop">
-     7.8.1. RMS prop
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#adam-optimizer">
-     7.8.2. ADAM optimizer
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#practical-tips">
-   7.9. Practical tips
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#automatic-differentiation">
-   7.10. Automatic differentiation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#replace-or-not">
-   7.11. Replace or not
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-autograd">
-   7.12. Using Autograd
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">
-   7.13. Same code but now with momentum gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">
-   7.14. Including Stochastic Gradient Descent with Autograd
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">
-     7.14.1. Similar (second order function now) problem but now with AdaGrad
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-jax">
-   7.15. Introducing JAX
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">7.1. Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">7.2. Convex functions</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">7.2.1. Some simple problems</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-steepest-descent">7.3. Standard steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method">7.4. Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-linear-regression-solvers">7.5. Revisiting our Linear Regression Solvers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">7.6. Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">7.7. Stochastic Gradient Descent (SGD)</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#program-for-stochastic-gradient">7.7.1. Program for stochastic gradient</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-based-gd">7.8. Momentum based GD</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#rms-prop">7.8.1. RMS prop</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#adam-optimizer">7.8.2. ADAM optimizer</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#practical-tips">7.9. Practical tips</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#automatic-differentiation">7.10. Automatic differentiation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#replace-or-not">7.11. Replace or not</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd">7.12. Using Autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">7.13. Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">7.14. Including Stochastic Gradient Descent with Autograd</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">7.14.1. Similar (second order function now) problem but now with AdaGrad</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-jax">7.15. Introducing JAX</a></li>
 </ul>
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-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#steepest-descent">
-   7.1. Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-functions">
-   7.2. Convex functions
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#some-simple-problems">
-     7.2.1. Some simple problems
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#standard-steepest-descent">
-   7.3. Standard steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conjugate-gradient-method">
-   7.4. Conjugate gradient method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-linear-regression-solvers">
-   7.5. Revisiting our Linear Regression Solvers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">
-   7.6. Using gradient descent methods, limitations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">
-   7.7. Stochastic Gradient Descent (SGD)
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#program-for-stochastic-gradient">
-     7.7.1. Program for stochastic gradient
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#momentum-based-gd">
-   7.8. Momentum based GD
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#rms-prop">
-     7.8.1. RMS prop
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#adam-optimizer">
-     7.8.2. ADAM optimizer
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#practical-tips">
-   7.9. Practical tips
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#automatic-differentiation">
-   7.10. Automatic differentiation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#replace-or-not">
-   7.11. Replace or not
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-autograd">
-   7.12. Using Autograd
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">
-   7.13. Same code but now with momentum gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">
-   7.14. Including Stochastic Gradient Descent with Autograd
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">
-     7.14.1. Similar (second order function now) problem but now with AdaGrad
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-jax">
-   7.15. Introducing JAX
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html chapteroptimization.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="optimization-the-central-part-of-any-machine-learning-algortithm">
-<h1><span class="section-number">7. </span>Optimization, the central part of any Machine Learning algortithm<a class="headerlink" href="#optimization-the-central-part-of-any-machine-learning-algortithm" title="Permalink to this headline">¶</a></h1>
+doconce format html chapteroptimization.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="optimization-the-central-part-of-any-machine-learning-algortithm">
+<h1><span class="section-number">7. </span>Optimization, the central part of any Machine Learning algortithm<a class="headerlink" href="#optimization-the-central-part-of-any-machine-learning-algortithm" title="Permalink to this heading">#</a></h1>
 <p>Almost every problem in machine learning and data science starts with
 a dataset <span class="math notranslate nohighlight">\(X\)</span>, a model <span class="math notranslate nohighlight">\(g(\beta)\)</span>, which is a function of the
 parameters <span class="math notranslate nohighlight">\(\beta\)</span> and a cost function <span class="math notranslate nohighlight">\(C(X, g(\beta))\)</span> that allows
@@ -762,8 +586,8 @@ is to understand that difficulties  may
 arise in case <span class="math notranslate nohighlight">\(\boldsymbol{J}\)</span> is nearly singular.</p>
 <p>It is rather straightforward to extend the above scheme to systems of
 more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.</p>
-<div class="section" id="steepest-descent">
-<h2><span class="section-number">7.1. </span>Steepest descent<a class="headerlink" href="#steepest-descent" title="Permalink to this headline">¶</a></h2>
+<section id="steepest-descent">
+<h2><span class="section-number">7.1. </span>Steepest descent<a class="headerlink" href="#steepest-descent" title="Permalink to this heading">#</a></h2>
 <p>The basic idea of gradient descent is
 that a function <span class="math notranslate nohighlight">\(F(\mathbf{x})\)</span>,
 <span class="math notranslate nohighlight">\(\mathbf{x} \equiv (x_1,\cdots,x_n)\)</span>, decreases fastest if one goes from <span class="math notranslate nohighlight">\(\bf {x}\)</span> in the
@@ -812,9 +636,9 @@ large we can experience erratic behavior.</p>
 <p>Many of these shortcomings can be alleviated by introducing
 randomness. One such method is that of Stochastic Gradient Descent
 (SGD), see below.</p>
-</div>
-<div class="section" id="convex-functions">
-<h2><span class="section-number">7.2. </span>Convex functions<a class="headerlink" href="#convex-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="convex-functions">
+<h2><span class="section-number">7.2. </span>Convex functions<a class="headerlink" href="#convex-functions" title="Permalink to this heading">#</a></h2>
 <p>Ideally we want our cost/loss function to be convex(concave).</p>
 <p>First we give the definition of a convex set: A set <span class="math notranslate nohighlight">\(C\)</span> in
 <span class="math notranslate nohighlight">\(\mathbb{R}^n\)</span> is said to be convex if, for all <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> in <span class="math notranslate nohighlight">\(C\)</span> and
@@ -868,9 +692,9 @@ is convex the following result provides invaluable information:</p>
 is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is convex and differentiable. Then, any point
 <span class="math notranslate nohighlight">\(x^*\)</span> that satisfies <span class="math notranslate nohighlight">\(\nabla f(x^*) = 0\)</span> is a global minimum.</p>
 <p>This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.</p>
-<div class="section" id="some-simple-problems">
-<h3><span class="section-number">7.2.1. </span>Some simple problems<a class="headerlink" href="#some-simple-problems" title="Permalink to this headline">¶</a></h3>
-<ol class="simple">
+<section id="some-simple-problems">
+<h3><span class="section-number">7.2.1. </span>Some simple problems<a class="headerlink" href="#some-simple-problems" title="Permalink to this heading">#</a></h3>
+<ol class="arabic simple">
 <li><p>Show that <span class="math notranslate nohighlight">\(f(x)=x^2\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span> using the definition of convexity. Hint: If you re-write the definition, <span class="math notranslate nohighlight">\(f\)</span> is convex if the following holds for all <span class="math notranslate nohighlight">\(x,y \in D_f\)</span> and any <span class="math notranslate nohighlight">\(\lambda \in [0,1]\)</span> <span class="math notranslate nohighlight">\(\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0\)</span>.</p></li>
 <li><p>Using the second order condition show that the following functions are convex on the specified domain.</p></li>
 </ol>
@@ -878,7 +702,7 @@ is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is con
 <li><p><span class="math notranslate nohighlight">\(f(x) = e^x\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>.</p></li>
 <li><p><span class="math notranslate nohighlight">\(g(x) = -\ln(x)\)</span> is convex for <span class="math notranslate nohighlight">\(x \in (0,\infty)\)</span>.</p></li>
 </ul>
-<ol class="simple">
+<ol class="arabic simple" start="3">
 <li><p>Let <span class="math notranslate nohighlight">\(f(x) = x^2\)</span> and <span class="math notranslate nohighlight">\(g(x) = e^x\)</span>. Show that <span class="math notranslate nohighlight">\(f(g(x))\)</span> and <span class="math notranslate nohighlight">\(g(f(x))\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>. Also show that if <span class="math notranslate nohighlight">\(f(x)\)</span> is any convex function than <span class="math notranslate nohighlight">\(h(x) = e^{f(x)}\)</span> is convex.</p></li>
 <li><p>A norm is any function that satisfy the following properties</p></li>
 </ol>
@@ -888,10 +712,10 @@ is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is con
 <li><p><span class="math notranslate nohighlight">\(f(x) \leq 0\)</span> for all <span class="math notranslate nohighlight">\(x \in \mathbb{R}^n\)</span> with equality if and only if <span class="math notranslate nohighlight">\(x = 0\)</span></p></li>
 </ul>
 <p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
-</div>
-</div>
-<div class="section" id="standard-steepest-descent">
-<h2><span class="section-number">7.3. </span>Standard steepest descent<a class="headerlink" href="#standard-steepest-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="standard-steepest-descent">
+<h2><span class="section-number">7.3. </span>Standard steepest descent<a class="headerlink" href="#standard-steepest-descent" title="Permalink to this heading">#</a></h2>
 <p>Before we proceed, we would like to discuss the approach called the
 <strong>standard Steepest descent</strong> (different from the above steepest descent discussion), which again leads to us having to be able
 to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).</p>
@@ -997,14 +821,55 @@ which equals</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7714/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
-  ax = fig.gca(projection=&quot;3d&quot;)
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy.linalg</span> <span class="k">as</span> <span class="nn">la</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11e77b070&gt;
-</pre></div>
-</div>
-<img alt="_images/chapteroptimization_61_2.png" src="_images/chapteroptimization_61_2.png" />
 </div>
 </div>
 <p>And then as countor plot</p>
@@ -1016,9 +881,6 @@ which equals</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapteroptimization_63_0.png" src="_images/chapteroptimization_63_0.png" />
-</div>
 </div>
 <p>Find guesses</p>
 <div class="cell docutils container">
@@ -1042,11 +904,6 @@ which equals</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 1.33333333 -0.26666667]
-</pre></div>
-</div>
-</div>
 </div>
 <p>What happened?</p>
 <div class="cell docutils container">
@@ -1058,16 +915,10 @@ which equals</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[&lt;matplotlib.lines.Line2D at 0x11ecf9850&gt;]
-</pre></div>
 </div>
-<img alt="_images/chapteroptimization_69_1.png" src="_images/chapteroptimization_69_1.png" />
-</div>
-</div>
-</div>
-<div class="section" id="conjugate-gradient-method">
-<h2><span class="section-number">7.4. </span>Conjugate gradient method<a class="headerlink" href="#conjugate-gradient-method" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="conjugate-gradient-method">
+<h2><span class="section-number">7.4. </span>Conjugate gradient method<a class="headerlink" href="#conjugate-gradient-method" title="Permalink to this heading">#</a></h2>
 <p>In the CG method we define so-called conjugate directions and two vectors
 <span class="math notranslate nohighlight">\(\boldsymbol{s}\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{t}\)</span>
 are said to be
@@ -1188,14 +1039,14 @@ This gives the following expression</p>
 \[
 \boldsymbol{r}_{k+1}=\boldsymbol{r}_k-\boldsymbol{A}\boldsymbol{p}_{k},
 \]</div>
-</div>
-<div class="section" id="revisiting-our-linear-regression-solvers">
-<h2><span class="section-number">7.5. </span>Revisiting our Linear Regression Solvers<a class="headerlink" href="#revisiting-our-linear-regression-solvers" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="revisiting-our-linear-regression-solvers">
+<h2><span class="section-number">7.5. </span>Revisiting our Linear Regression Solvers<a class="headerlink" href="#revisiting-our-linear-regression-solvers" title="Permalink to this heading">#</a></h2>
 <p>We will use linear regression as a case study for the gradient descent
 methods. Linear regression is a great test case for the gradient
 descent methods discussed in the lectures since it has several
 desirable properties such as:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>An analytical solution.</p></li>
 <li><p>The gradient can be computed analytically.</p></li>
 <li><p>The cost function is convex which guarantees that gradient descent converges for small enough learning rates</p></li>
@@ -1315,16 +1166,6 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.33196524 4.36593124]
-[[4.09963157]
- [2.99760425]]
-[[4.09963157]
- [2.99760425]]
-</pre></div>
-</div>
-<img alt="_images/chapteroptimization_123_1.png" src="_images/chapteroptimization_123_1.png" />
-</div>
 </div>
 <p>Alternatively, we can use <strong>Scikit-Learn</strong> as done here</p>
 <div class="cell docutils container">
@@ -1348,13 +1189,6 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[4.21639245]
- [2.82985482]]
-[4.15172236] [2.79589065]
-</pre></div>
-</div>
-</div>
 </div>
 <p>We have also discussed Ridge regression where the loss function contains a regularized term given by the <span class="math notranslate nohighlight">\(L_2\)</span> norm of <span class="math notranslate nohighlight">\(\beta\)</span>,</p>
 <div class="math notranslate nohighlight">
@@ -1421,19 +1255,10 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[3.98919197]
- [2.94015598]]
-[[3.94925462]
- [2.97087408]]
-</pre></div>
 </div>
-<img alt="_images/chapteroptimization_132_1.png" src="_images/chapteroptimization_132_1.png" />
-</div>
-</div>
-</div>
-<div class="section" id="using-gradient-descent-methods-limitations">
-<h2><span class="section-number">7.6. </span>Using gradient descent methods, limitations<a class="headerlink" href="#using-gradient-descent-methods-limitations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="using-gradient-descent-methods-limitations">
+<h2><span class="section-number">7.6. </span>Using gradient descent methods, limitations<a class="headerlink" href="#using-gradient-descent-methods-limitations" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><strong>Gradient descent (GD) finds local minima of our function</strong>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</p></li>
 <li><p><strong>GD is sensitive to initial conditions</strong>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</p></li>
@@ -1442,9 +1267,9 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
 <li><p><strong>GD treats all directions in parameter space uniformly.</strong> Another major drawback of GD is that unlike Newton’s method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</p></li>
 <li><p>GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</p></li>
 </ul>
-</div>
-<div class="section" id="stochastic-gradient-descent-sgd">
-<h2><span class="section-number">7.7. </span>Stochastic Gradient Descent (SGD)<a class="headerlink" href="#stochastic-gradient-descent-sgd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="stochastic-gradient-descent-sgd">
+<h2><span class="section-number">7.7. </span>Stochastic Gradient Descent (SGD)<a class="headerlink" href="#stochastic-gradient-descent-sgd" title="Permalink to this heading">#</a></h2>
 <p>In stochastic gradient descent, the extreme case is the case where we
 have only one batch, that is we include the whole data set.</p>
 <p>This process is called Stochastic Gradient
@@ -1590,15 +1415,10 @@ function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>gamma_j after 500 epochs: 9.97108e-05
-</pre></div>
-</div>
-</div>
 </div>
 <p>We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters <span class="math notranslate nohighlight">\(t_0\)</span> and <span class="math notranslate nohighlight">\(t_1\)</span>.</p>
-<div class="section" id="program-for-stochastic-gradient">
-<h3><span class="section-number">7.7.1. </span>Program for stochastic gradient<a class="headerlink" href="#program-for-stochastic-gradient" title="Permalink to this headline">¶</a></h3>
+<section id="program-for-stochastic-gradient">
+<h3><span class="section-number">7.7.1. </span>Program for stochastic gradient<a class="headerlink" href="#program-for-stochastic-gradient" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Importing various packages</span>
@@ -1673,30 +1493,15 @@ function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Own inversion
-[[4.5424657 ]
- [2.40026896]]
-Eigenvalues of Hessian Matrix:[0.29830651 3.89658408]
-theta from own gd
-[[4.5424657 ]
- [2.40026896]]
-theta from own sdg
-[[4.55687658]
- [2.41165766]]
-</pre></div>
-</div>
-<img alt="_images/chapteroptimization_148_1.png" src="_images/chapteroptimization_148_1.png" />
-</div>
 </div>
 <p>In the above code, we have use replacement in setting up the
 mini-batches. The discussion
 <a class="reference external" href="https://sebastianraschka.com/faq/docs/sgd-methods.html">here</a> may be
 useful.  More material will be added later.</p>
-</div>
-</div>
-<div class="section" id="momentum-based-gd">
-<h2><span class="section-number">7.8. </span>Momentum based GD<a class="headerlink" href="#momentum-based-gd" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="momentum-based-gd">
+<h2><span class="section-number">7.8. </span>Momentum based GD<a class="headerlink" href="#momentum-based-gd" title="Permalink to this heading">#</a></h2>
 <p>The stochastic gradient descent (SGD) is almost always used with a
 <em>momentum</em> or inertia term that serves as a memory of the direction we
 are moving in parameter space.  This is typically implemented as
@@ -1811,8 +1616,8 @@ Hessians.</p>
 this by tracking not only the gradient, but also the second moment of
 the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and
 ADAM.</p>
-<div class="section" id="rms-prop">
-<h3><span class="section-number">7.8.1. </span>RMS prop<a class="headerlink" href="#rms-prop" title="Permalink to this headline">¶</a></h3>
+<section id="rms-prop">
+<h3><span class="section-number">7.8.1. </span>RMS prop<a class="headerlink" href="#rms-prop" title="Permalink to this heading">#</a></h3>
 <p>In RMS prop, in addition to keeping a running average of the first
 moment of the gradient, we also keep track of the second moment
 denoted by <span class="math notranslate nohighlight">\(\mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2]\)</span>. The update rule
@@ -1843,9 +1648,9 @@ is clear from this formula that the learning rate is reduced in
 directions where the norm of the gradient is consistently large. This
 greatly speeds up the convergence by allowing us to use a larger
 learning rate for flat directions.</p>
-</div>
-<div class="section" id="adam-optimizer">
-<h3><span class="section-number">7.8.2. </span>ADAM optimizer<a class="headerlink" href="#adam-optimizer" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="adam-optimizer">
+<h3><span class="section-number">7.8.2. </span>ADAM optimizer<a class="headerlink" href="#adam-optimizer" title="Permalink to this heading">#</a></h3>
 <p>A related algorithm is the ADAM optimizer. In ADAM, we keep a running
 average of both the first and second moment of the gradient and use
 this information to adaptively change the learning rate for different
@@ -1908,19 +1713,19 @@ update rule for this parameter is given by</p>
 \[
 \Delta \theta_{t+1}= -\eta_t { \boldsymbol{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
 \]</div>
-</div>
-</div>
-<div class="section" id="practical-tips">
-<h2><span class="section-number">7.9. </span>Practical tips<a class="headerlink" href="#practical-tips" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="practical-tips">
+<h2><span class="section-number">7.9. </span>Practical tips<a class="headerlink" href="#practical-tips" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><strong>Randomize the data when making mini-batches</strong>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</p></li>
 <li><p><strong>Transform your inputs</strong>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</p></li>
 <li><p><strong>Monitor the out-of-sample performance.</strong> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</p></li>
 <li><p><strong>Adaptive optimization methods don’t always have good generalization.</strong> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</p></li>
 </ul>
-</div>
-<div class="section" id="automatic-differentiation">
-<h2><span class="section-number">7.10. </span>Automatic differentiation<a class="headerlink" href="#automatic-differentiation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="automatic-differentiation">
+<h2><span class="section-number">7.10. </span>Automatic differentiation<a class="headerlink" href="#automatic-differentiation" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="https://en.wikipedia.org/wiki/Automatic_differentiation">Automatic differentiation (AD)</a>,
 also called algorithmic
 differentiation or computational differentiation,is a set of
@@ -1994,12 +1799,6 @@ f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/chapteroptimization_188_0.png" src="_images/chapteroptimization_188_0.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The max absolute difference is: 1.77636e-15
-</pre></div>
-</div>
-</div>
 </div>
 <p>Here we
 experiment with what kind of functions Autograd is capable
@@ -2028,12 +1827,6 @@ experiment with other, possibly more complicated, functions as well.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The gradient of f1 evaluated at a = 1 using autograd is: 3
-The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3
-</pre></div>
-</div>
-</div>
 </div>
 <p>To differentiate with respect to two (or more) arguments of a Python
 function, Autograd need to know at which variable the function if
@@ -2076,17 +1869,6 @@ being differentiated with respect to.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Evaluating at x1 = 1, x2 = 3
-------------------------------
-The derivative of f2 w.r.t x1: 12
-The analytical derivative of f2 w.r.t x1: 12
-
-The derivative of f2 w.r.t x2: -4
-The analytical derivative of f2 w.r.t x2: -4
-</pre></div>
-</div>
-</div>
 </div>
 <p>Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.</p>
 <div class="cell docutils container">
@@ -2111,12 +1893,6 @@ The analytical derivative of f2 w.r.t x2: -4
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The computed gradient of f3 is:  [ 2.  3.  5.  7. 88.]
-The analytical gradient of f3 is:  [ 2.  3.  5.  7. 88.]
-</pre></div>
-</div>
-</div>
 </div>
 <p>Note that in this case, when sending an array as input argument, the
 output from Autograd is another array. This is the true gradient of
@@ -2146,12 +1922,6 @@ could expect form a gradient-evaluting function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The computed derivative of f4 at x = 2.7 is: 13.8759
-The analytical gradient of f4 at x = 2.7 is: 13.8759
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2172,11 +1942,6 @@ The analytical gradient of f4 at x = 2.7 is: 13.8759
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The computed derivative of f5 at x = 2.7 is: 5.4
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2207,12 +1972,6 @@ The analytical gradient of f4 at x = 2.7 is: 13.8759
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The computed derivative of f6_for at x = 0.5 is: 3.95703
-The computed derivative of f6_while at x = 0.5 is: 3.95703
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2228,11 +1987,6 @@ The computed derivative of f6_while at x = 0.5 is: 3.95703
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The analytical derivative of f6 at x = 0.5 is: 3.95703
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2266,12 +2020,6 @@ The computed derivative of f6_while at x = 0.5 is: 3.95703
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The computed derivative of f7 at n = 2 is: 1
-The analytical derivative of f7 at n = 2 is: 1
-</pre></div>
-</div>
-</div>
 </div>
 <p>Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.</p>
 <p>Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.</p>
@@ -2294,11 +2042,6 @@ The analytical derivative of f7 at n = 2 is: 1
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;\nimport autograd.numpy as np\nfrom autograd import grad\ndef f8(x): # Assume x is an array\n    x[2] = 3\n    return x*2\n\nf8_grad = grad(f8)\n\nx = 8.4\n\nprint(&quot;The derivative of f8 is:&quot;,f8_grad(x))\n&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>Here, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.</p>
 <div class="cell docutils container">
@@ -2317,60 +2060,6 @@ The analytical derivative of f7 at n = 2 is: 1
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">AttributeError</span><span class="g g-Whitespace">                            </span>Traceback (most recent call last)
-<span class="nn">Input In [23],</span> in <span class="ni">&lt;cell line: 11&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="n">f9_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f9</span><span class="p">)</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">])</span>
-<span class="ne">---&gt; </span><span class="mi">11</span> <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The derivative of f9 is:&quot;</span><span class="p">,</span><span class="n">f9_grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>     <span class="n">x</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">args</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">argnum</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">20</span> <span class="k">return</span> <span class="n">unary_operator</span><span class="p">(</span><span class="n">unary_f</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">nary_op_args</span><span class="p">,</span> <span class="o">**</span><span class="n">nary_op_kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25,</span> in <span class="ni">grad</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="nd">@unary_to_nary</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span> <span class="k">def</span> <span class="nf">grad</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>     <span class="sd">&quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span><span class="sd">     Returns a function which computes the gradient of `fun` with respect to</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span><span class="sd">     positional argument number `argnum`. The returned function takes the same</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span><span class="sd">     arguments as `fun`, but returns the gradient instead. The function `fun`</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span><span class="sd">     should be scalar-valued. The gradient has the same type as the argument.&quot;&quot;&quot;</span>
-<span class="ne">---&gt; </span><span class="mi">25</span>     <span class="n">vjp</span><span class="p">,</span> <span class="n">ans</span> <span class="o">=</span> <span class="n">_make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span>     <span class="k">if</span> <span class="ow">not</span> <span class="n">vspace</span><span class="p">(</span><span class="n">ans</span><span class="p">)</span><span class="o">.</span><span class="n">size</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span>         <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s2">&quot;Grad only applies to real scalar-output functions. &quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span>                         <span class="s2">&quot;Try jacobian, elementwise_grad or holomorphic_grad.&quot;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10,</span> in <span class="ni">make_vjp</span><span class="nt">(fun, x)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="k">def</span> <span class="nf">make_vjp</span><span class="p">(</span><span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span>     <span class="n">start_node</span> <span class="o">=</span> <span class="n">VJPNode</span><span class="o">.</span><span class="n">new_root</span><span class="p">()</span>
-<span class="ne">---&gt; </span><span class="mi">10</span>     <span class="n">end_value</span><span class="p">,</span> <span class="n">end_node</span> <span class="o">=</span>  <span class="n">trace</span><span class="p">(</span><span class="n">start_node</span><span class="p">,</span> <span class="n">fun</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span>     <span class="k">if</span> <span class="n">end_node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">12</span>         <span class="k">def</span> <span class="nf">vjp</span><span class="p">(</span><span class="n">g</span><span class="p">):</span> <span class="k">return</span> <span class="n">vspace</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">zeros</span><span class="p">()</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10,</span> in <span class="ni">trace</span><span class="nt">(start_node, fun, x)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="k">with</span> <span class="n">trace_stack</span><span class="o">.</span><span class="n">new_trace</span><span class="p">()</span> <span class="k">as</span> <span class="n">t</span><span class="p">:</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span>     <span class="n">start_box</span> <span class="o">=</span> <span class="n">new_box</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="n">start_node</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">10</span>     <span class="n">end_box</span> <span class="o">=</span> <span class="n">fun</span><span class="p">(</span><span class="n">start_box</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span>     <span class="k">if</span> <span class="n">isbox</span><span class="p">(</span><span class="n">end_box</span><span class="p">)</span> <span class="ow">and</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_trace</span> <span class="o">==</span> <span class="n">start_box</span><span class="o">.</span><span class="n">_trace</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">12</span>         <span class="k">return</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_value</span><span class="p">,</span> <span class="n">end_box</span><span class="o">.</span><span class="n">_node</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15,</span> in <span class="ni">unary_to_nary.&lt;locals&gt;.nary_operator.&lt;locals&gt;.nary_f.&lt;locals&gt;.unary_f</span><span class="nt">(x)</span>
-<span class="g g-Whitespace">     </span><span class="mi">13</span> <span class="k">else</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">14</span>     <span class="n">subargs</span> <span class="o">=</span> <span class="n">subvals</span><span class="p">(</span><span class="n">args</span><span class="p">,</span> <span class="nb">zip</span><span class="p">(</span><span class="n">argnum</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
-<span class="ne">---&gt; </span><span class="mi">15</span> <span class="k">return</span> <span class="n">fun</span><span class="p">(</span><span class="o">*</span><span class="n">subargs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">Input In [23],</span> in <span class="ni">f9</span><span class="nt">(a)</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="k">def</span> <span class="nf">f9</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="c1"># Assume a is an array with 2 elements</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span>     <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">])</span>
-<span class="ne">----&gt; </span><span class="mi">5</span>     <span class="k">return</span> <span class="n">a</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
-
-<span class="ne">AttributeError</span>: &#39;ArrayBox&#39; object has no attribute &#39;dot&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>Here we are told that the ‘dot’ function does not belong to Autograd’s
 version of a Numpy array.  To overcome this, an alternative syntax
@@ -2406,16 +2095,16 @@ which also computed the dot product can be used:</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="replace-or-not">
-<h2><span class="section-number">7.11. </span>Replace or not<a class="headerlink" href="#replace-or-not" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="replace-or-not">
+<h2><span class="section-number">7.11. </span>Replace or not<a class="headerlink" href="#replace-or-not" title="Permalink to this heading">#</a></h2>
 <p>In the above code, we have use replacement in setting up the
 mini-batches. The discussion
 <a class="reference external" href="https://sebastianraschka.com/faq/docs/sgd-methods.html">here</a> may be
 useful.</p>
-</div>
-<div class="section" id="using-autograd">
-<h2><span class="section-number">7.12. </span>Using Autograd<a class="headerlink" href="#using-autograd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="using-autograd">
+<h2><span class="section-number">7.12. </span>Using Autograd<a class="headerlink" href="#using-autograd" title="Permalink to this heading">#</a></h2>
 <p>We conclude the part on optmization by showing how we can make codes
 for linear regression and logistic regression using <strong>autograd</strong>. The
 first example shows results with ordinary leats squares.</p>
@@ -2474,9 +2163,9 @@ first example shows results with ordinary leats squares.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="same-code-but-now-with-momentum-gradient-descent">
-<h2><span class="section-number">7.13. </span>Same code but now with momentum gradient descent<a class="headerlink" href="#same-code-but-now-with-momentum-gradient-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="same-code-but-now-with-momentum-gradient-descent">
+<h2><span class="section-number">7.13. </span>Same code but now with momentum gradient descent<a class="headerlink" href="#same-code-but-now-with-momentum-gradient-descent" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients for OLS</span>
@@ -2582,9 +2271,9 @@ However, if we can invert the Hessian matrix, this is the preferred approach, as
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="including-stochastic-gradient-descent-with-autograd">
-<h2><span class="section-number">7.14. </span>Including Stochastic Gradient Descent with Autograd<a class="headerlink" href="#including-stochastic-gradient-descent-with-autograd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="including-stochastic-gradient-descent-with-autograd">
+<h2><span class="section-number">7.14. </span>Including Stochastic Gradient Descent with Autograd<a class="headerlink" href="#including-stochastic-gradient-descent-with-autograd" title="Permalink to this heading">#</a></h2>
 <p>In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using <strong>autograd</strong>.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2739,8 +2428,8 @@ However, if we can invert the Hessian matrix, this is the preferred approach, as
 </div>
 </div>
 </div>
-<div class="section" id="similar-second-order-function-now-problem-but-now-with-adagrad">
-<h3><span class="section-number">7.14.1. </span>Similar (second order function now) problem but now with AdaGrad<a class="headerlink" href="#similar-second-order-function-now-problem-but-now-with-adagrad" title="Permalink to this headline">¶</a></h3>
+<section id="similar-second-order-function-now-problem-but-now-with-adagrad">
+<h3><span class="section-number">7.14.1. </span>Similar (second order function now) problem but now with AdaGrad<a class="headerlink" href="#similar-second-order-function-now-problem-but-now-with-adagrad" title="Permalink to this heading">#</a></h3>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent</span>
@@ -2866,10 +2555,10 @@ However, if we can invert the Hessian matrix, this is the preferred approach, as
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="introducing-jax">
-<h2><span class="section-number">7.15. </span>Introducing <a class="reference external" href="https://jax.readthedocs.io/en/latest/">JAX</a><a class="headerlink" href="#introducing-jax" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="introducing-jax">
+<h2><span class="section-number">7.15. </span>Introducing <a class="reference external" href="https://jax.readthedocs.io/en/latest/">JAX</a><a class="headerlink" href="#introducing-jax" title="Permalink to this heading">#</a></h2>
 <p>Presently, instead of using <strong>autograd</strong>, we recommend using <a class="reference external" href="https://jax.readthedocs.io/en/latest/">JAX</a></p>
 <p><strong>JAX</strong> is Autograd and <a class="reference external" href="https://www.tensorflow.org/xla">XLA (Accelerated Linear Algebra))</a>,
 brought together for high-performance numerical computing and machine learning research.
@@ -2890,8 +2579,8 @@ It provides composable transformations of Python+NumPy programs: differentiate,
 </div>
 </div>
 </div>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2905,7 +2594,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -2913,44 +2602,128 @@ It provides composable transformations of Python+NumPy programs: differentiate,
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">7.1. Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">7.2. Convex functions</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">7.2.1. Some simple problems</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-steepest-descent">7.3. Standard steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method">7.4. Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-linear-regression-solvers">7.5. Revisiting our Linear Regression Solvers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">7.6. Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">7.7. Stochastic Gradient Descent (SGD)</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#program-for-stochastic-gradient">7.7.1. Program for stochastic gradient</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-based-gd">7.8. Momentum based GD</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#rms-prop">7.8.1. RMS prop</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#adam-optimizer">7.8.2. ADAM optimizer</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#practical-tips">7.9. Practical tips</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#automatic-differentiation">7.10. Automatic differentiation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#replace-or-not">7.11. Replace or not</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd">7.12. Using Autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">7.13. Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">7.14. Including Stochastic Gradient Descent with Autograd</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">7.14.1. Similar (second order function now) problem but now with AdaGrad</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-jax">7.15. Introducing JAX</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
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+    <h1>Clustering and Unsupervised Learning</h1>
+    <!-- Table of contents -->
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-   12.1. Codes and Approaches
-  </a>
- </li>
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-                <h1>Clustering and Unsupervised Learning</h1>
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- <li class="toc-h2 nav-item toc-entry">
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-   12.1. Codes and Approaches
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html clustering.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="clustering-and-unsupervised-learning">
-<h1><span class="section-number">12. </span>Clustering and Unsupervised Learning<a class="headerlink" href="#clustering-and-unsupervised-learning" title="Permalink to this headline">¶</a></h1>
+doconce format html clustering.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="clustering-and-unsupervised-learning">
+<h1><span class="section-number">12. </span>Clustering and Unsupervised Learning<a class="headerlink" href="#clustering-and-unsupervised-learning" title="Permalink to this heading">#</a></h1>
 <p>In general terms cluster analysis, or clustering, is the task of grouping a
 data-set into different distinct categories based on some measure of equality of
 the data. This measure is often referred to as a <strong>metric</strong> or <strong>similarity
@@ -437,7 +440,7 @@ one cluster <span class="math notranslate nohighlight">\(k\)</span>, and these a
 can think of these mappings as an encoder <span class="math notranslate nohighlight">\(k = C(i)\)</span>, which assigns the <span class="math notranslate nohighlight">\(i\)</span>-th
 data-point <span class="math notranslate nohighlight">\(\bf x_i\)</span> to the <span class="math notranslate nohighlight">\(k\)</span>-th cluster.</p>
 <p><span class="math notranslate nohighlight">\(k\)</span>-means algorithm in words:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>We start with guesses / random initializations of our <span class="math notranslate nohighlight">\(k\)</span> cluster centers/centroids</p></li>
 <li><p>For each centroid the points that are most similar are identified</p></li>
 <li><p>Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid.</p></li>
@@ -513,14 +516,14 @@ conserved.</p>
 \]</div>
 <p>Now we have all the pieces necessary to formally revisit the <span class="math notranslate nohighlight">\(k\)</span>-means algorithm.</p>
 <p>The <span class="math notranslate nohighlight">\(k\)</span>-means clustering algorithm goes as follows</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>For a given cluster assignment <span class="math notranslate nohighlight">\(C\)</span>, and <span class="math notranslate nohighlight">\(k\)</span> cluster means <span class="math notranslate nohighlight">\(\left\{m_1, \cdots, m_k\right\}\)</span>. We minimize the total cluster variance with respect to the cluster means <span class="math notranslate nohighlight">\(\{m_k\}\)</span> yielding the means of the currently assigned clusters.</p></li>
 <li><p>Given a current set of <span class="math notranslate nohighlight">\(k\)</span> means <span class="math notranslate nohighlight">\(\{m_k\}\)</span> the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $<span class="math notranslate nohighlight">\(C(i) = \underset{1\leq k\leq K}{\mathrm{argmin}} ||\boldsymbol{x_i} - \boldsymbol{m_k}||^2\)</span>$</p></li>
 <li><p>Steps 1 and 2 are repeated until the assignments do not change.</p></li>
 </ol>
-<div class="section" id="codes-and-approaches">
-<h2><span class="section-number">12.1. </span>Codes and Approaches<a class="headerlink" href="#codes-and-approaches" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+<section id="codes-and-approaches">
+<h2><span class="section-number">12.1. </span>Codes and Approaches<a class="headerlink" href="#codes-and-approaches" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>Before we start we specify a number <span class="math notranslate nohighlight">\(k\)</span> which is the number of clusters we want to try to separate our data into.</p></li>
 <li><p>We initially choose <span class="math notranslate nohighlight">\(k\)</span> random data points in our data as our initial centroids, <em>or means</em> (this is where the name comes from).</p></li>
 <li><p>Assign each data point to their closest centroid, based on the squared Euclidean distance.</p></li>
@@ -551,215 +554,53 @@ Gaussian distribution.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.
-  warnings.warn(&quot;JAX on Mac ARM machines is experimental and minimally tested. &quot;
-</pre></div>
-</div>
 <div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">AttributeError</span><span class="g g-Whitespace">                            </span>Traceback (most recent call last)
-<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 5&gt;</span><span class="nt">()</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
 <span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">time</span>
 <span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="ne">----&gt; </span><span class="mi">5</span> <span class="kn">import</span> <span class="nn">tensorflow</span> <span class="k">as</span> <span class="nn">tf</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">image</span>
-<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">51</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._api.v2</span> <span class="kn">import</span> <span class="n">data</span>
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
 <span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">30</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">autograph</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">bitwise</span>
-<span class="ne">---&gt; </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">compat</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">config</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">data</span>
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">37</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Compatibility functions.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> </span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span><span class="sd"> The `tf.compat` module contains two sets of compatibility functions.</span>
-<span class="sd">   (...)</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span><span class="sd"> </span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">---&gt; </span><span class="mi">37</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v1</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">v2</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">from</span> <span class="nn">tensorflow.python.compat.compat</span> <span class="kn">import</span> <span class="n">forward_compatibility_horizon</span>
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
 
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">47</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">layers</span>
-<span class="g g-Whitespace">     </span><span class="mi">46</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">linalg</span>
-<span class="ne">---&gt; </span><span class="mi">47</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">logging</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="kn">from</span> <span class="nn">tensorflow._api.v2.compat.v1</span> <span class="kn">import</span> <span class="n">lookup</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">9</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">constants</span>
-<span class="ne">----&gt; </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">experimental</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">Interpreter</span>
-<span class="g g-Whitespace">     </span><span class="mi">11</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpHint</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">authoring</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.analyzer</span> <span class="kn">import</span> <span class="n">ModelAnalyzer</span> <span class="k">as</span> <span class="n">Analyzer</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.lite</span> <span class="kn">import</span> <span class="n">OpResolverType</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">_api</span><span class="o">/</span><span class="n">v2</span><span class="o">/</span><span class="n">compat</span><span class="o">/</span><span class="n">v1</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">8</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="sd">&quot;&quot;&quot;Public API for tf.lite.experimental.authoring namespace.</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span><span class="sd"> &quot;&quot;&quot;</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">sys</span> <span class="k">as</span> <span class="nn">_sys</span>
-<span class="ne">----&gt; </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.authoring.authoring</span> <span class="kn">import</span> <span class="n">compatible</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">authoring</span><span class="o">/</span><span class="n">authoring</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">43</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="kn">import</span> <span class="nn">functools</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="ne">---&gt; </span><span class="mi">43</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">convert</span>
-<span class="g g-Whitespace">     </span><span class="mi">44</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite</span>
-<span class="g g-Whitespace">     </span><span class="mi">45</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.metrics</span> <span class="kn">import</span> <span class="n">converter_error_data_pb2</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">convert</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">29</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span> <span class="kn">import</span> <span class="nn">six</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">lite_constants</span>
-<span class="ne">---&gt; </span><span class="mi">29</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">util</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python</span> <span class="kn">import</span> <span class="n">wrap_toco</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span> <span class="kn">from</span> <span class="nn">tensorflow.lite.python.convert_phase</span> <span class="kn">import</span> <span class="n">Component</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">tensorflow</span><span class="o">/</span><span class="n">lite</span><span class="o">/</span><span class="n">python</span><span class="o">/</span><span class="n">util</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">51</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">47</span> <span class="c1"># Jax functions used by TFLite</span>
-<span class="g g-Whitespace">     </span><span class="mi">48</span> <span class="c1"># pylint: disable=g-import-not-at-top</span>
-<span class="g g-Whitespace">     </span><span class="mi">49</span> <span class="c1"># pylint: disable=unused-import</span>
-<span class="g g-Whitespace">     </span><span class="mi">50</span> <span class="k">try</span><span class="p">:</span>
-<span class="ne">---&gt; </span><span class="mi">51</span>   <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">_xla_computation</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="k">except</span> <span class="ne">ImportError</span><span class="p">:</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span>   <span class="n">_xla_computation</span> <span class="o">=</span> <span class="kc">None</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">116</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="kn">from</span> <span class="nn">._src.config</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">41</span>   <span class="n">config</span> <span class="k">as</span> <span class="n">config</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">42</span>   <span class="n">enable_checks</span> <span class="k">as</span> <span class="n">enable_checks</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">51</span>   <span class="n">numpy_rank_promotion</span> <span class="k">as</span> <span class="n">numpy_rank_promotion</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">52</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">53</span> <span class="kn">from</span> <span class="nn">._src.api</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">54</span>   <span class="n">ad</span><span class="p">,</span>  <span class="c1"># TODO(phawkins): update users to avoid this.</span>
-<span class="g g-Whitespace">     </span><span class="mi">55</span>   <span class="n">checkpoint</span> <span class="k">as</span> <span class="n">checkpoint</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">114</span>   <span class="n">xla_computation</span> <span class="k">as</span> <span class="n">xla_computation</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">115</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">116</span> <span class="kn">from</span> <span class="nn">.experimental.maps</span> <span class="kn">import</span> <span class="n">soft_pmap</span> <span class="k">as</span> <span class="n">soft_pmap</span>
-<span class="g g-Whitespace">    </span><span class="mi">117</span> <span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">__version__</span> <span class="k">as</span> <span class="n">__version__</span>
-<span class="g g-Whitespace">    </span><span class="mi">119</span> <span class="c1"># These submodules are separate because they are in an import cycle with</span>
-<span class="g g-Whitespace">    </span><span class="mi">120</span> <span class="c1"># jax and rely on the names imported above.</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">experimental</span><span class="o">/</span><span class="n">maps</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">26</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span> <span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">wraps</span><span class="p">,</span> <span class="n">partial</span><span class="p">,</span> <span class="n">partialmethod</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span> <span class="kn">from</span> <span class="nn">enum</span> <span class="kn">import</span> <span class="n">Enum</span>
-<span class="ne">---&gt; </span><span class="mi">26</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">numpy</span> <span class="k">as</span> <span class="n">jnp</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">core</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span> <span class="kn">from</span> <span class="nn">..</span> <span class="kn">import</span> <span class="n">linear_util</span> <span class="k">as</span> <span class="n">lu</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2018 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> 
-<span class="g g-Whitespace">     </span><span class="mi">18</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span> <span class="k">as</span> <span class="n">linalg</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span> <span class="kn">from</span> <span class="nn">jax.interpreters.xla</span> <span class="kn">import</span> <span class="n">DeviceArray</span> <span class="k">as</span> <span class="n">DeviceArray</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">17</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Copyright 2020 Google LLC</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="c1">#</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">14</span> 
-<span class="g g-Whitespace">     </span><span class="mi">15</span> <span class="c1"># flake8: noqa: F401</span>
-<span class="ne">---&gt; </span><span class="mi">17</span> <span class="kn">from</span> <span class="nn">jax._src.numpy.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">     </span><span class="mi">18</span>   <span class="n">ifft</span> <span class="k">as</span> <span class="n">ifft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">19</span>   <span class="n">ifft2</span> <span class="k">as</span> <span class="n">ifft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span>   <span class="n">ifftn</span> <span class="k">as</span> <span class="n">ifftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span>   <span class="n">ifftshift</span> <span class="k">as</span> <span class="n">ifftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">22</span>   <span class="n">ihfft</span> <span class="k">as</span> <span class="n">ihfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">23</span>   <span class="n">irfft</span> <span class="k">as</span> <span class="n">irfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">24</span>   <span class="n">irfft2</span> <span class="k">as</span> <span class="n">irfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">25</span>   <span class="n">irfftn</span> <span class="k">as</span> <span class="n">irfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">26</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">27</span>   <span class="n">fft2</span> <span class="k">as</span> <span class="n">fft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">28</span>   <span class="n">fftfreq</span> <span class="k">as</span> <span class="n">fftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">29</span>   <span class="n">fftn</span> <span class="k">as</span> <span class="n">fftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">30</span>   <span class="n">fftshift</span> <span class="k">as</span> <span class="n">fftshift</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">31</span>   <span class="n">hfft</span> <span class="k">as</span> <span class="n">hfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span>   <span class="n">rfft</span> <span class="k">as</span> <span class="n">rfft</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span>   <span class="n">rfft2</span> <span class="k">as</span> <span class="n">rfft2</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">34</span>   <span class="n">rfftfreq</span> <span class="k">as</span> <span class="n">rfftfreq</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span>   <span class="n">rfftn</span> <span class="k">as</span> <span class="n">rfftn</span><span class="p">,</span>
-<span class="g g-Whitespace">     </span><span class="mi">36</span> <span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">38</span> <span class="c1"># Module initialization is encapsulated in a function to avoid accidental</span>
-<span class="g g-Whitespace">     </span><span class="mi">39</span> <span class="c1"># namespace pollution.</span>
-<span class="g g-Whitespace">     </span><span class="mi">40</span> <span class="n">_NOT_IMPLEMENTED</span> <span class="o">=</span> <span class="p">[]</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">numpy</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">19</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">     </span><span class="mi">16</span> <span class="kn">import</span> <span class="nn">operator</span>
-<span class="g g-Whitespace">     </span><span class="mi">17</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
-<span class="ne">---&gt; </span><span class="mi">19</span> <span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">lax</span>
-<span class="g g-Whitespace">     </span><span class="mi">20</span> <span class="kn">from</span> <span class="nn">jax._src.lib</span> <span class="kn">import</span> <span class="n">xla_client</span>
-<span class="g g-Whitespace">     </span><span class="mi">21</span> <span class="kn">from</span> <span class="nn">jax._src.util</span> <span class="kn">import</span> <span class="n">safe_zip</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">332</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">299</span> <span class="kn">from</span> <span class="nn">jax._src.lax.lax</span> <span class="kn">import</span> <span class="p">(</span><span class="n">_reduce_sum</span><span class="p">,</span> <span class="n">_reduce_max</span><span class="p">,</span> <span class="n">_reduce_min</span><span class="p">,</span> <span class="n">_reduce_or</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">300</span>                   <span class="n">_reduce_and</span><span class="p">,</span> <span class="n">_reduce_window_sum</span><span class="p">,</span> <span class="n">_reduce_window_max</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">301</span>                   <span class="n">_reduce_window_min</span><span class="p">,</span> <span class="n">_reduce_window_prod</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">306</span>                   <span class="n">_upcast_fp16_for_computation</span><span class="p">,</span> <span class="n">_broadcasting_shape_rule</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">307</span>                   <span class="n">_eye</span><span class="p">,</span> <span class="n">_tri</span><span class="p">,</span> <span class="n">_delta</span><span class="p">,</span> <span class="n">_ones</span><span class="p">,</span> <span class="n">_zeros</span><span class="p">,</span> <span class="n">_dilate_shape</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">308</span> <span class="kn">from</span> <span class="nn">jax._src.lax.control_flow</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">309</span>   <span class="n">associative_scan</span> <span class="k">as</span> <span class="n">associative_scan</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">310</span>   <span class="n">cond</span> <span class="k">as</span> <span class="n">cond</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">330</span>   <span class="n">while_p</span> <span class="k">as</span> <span class="n">while_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">331</span> <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">332</span> <span class="kn">from</span> <span class="nn">jax._src.lax.fft</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">333</span>   <span class="n">fft</span> <span class="k">as</span> <span class="n">fft</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">334</span>   <span class="n">fft_p</span> <span class="k">as</span> <span class="n">fft_p</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">335</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">336</span> <span class="kn">from</span> <span class="nn">jax._src.lax.parallel</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">337</span>   <span class="n">all_gather</span> <span class="k">as</span> <span class="n">all_gather</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">338</span>   <span class="n">all_to_all</span> <span class="k">as</span> <span class="n">all_to_all</span><span class="p">,</span>
-   <span class="p">(</span><span class="o">...</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">355</span>   <span class="n">xeinsum</span> <span class="k">as</span> <span class="n">xeinsum</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">356</span> <span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">357</span> <span class="kn">from</span> <span class="nn">jax._src.lax.other</span> <span class="kn">import</span> <span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">358</span>   <span class="n">conv_general_dilated_patches</span> <span class="k">as</span> <span class="n">conv_general_dilated_patches</span>
-<span class="g g-Whitespace">    </span><span class="mi">359</span> <span class="p">)</span>
-
-<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">envs</span><span class="o">/</span><span class="n">myenv</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">jax</span><span class="o">/</span><span class="n">_src</span><span class="o">/</span><span class="n">lax</span><span class="o">/</span><span class="n">fft</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">145</span><span class="p">,</span> <span class="ow">in</span> <span class="o">&lt;</span><span class="n">module</span><span class="o">&gt;</span>
-<span class="g g-Whitespace">    </span><span class="mi">143</span> <span class="n">batching</span><span class="o">.</span><span class="n">primitive_batchers</span><span class="p">[</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">fft_batching_rule</span>
-<span class="g g-Whitespace">    </span><span class="mi">144</span> <span class="k">if</span> <span class="n">pocketfft</span><span class="p">:</span>
-<span class="ne">--&gt; </span><span class="mi">145</span>   <span class="n">xla</span><span class="o">.</span><span class="n">backend_specific_translations</span><span class="p">[</span><span class="s1">&#39;cpu&#39;</span><span class="p">][</span><span class="n">fft_p</span><span class="p">]</span> <span class="o">=</span> <span class="n">pocketfft</span><span class="o">.</span><span class="n">pocketfft</span>
-
-<span class="ne">AttributeError</span>: module &#39;jaxlib.pocketfft&#39; has no attribute &#39;pocketfft&#39;
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
 </div>
@@ -770,7 +611,7 @@ set up our toy data set.</p>
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">gaussian_points</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">mean_vector</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span>
                     <span class="n">sample_variance</span><span class="o">=</span><span class="mi">1</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Very simple custom function to generate gaussian distributed point clusters</span>
 <span class="sd">    with variable dimension, number of points, means in each direction</span>
 <span class="sd">    (must match dim) and sample variance.</span>
@@ -795,7 +636,7 @@ set up our toy data set.</p>
 
 <span class="k">def</span> <span class="nf">generate_simple_clustering_dataset</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">plotting</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
                                     <span class="n">return_data</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;</span>
+<span class="w">    </span><span class="sd">&quot;&quot;&quot;</span>
 <span class="sd">    Toy model to illustrate k-means clustering</span>
 <span class="sd">    &quot;&quot;&quot;</span>
 
@@ -1024,20 +865,20 @@ clustering implementation. Lets plot the final result</p>
         <span class="n">centroid_difference</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">centroids</span> <span class="o">-</span> <span class="n">prev_centroids</span><span class="p">))</span>
         <span class="k">if</span> <span class="n">centroid_difference</span> <span class="o">&lt;</span> <span class="n">tolerance</span><span class="p">:</span>
             <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Converged at iteration </span><span class="si">{</span><span class="n">iteration</span><span class="si">}</span><span class="s1">&#39;</span><span class="p">)</span>
-            <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Runtime: </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start_time</span><span class="si">}</span><span class="s1"> seconds&#39;</span><span class="p">)</span>
+            <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Runtime: </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start_time</span><span class="si">}</span><span class="s1"> seconds&#39;</span><span class="p">)</span>
 
             <span class="k">return</span> <span class="n">cluster_labels</span><span class="p">,</span> <span class="n">centroids</span>
 
     <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Did not converge in </span><span class="si">{</span><span class="n">max_iterations</span><span class="si">}</span><span class="s1"> iterations&#39;</span><span class="p">)</span>
-    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Runtime: </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span> <span class="o">-</span> <span class="n">start_time</span><span class="si">}</span><span class="s1"> seconds&#39;</span><span class="p">)</span>
+    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s1">&#39;Runtime: </span><span class="si">{</span><span class="n">time</span><span class="o">.</span><span class="n">time</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">start_time</span><span class="si">}</span><span class="s1"> seconds&#39;</span><span class="p">)</span>
 
     <span class="k">return</span> <span class="n">cluster_labels</span><span class="p">,</span> <span class="n">centroids</span>
 </pre></div>
 </div>
 </div>
 </div>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1051,7 +892,7 @@ clustering implementation. Lets plot the final result</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1059,44 +900,101 @@ clustering implementation. Lets plot the final result</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter2.html">
-   4. Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter3.html">
-   5. Resampling Methods
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter4.html">
-   6. Logistic Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapteroptimization.html">
-   7. Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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-   9. Decision trees, overarching aims
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-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
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-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">Exercise 3: Split data in test and training data</a></li>
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html exercisesweek34.do.txt  -->
-<!-- dom:TITLE: Exercises week 34 --><div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-34">
-<h1>Exercises week 34<a class="headerlink" href="#exercises-week-34" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Exercises week 34 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-34">
+<h1>Exercises week 34<a class="headerlink" href="#exercises-week-34" title="Permalink to this heading">#</a></h1>
 <p><strong>FYS-STK3155/4155</strong></p>
 <p>Date: <strong>August 21-25, 2023</strong></p>
-<div class="section" id="exercises">
-<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this headline">¶</a></h2>
+<section id="exercises">
+<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this heading">#</a></h2>
 <p>Here are three possible exercises for week 34</p>
-</div>
-<div class="section" id="exercise-1-setting-up-various-python-environments">
-<h2>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-1-setting-up-various-python-environments">
+<h2>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this heading">#</a></h2>
 <p>The first exercise here is of a mere technical art. We want you to have</p>
 <ul class="simple">
 <li><p>git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo <a class="reference external" href="https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html">GitHub facilities</a>.</p></li>
@@ -467,7 +443,7 @@ on Python.</p>
 <p>If you have Python installed (we recommend Python3) and you feel
 pretty familiar with installing different packages, we recommend that
 you install the following Python packages via <strong>pip</strong> as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>pip install numpy scipy matplotlib ipython scikit-learn sympy pandas pillow</p></li>
 </ol>
 <p>For <strong>Tensorflow</strong>, we recommend following the instructions in the text of
@@ -477,12 +453,12 @@ you install the following Python packages via <strong>pip</strong> as</p>
 <p>For OSX users we recommend, after having installed Xcode, to
 install <strong>brew</strong>. Brew allows for a seamless installation of additional
 software via for example</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>brew install python3</p></li>
 </ol>
 <p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
 you can use <strong>pip</strong> as well and simply install Python as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>sudo apt-get install python3  (or python for Python2.7)</p></li>
 </ol>
 <p>If you don’t want to perform these operations separately and venture
@@ -505,9 +481,9 @@ distribution for scientific and analytic computing distribution and
 analysis environment, available for free and under a commercial
 license.</p>
 <p>We recommend using <strong>Anaconda</strong> if you are not too familiar with setting paths in a terminal environment.</p>
-</div>
-<div class="section" id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
-<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
+<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>We will generate our own dataset for a function <span class="math notranslate nohighlight">\(y(x)\)</span> where <span class="math notranslate nohighlight">\(x \in [0,1]\)</span> and defined by random numbers computed with the uniform distribution. The function <span class="math notranslate nohighlight">\(y\)</span> is a quadratic polynomial in <span class="math notranslate nohighlight">\(x\)</span> with added stochastic noise according to the normal distribution <span class="math notranslate nohighlight">\(\cal {N}(0,1)\)</span>.
 The following simple Python instructions define our <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> values (with 100 data points).</p>
 <div class="cell docutils container">
@@ -520,7 +496,7 @@ The following simple Python instructions define our <span class="math notranslat
 <div class="cell_output docutils container">
 <div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
 <span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
 <span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
 <span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">y</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">+</span><span class="mi">5</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="mf">0.1</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">100</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
 
@@ -529,7 +505,7 @@ The following simple Python instructions define our <span class="math notranslat
 </div>
 </div>
 </div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Write your own code (following the examples under the <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter1.html">regression notes</a>) for computing the parametrization of the data set fitting a second-order polynomial.</p></li>
 <li><p>Use thereafter <strong>scikit-learn</strong> (see again the examples in the regression slides) and compare with your own code.</p></li>
 <li><p>Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</p></li>
@@ -552,9 +528,9 @@ R^2(\boldsymbol{y}, \tilde{\boldsymbol{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i
 \]</div>
 <p>You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
 Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.</p>
-</div>
-<div class="section" id="exercise-3-split-data-in-test-and-training-data">
-<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-3-split-data-in-test-and-training-data">
+<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this heading">#</a></h2>
 <p>In this exercise we want you to to compute the MSE for the training
 data and the test data as function of the complexity of a polynomial,
 that is the degree of a given polynomial.</p>
@@ -579,8 +555,8 @@ Write thereafter (using either <strong>scikit-learn</strong> or your matrix inve
 and perform an ordinary least squares fitting and compute the mean squared error for the training data and the test data. These calculations should apply to a model given by a fifth-order polynomial.</p>
 <p><strong>c)</strong>
 Add now a model which allows you to make polynomials up to degree <span class="math notranslate nohighlight">\(15\)</span>.  Perform a standard OLS fitting of the training data and compute the MSE for the training and test data and plot both test and training data MSE as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -594,7 +570,7 @@ Add now a model which allows you to make polynomials up to degree <span class="m
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -602,44 +578,104 @@ Add now a model which allows you to make polynomials up to degree <span class="m
     </script>
     <script>kernelName = 'python3'</script>
 
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- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter1.html">
-   3. Linear Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter2.html">
-   4. Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter3.html">
-   5. Resampling Methods
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter4.html">
-   6. Logistic Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapteroptimization.html">
-   7. Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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- <li class="toctree-l1">
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-   9. Decision trees, overarching aims
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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-   Exercise 1: Analytical exercises
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-  <a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">Exercise 3: Split data in test and training data</a></li>
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html exercisesweek35.do.txt  -->
-<!-- dom:TITLE: Exercises week 35 --><div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-35">
-<h1>Exercises week 35<a class="headerlink" href="#exercises-week-35" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Exercises week 35 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-35">
+<h1>Exercises week 35<a class="headerlink" href="#exercises-week-35" title="Permalink to this heading">#</a></h1>
 <p><strong>August 28-September 1, 2023</strong></p>
 <p>Date: <strong>Deadline is Friday September 1 at midnight</strong></p>
-<div class="section" id="exercise-1-analytical-exercises">
-<h2>Exercise 1: Analytical exercises<a class="headerlink" href="#exercise-1-analytical-exercises" title="Permalink to this headline">¶</a></h2>
+<section id="exercise-1-analytical-exercises">
+<h2>Exercise 1: Analytical exercises<a class="headerlink" href="#exercise-1-analytical-exercises" title="Permalink to this heading">#</a></h2>
 <p>In this exercise we derive the expressions for various derivatives of
 products of vectors and matrices. Such derivatives are central to the
 optimization of various cost functions. Although we will often use
@@ -485,9 +470,9 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
 \[
 \frac{\partial f(\boldsymbol{x})}{\partial \boldsymbol{x}}= \boldsymbol{A}.
 \]</div>
-</div>
-<div class="section" id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
-<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
+<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>We will generate our own dataset for a function <span class="math notranslate nohighlight">\(y(x)\)</span> where <span class="math notranslate nohighlight">\(x \in
 [0,1]\)</span> and defined by random numbers computed with the uniform
 distribution. The function <span class="math notranslate nohighlight">\(y\)</span> is a quadratic polynomial in <span class="math notranslate nohighlight">\(x\)</span> with
@@ -503,7 +488,7 @@ and <span class="math notranslate nohighlight">\(y\)</span> values (with 100 dat
 </div>
 </div>
 </div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Write your own code (following the examples under the <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter1.html">regression notes</a>) for computing the parametrization of the data set fitting a second-order polynomial.</p></li>
 <li><p>Use thereafter <strong>scikit-learn</strong> (see again the examples in the slides for week 35) and compare with your own code. Note here that <strong>scikit-learn</strong> does not include, by default, the intercept. See the discussions on scaling your data in the slides for this week. This type of problems appear in particular if we fit a polynomial with an intercept.</p></li>
 <li><p>Using scikit-learn, compute also the mean squared error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</p></li>
@@ -526,9 +511,9 @@ R^2(\boldsymbol{y}, \tilde{\boldsymbol{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i
 \]</div>
 <p>You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
 Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.</p>
-</div>
-<div class="section" id="exercise-3-split-data-in-test-and-training-data">
-<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-3-split-data-in-test-and-training-data">
+<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this heading">#</a></h2>
 <p>In this exercise we want you to to compute the MSE for the training
 data and the test data as function of the complexity of a polynomial,
 that is the degree of a given polynomial.</p>
@@ -554,8 +539,8 @@ Write thereafter (using either <strong>scikit-learn</strong> or your matrix inve
 and perform an ordinary least squares fitting and compute the mean squared error for the training data and the test data. These calculations should apply to a model given by a fifth-order polynomial.  If you compare your own code with <em>scikit_learn</em>, not that the latter does not include by default the intercept. See the discussions on scaling your data in the slides for this week.</p>
 <p><strong>c)</strong>
 Add now a model which allows you to make polynomials up to degree <span class="math notranslate nohighlight">\(15\)</span>.  Perform a standard OLS fitting of the training data and compute the MSE for the training and test data and plot both test and training data MSE as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -569,7 +554,7 @@ Add now a model which allows you to make polynomials up to degree <span class="m
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -577,44 +562,103 @@ Add now a model which allows you to make polynomials up to degree <span class="m
     </script>
     <script>kernelName = 'python3'</script>
 
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-  Decision Trees, Ensemble Methods and Boosting
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 </ul>
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-   13. Neural networks
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-   14. Building a Feed Forward Neural Network
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
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-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#a-expression-for-ridge-regression">a) Expression for Ridge regression</a></li>
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html exercisesweek36.do.txt --no_mako -->
-<!-- dom:TITLE: Exercises week 36 --><div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-36">
-<h1>Exercises week 36<a class="headerlink" href="#exercises-week-36" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Exercises week 36 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-36">
+<h1>Exercises week 36<a class="headerlink" href="#exercises-week-36" title="Permalink to this heading">#</a></h1>
 <p><strong>September 4-8, 2023</strong></p>
 <p>Date: <strong>Deadline is Sunday September 10 at midnight</strong></p>
-<div class="section" id="overarching-aims-of-the-exercises-this-week">
-<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this headline">¶</a></h2>
+<section id="overarching-aims-of-the-exercises-this-week">
+<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this heading">#</a></h2>
 <p>This set of exercises form an important part of the first project. The
 analytical exercises deal with the material covered last week on the
 mathematical interpretations of ordinary least squares and of Ridge
 regression. The numerical exercises can be seen as a continuation of
 exercise 3 from week 35, with the inclusion of Ridge regression. This
 material enters also the discussions of the first project.</p>
-</div>
-<div class="section" id="exercise-1-analytical-exercises">
-<h2>Exercise 1: Analytical exercises<a class="headerlink" href="#exercise-1-analytical-exercises" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-1-analytical-exercises">
+<h2>Exercise 1: Analytical exercises<a class="headerlink" href="#exercise-1-analytical-exercises" title="Permalink to this heading">#</a></h2>
 <p>The aim here is to derive the expression for the optimal parameters
 using Ridge regression. Furthermore, using the singular value
 decomposition, we will analyze the difference between the ordinary
@@ -505,8 +470,8 @@ defining a new cost function to be optimized, that is</p>
 <p>which leads to the Ridge regression minimization problem. One can require as part of the optimization problem
 that <span class="math notranslate nohighlight">\(\vert\vert \boldsymbol{\beta}\vert\vert_2^2\le t\)</span>, where <span class="math notranslate nohighlight">\(t\)</span> is
 a finite number larger than zero. We will not implement that here.</p>
-<div class="section" id="a-expression-for-ridge-regression">
-<h3>a) Expression for Ridge regression<a class="headerlink" href="#a-expression-for-ridge-regression" title="Permalink to this headline">¶</a></h3>
+<section id="a-expression-for-ridge-regression">
+<h3>a) Expression for Ridge regression<a class="headerlink" href="#a-expression-for-ridge-regression" title="Permalink to this heading">#</a></h3>
 <p>Show that the optimal parameters</p>
 <div class="math notranslate nohighlight">
 \[
@@ -523,9 +488,9 @@ a finite number larger than zero. We will not implement that here.</p>
 \[
 \hat{\boldsymbol{\beta}}_{\mathrm{OLS}} = \left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y},
 \]</div>
-</div>
-<div class="section" id="b-the-singular-value-decomposition">
-<h3>b) The singular value decomposition<a class="headerlink" href="#b-the-singular-value-decomposition" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="b-the-singular-value-decomposition">
+<h3>b) The singular value decomposition<a class="headerlink" href="#b-the-singular-value-decomposition" title="Permalink to this heading">#</a></h3>
 <p>Here we will use the singular value decomposition of an <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> (our design matrix)</p>
 <div class="math notranslate nohighlight">
 \[
@@ -548,16 +513,16 @@ OLS solutions in terms of the eigenvectors (the columns) of the orthogonal matri
 \]</div>
 <p>with the vectors <span class="math notranslate nohighlight">\(\boldsymbol{u}_j\)</span> being the columns of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> from the SVD of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
 <p>Give an interpretation of the results.  <a class="reference external" href="https://link.springer.com/book/10.1007/978-0-387-84858-7">Section 3.4 of Hastie et al’s textbook gives a good discussion of the above results</a>.</p>
-</div>
-</div>
-<div class="section" id="exercise-2-adding-ridge-regression">
-<h2>Exercise 2: Adding Ridge Regression<a class="headerlink" href="#exercise-2-adding-ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="exercise-2-adding-ridge-regression">
+<h2>Exercise 2: Adding Ridge Regression<a class="headerlink" href="#exercise-2-adding-ridge-regression" title="Permalink to this heading">#</a></h2>
 <p>This exercise is a continuation of exercise 3 from week 35, see <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/exercisesweek35.html">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/exercisesweek35.html</a>. We will use the same function to
 generate our data set, still staying with a simple function <span class="math notranslate nohighlight">\(y(x)\)</span>
 which we want to fit using linear regression, but now extending the
 analysis to include the Ridge regression method.</p>
 <p>In this exercise you need to include the same elements from last week, that is</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>scale your data by subtracting the mean value from each column in the design matrix.</p></li>
 <li><p>perform a split of the data in a training set and a test set.</p></li>
 </ol>
@@ -579,8 +544,8 @@ with <span class="math notranslate nohighlight">\(n=100\)</span> data points and
 squared error for the same values of <span class="math notranslate nohighlight">\(\lambda\)</span> for polynomials of degree ten
 and <span class="math notranslate nohighlight">\(15\)</span>. Discuss your results for the training MSE and test MSE with
 Ridge regression and ordinary least squares.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -594,7 +559,7 @@ Ridge regression and ordinary least squares.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -602,44 +567,107 @@ Ridge regression and ordinary least squares.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
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-</p>
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 </ul>
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-  Deep Learning Methods
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-expectation-values-for-ridge-regression">Exercise 2: Expectation values for Ridge regression</a></li>
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   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html exercisesweek37.do.txt  -->
-<!-- dom:TITLE: Exercises week 37 --><div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-37">
-<h1>Exercises week 37<a class="headerlink" href="#exercises-week-37" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Exercises week 37 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-37">
+<h1>Exercises week 37<a class="headerlink" href="#exercises-week-37" title="Permalink to this heading">#</a></h1>
 <p><strong>September 11-15, 2023</strong></p>
 <p>Date: <strong>Deadline is Sunday September 17 at midnight</strong></p>
-<div class="section" id="overarching-aims-of-the-exercises-this-week">
-<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this headline">¶</a></h2>
+<section id="overarching-aims-of-the-exercises-this-week">
+<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this heading">#</a></h2>
 <p>This exercise deals with various mean values and variances in linear
 regression method (here it may be useful to look up chapter 3,
 equation (3.8) of <a class="reference external" href="https://www.springer.com/gp/book/9780387848570">Trevor Hastie, Robert Tibshirani, Jerome
@@ -463,9 +448,9 @@ function <span class="math notranslate nohighlight">\(f\)</span> is approximated
 \boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
 \]</div>
 <p>The matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is the so-called design or feature matrix.</p>
-</div>
-<div class="section" id="exercise-1-expectation-values-for-ordinary-least-squares-expressions">
-<h2>Exercise 1: Expectation values for ordinary least squares expressions<a class="headerlink" href="#exercise-1-expectation-values-for-ordinary-least-squares-expressions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-1-expectation-values-for-ordinary-least-squares-expressions">
+<h2>Exercise 1: Expectation values for ordinary least squares expressions<a class="headerlink" href="#exercise-1-expectation-values-for-ordinary-least-squares-expressions" title="Permalink to this heading">#</a></h2>
 <p>Show that  the expectation value of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> for a given element <span class="math notranslate nohighlight">\(i\)</span></p>
 <div class="math notranslate nohighlight">
 \[
@@ -491,9 +476,9 @@ mean value <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbo
 \]</div>
 <p>We can use the last expression when we define a <a class="reference external" href="https://en.wikipedia.org/wiki/Confidence_interval">so-called confidence interval</a> for the parameters <span class="math notranslate nohighlight">\(\beta\)</span>.
 A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span> is given by the diagonal matrix element of the above matrix.</p>
-</div>
-<div class="section" id="exercise-2-expectation-values-for-ridge-regression">
-<h2>Exercise 2: Expectation values for Ridge regression<a class="headerlink" href="#exercise-2-expectation-values-for-ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-2-expectation-values-for-ridge-regression">
+<h2>Exercise 2: Expectation values for Ridge regression<a class="headerlink" href="#exercise-2-expectation-values-for-ridge-regression" title="Permalink to this heading">#</a></h2>
 <p>Show that</p>
 <div class="math notranslate nohighlight">
 \[
@@ -507,8 +492,8 @@ A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span>
 \mbox{Var}[\hat{\boldsymbol{\beta}}^{\mathrm{Ridge}}]=\sigma^2[  \mathbf{X}^{T} \mathbf{X} + \lambda \mathbf{I} ]^{-1}  \mathbf{X}^{T}\mathbf{X} \{ [  \mathbf{X}^{\top} \mathbf{X} + \lambda \mathbf{I} ]^{-1}\}^{T},
 \]</div>
 <p>and it is easy to see that if the parameter <span class="math notranslate nohighlight">\(\lambda\)</span> goes to infinity then the variance of the Ridge parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> goes to zero.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -522,7 +507,7 @@ A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -530,44 +515,103 @@ A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span>
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-1-expectation-values-for-ordinary-least-squares-expressions">Exercise 1: Expectation values for ordinary least squares expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-expectation-values-for-ridge-regression">Exercise 2: Expectation values for Ridge regression</a></li>
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index 8e99eb03f..8db9be131 100644
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
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-   1. Elements of Probability Theory and Statistical Data Analysis
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- <li class="toctree-l1">
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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- <li class="toctree-l1">
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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-   7. Optimization, the central part of any Machine Learning algortithm
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-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
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-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
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+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
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-   11. Basic ideas of the Principal Component Analysis (PCA)
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-   12. Clustering and Unsupervised Learning
-  </a>
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+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   13. Neural networks
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-   14. Building a Feed Forward Neural Network
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
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-   Week 37: Statistical interpretations and Resampling Methods
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-   Exercises week 38
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- <li class="toctree-l1">
-  <a class="reference internal" href="week38.html">
-   Week 38: Logistic Regression and Optimization
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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-<!-- dom:TITLE: Exercises week 38 --><div class="tex2jax_ignore mathjax_ignore section" id="exercises-week-38">
-<h1>Exercises week 38<a class="headerlink" href="#exercises-week-38" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Exercises week 38 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-38">
+<h1>Exercises week 38<a class="headerlink" href="#exercises-week-38" title="Permalink to this heading">#</a></h1>
 <p><strong>September 18-22, 2023</strong></p>
 <p>Date: <strong>Deadline is Sunday September 24 at midnight</strong></p>
-<div class="section" id="overarching-aims-of-the-exercises-this-week">
-<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this headline">¶</a></h2>
+<section id="overarching-aims-of-the-exercises-this-week">
+<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this heading">#</a></h2>
 <p>The aim of the exercises this week is to derive the equations for the bias-variance tradeoff to be used in project 1 as well as testing this for a simpler function using the bootstrap method. The exercises here can be reused in project 1 as well.</p>
 <p>Consider a
 dataset <span class="math notranslate nohighlight">\(\mathcal{L}\)</span> consisting of the data
@@ -474,9 +467,9 @@ studying the MSE value as function of the complexity of your model. Use ordinary
 of your model complexity (the degree of the polynomial) and the number
 of data points, and possibly also your training and test data using the <strong>bootstrap</strong> resampling method.
 You can follow the code example in the jupyter-book at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#the-bias-variance-tradeoff">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#the-bias-variance-tradeoff</a>.</p>
-<p>See also the whiteboard notes from week 37 at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf</a></p>
-</div>
-</div>
+<p>See also the whiteboard notes from week 37 at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">CompPhysics/MachineLearning</a></p>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
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@@ -490,7 +483,7 @@ You can follow the code example in the jupyter-book at <a class="reference exter
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -498,44 +491,101 @@ You can follow the code example in the jupyter-book at <a class="reference exter
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toctree-l1"><a class="reference internal" href="textbooks.html">Textbooks</a></li>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
+<ul class="current nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 39</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Optimization and  Gradient Methods</a></li>
+</ul>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#overarching-aims-of-the-exercises-this-week">Overarching aims of the exercises this week</a></li>
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+doconce format html exercisesweek39.do.txt  -->
+<!-- dom:TITLE: Exercises week 39 --><section class="tex2jax_ignore mathjax_ignore" id="exercises-week-39">
+<h1>Exercises week 39<a class="headerlink" href="#exercises-week-39" title="Permalink to this heading">#</a></h1>
+<p><strong>September 25-29, 2023</strong></p>
+<p>Date: <strong>Deadline is Sunday October 1 at midnight</strong></p>
+<section id="overarching-aims-of-the-exercises-this-week">
+<h2>Overarching aims of the exercises this week<a class="headerlink" href="#overarching-aims-of-the-exercises-this-week" title="Permalink to this heading">#</a></h2>
+<p>The aim of the exercises this week is to aid you in getting started
+with writing the report. This will be discussed during the lab
+sessions as well. One of the lab sessions will be recorded.</p>
+<p>A general guideline can be found at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">CompPhysics/MachineLearning</a>.</p>
+<p>Similarly, an example of an earlier project can be found at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf">CompPhysics/MachineLearning</a></p>
+<p>Your task this week is to</p>
+<ol class="arabic simple">
+<li><p>Write an abstract for your project</p></li>
+<li><p>Write an introduction</p></li>
+<li><p>Include references</p></li>
+</ol>
+<p>Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report.</p>
+</section>
+</section>
+
+    <script type="text/x-thebe-config">
+    {
+        requestKernel: true,
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+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
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+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
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+<ul class="nav bd-sidenav">
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Optimization and  Gradient Methods</a></li>
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 </ul>
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-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
 <ul class="nav bd-sidenav">
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
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+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
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-   12. Clustering and Unsupervised Learning
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+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
 <ul class="nav bd-sidenav">
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-   14. Building a Feed Forward Neural Network
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
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-</p>
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 <ul class="nav bd-sidenav">
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-   Exercises week 38
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-   Week 38: Logistic Regression and Optimization
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Optimization and  Gradient Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Projects
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+    <h1>Applied Data Analysis and Machine Learning</h1>
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- <li class="toc-h2 nav-item toc-entry">
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-   Introduction
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-     Useful Python libraries
-    </a>
-   </li>
-  </ul>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-outcomes">Learning outcomes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites-and-background">Prerequisites and background</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-course-has-two-central-parts">The course has two central parts</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#statistical-analysis-and-optimization-of-data">Statistical analysis and optimization of data</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#machine-learning">Machine learning</a></li>
+</ul>
+</li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#useful-python-libraries">Useful Python libraries</a></li>
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-                <h1>Applied Data Analysis and Machine Learning</h1>
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-                            <h2> Contents </h2>
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+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="applied-data-analysis-and-machine-learning">
-<h1>Applied Data Analysis and Machine Learning<a class="headerlink" href="#applied-data-analysis-and-machine-learning" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="introduction">
-<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="applied-data-analysis-and-machine-learning">
+<h1>Applied Data Analysis and Machine Learning<a class="headerlink" href="#applied-data-analysis-and-machine-learning" title="Permalink to this heading">#</a></h1>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
 <p>Probability theory and statistical methods play a central role in Science. Nowadays we are
 surrounded by huge amounts of data. For example, there are more than one trillion web pages; more than one
 hour of video is uploaded to YouTube every second, amounting to years of content every
 day; the genomes of 1000s of people, each of which has a length of more than a billion  base pairs, have
 been sequenced by various labs and so on. This deluge of data calls for automated methods of data analysis,
 which is exactly what machine learning aims at providing.</p>
-</div>
-<div class="section" id="learning-outcomes">
-<h2>Learning outcomes<a class="headerlink" href="#learning-outcomes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="learning-outcomes">
+<h2>Learning outcomes<a class="headerlink" href="#learning-outcomes" title="Permalink to this heading">#</a></h2>
 <p>This course aims at giving you insights and knowledge about  many of the central algorithms used in Data Analysis and Machine Learning.  The course is project based and through  various numerical projects and weekly exercises you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach with an emphasis on predictions and correaltions. However, we will try, where appropriate, to link our machine learning models with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will</p>
 <ul class="simple">
 <li><p>Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;</p></li>
@@ -531,20 +419,20 @@ which is exactly what machine learning aims at providing.</p>
 <li><p>Autoencoders and Reinforcement Learning;</p></li>
 <li><p>Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later).</p></li>
 </ul>
-</div>
-<div class="section" id="prerequisites-and-background">
-<h2>Prerequisites and background<a class="headerlink" href="#prerequisites-and-background" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="prerequisites-and-background">
+<h2>Prerequisites and background<a class="headerlink" href="#prerequisites-and-background" title="Permalink to this heading">#</a></h2>
 <p>Basic knowledge in programming and mathematics, with an emphasis on linear algebra. Knowledge of Python or/and C++ as programming languages is strongly recommended and experience with Jupyter notebooks is recommended. Required courses are the equivalents to the University of Oslo mathematics courses MAT1100, MAT1110, MAT1120 and at least one of the corresponding computing and programming courses INF1000/INF1110 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1100. Most universities offer nowadays a basic programming course (often compulsory) where Python is the recurring programming language.
 We recommend also refreshing your knowledge on Statistics and Probability theory. The lecture notes at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html</a> offer a review of Statistics and Probability theory.</p>
-</div>
-<div class="section" id="the-course-has-two-central-parts">
-<h2>The course has two central parts<a class="headerlink" href="#the-course-has-two-central-parts" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="the-course-has-two-central-parts">
+<h2>The course has two central parts<a class="headerlink" href="#the-course-has-two-central-parts" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>Statistical analysis and optimization of data</p></li>
 <li><p>Machine learning</p></li>
 </ol>
-<div class="section" id="statistical-analysis-and-optimization-of-data">
-<h3>Statistical analysis and optimization of data<a class="headerlink" href="#statistical-analysis-and-optimization-of-data" title="Permalink to this headline">¶</a></h3>
+<section id="statistical-analysis-and-optimization-of-data">
+<h3>Statistical analysis and optimization of data<a class="headerlink" href="#statistical-analysis-and-optimization-of-data" title="Permalink to this heading">#</a></h3>
 <p>The following topics will be covered</p>
 <ul class="simple">
 <li><p>Basic concepts, expectation values, variance, covariance, correlation functions and errors;</p></li>
@@ -555,9 +443,9 @@ We recommend also refreshing your knowledge on Statistics and Probability theory
 <li><p>Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;</p></li>
 <li><p>Principal Component Analysis (PCA) and its mathematical foundation</p></li>
 </ul>
-</div>
-<div class="section" id="machine-learning">
-<h3>Machine learning<a class="headerlink" href="#machine-learning" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="machine-learning">
+<h3>Machine learning<a class="headerlink" href="#machine-learning" title="Permalink to this heading">#</a></h3>
 <p>The following topics will be covered:</p>
 <ul class="simple">
 <li><p>Linear Regression and Logistic Regression;</p></li>
@@ -573,11 +461,11 @@ We recommend also refreshing your knowledge on Statistics and Probability theory
 <p>Computational aspects play a central role and you are
 expected to work on numerical examples and projects which illustrate
 the theory and various algorithms discussed during the lectures. We recommend strongly to form small project groups of 2-3 participants, if possible.</p>
-</div>
-</div>
-<div class="section" id="required-technologies">
-<h2>Required Technologies<a class="headerlink" href="#required-technologies" title="Permalink to this headline">¶</a></h2>
-<p>Course participants are expected to have their own laptops/PCs. We use <em>Git</em> as version control software and the usage of providers like <em>GitHub</em>, <em>GitLab</em> or similar are strongly recommended. If you are not familiar with Git as version control software, the following video may be of interest, see <a class="reference external" href="https://www.youtube.com/watch?v=RGOj5yH7evk&amp;ab_channel=freeCodeCamp.org">https://www.youtube.com/watch?v=RGOj5yH7evk&amp;ab_channel=freeCodeCamp.org</a></p>
+</section>
+</section>
+<section id="required-technologies">
+<h2>Required Technologies<a class="headerlink" href="#required-technologies" title="Permalink to this heading">#</a></h2>
+<p>Course participants are expected to have their own laptops/PCs. We use <em>Git</em> as version control software and the usage of providers like <em>GitHub</em>, <em>GitLab</em> or similar are strongly recommended. If you are not familiar with Git as version control software, the following video may be of interest, see <a class="reference external" href="https://www.youtube.com/watch?v=RGOj5yH7evk&amp;amp;ab_channel=freeCodeCamp.org">https://www.youtube.com/watch?v=RGOj5yH7evk&amp;ab_channel=freeCodeCamp.org</a></p>
 <p>We will make extensive use of Python as programming language and its
 myriad of available libraries.  You will find
 Jupyter notebooks invaluable in your work.  You can run <em>R</em>
@@ -602,8 +490,8 @@ you can use <em>pip</em> as well and simply install Python as</p>
 <ul class="simple">
 <li><p>sudo apt-get install python3</p></li>
 </ul>
-<div class="section" id="python-installers">
-<h3>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this headline">¶</a></h3>
+<section id="python-installers">
+<h3>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this heading">#</a></h3>
 <p>If you don’t want to perform these operations separately and venture
 into the hassle of exploring how to set up dependencies and paths, we
 recommend two widely used distrubutions which set up all relevant
@@ -625,9 +513,9 @@ analysis environment, available for free and under a commercial
 license.</p>
 <p>Furthermore, Google’s Colab:<a class="reference external" href="https://colab.research.google.com/notebooks/welcome.ipynb">https://colab.research.google.com/notebooks/welcome.ipynb</a> is a free Jupyter notebook environment that requires
 no setup and runs entirely in the cloud. Try it out!</p>
-</div>
-<div class="section" id="useful-python-libraries">
-<h3>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="useful-python-libraries">
+<h3>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this heading">#</a></h3>
 <p>Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)</p>
 <ul class="simple">
 <li><p><em>NumPy</em>:<a class="reference external" href="https://www.numpy.org/">https://www.numpy.org/</a> is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays</p></li>
@@ -635,7 +523,7 @@ no setup and runs entirely in the cloud. Try it out!</p>
 <li><p><em>Xarray</em>:<a class="reference external" href="http://xarray.pydata.org/en/stable/">http://xarray.pydata.org/en/stable/</a> is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!</p></li>
 <li><p><em>Scipy</em>:<a class="reference external" href="https://www.scipy.org/">https://www.scipy.org/</a> (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.</p></li>
 <li><p><em>Matplotlib</em>:<a class="reference external" href="https://matplotlib.org/">https://matplotlib.org/</a> is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.</p></li>
-<li><p><em>Autograd</em>:<a class="reference external" href="https://github.com/HIPS/autograd">https://github.com/HIPS/autograd</a> can automatically differentiate native Python and Numpy code. It can handle a large subset of Python’s features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives</p></li>
+<li><p><em>Autograd</em>:<a class="github reference external" href="https://github.com/HIPS/autograd">HIPS/autograd</a> can automatically differentiate native Python and Numpy code. It can handle a large subset of Python’s features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives</p></li>
 <li><p><em>JAX</em> <a class="reference external" href="https://jax.readthedocs.io/en/latest/index.html">https://jax.readthedocs.io/en/latest/index.html</a> has now more or less replaced <em>Autograd</em>.
 JAX is Autograd and XLA, brought together for high-performance numerical computing and machine learning research.
 It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.</p></li>
@@ -645,8 +533,8 @@ It provides composable transformations of Python+NumPy programs: differentiate,
 <li><p><em>Keras</em>:<a class="reference external" href="https://keras.io/">https://keras.io/</a> is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano</p></li>
 <li><p>And many more such as <em>pytorch</em>:<a class="reference external" href="https://pytorch.org/">https://pytorch.org/</a>,  <em>Theano</em>:<a class="reference external" href="https://pypi.org/project/Theano/">https://pypi.org/project/Theano/</a> etc</p></li>
 </ul>
-</div>
-</div>
+</section>
+</section>
 <div class="toctree-wrapper compound">
 </div>
 <div class="toctree-wrapper compound">
@@ -663,7 +551,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
 </div>
 <div class="toctree-wrapper compound">
 </div>
-</div>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -677,7 +565,7 @@ It provides composable transformations of Python+NumPy programs: differentiate,
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -685,37 +573,104 @@ It provides composable transformations of Python+NumPy programs: differentiate,
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
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-<p aria-level="2" class="caption" role="heading">
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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 </ul>
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-  Dimensionality Reduction
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+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-<p aria-level="2" class="caption" role="heading">
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-   Exercises week 37
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-<p aria-level="2" class="caption" role="heading">
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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- <li class="toc-h2 nav-item toc-entry">
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-   2.1. Introduction
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-  <a class="reference internal nav-link" href="#important-matrix-and-vector-handling-packages">
-   2.2. Important Matrix and vector handling packages
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-     2.6.1. LU Decomposition, the inverse of a matrix
-    </a>
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- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">2.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#important-matrix-and-vector-handling-packages">2.2. Important Matrix and vector handling packages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-matrix-features">2.3. Basic Matrix Features</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#some-famous-matrices">2.3.1. Some famous Matrices</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-and-arrays">2.4. Numpy and arrays</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-matrix-and-vector-operations">2.5. Other Matrix and Vector Operations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gaussian-elimination">2.6. Gaussian Elimination</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#lu-decomposition-the-inverse-of-a-matrix">2.6.1. LU Decomposition, the inverse of a matrix</a></li>
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+</li>
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- </li>
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-   2.2. Important Matrix and vector handling packages
-  </a>
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-    </a>
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+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html linalg.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="linear-algebra-handling-of-arrays-and-more-python-features">
-<h1><span class="section-number">2. </span>Linear Algebra, Handling of Arrays and more Python Features<a class="headerlink" href="#linear-algebra-handling-of-arrays-and-more-python-features" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="introduction">
-<h2><span class="section-number">2.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+doconce format html linalg.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="linear-algebra-handling-of-arrays-and-more-python-features">
+<h1><span class="section-number">2. </span>Linear Algebra, Handling of Arrays and more Python Features<a class="headerlink" href="#linear-algebra-handling-of-arrays-and-more-python-features" title="Permalink to this heading">#</a></h1>
+<section id="introduction">
+<h2><span class="section-number">2.1. </span>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
 <p>The aim of this set of lectures is to review some central linear algebra algorithms that we will need in our
 data analysis part and in the construction of Machine Learning algorithms (ML).
 This will allow us to introduce some central programming features of high-level languages like Python and
@@ -503,9 +439,9 @@ as writing your own codes for some central ML algorithms. The
 latter can be written in a language of your choice, be it Python, Julia, R,
 Rust, C++, Fortran etc. In order to avoid confusion however, in these lectures we will limit our
 attention to Python, C++ and Fortran.</p>
-</div>
-<div class="section" id="important-matrix-and-vector-handling-packages">
-<h2><span class="section-number">2.2. </span>Important Matrix and vector handling packages<a class="headerlink" href="#important-matrix-and-vector-handling-packages" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="important-matrix-and-vector-handling-packages">
+<h2><span class="section-number">2.2. </span>Important Matrix and vector handling packages<a class="headerlink" href="#important-matrix-and-vector-handling-packages" title="Permalink to this heading">#</a></h2>
 <p>There are several central software packages for linear algebra and eigenvalue problems. Several of the more
 popular ones have been wrapped into ofter software packages like those from the widely used text <strong>Numerical Recipes</strong>. The original source codes in many of the available packages are often taken from the widely used
 software package LAPACK, which follows two other popular packages
@@ -531,9 +467,9 @@ linear algebra and eigenvalue problems. In addition it offers a
 convenient way to handle and organize arrays. We discuss this library
 as well.   Before we proceed we believe  it may be convenient to repeat some basic features of
 matrices and vectors.</p>
-</div>
-<div class="section" id="basic-matrix-features">
-<h2><span class="section-number">2.3. </span>Basic Matrix Features<a class="headerlink" href="#basic-matrix-features" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="basic-matrix-features">
+<h2><span class="section-number">2.3. </span>Basic Matrix Features<a class="headerlink" href="#basic-matrix-features" title="Permalink to this heading">#</a></h2>
 <p>Matrix properties reminder</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -566,8 +502,8 @@ matrices and vectors.</p>
 <tr><td align="center">   $A = A^{\dagger}$                         </td> <td align="center">   hermitian          </td> <td align="center">   $a_{ij} = a_{ji}^{ * }$                                                    </td> </tr>
 <tr><td align="center">   $A = \left (A^{\dagger} \right )^{-1}$    </td> <td align="center">   unitary            </td> <td align="center">   $\sum_k a_{ik} a_{jk}^{ * } = \sum_k a_{ki}^{ * } a_{kj} = \delta_{ij}$    </td> </tr>
 </tbody>
-</table><div class="section" id="some-famous-matrices">
-<h3><span class="section-number">2.3.1. </span>Some famous Matrices<a class="headerlink" href="#some-famous-matrices" title="Permalink to this headline">¶</a></h3>
+</table><section id="some-famous-matrices">
+<h3><span class="section-number">2.3.1. </span>Some famous Matrices<a class="headerlink" href="#some-famous-matrices" title="Permalink to this heading">#</a></h3>
 <ul class="simple">
 <li><p>Diagonal if <span class="math notranslate nohighlight">\(a_{ij}=0\)</span> for <span class="math notranslate nohighlight">\(i\ne j\)</span></p></li>
 <li><p>Upper triangular if <span class="math notranslate nohighlight">\(a_{ij}=0\)</span> for <span class="math notranslate nohighlight">\(i &gt; j\)</span></p></li>
@@ -588,10 +524,10 @@ matrices and vectors.</p>
 <li><p><span class="math notranslate nohighlight">\(\mathbf{A}\)</span> is a product of elementary matrices.</p></li>
 <li><p><span class="math notranslate nohighlight">\(0\)</span> is not eigenvalue of <span class="math notranslate nohighlight">\(\mathbf{A}\)</span>.</p></li>
 </ul>
-</div>
-</div>
-<div class="section" id="numpy-and-arrays">
-<h2><span class="section-number">2.4. </span>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="numpy-and-arrays">
+<h2><span class="section-number">2.4. </span>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="http://www.numpy.org/">Numpy</a> provides an easy way to handle arrays in Python. The standard way to import this library is as</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -603,8 +539,8 @@ matrices and vectors.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.28587856 -0.73509675  0.35559283 -0.62819534 -0.15254784 -0.44792888
-  1.5393681  -0.81784072  0.53476918  1.02055673]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-0.1223405   0.96602098 -0.42045733  2.00897328  0.96178833 -0.30742211
+  0.23867951 -1.84775931 -0.3804507  -0.47953891]
 </pre></div>
 </div>
 </div>
@@ -825,26 +761,26 @@ as (recall that we user lowercase letters for vectors and uppercase letters for
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.99218609 0.13120126 0.8260149  0.70761641 0.8634474  0.47202234
-  0.09862064 0.8970168  0.40947888 0.19121744]
- [0.93969474 0.4378299  0.23405814 0.52872817 0.00229179 0.41050604
-  0.846471   0.78027207 0.11551515 0.18573652]
- [0.80515205 0.40984037 0.61970354 0.03608726 0.90793026 0.45494697
-  0.41718305 0.77288474 0.94404545 0.09218919]
- [0.24566623 0.18632646 0.82113506 0.01710429 0.88981061 0.77756468
-  0.94073014 0.89779302 0.97936584 0.69051742]
- [0.84924359 0.43533824 0.62420578 0.02185737 0.36336962 0.10056192
-  0.19468989 0.96562567 0.770356   0.4756968 ]
- [0.05851756 0.43471448 0.80088524 0.62083489 0.88778045 0.56821272
-  0.7133574  0.10148978 0.54861905 0.45917334]
- [0.15939618 0.47756853 0.08791994 0.87602519 0.11470382 0.67142502
-  0.7600498  0.81709481 0.85895314 0.33874172]
- [0.21561586 0.65011691 0.1897755  0.5538822  0.75747652 0.27898999
-  0.35128114 0.27674224 0.47513129 0.59366475]
- [0.5916751  0.82365318 0.16026316 0.533142   0.93265898 0.05881845
-  0.10326551 0.95604667 0.8617319  0.74199799]
- [0.21089449 0.0402861  0.12611267 0.49197115 0.59203799 0.74577306
-  0.14491591 0.71135895 0.84723978 0.03416188]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.69846205 0.78851232 0.08308983 0.5305063  0.12815515 0.72072214
+  0.67232869 0.76697449 0.58848856 0.9904943 ]
+ [0.75838023 0.80529041 0.6484163  0.10609258 0.41344691 0.48942943
+  0.92662338 0.88338811 0.12254643 0.81520361]
+ [0.55042787 0.34048788 0.25737687 0.7565813  0.30552745 0.25529596
+  0.44101674 0.95844886 0.86670783 0.3992021 ]
+ [0.62482386 0.98232786 0.5248769  0.48823898 0.944291   0.88340778
+  0.96704933 0.5255844  0.38941883 0.29239286]
+ [0.65680942 0.65466708 0.96617085 0.42214481 0.99932624 0.96546053
+  0.48953049 0.26725306 0.57937269 0.36135213]
+ [0.73623167 0.23284855 0.36113667 0.61429341 0.91951571 0.84545016
+  0.37857094 0.76168988 0.96457138 0.61999335]
+ [0.89635517 0.52058686 0.41240055 0.94738767 0.74171774 0.96592507
+  0.63880898 0.44499556 0.21026792 0.92965555]
+ [0.30230092 0.9347861  0.56187437 0.3860215  0.58467645 0.27058589
+  0.67628977 0.01494766 0.30681968 0.30491305]
+ [0.00860818 0.97140208 0.86478154 0.68302636 0.72968415 0.5859337
+  0.88898063 0.25024282 0.07427349 0.65046291]
+ [0.01924293 0.54705652 0.01611258 0.47220243 0.36688196 0.47846644
+  0.17072424 0.48396466 0.7900928  0.28490342]]
 </pre></div>
 </div>
 </div>
@@ -904,13 +840,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.041129694365319464
-4.025325212488352
-0.010687707010849668
-[[ 1.23319332  3.73704762  4.12446443]
- [ 3.73704762 12.59095724 12.81409445]
- [ 4.12446443 12.81409445 20.04983109]]
-[30.70850263  0.10254846  3.06293056]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.0017018997030592974
+3.9531810558360623
+-0.018173592942955955
+[[ 1.06833761  3.33062366  3.10248906]
+ [ 3.33062366 11.28977247 10.01231809]
+ [ 3.10248906 10.01231809 13.75855891]]
+[23.52658256  0.07563718  2.51444926]
 </pre></div>
 </div>
 </div>
@@ -934,22 +870,60 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[1. 0. 0. 0.]
- [0. 1. 0. 0.]
- [0. 0. 1. 0.]
- [0. 0. 0. 1.]]
-  (0, 0)	1.0
-  (1, 1)	1.0
-  (2, 2)	1.0
-  (3, 3)	1.0
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">15</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/linalg_44_1.png" src="_images/linalg_44_1.png" />
 </div>
 </div>
-</div>
-<div class="section" id="other-matrix-and-vector-operations">
-<h2><span class="section-number">2.5. </span>Other Matrix and Vector Operations<a class="headerlink" href="#other-matrix-and-vector-operations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-matrix-and-vector-operations">
+<h2><span class="section-number">2.5. </span>Other Matrix and Vector Operations<a class="headerlink" href="#other-matrix-and-vector-operations" title="Permalink to this heading">#</a></h2>
 <p>The following examples show how to compute various quantities like the <strong>mean</strong> value of a matrix or a vector and how to use functions like <strong>reshape</strong> and <strong>ravel</strong>. These are all useful quantities when scaling the data and preparing the data for various machine learning algorithms and when calculating quantities like the mean squared error or the variance.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -964,28 +938,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 <span class="c1"># This is the total mean summed over all elements, which here has to be 6.5</span>
 <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the total mean summed over all elements:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="c1"># This is the mean for each column, it returns an array with the mean values for each column. It returns a row-like vector</span>
-<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean for each column:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean for each column:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="c1"># This is the mean value for each row, it returns an array via the keepdims option which is a column-like vector if</span>
 <span class="c1"># keepdims=True. Else it return a row-like vector</span>
 <span class="c1"># Try setting keepdims=False</span>
-<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean value for each row:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean value for each row:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">keepdims</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 <span class="c1"># We print then the mean value for each row by  setting keepdims=False</span>
-<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean value for each row with keepdims false:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
-</pre></div>
-</div>
-</div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The test matrix:[[ 1.  2.  3.]
- [ 4.  5.  6.]
- [ 7.  8.  9.]
- [10. 11. 12.]]
-This is the total mean summed over all elements:6.5
-This is the mean for each column:[[5.5 6.5 7.5]]
-This is the mean value for each row:[[ 2.]
- [ 5.]
- [ 8.]
- [11.]]
-This is the mean value for each row with keepdims false:[ 2.  5.  8. 11.]
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;This is the mean value for each row with keepdims false:</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">keepdims</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span><span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
@@ -1009,19 +968,10 @@ This is the mean value for each row with keepdims false:[ 2.  5.  8. 11.]
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Flatten  the matrix:[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]
-Reshape the matrix to a one-dim array:[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]
-[ 1.  4.  7. 10.  2.  5.  8. 11.  3.  6.  9. 12.]
-[ 1.  4.  7. 10.  2.  5.  8. 11.  3.  6.  9. 12.]
-[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="gaussian-elimination">
-<h2><span class="section-number">2.6. </span>Gaussian Elimination<a class="headerlink" href="#gaussian-elimination" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gaussian-elimination">
+<h2><span class="section-number">2.6. </span>Gaussian Elimination<a class="headerlink" href="#gaussian-elimination" title="Permalink to this heading">#</a></h2>
 <p>We start with the linear set of equations</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1374,8 +1324,8 @@ needed to solve the set of <span class="math notranslate nohighlight">\(n\)</spa
 <li><p>Then LU decompose the matrix <span class="math notranslate nohighlight">\(\bf A\)</span> through a call to the function <code class="docutils literal notranslate"><span class="pre">ludcmp(double</span> <span class="pre">a,</span> <span class="pre">int</span> <span class="pre">n,</span> <span class="pre">int</span> <span class="pre">indx,</span> <span class="pre">double</span> <span class="pre">&amp;d)</span></code>. This functions returns the LU decomposed matrix <span class="math notranslate nohighlight">\(\bf A\)</span>, its determinant and the vector indx which keeps track of the number of interchanges of rows. If the determinant is zero, the solution is malconditioned.</p></li>
 <li><p>Thereafter you call the function  <code class="docutils literal notranslate"><span class="pre">lubksb(double</span> <span class="pre">a,</span> <span class="pre">int</span> <span class="pre">n,</span> <span class="pre">int</span> <span class="pre">indx,</span> <span class="pre">double</span> <span class="pre">w)</span></code> which uses the LU decomposed matrix <span class="math notranslate nohighlight">\(\bf A\)</span> and the vector <span class="math notranslate nohighlight">\(\bf w\)</span> and returns <span class="math notranslate nohighlight">\(\bf x\)</span> in the same place as <span class="math notranslate nohighlight">\(\bf w\)</span>. Upon exit the original content in <span class="math notranslate nohighlight">\(\bf w\)</span> is destroyed. If you wish to keep this information, you should make a backup of it in your calling function.</p></li>
 </ul>
-<div class="section" id="lu-decomposition-the-inverse-of-a-matrix">
-<h3><span class="section-number">2.6.1. </span>LU Decomposition, the inverse of a matrix<a class="headerlink" href="#lu-decomposition-the-inverse-of-a-matrix" title="Permalink to this headline">¶</a></h3>
+<section id="lu-decomposition-the-inverse-of-a-matrix">
+<h3><span class="section-number">2.6.1. </span>LU Decomposition, the inverse of a matrix<a class="headerlink" href="#lu-decomposition-the-inverse-of-a-matrix" title="Permalink to this heading">#</a></h3>
 <p>If the inverse exists then</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1434,9 +1384,9 @@ linear dependencies among the various columns and/or rows. In our
 discussions of linear regression we will dive into the mathematics of
 the singular value decomposition, an algorithm which will allow us to calculate the so-called pseudo-inverse.
 These details will be presented in our linear regression chapter.</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1450,7 +1400,7 @@ These details will be presented in our linear regression chapter.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1458,44 +1408,112 @@ These details will be presented in our linear regression chapter.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">2.1. Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#important-matrix-and-vector-handling-packages">2.2. Important Matrix and vector handling packages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-matrix-features">2.3. Basic Matrix Features</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#some-famous-matrices">2.3.1. Some famous Matrices</a></li>
+</ul>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-and-arrays">2.4. Numpy and arrays</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-matrix-and-vector-operations">2.5. Other Matrix and Vector Operations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gaussian-elimination">2.6. Gaussian Elimination</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#lu-decomposition-the-inverse-of-a-matrix">2.6.1. LU Decomposition, the inverse of a matrix</a></li>
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-  About the course
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+                    Applied Data Analysis and Machine Learning
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+        <p aria-level="2" class="caption" role="heading"><span class="caption-text">About the course</span></p>
 <ul class="nav bd-sidenav">
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 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="statistics.html">
-   1. Elements of Probability Theory and Statistical Data Analysis
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="linalg.html">
-   2. Linear Algebra, Handling of Arrays and more Python Features
-  </a>
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter1.html">
-   3. Linear Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter2.html">
-   4. Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter3.html">
-   5. Resampling Methods
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter4.html">
-   6. Logistic Regression
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapteroptimization.html">
-   7. Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
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-   9. Decision trees, overarching aims
-  </a>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
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- <li class="toctree-l1">
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-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
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-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
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- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-  <a class="reference internal" href="week35.html">
-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
-  </a>
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- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statistical interpretations and Resampling Methods
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek38.html">
-   Exercises week 38
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week38.html">
-   Week 38: Logistic Regression and Optimization
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1 current active">
-  <a class="current reference internal" href="#">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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-   Regression analysis and resampling methods
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-   Background literature
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-   Introduction to numerical projects
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+<div id="jb-print-docs-body" class="onlyprint">
+    <h1>Project 1 on Machine Learning, deadline October 9 (midnight), 2023</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
+            
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-and-resampling-methods">Regression analysis and resampling methods</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#description-of-two-dimensional-function">Description of two-dimensional function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-a-ordinary-least-square-ols-on-the-franke-function">Part a) : Ordinary Least Square (OLS) on the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-b-adding-ridge-regression-for-the-franke-function">Part b): Adding Ridge regression for  the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-c-adding-lasso-for-the-franke-function">Part c): Adding Lasso for the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-d-paper-and-pencil-part">Part d): Paper and pencil part</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-e-bias-variance-trade-off-and-resampling-techniques">Part e): Bias-variance trade-off and resampling techniques</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity">Part f):  Cross-validation as resampling techniques, adding more complexity</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-g-analysis-of-real-data">Part g): Analysis of real data</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#background-literature">Background literature</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction-to-numerical-projects">Introduction to numerical projects</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#format-for-electronic-delivery-of-report-and-programs">Format for electronic delivery of report and programs</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#software-and-needed-installations">Software and needed installations</a></li>
+</ul>
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Project 1 on Machine Learning, deadline October 9 (midnight), 2023</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-analysis-and-resampling-methods">
-   Regression analysis and resampling methods
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#description-of-two-dimensional-function">
-     Description of two-dimensional function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-a-ordinary-least-square-ols-on-the-franke-function">
-     Part a) : Ordinary Least Square (OLS) on the Franke function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-b-adding-ridge-regression-for-the-franke-function">
-     Part b): Adding Ridge regression for  the Franke function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-c-adding-lasso-for-the-franke-function">
-     Part c): Adding Lasso for the Franke function
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-d-paper-and-pencil-part">
-     Part d): Paper and pencil part
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-e-bias-variance-trade-off-and-resampling-techniques">
-     Part e): Bias-variance trade-off and resampling techniques
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity">
-     Part f):  Cross-validation as resampling techniques, adding more complexity
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#part-g-analysis-of-real-data">
-     Part g): Analysis of real data
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#background-literature">
-   Background literature
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction-to-numerical-projects">
-   Introduction to numerical projects
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#format-for-electronic-delivery-of-report-and-programs">
-   Format for electronic delivery of report and programs
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#software-and-needed-installations">
-   Software and needed installations
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
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+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html Project1.do.txt  -->
-<!-- dom:TITLE: Project 1 on Machine Learning, deadline October 9 (midnight), 2023 --><div class="tex2jax_ignore mathjax_ignore section" id="project-1-on-machine-learning-deadline-october-9-midnight-2023">
-<h1>Project 1 on Machine Learning, deadline October 9 (midnight), 2023<a class="headerlink" href="#project-1-on-machine-learning-deadline-october-9-midnight-2023" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Project 1 on Machine Learning, deadline October 9 (midnight), 2023 --><section class="tex2jax_ignore mathjax_ignore" id="project-1-on-machine-learning-deadline-october-9-midnight-2023">
+<h1>Project 1 on Machine Learning, deadline October 9 (midnight), 2023<a class="headerlink" href="#project-1-on-machine-learning-deadline-october-9-midnight-2023" title="Permalink to this heading">#</a></h1>
 <p><strong><a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a></strong>, University of Oslo, Norway</p>
 <p>Date: <strong>September 3</strong></p>
-<div class="section" id="regression-analysis-and-resampling-methods">
-<h2>Regression analysis and resampling methods<a class="headerlink" href="#regression-analysis-and-resampling-methods" title="Permalink to this headline">¶</a></h2>
+<section id="regression-analysis-and-resampling-methods">
+<h2>Regression analysis and resampling methods<a class="headerlink" href="#regression-analysis-and-resampling-methods" title="Permalink to this heading">#</a></h2>
 <p>The main aim of this project is to study in more detail various
 regression methods, including the Ordinary Least Squares (OLS) method.
 In addition to the scientific part, in this course we want also to
 give you an experience in writing scientific reports.  The format for
 the delivery of your answers is namely that of a scientific report. At
 for example
-<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md</a>
+<a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">CompPhysics/MachineLearning</a>
 we detail how to write a report. Furthermore, at
-<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/</a>
+<a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/">CompPhysics/MachineLearning</a>
 you can find examples of previous reports. How to write reports will
 also be discussed during the various lab sessions.</p>
 <p><strong>A small recommendation when developing the codes here</strong>. Instead of
@@ -574,8 +457,8 @@ the one-dimensional test function with the two-dimensional <strong>Franke</stron
 discussed here.</p>
 <p>The Franke function serves as a stepping stone towards the analysis of
 real topographic data. The latter is the last part of this project.</p>
-<div class="section" id="description-of-two-dimensional-function">
-<h3>Description of two-dimensional function<a class="headerlink" href="#description-of-two-dimensional-function" title="Permalink to this headline">¶</a></h3>
+<section id="description-of-two-dimensional-function">
+<h3>Description of two-dimensional function<a class="headerlink" href="#description-of-two-dimensional-function" title="Permalink to this heading">#</a></h3>
 <p>We will first study how to fit polynomials to a specific
 two-dimensional function called <a class="reference external" href="http://www.dtic.mil/dtic/tr/fulltext/u2/a081688.pdf">Franke’s
 function</a>.  This
@@ -659,16 +542,60 @@ which polynomial fits the data best.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22981/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
-  ax = fig.gca(projection=&#39;3d&#39;)
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/project1_6_1.png" src="_images/project1_6_1.png" />
 </div>
 </div>
-</div>
-<div class="section" id="part-a-ordinary-least-square-ols-on-the-franke-function">
-<h3>Part a) : Ordinary Least Square (OLS) on the Franke function<a class="headerlink" href="#part-a-ordinary-least-square-ols-on-the-franke-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-a-ordinary-least-square-ols-on-the-franke-function">
+<h3>Part a) : Ordinary Least Square (OLS) on the Franke function<a class="headerlink" href="#part-a-ordinary-least-square-ols-on-the-franke-function" title="Permalink to this heading">#</a></h3>
 <p>We will generate our own dataset for a function
 <span class="math notranslate nohighlight">\(\mathrm{FrankeFunction}(x,y)\)</span> with <span class="math notranslate nohighlight">\(x,y \in [0,1]\)</span>. The function
 <span class="math notranslate nohighlight">\(f(x,y)\)</span> is the Franke function. You should explore also the addition
@@ -712,27 +639,27 @@ data and say test data.  An accepted rule of thumb is to use
 approximately <span class="math notranslate nohighlight">\(2/3\)</span> to <span class="math notranslate nohighlight">\(4/5\)</span> of the data as training data.</p>
 <p>You can easily reuse the solutions to your exercises from week 35 and week 36.
 See also the lecture slides from week 35 and week 36.</p>
-</div>
-<div class="section" id="part-b-adding-ridge-regression-for-the-franke-function">
-<h3>Part b): Adding Ridge regression for  the Franke function<a class="headerlink" href="#part-b-adding-ridge-regression-for-the-franke-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-b-adding-ridge-regression-for-the-franke-function">
+<h3>Part b): Adding Ridge regression for  the Franke function<a class="headerlink" href="#part-b-adding-ridge-regression-for-the-franke-function" title="Permalink to this heading">#</a></h3>
 <p>Write your own code for the Ridge method, either using matrix
 inversion or the singular value decomposition as done in the previous
 exercise. The lecture notes from week 35 and 36 contain more information. Furthermore, the numerical exercise from week 36 is something you can reuse here.</p>
 <p>Perform the same analysis as you did in the previous exercise but now for different values of <span class="math notranslate nohighlight">\(\lambda\)</span>. Compare and
 analyze your results with those obtained in part a) with the ordinary least squares method. Study the
 dependence on <span class="math notranslate nohighlight">\(\lambda\)</span>.</p>
-</div>
-<div class="section" id="part-c-adding-lasso-for-the-franke-function">
-<h3>Part c): Adding Lasso for the Franke function<a class="headerlink" href="#part-c-adding-lasso-for-the-franke-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-c-adding-lasso-for-the-franke-function">
+<h3>Part c): Adding Lasso for the Franke function<a class="headerlink" href="#part-c-adding-lasso-for-the-franke-function" title="Permalink to this heading">#</a></h3>
 <p>This exercise is essentially a repeat of the previous two ones, but now
 with Lasso regression. Write either your own code (difficult and optional) or, in this case,
 you can also use the functionalities of <strong>Scikit-Learn</strong> (recommended). Keep in mind that the library <strong>Scikit-Learn</strong> excludes the intercept by default.
 Give a
 critical discussion of the three methods and a judgement of which
 model fits the data best.</p>
-</div>
-<div class="section" id="part-d-paper-and-pencil-part">
-<h3>Part d): Paper and pencil part<a class="headerlink" href="#part-d-paper-and-pencil-part" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-d-paper-and-pencil-part">
+<h3>Part d): Paper and pencil part<a class="headerlink" href="#part-d-paper-and-pencil-part" title="Permalink to this heading">#</a></h3>
 <p>This exercise deals with various mean values and variances in  linear regression method (here it may be useful to look up chapter 3, equation (3.8) of <a class="reference external" href="https://www.springer.com/gp/book/9780387848570">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>). The exercise is also part of the weekly exercises for week 37.</p>
 <p>The assumption we have made is
 that there exists a continuous function <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and  a normal distributed error <span class="math notranslate nohighlight">\(\boldsymbol{\varepsilon}\sim N(0, \sigma^2)\)</span>
@@ -773,9 +700,9 @@ mean value <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbo
 \]</div>
 <p>We can use the last expression when we define a so-called confidence interval for the parameters <span class="math notranslate nohighlight">\(\beta\)</span>.
 A given parameter <span class="math notranslate nohighlight">\(\beta_j\)</span> is given by the diagonal matrix element of the above matrix.</p>
-</div>
-<div class="section" id="part-e-bias-variance-trade-off-and-resampling-techniques">
-<h3>Part e): Bias-variance trade-off and resampling techniques<a class="headerlink" href="#part-e-bias-variance-trade-off-and-resampling-techniques" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-e-bias-variance-trade-off-and-resampling-techniques">
+<h3>Part e): Bias-variance trade-off and resampling techniques<a class="headerlink" href="#part-e-bias-variance-trade-off-and-resampling-techniques" title="Permalink to this heading">#</a></h3>
 <p>Our aim here is to study the bias-variance trade-off by implementing the <strong>bootstrap</strong> resampling technique.
 <strong>We will only use the simpler ordinary least squares here</strong>.</p>
 <p>With a code which does OLS and includes resampling techniques,
@@ -835,9 +762,9 @@ studying the MSE value as function of the complexity of your model.</p>
 of your model complexity (the degree of the polynomial) and the number
 of data points, and possibly also your training and test data using the <strong>bootstrap</strong> resampling method.
 You can follow the code example in the jupyter-book at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#the-bias-variance-tradeoff">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#the-bias-variance-tradeoff</a>.</p>
-</div>
-<div class="section" id="part-f-cross-validation-as-resampling-techniques-adding-more-complexity">
-<h3>Part f):  Cross-validation as resampling techniques, adding more complexity<a class="headerlink" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-f-cross-validation-as-resampling-techniques-adding-more-complexity">
+<h3>Part f):  Cross-validation as resampling techniques, adding more complexity<a class="headerlink" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity" title="Permalink to this heading">#</a></h3>
 <p>The aim here is to write your own code for another widely popular
 resampling technique, the so-called cross-validation method.</p>
 <p>Implement the <span class="math notranslate nohighlight">\(k\)</span>-fold cross-validation algorithm (write your own
@@ -849,16 +776,16 @@ you got from your <strong>bootstrap</strong> code. Comment your results. Try <sp
 folds.  You can also compare your own cross-validation code with the
 one provided by <strong>Scikit-Learn</strong>.</p>
 <p>In addition to using the ordinary least squares method, you should include both Ridge and Lasso regression.</p>
-</div>
-<div class="section" id="part-g-analysis-of-real-data">
-<h3>Part g): Analysis of real data<a class="headerlink" href="#part-g-analysis-of-real-data" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="part-g-analysis-of-real-data">
+<h3>Part g): Analysis of real data<a class="headerlink" href="#part-g-analysis-of-real-data" title="Permalink to this heading">#</a></h3>
 <p>With our codes functioning and having been tested properly on a
 simpler function we are now ready to look at real data. We will
 essentially repeat in this exercise what was done in exercises a-f. However, we
 need first to download the data and prepare properly the inputs to our
 codes.  We are going to download digital terrain data from the website
 <a class="reference external" href="https://earthexplorer.usgs.gov/">https://earthexplorer.usgs.gov/</a>,</p>
-<p>Or, if you prefer, we have placed selected datafiles at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2023/Project1/DataFiles">https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2023/Project1/DataFiles</a></p>
+<p>Or, if you prefer, we have placed selected datafiles at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Projects/2023/Project1/DataFiles">CompPhysics/MachineLearning</a></p>
 <p>In order to obtain data for a specific region, you need to register as
 a user (free) at this website and then decide upon which area you want
 to fetch the digital terrain data from.  In order to be able to read
@@ -872,16 +799,6 @@ Python program using</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [2],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
-<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">scipy</span><span class="o">.</span><span class="n">misc</span><span class="o">.</span><span class="n">imread</span>
-
-<span class="ne">NameError</span>: name &#39;scipy&#39; is not defined
-</pre></div>
-</div>
-</div>
 </div>
 <p>Here is a simple part of a Python code which reads and plots the data
 from such files</p>
@@ -919,17 +836,17 @@ model fits the data best.</p>
 <p>At the end, you should present a critical evaluation of your results
 and discuss the applicability of these regression methods to the type
 of data presented here (either the terrain data we propose or other data sets).</p>
-</div>
-</div>
-<div class="section" id="background-literature">
-<h2>Background literature<a class="headerlink" href="#background-literature" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+</section>
+<section id="background-literature">
+<h2>Background literature<a class="headerlink" href="#background-literature" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>For a discussion and derivation of the variances and mean squared errors using linear regression, see the <a class="reference external" href="https://arxiv.org/abs/1509.09169">Lecture notes on ridge regression by Wessel N. van Wieringen</a></p></li>
 <li><p>The textbook of <a class="reference external" href="https://www.springer.com/gp/book/9780387848570">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a>, chapters 3 and 7 are the most relevant ones for the analysis here.</p></li>
 </ol>
-</div>
-<div class="section" id="introduction-to-numerical-projects">
-<h2>Introduction to numerical projects<a class="headerlink" href="#introduction-to-numerical-projects" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="introduction-to-numerical-projects">
+<h2>Introduction to numerical projects<a class="headerlink" href="#introduction-to-numerical-projects" title="Permalink to this heading">#</a></h2>
 <p>Here follows a brief recipe and recommendation on how to answer the various questions when preparing your answers.</p>
 <ul class="simple">
 <li><p>Give a short description of the nature of the problem and the eventual  numerical methods you have used.</p></li>
@@ -942,9 +859,9 @@ of data presented here (either the terrain data we propose or other data sets).<
 <li><p>Critique: if possible include your comments and reflections about the  exercise, whether you felt you learnt something, ideas for improvements and  other thoughts you’ve made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.</p></li>
 <li><p>Try to establish a practice where you log your work at the  computerlab. You may find such a logbook very handy at later stages in your work, especially when you don’t properly remember  what a previous test version  of your program did. Here you could also record  the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.</p></li>
 </ul>
-</div>
-<div class="section" id="format-for-electronic-delivery-of-report-and-programs">
-<h2>Format for electronic delivery of report and programs<a class="headerlink" href="#format-for-electronic-delivery-of-report-and-programs" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="format-for-electronic-delivery-of-report-and-programs">
+<h2>Format for electronic delivery of report and programs<a class="headerlink" href="#format-for-electronic-delivery-of-report-and-programs" title="Permalink to this heading">#</a></h2>
 <p>The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file.  As programming language we prefer that you choose between C/C++, Fortran2008, Julia or Python. The following prescription should be followed when preparing the report:</p>
 <ul class="simple">
 <li><p>Use Canvas to hand in your projects, log in  at  <a class="reference external" href="https://www.uio.no/english/services/it/education/canvas/">https://www.uio.no/english/services/it/education/canvas/</a> with your normal UiO username and password.</p></li>
@@ -954,29 +871,29 @@ of data presented here (either the terrain data we propose or other data sets).<
 <p>Finally,
 we encourage you to collaborate. Optimal working groups consist of
 2-3 students. You can then hand in a common report.</p>
-</div>
-<div class="section" id="software-and-needed-installations">
-<h2>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="software-and-needed-installations">
+<h2>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this heading">#</a></h2>
 <p>If you have Python installed (we recommend Python3) and you feel pretty familiar with installing different packages,
 we recommend that you install the following Python packages via <strong>pip</strong> as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>pip install numpy scipy matplotlib ipython scikit-learn tensorflow sympy pandas pillow</p></li>
 </ol>
 <p>For Python3, replace <strong>pip</strong> with <strong>pip3</strong>.</p>
 <p>See below for a discussion of <strong>tensorflow</strong> and <strong>scikit-learn</strong>.</p>
 <p>For OSX users we recommend also, after having installed Xcode, to install <strong>brew</strong>. Brew allows
 for a seamless installation of additional software via for example</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>brew install python3</p></li>
 </ol>
 <p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution
 you can use <strong>pip</strong> as well and simply install Python as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>sudo apt-get install python3  (or python for python2.7)</p></li>
 </ol>
 <p>etc etc.</p>
 <p>If you don’t want to install various Python packages with their dependencies separately, we recommend two widely used distrubutions which set up  all relevant dependencies for Python, namely</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p><a class="reference external" href="https://docs.anaconda.com/">Anaconda</a> Anaconda is an open source distribution of the Python and R programming languages for large-scale data processing, predictive analytics, and scientific computing, that aims to simplify package management and deployment. Package versions are managed by the package management system <strong>conda</strong></p></li>
 <li><p><a class="reference external" href="https://www.enthought.com/product/canopy/">Enthought canopy</a>  is a Python distribution for scientific and analytic computing distribution and analysis environment, available for free and under a commercial license.</p></li>
 </ol>
@@ -990,8 +907,8 @@ you can use <strong>pip</strong> as well and simply install Python as</p>
 <p>These are all freely available at their respective GitHub sites. They
 encompass communities of developers in the thousands or more. And the number
 of code developers and contributors keeps increasing.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1005,7 +922,7 @@ of code developers and contributors keeps increasing.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1013,37 +930,106 @@ of code developers and contributors keeps increasing.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-and-resampling-methods">Regression analysis and resampling methods</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#description-of-two-dimensional-function">Description of two-dimensional function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-a-ordinary-least-square-ols-on-the-franke-function">Part a) : Ordinary Least Square (OLS) on the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-b-adding-ridge-regression-for-the-franke-function">Part b): Adding Ridge regression for  the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-c-adding-lasso-for-the-franke-function">Part c): Adding Lasso for the Franke function</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-d-paper-and-pencil-part">Part d): Paper and pencil part</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-e-bias-variance-trade-off-and-resampling-techniques">Part e): Bias-variance trade-off and resampling techniques</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity">Part f):  Cross-validation as resampling techniques, adding more complexity</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-g-analysis-of-real-data">Part g): Analysis of real data</a></li>
+</ul>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#background-literature">Background literature</a></li>
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diff --git a/doc/LectureNotes/_build/html/schedule.html b/doc/LectureNotes/_build/html/schedule.html
index 632c2fd70..f02ec15ec 100644
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@@ -1,417 +1,389 @@
 
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-<p aria-level="2" class="caption" role="heading">
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-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
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-   1. Elements of Probability Theory and Statistical Data Analysis
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
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-   9. Decision trees, overarching aims
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-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
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-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
 <ul class="nav bd-sidenav">
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-   13. Neural networks
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-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Exercises week 35
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
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- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
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- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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-<h1>Teaching schedule with links to material<a class="headerlink" href="#teaching-schedule-with-links-to-material" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
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+  <section class="tex2jax_ignore mathjax_ignore" id="teaching-schedule-with-links-to-material">
+<h1>Teaching schedule with links to material<a class="headerlink" href="#teaching-schedule-with-links-to-material" title="Permalink to this heading">#</a></h1>
 <p>This course will be delivered in a hybrid mode, with online lectures and on site or online laboratory sessions.</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Four lectures per week, Fall semester, 10 ECTS. The lectures are in person but will be recorded and linked to this site and the official University of Oslo website for the course;</p></li>
 <li><p>Two hours of laboratory sessions for work on computational projects and exercises for each group. There will  also be fully digital laboratory sessions for those who cannot attend;</p></li>
 <li><p>Three projects which are graded and count 1/3 each of the final grade. The deadlines for the projects are October 7 for project 1, November 11 for project 2 and December 9 for project 3.</p></li>
@@ -421,8 +393,8 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p>Videos of teaching material are available via the links at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/web/course.html">https://compphysics.github.io/MachineLearning/doc/web/course.html</a>;</p></li>
 <li><p>Weekly emails with summary of activities will be mailed to all participants;</p></li>
 </ol>
-<div class="section" id="weekly-schedule">
-<h2>Weekly Schedule<a class="headerlink" href="#weekly-schedule" title="Permalink to this headline">¶</a></h2>
+<section id="weekly-schedule">
+<h2>Weekly Schedule<a class="headerlink" href="#weekly-schedule" title="Permalink to this heading">#</a></h2>
 <p>For the reading assignments we use the following abbreviations:</p>
 <ul class="simple">
 <li><p>GBC: Goodfellow, Bengio, and Courville, Deep Learning</p></li>
@@ -430,8 +402,8 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p>HTF: Hastie, Tibshirani, and Friedman, The Elements of Statistical Learning</p></li>
 <li><p>AG: Aurelien Geron, Hands‑On Machine Learning with Scikit‑Learn and TensorFlow</p></li>
 </ul>
-</div>
-</div>
+</section>
+</section>
 
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@@ -453,44 +425,101 @@ const thebe_selector_output = ".output, .cell_output"
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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Exercises week 37","Exercises week 38","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Statistical interpretation of Linear Regression and Resampling techniques","Week 37: Statistical interpretations and Resampling Methods","Week 38: Logistic Regression and 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+Search.setIndex({"docnames": ["chapter1", "chapter10", "chapter11", "chapter12", "chapter13", "chapter2", "chapter3", "chapter4", "chapter5", "chapter6", "chapter7", "chapter8", "chapter9", "chapteroptimization", "clustering", "exercisesweek34", "exercisesweek35", "exercisesweek36", "exercisesweek37", "exercisesweek38", "exercisesweek39", "intro", "linalg", "project1", "schedule", "statistics", "teachers", "textbooks", "week34", "week35", "week36", "week37", "week38", "week39"], "filenames": ["chapter1.ipynb", "chapter10.ipynb", "chapter11.ipynb", "chapter12.ipynb", "chapter13.ipynb", "chapter2.ipynb", "chapter3.ipynb", "chapter4.ipynb", "chapter5.ipynb", "chapter6.ipynb", "chapter7.ipynb", "chapter8.ipynb", "chapter9.ipynb", "chapteroptimization.ipynb", "clustering.ipynb", "exercisesweek34.ipynb", "exercisesweek35.ipynb", "exercisesweek36.ipynb", "exercisesweek37.ipynb", "exercisesweek38.ipynb", "exercisesweek39.ipynb", "intro.md", "linalg.ipynb", "project1.ipynb", "schedule.md", 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Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods", "<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)", "<span class=\"section-number\">13. </span>Neural networks", "<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm", "<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning", "Exercises week 34", "Exercises week 35", "Exercises week 36", "Exercises week 37", "Exercises week 38", "Exercises week 39", "Applied Data Analysis and Machine Learning", "<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features", "Project 1 on Machine Learning, deadline October 9 (midnight), 2023", "Teaching schedule with links to material", "<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis", "Teachers and Grading", "Textbooks", "Week 34: Introduction to the course, Logistics and Practicalities", "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression", "Week 36: Statistical interpretation of Linear Regression and Resampling techniques", "Week 37: Statistical interpretations and Resampling Methods", "Week 38: Logistic Regression and Optimization", "Week 39: Optimization and  Gradient Methods"], "terms": {"emphasi": [0, 21, 27, 28], "throughout": [0, 4, 5, 14, 21, 22, 25, 28], "thi": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33], "seri": [0, 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 22, 28, 29, 30, 31, 32, 33], "lectur": [0, 1, 5, 10, 11, 12, 13, 15, 17, 21, 22, 23, 24, 26, 27, 33], "understand": [0, 1, 3, 5, 6, 10, 13, 14, 21, 28, 29, 30, 32, 33], "mathemat": [0, 6, 11, 12, 13, 17, 21, 22, 25, 27, 28, 30, 31, 32], "aspect": [0, 6, 21, 23, 28, 29, 30], "differ": [0, 1, 2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32], "algorithm": [0, 1, 2, 4, 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[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 22, 25, 28, 29, 30, 31, 32, 33], "deduc": [0, 28], "behind": [0, 1, 6, 8, 13, 28, 32, 33], "On": [0, 3, 15, 24, 25, 26, 27, 28], "other": [0, 1, 2, 3, 5, 6, 7, 8, 10, 13, 14, 15, 19, 21, 23, 24, 25, 26, 27, 30, 31, 33], "unsupervis": [0, 1, 4, 12, 21, 28], "relationship": [0, 4, 9, 28], "ani": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 18, 25, 28, 29, 30, 31], "prior": [0, 5, 6, 28, 29, 30, 31], "oper": [0, 1, 3, 5, 6, 10, 11, 12, 13, 15, 21, 25, 28, 29, 30, 31, 33], "third": [0, 3, 6, 13, 26, 28, 31, 32, 33], "name": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32, 33], "reinforc": [0, 8, 21, 28], "paradigm": [0, 28], "inspir": [0, 1, 12, 28], "behavior": [0, 1, 13, 28, 32, 33], "psycholog": [0, 28], "achiev": [0, 1, 5, 6, 8, 12, 22, 28, 30, 31], "sole": [0, 6, 28], "reward": [0, 4, 28], "punish": [0, 1, 28], "anoth": [0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 22, 23, 25, 28, 29, 32, 33], "wai": [0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 17, 22, 25, 28, 29, 30, 32, 33], "categor": [0, 1, 3, 9, 11, 28], "consid": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 16, 19, 22, 23, 25, 28, 29, 30, 31, 32, 33], "desir": [0, 2, 4, 5, 13, 14, 28, 29, 32, 33], "output": [0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 16, 22, 23, 25, 28, 29, 30, 31, 32, 33], "classif": [0, 3, 5, 6, 7, 8, 11, 12, 21, 23, 27, 28, 29, 30, 31, 33], "divid": [0, 1, 3, 5, 6, 7, 8, 9, 11, 12, 25, 28, 29, 30, 31, 32], "goal": [0, 7, 9, 28, 32], "assign": [0, 7, 8, 9, 12, 13, 14, 24, 26, 27, 28, 29, 32, 33], "identifi": [0, 1, 7, 9, 11, 12, 13, 14, 28, 29, 32, 33], "digit": [0, 1, 3, 4, 6, 23, 24, 26, 28], "pictur": [0, 28], "ones": [0, 2, 5, 6, 8, 9, 10, 11, 13, 22, 23, 28, 29, 30, 31, 32, 33], "typic": [0, 1, 2, 3, 4, 5, 7, 9, 10, 12, 13, 25, 28, 29, 30, 31, 32, 33], "between": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 23, 25, 28, 29, 30, 31, 32, 33], "refer": [0, 1, 2, 3, 5, 6, 11, 12, 13, 14, 20, 22, 23, 27, 28, 29, 31, 32, 33], "construct": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 22, 25, 28, 29, 30, 31, 32], "map": [0, 1, 2, 6, 7, 8, 11, 12, 14, 23, 25, 28, 32], "continu": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 17, 18, 22, 23, 25, 28, 29, 30, 31, 32, 33], "valu": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 19, 21, 22, 23, 28, 33], "cluster": [0, 1, 4, 6, 11, 21, 28, 31], "group": [0, 6, 7, 9, 14, 21, 23, 24, 26, 28, 31], "certain": [0, 3, 6, 7, 9, 25, 28, 29, 31, 32], "trait": [0, 28], "beforehand": [0, 25, 28], "cover": [0, 5, 17, 21, 26, 27, 29, 30], "irrespect": [0, 28], "deal": [0, 1, 3, 5, 6, 8, 11, 13, 14, 17, 18, 22, 23, 25, 28, 29, 30, 31, 32, 33], "first": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 22, 23, 25, 26, 27, 31], "ingredi": [0, 9, 28], "subdivid": [0, 22, 28], "valid": [0, 1, 4, 7, 9, 10, 13, 21, 25, 28, 29, 33], "difficult": [0, 1, 6, 10, 13, 23, 25, 28, 31, 33], "part": [0, 1, 3, 5, 6, 10, 17, 18, 22, 24, 25, 26, 28, 30, 31], "meaning": 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13, 22, 23, 28, 30, 31], "risk": [0, 13, 15, 16, 28, 32, 33], "present": [0, 5, 6, 7, 9, 12, 13, 22, 23, 25, 28, 29, 30, 33], "estim": [0, 1, 5, 6, 7, 10, 11, 13, 21, 25, 28, 29, 32, 33], "reproduc": [0, 5, 6, 9, 12, 15, 16, 21, 23, 25, 28, 29], "suppos": [0, 5, 6, 7, 8, 10, 11, 12, 13, 22, 28, 29, 30, 31, 32, 33], "At": [0, 4, 6, 13, 23, 28, 33], "heart": [0, 7, 28, 32], "encount": [0, 1, 5, 7, 13, 25, 28, 29, 32, 33], "minim": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 23, 29, 30, 31, 33], "optim": [0, 2, 3, 4, 5, 6, 7, 9, 10, 11, 14, 15, 16, 17, 18, 19, 23, 30, 31], "famili": [0, 7, 8, 25, 32], "gradient": [0, 3, 4, 7, 8, 9, 12, 21, 28, 29], "hear": [0, 13, 28, 33], "phrase": [0, 28], "causat": [0, 28], "do": [0, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 22, 23, 29, 32], "think": [0, 1, 3, 4, 6, 9, 12, 13, 14, 25, 28, 31, 32, 33], "mai": [0, 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 18, 21, 22, 23, 25, 29, 30, 31, 32, 33], "classifi": [0, 1, 4, 7, 9, 10, 11, 28], "point": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 22, 23, 25, 26, 28, 29, 31, 32, 33], "Or": [0, 1, 6, 23, 28, 32], "perhap": [0, 5, 13, 28, 29, 30, 32, 33], "kind": [0, 2, 3, 4, 8, 12, 13, 14, 28, 29, 33], "symmetr": [0, 5, 8, 11, 12, 13, 22, 28, 29, 33], "statement": [0, 7, 22, 32], "b": [0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 25, 26, 28, 29, 30, 31, 32], "caus": [0, 5, 6, 25, 28, 29, 30, 31], "doe": [0, 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 16, 22, 23, 25, 28, 31, 32, 33], "necessarili": [0, 4, 11, 25, 28], "sens": [0, 4, 6, 8, 23, 28, 31], "autom": [0, 21, 27, 28], "fashion": [0, 9, 10, 28], "assess": [0, 6, 23, 28, 29, 30, 31], "newli": [0, 28], "primari": [0, 7, 28, 32], "concern": [0, 1, 4, 7, 28, 32], "qualiti": [0, 9, 15, 16, 21, 28, 29], "less": [0, 1, 3, 4, 5, 6, 8, 9, 13, 21, 25, 28, 29, 30, 31, 32, 33], "were": [0, 1, 3, 4, 5, 6, 7, 8, 10, 11, 12, 14, 25, 28, 29, 31, 32], "order": [0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 22, 23, 25, 28, 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4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33], "instanc": [0, 1, 2, 4, 6, 9, 11, 13, 28, 29, 31, 32, 33], "discov": [0, 28], "interpret": [0, 1, 6, 9, 10, 12, 13, 17, 19, 22, 23, 25], "addit": [0, 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 15, 17, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33], "simplifi": [0, 6, 9, 15, 21, 23, 28, 29, 30, 31], "represent": [0, 1, 3, 6, 25, 28, 31, 32], "help": [0, 1, 4, 12, 13, 16, 23, 28, 33], "futur": [0, 4, 8, 9, 28], "consider": [0, 1, 5, 13, 28, 29, 30, 31, 32, 33], "correct": [0, 1, 2, 3, 4, 5, 7, 13, 22, 25, 28, 29, 30, 31, 33], "elus": [0, 28], "imposs": [0, 5, 28, 29], "fundament": [0, 6, 21, 28, 31], "difficulti": [0, 1, 13, 28, 32, 33], "equal": [0, 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 22, 23, 25, 28, 29, 30, 31, 32, 33], "question": [0, 5, 6, 9, 11, 12, 13, 23, 26, 28, 29, 30, 31, 33], "lead": [0, 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 17, 22, 25, 28, 29, 30, 31, 32, 33], "To": [0, 1, 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"specifi": [0, 3, 5, 6, 7, 9, 11, 13, 14, 23, 25, 28, 30, 31, 32, 33], "strategi": [0, 1, 9, 28], "simplest": [0, 1, 3, 4, 9, 10, 12, 14, 28], "necessari": [0, 1, 3, 4, 8, 14, 28], "solv": [0, 1, 3, 5, 6, 8, 10, 11, 12, 13, 22, 23, 28, 29], "precis": [0, 2, 5, 11, 13, 22, 23, 25, 28, 29, 30, 31, 33], "enough": [0, 6, 13, 28, 31, 32, 33], "contain": [0, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 17, 19, 22, 23, 25, 27, 28, 29, 30, 31, 32, 33], "least": [0, 7, 8, 10, 11, 15, 16, 17, 19, 21, 22, 25, 31, 32], "accuraci": [0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 28, 29, 32], "yet": [0, 1, 6, 8, 11, 13, 28, 32, 33], "rel": [0, 4, 6, 7, 9, 12, 13, 25, 28, 29, 31, 32, 33], "onli": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 22, 23, 25, 28, 29, 30, 31, 32, 33], "simpler": [0, 1, 5, 6, 7, 13, 16, 19, 21, 23, 28, 30, 33], "inadequ": [0, 28], "work": [0, 1, 4, 6, 7, 8, 9, 13, 15, 21, 23, 24, 25, 26, 28, 29, 31, 32, 33], "obvious": [0, 4, 5, 6, 22, 28, 30, 31], "evalu": [0, 2, 3, 4, 5, 6, 9, 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33], "98": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "els": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "gui": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "shell": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "enable_matplotlib": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "lower": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 22, 23, 25, 28, 29, 31, 32, 33], "isinst": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "str": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "_show_matplotlib_backend": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "3606": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "3585": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "def": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 22, 23, 25, 28, 29, 30, 31, 32, 33], "none": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 22, 23, 25, 28, 29, 30, 31, 32, 33], "3586": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "enabl": [0, 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "interact": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 21, 22, 23, 25, 28, 29, 31, 32, 33], "support": [0, 1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 21, 22, 23, 25, 28, 29, 31, 32, 33], "3587": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "3588": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "take": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 21, 22, 23, 25, 28, 29, 30, 31, 32, 33], "step": [0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 22, 23, 25, 28, 29], "3604": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "3605": [0, 1, 2, 3, 4, 6, 7, 8, 9, 12, 13, 14, 22, 23, 25, 28, 29, 31, 32, 33], "matplotlib_inlin": [0, 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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   1. Elements of Probability Theory and Statistical Data Analysis
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-  <a class="reference internal" href="linalg.html">
-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1 current active"><a class="current reference internal" href="#">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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- <li class="toctree-l1">
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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-   7. Optimization, the central part of any Machine Learning algortithm
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-   8. Support Vector Machines, overarching aims
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+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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-   9. Decision trees, overarching aims
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-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
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+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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-   12. Clustering and Unsupervised Learning
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+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
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- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#domains-and-probabilities">
-   1.1. Domains and probabilities
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#stochastic-variables-and-the-main-concepts-the-discrete-case">
-     1.1.1. Stochastic variables and the main concepts, the discrete case
-    </a>
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-     1.1.4. Probability Distribution Functions
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-    <a class="reference internal nav-link" href="#numerical-experiments-and-the-covariance-central-limit-theorem">
-     1.1.6. Numerical experiments and the covariance, central limit theorem
-    </a>
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+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#domains-and-probabilities">1.1. Domains and probabilities</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-variables-and-the-main-concepts-the-discrete-case">1.1.1. Stochastic variables and the main concepts, the discrete case</a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance">1.1.5. Meet the  covariance!</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#numerical-experiments-and-the-covariance-central-limit-theorem">1.1.6. Numerical experiments and the covariance, central limit theorem</a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#autocorrelation-function">1.1.8. Autocorrelation function</a></li>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#domains-and-probabilities">
-   1.1. Domains and probabilities
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#stochastic-variables-and-the-main-concepts-the-discrete-case">
-     1.1.1. Stochastic variables and the main concepts, the discrete case
-    </a>
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-   <li class="toc-h3 nav-item toc-entry">
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-     1.1.4. Probability Distribution Functions
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-    <a class="reference internal nav-link" href="#meet-the-covariance">
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-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#numerical-experiments-and-the-covariance-central-limit-theorem">
-     1.1.6. Numerical experiments and the covariance, central limit theorem
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#random-numbers">
-     1.1.7. Random Numbers
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#autocorrelation-function">
-     1.1.8. Autocorrelation function
-    </a>
-   </li>
-  </ul>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
-doconce format html statistics.do.txt  --><div class="tex2jax_ignore mathjax_ignore section" id="elements-of-probability-theory-and-statistical-data-analysis">
-<h1><span class="section-number">1. </span>Elements of Probability Theory and Statistical Data Analysis<a class="headerlink" href="#elements-of-probability-theory-and-statistical-data-analysis" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="domains-and-probabilities">
-<h2><span class="section-number">1.1. </span>Domains and probabilities<a class="headerlink" href="#domains-and-probabilities" title="Permalink to this headline">¶</a></h2>
+doconce format html statistics.do.txt  --><section class="tex2jax_ignore mathjax_ignore" id="elements-of-probability-theory-and-statistical-data-analysis">
+<h1><span class="section-number">1. </span>Elements of Probability Theory and Statistical Data Analysis<a class="headerlink" href="#elements-of-probability-theory-and-statistical-data-analysis" title="Permalink to this heading">#</a></h1>
+<section id="domains-and-probabilities">
+<h2><span class="section-number">1.1. </span>Domains and probabilities<a class="headerlink" href="#domains-and-probabilities" title="Permalink to this heading">#</a></h2>
 <p>Consider the following simple example, namely the tossing of two dice, resulting in  the following possible values</p>
 <div class="math notranslate nohighlight">
 \[
@@ -528,8 +457,8 @@ registering the sequence of outcomes, we will note that the numbers in the above
 \{10,8,6,3,6,9,11,8,12,4,5\}.
 \]</div>
 <p><strong>Random variables are characterized by a domain which contains all possible values that the random value may take. This domain has a corresponding probability distribution function(PDF)</strong>.</p>
-<div class="section" id="stochastic-variables-and-the-main-concepts-the-discrete-case">
-<h3><span class="section-number">1.1.1. </span>Stochastic variables and the main concepts, the discrete case<a class="headerlink" href="#stochastic-variables-and-the-main-concepts-the-discrete-case" title="Permalink to this headline">¶</a></h3>
+<section id="stochastic-variables-and-the-main-concepts-the-discrete-case">
+<h3><span class="section-number">1.1.1. </span>Stochastic variables and the main concepts, the discrete case<a class="headerlink" href="#stochastic-variables-and-the-main-concepts-the-discrete-case" title="Permalink to this heading">#</a></h3>
 <p>There are two main concepts associated with a stochastic variable. The
 <em>domain</em> is the set <span class="math notranslate nohighlight">\(\mathbb D = \{x\}\)</span> of all accessible values
 the variable can assume, so that <span class="math notranslate nohighlight">\(X \in \mathbb D\)</span>. An example of a
@@ -570,9 +499,9 @@ P(x)=\mathrm{Prob(}X\leq x\mathrm{)} =
 \[
 p(x) = \frac{d}{dx}P(x).
 \]</div>
-</div>
-<div class="section" id="properties-of-pdfs">
-<h3><span class="section-number">1.1.2. </span>Properties of PDFs<a class="headerlink" href="#properties-of-pdfs" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="properties-of-pdfs">
+<h3><span class="section-number">1.1.2. </span>Properties of PDFs<a class="headerlink" href="#properties-of-pdfs" title="Permalink to this heading">#</a></h3>
 <p>There are two properties that all PDFs must satisfy. The first one is
 positivity (assuming that the PDF is normalized)</p>
 <div class="math notranslate nohighlight">
@@ -666,7 +595,55 @@ p(x) = \frac{1}{\sqrt{2\pi}} \exp{(-\frac{x^2}{2})},
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/statistics_32_0.png" src="_images/statistics_32_0.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">acos</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
+</div>
 </div>
 </div>
 <p>Another important distribution in science is the exponential distribution</p>
@@ -674,9 +651,9 @@ p(x) = \frac{1}{\sqrt{2\pi}} \exp{(-\frac{x^2}{2})},
 \[
 p(x) = \alpha\exp{-(\alpha x)}.
 \]</div>
-</div>
-<div class="section" id="expectation-values">
-<h3><span class="section-number">1.1.3. </span>Expectation values<a class="headerlink" href="#expectation-values" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="expectation-values">
+<h3><span class="section-number">1.1.3. </span>Expectation values<a class="headerlink" href="#expectation-values" title="Permalink to this heading">#</a></h3>
 <p>Let <span class="math notranslate nohighlight">\(h(x)\)</span> be an arbitrary continuous function on the domain of the stochastic
 variable <span class="math notranslate nohighlight">\(X\)</span> whose PDF is <span class="math notranslate nohighlight">\(p(x)\)</span>. We define the <em>expectation value</em>
 of <span class="math notranslate nohighlight">\(h\)</span> with respect to <span class="math notranslate nohighlight">\(p\)</span> as follows</p>
@@ -736,9 +713,9 @@ variable <span class="math notranslate nohighlight">\(X\)</span>, the variance i
 <strong>standard deviation</strong> of <span class="math notranslate nohighlight">\(p\)</span>. It is the RMS (root-mean-square)
 value of the deviation of the PDF from its mean value, interpreted
 qualitatively as the “spread” of <span class="math notranslate nohighlight">\(p\)</span> around its mean.</p>
-</div>
-<div class="section" id="probability-distribution-functions">
-<h3><span class="section-number">1.1.4. </span>Probability Distribution Functions<a class="headerlink" href="#probability-distribution-functions" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="probability-distribution-functions">
+<h3><span class="section-number">1.1.4. </span>Probability Distribution Functions<a class="headerlink" href="#probability-distribution-functions" title="Permalink to this heading">#</a></h3>
 <p>The following table collects properties of probability distribution functions.
 In our notation we reserve the label <span class="math notranslate nohighlight">\(p(x)\)</span> for the probability of a certain event,
 while <span class="math notranslate nohighlight">\(P(x)\)</span> is the cumulative probability.</p>
@@ -904,9 +881,9 @@ the binomial distribution we can show that</p>
 \[\begin{split}
 \lim_{n\rightarrow \infty}\left(\begin{array}{c} n \\ x\end{array}\right)y^x(1-y)^{n-x} e^{-\lambda}=\sum_{x=1}^{\infty}\frac{\lambda^x}{x!} e^{-\lambda}.
 \end{split}\]</div>
-</div>
-<div class="section" id="meet-the-covariance">
-<h3><span class="section-number">1.1.5. </span>Meet the  covariance!<a class="headerlink" href="#meet-the-covariance" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="meet-the-covariance">
+<h3><span class="section-number">1.1.5. </span>Meet the  covariance!<a class="headerlink" href="#meet-the-covariance" title="Permalink to this heading">#</a></h3>
 <p>An important quantity in a statistical analysis is the so-called covariance.</p>
 <p>Consider the set <span class="math notranslate nohighlight">\(\{X_i\}\)</span> of <span class="math notranslate nohighlight">\(n\)</span>
 stochastic variables (not necessarily uncorrelated) with the
@@ -974,31 +951,6 @@ uncorrelated.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>2.0543653729690416
-[[ 8.75352505  9.52812155  6.26350283  2.23593659  5.0058263  12.34270689
-   3.69987647 18.4524458   5.51178587  5.67743788]
- [ 9.52812155 10.37126183  6.8177581   2.43379387  5.44879019 13.43490889
-   4.0272773  20.08529655  5.99952195  6.17983246]
- [ 6.26350283  6.8177581   4.48179077  1.59990347  3.58187211  8.83170827
-   2.64741194 13.2034747   3.94390673  4.06243748]
- [ 2.23593659  2.43379387  1.59990347  0.57113133  1.27865175  3.15273101
-   0.94506946  4.71335815  1.40789038  1.45020332]
- [ 5.0058263   5.44879019  3.58187211  1.27865175  2.86265211  7.05835037
-   2.11582635 10.55229041  3.1519922   3.24672263]
- [12.34270689 13.43490889  8.83170827  3.15273101  7.05835037 17.40355028
-   5.21692581 26.01844727  7.77176703  8.00534085]
- [ 3.69987647  4.0272773   2.64741194  0.94506946  2.11582635  5.21692581
-   1.56383695  7.79934594  2.32968167  2.39969826]
- [18.4524458  20.08529655 13.2034747   4.71335815 10.55229041 26.01844727
-   7.79934594 38.89778737 11.61885405 11.96804878]
- [ 5.51178587  5.99952195  3.94390673  1.40789038  3.1519922   7.77176703
-   2.32968167 11.61885405  3.47057708  3.57488231]
- [ 5.67743788  6.17983246  4.06243748  1.45020332  3.24672263  8.00534085
-   2.39969826 11.96804878  3.57488231  3.68232235]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>Consider the stochastic variables <span class="math notranslate nohighlight">\(X_i\)</span> and <span class="math notranslate nohighlight">\(X_j\)</span>, (<span class="math notranslate nohighlight">\(i\neq j\)</span>). We have</p>
 <div class="math notranslate nohighlight">
@@ -1103,9 +1055,9 @@ may differ, in some cases
 significantly,  from the similarly named
 exact values for the mean value <span class="math notranslate nohighlight">\(\mu_X\)</span>, the variance <span class="math notranslate nohighlight">\(\mathrm{Var}(X)\)</span>
 and the covariance <span class="math notranslate nohighlight">\(\mathrm{Cov}(X,Y)\)</span>.</p>
-</div>
-<div class="section" id="numerical-experiments-and-the-covariance-central-limit-theorem">
-<h3><span class="section-number">1.1.6. </span>Numerical experiments and the covariance, central limit theorem<a class="headerlink" href="#numerical-experiments-and-the-covariance-central-limit-theorem" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="numerical-experiments-and-the-covariance-central-limit-theorem">
+<h3><span class="section-number">1.1.6. </span>Numerical experiments and the covariance, central limit theorem<a class="headerlink" href="#numerical-experiments-and-the-covariance-central-limit-theorem" title="Permalink to this heading">#</a></h3>
 <p>The central limit theorem states that the PDF <span class="math notranslate nohighlight">\(\tilde{p}(z)\)</span> of
 the average of <span class="math notranslate nohighlight">\(m\)</span> random values corresponding to a PDF <span class="math notranslate nohighlight">\(p(x)\)</span>
 is a normal distribution whose mean is the
@@ -1124,7 +1076,7 @@ standard deviation, given by</p>
 \[
 \mu_{X}^{\phantom X} \approx X_m=\frac{1}{mn}\sum_{\alpha=1}^m\sum_{k=1}^n x_{\alpha,k}.
 \]</div>
-<p>We can then use Eq. (<a class="reference external" href="#eq:exptvariance">7</a>)</p>
+<p>We can then use Eq. (<span class="xref myst">7</span>)</p>
 <div class="math notranslate nohighlight">
 \[
 \sigma^2_m=\frac{1}{mn^2}\sum_{\alpha=1}^m\sum_{kl=1}^n (x_{\alpha,k}-\langle X_m \rangle)(x_{\alpha,l}-\langle X_m \rangle),
@@ -1206,7 +1158,7 @@ correction factor the <em>autocorrelation time</em></p>
 <p>For a correlation free experiment, <span class="math notranslate nohighlight">\(\tau\)</span>
 equals 1.</p>
 <p>From the point of view of
-Eq. (<a class="reference external" href="#eq:error_estimate_corr_time">10</a>) we can interpret a sequential
+Eq. (<span class="xref myst">10</span>) we can interpret a sequential
 correlation as an effective reduction of the number of measurements by
 a factor <span class="math notranslate nohighlight">\(\tau\)</span>. The effective number of measurements becomes</p>
 <div class="math notranslate nohighlight">
@@ -1262,23 +1214,10 @@ more practically oriented methods like the blocking technique.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.1999902359008225
-4.487000566129411
-1.3211480515121596
-1.0120561022775605 9.785157020098348 24.0365416391166
-2.9740940821517547 3.838584583553216 11.184094793957168
-[[ 1.0120561   2.97409408  3.83858458]
- [ 2.97409408  9.78515702 11.18409479]
- [ 3.83858458 11.18409479 24.03654164]]
-[30.9410965   0.08502185  3.80763641]
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="random-numbers">
-<h3><span class="section-number">1.1.7. </span>Random Numbers<a class="headerlink" href="#random-numbers" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="random-numbers">
+<h3><span class="section-number">1.1.7. </span>Random Numbers<a class="headerlink" href="#random-numbers" title="Permalink to this heading">#</a></h3>
 <p>Uniform deviates are just random numbers that lie within a specified range
 (typically 0 to 1), with any one number in the range just as likely as any other. They
 are, in other words, what you probably think random numbers are. However,
@@ -1426,7 +1365,7 @@ r = M\hspace{0.1cm}\mathrm{MOD} \hspace{0.1cm}a.
 <p>since we can add or subtract any integer multiple of <span class="math notranslate nohighlight">\(M\)</span> from <span class="math notranslate nohighlight">\(aN_{i-1}\)</span>.
 The last term <span class="math notranslate nohighlight">\([N_{i-1}/q]M\mathrm{MOD}(M)\)</span> is zero since the integer division
 <span class="math notranslate nohighlight">\([N_{i-1}/q]\)</span> just yields a constant which is multiplied with <span class="math notranslate nohighlight">\(M\)</span>.</p>
-<p>We can now rewrite Eq. (<a class="reference external" href="#eq:rntrick1">14</a>) as</p>
+<p>We can now rewrite Eq. (<span class="xref myst">14</span>) as</p>
 <!-- Equation labels as ordinary links -->
 <div id="eq:rntrick2"></div>
 <div class="math notranslate nohighlight">
@@ -1538,14 +1477,11 @@ these limiting values.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/statistics_181_0.png" src="_images/statistics_181_0.png" />
-</div>
 </div>
 <p>Since our random numbers, which are typically generated via a linear congruential algorithm,
 are never fully independent, we can then define
 an important test which measures the degree of correlation, namely the  so-called<br />
-auto-correlation function defined previously, see again Eq. (<a class="reference external" href="#eq:autocorrelformal">9</a>).
+auto-correlation function defined previously, see again Eq. (<span class="xref myst">9</span>).
 We rewrite it here as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1562,9 +1498,9 @@ f_d = \frac{1}{nm}\sum_{\alpha=1}^m\sum_{k=1}^{n-d}(x_{\alpha,k}-\langle X_m \ra
 numbers are not independent. The independence of the random numbers is crucial
 in the evaluation of other expectation values. If they are not independent, our
 assumption for approximating <span class="math notranslate nohighlight">\(\sigma_N\)</span> is no longer valid.</p>
-</div>
-<div class="section" id="autocorrelation-function">
-<h3><span class="section-number">1.1.8. </span>Autocorrelation function<a class="headerlink" href="#autocorrelation-function" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="autocorrelation-function">
+<h3><span class="section-number">1.1.8. </span>Autocorrelation function<a class="headerlink" href="#autocorrelation-function" title="Permalink to this heading">#</a></h3>
 <p>This program computes the autocorrelation function as discussed in the equation on the previous slide for random numbers generated with the normal distribution <span class="math notranslate nohighlight">\(N(0,1)\)</span>.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1600,18 +1536,12 @@ assumption for approximating <span class="math notranslate nohighlight">\(\sigma
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.026121042099059435 1.0617129312534124
-</pre></div>
-</div>
-<img alt="_images/statistics_188_1.png" src="_images/statistics_188_1.png" />
-</div>
 </div>
 <p>As can be seen from the plot, the first point gives back the variance and a value of one.
 For the remaining values we notice that there are still non-zero values for the auto-correlation function.</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -1625,7 +1555,7 @@ For the remaining values we notice that there are still non-zero values for the
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -1633,44 +1563,111 @@ For the remaining values we notice that there are still non-zero values for the
     </script>
     <script>kernelName = 'python3'</script>
 
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-variables-and-the-main-concepts-the-discrete-case">1.1.1. Stochastic variables and the main concepts, the discrete case</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#properties-of-pdfs">1.1.2. Properties of PDFs</a></li>
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+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#probability-distribution-functions">1.1.4. Probability Distribution Functions</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance">1.1.5. Meet the  covariance!</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#numerical-experiments-and-the-covariance-central-limit-theorem">1.1.6. Numerical experiments and the covariance, central limit theorem</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#random-numbers">1.1.7. Random Numbers</a></li>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapteroptimization.html">
-   7. Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter5.html">
-   8. Support Vector Machines, overarching aims
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter6.html">
-   9. Decision trees, overarching aims
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter7.html">
-   10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
-  </a>
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- <li class="toctree-l1">
-  <a class="reference internal" href="week37.html">
-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+              
                 
-  <div class="tex2jax_ignore mathjax_ignore section" id="teachers-and-grading">
-<h1>Teachers and Grading<a class="headerlink" href="#teachers-and-grading" title="Permalink to this headline">¶</a></h1>
-<div class="section" id="instructor-information">
-<h2>Instructor information<a class="headerlink" href="#instructor-information" title="Permalink to this headline">¶</a></h2>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section class="tex2jax_ignore mathjax_ignore" id="teachers-and-grading">
+<h1>Teachers and Grading<a class="headerlink" href="#teachers-and-grading" title="Permalink to this heading">#</a></h1>
+<section id="instructor-information">
+<h2>Instructor information<a class="headerlink" href="#instructor-information" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><em>Name</em>: Morten Hjorth-Jensen</p></li>
 <li><p><em>Email</em>: <a class="reference external" href="mailto:morten&#46;hjorth-jensen&#37;&#52;&#48;fys&#46;uio&#46;no">morten<span>&#46;</span>hjorth-jensen<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
@@ -463,9 +397,9 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p><em>Office</em>: Department of Physics, University of Oslo, Eastern wing, room FØ470</p></li>
 <li><p><em>Office hours</em>: <em>Anytime</em>! Feel free to send an email for planning. Both in person meetings or digital meetings are possible.</p></li>
 </ul>
-</div>
-<div class="section" id="teaching-assistants-fall-semester-2023">
-<h2>Teaching Assistants Fall semester 2023<a class="headerlink" href="#teaching-assistants-fall-semester-2023" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="teaching-assistants-fall-semester-2023">
+<h2>Teaching Assistants Fall semester 2023<a class="headerlink" href="#teaching-assistants-fall-semester-2023" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Karl Henrik Fredly, <a class="reference external" href="mailto:k&#46;h&#46;fredly&#37;&#52;&#48;fys&#46;uio&#46;no">k<span>&#46;</span>h<span>&#46;</span>fredly<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
 <li><p>Daniel Haas Becattini Lima, <a class="reference external" href="mailto:d&#46;h&#46;b&#46;lima&#37;&#52;&#48;fys&#46;uio&#46;no">d<span>&#46;</span>h<span>&#46;</span>b<span>&#46;</span>lima<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
@@ -474,10 +408,10 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p>Ida Torkjellsdatter Storehaug, <a class="reference external" href="mailto:i&#46;t&#46;storehaug&#37;&#52;&#48;fys&#46;uio&#46;no">i<span>&#46;</span>t<span>&#46;</span>storehaug<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
 <li><p>Mia-Katrin Ose Kvalsund, <a class="reference external" href="mailto:m&#46;k&#46;o&#46;kvalsund&#37;&#52;&#48;fys&#46;uio&#46;no">m<span>&#46;</span>k<span>&#46;</span>o<span>&#46;</span>kvalsund<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
 </ul>
-</div>
-<div class="section" id="practicalities">
-<h2>Practicalities<a class="headerlink" href="#practicalities" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="practicalities">
+<h2>Practicalities<a class="headerlink" href="#practicalities" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>The sessions on Tuesdays and Wednesdays last four hours for each group (four in total) and will include lectures in a flipped mode (promoting active learning) and work on exercices and projects.  The sessions will begin with lectures and questions and answers about the material to be covered every week.</p></li>
 <li><p>There are four groups, Tuesdays 815am-12pm and 1215pm-4pm and Wednesdays 815am-12pm and 1215pm-4pm. Please sign up as soon as possible for one of the groups. Max capacity per group is 30-40 participants.</p></li>
 <li><p>On Thursdays we have a regular lecture. These lectures start at 1215pm and end at 2pm. The lectures are recorded.</p></li>
@@ -488,9 +422,9 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p>Videos of teaching material are available via the links at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/web/course.html">https://compphysics.github.io/MachineLearning/doc/web/course.html</a>;</p></li>
 <li><p>Weekly email with summary of activities will be mailed to all participants;</p></li>
 </ol>
-</div>
-<div class="section" id="grading">
-<h2>Grading<a class="headerlink" href="#grading" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="grading">
+<h2>Grading<a class="headerlink" href="#grading" title="Permalink to this heading">#</a></h2>
 <p>Grading scale: Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. There are three projects which are graded and each project counts 1/3 of the final grade. The total score is thus the average from all three projects.</p>
 <p>The final number of points is based on the average of all projects (including eventual additional points) and the grade follows the following table:</p>
 <ul class="simple">
@@ -501,9 +435,9 @@ const thebe_selector_output = ".output, .cell_output"
 <li><p>40-45 points: E</p></li>
 <li><p>0-39 points: F-failed</p></li>
 </ul>
-<div class="section" id="in-summary">
-<h3>In summary<a class="headerlink" href="#in-summary" title="Permalink to this headline">¶</a></h3>
-<table class="colwidths-auto table">
+<section id="in-summary">
+<h3>In summary<a class="headerlink" href="#in-summary" title="Permalink to this heading">#</a></h3>
+<table class="table">
 <thead>
 <tr class="row-odd"><th class="head"><p>Activity</p></th>
 <th class="head"><p>Percentage of total score</p></th>
@@ -525,9 +459,9 @@ const thebe_selector_output = ".output, .cell_output"
 </tbody>
 </table>
 <p>The first weekly exercise set is scheduled for week 35.</p>
-</div>
-</div>
-</div>
+</section>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
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@@ -549,44 +483,107 @@ const thebe_selector_output = ".output, .cell_output"
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 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Review of Statistics with Resampling Techniques and Linear Algebra
- </span>
-</p>
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- <li class="toctree-l1">
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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-   7. Optimization, the central part of any Machine Learning algortithm
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+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
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 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
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-   12. Clustering and Unsupervised Learning
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+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
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-<p aria-level="2" class="caption" role="heading">
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-   14. Building a Feed Forward Neural Network
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-   15. Solving Differential Equations  with Deep Learning
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-<p aria-level="2" class="caption" role="heading">
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-  Weekly material, notes and exercises
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-   Links to relevant courses at the University of Oslo
-  </a>
- </li>
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#">Textbooks</a></li>
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#links-to-relevant-courses-at-the-university-of-oslo">Links to relevant courses at the University of Oslo</a></li>
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-            
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+              
                 
-  <div class="section" id="textbooks">
-<h1>Textbooks<a class="headerlink" href="#textbooks" title="Permalink to this headline">¶</a></h1>
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <section id="textbooks">
+<h1>Textbooks<a class="headerlink" href="#textbooks" title="Permalink to this heading">#</a></h1>
 <p><em>Recommended textbooks</em>:
 The lecture notes are collected as a jupyter-book at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html</a>. In addition to the lecture notes, we recommend the books of Bishop, Murphy and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these two texts.</p>
 <ul class="simple">
@@ -444,9 +408,9 @@ The lecture notes are collected as a jupyter-book at <a class="reference externa
 <li><p>David J.C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press</p></li>
 <li><p>David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press</p></li>
 </ul>
-</div>
-<div class="section" id="links-to-relevant-courses-at-the-university-of-oslo">
-<h1>Links to relevant courses at the University of Oslo<a class="headerlink" href="#links-to-relevant-courses-at-the-university-of-oslo" title="Permalink to this headline">¶</a></h1>
+</section>
+<section id="links-to-relevant-courses-at-the-university-of-oslo">
+<h1>Links to relevant courses at the University of Oslo<a class="headerlink" href="#links-to-relevant-courses-at-the-university-of-oslo" title="Permalink to this heading">#</a></h1>
 <ul class="simple">
 <li><p><em>FYS5429 Advanced Machine Learning for the Physical Sciences</em> <a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS5429/index-eng.html">https://www.uio.no/studier/emner/matnat/fys/FYS5429/index-eng.html</a></p></li>
 <li><p><em>FYS5419 Quantum Computing and Quantum Machine Learning</em> <a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS5419/index-eng.html">https://www.uio.no/studier/emner/matnat/fys/FYS5419/index-eng.html</a></p></li>
@@ -460,7 +424,7 @@ The lecture notes are collected as a jupyter-book at <a class="reference externa
 <li><p><em>STK4051 Computational Statistics</em> <a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html">https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html</a></p></li>
 <li><p><em>STK4021 Applied Bayesian Analysis and Numerical Methods</em> <a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/STK4021/">https://www.uio.no/studier/emner/matnat/math/STK4021/</a></p></li>
 </ul>
-</div>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -474,7 +438,7 @@ The lecture notes are collected as a jupyter-book at <a class="reference externa
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -482,44 +446,103 @@ The lecture notes are collected as a jupyter-book at <a class="reference externa
     </script>
     <script>kernelName = 'python3'</script>
 
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diff --git a/doc/LectureNotes/_build/html/week34.html b/doc/LectureNotes/_build/html/week34.html
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   3. Linear Regression
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   15. Solving Differential Equations  with Deep Learning
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Week 37: Statitsitcal interpretations and Resampling Methods
-  </a>
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
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-</p>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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-                <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#overview-of-first-week">
-   Overview of first week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#schedule-first-week">
-   Schedule first week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lectures-and-computerlab">
-   Lectures and ComputerLab
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#communication-channels">
-   Communication channels
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#course-format">
-   Course Format
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-  <a class="reference internal nav-link" href="#teachers">
-   Teachers
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-  <a class="reference internal nav-link" href="#deadlines-for-projects-tentative">
-   Deadlines for projects (tentative)
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- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#grading">
-   Grading
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- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reading-material">
-   Reading material
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- <li class="toc-h2 nav-item toc-entry">
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-   Textbooks
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- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reading-suggestions-week-34">
-   Reading suggestions week 34
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#prerequisites">
-   Prerequisites
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">
-   Topics covered in this course: Statistical analysis and optimization of data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#statistical-analysis-and-optimization-of-data">
-   Statistical analysis and optimization of data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#machine-learning">
-   Machine Learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extremely-useful-tools-strongly-recommended">
-   Extremely useful tools, strongly recommended
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio">
-   Other courses on Data science and Machine Learning  at UiO
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn">
-   Other courses on Data science and Machine Learning  at UiO, contn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#learning-outcomes">
-   Learning outcomes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction">
-   Introduction
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">
-   AI/ML and some statements you may have heard (and what do they mean?)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-machine-learning">
-   What is Machine Learning?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#types-of-machine-learning">
-   Types of Machine Learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#essential-elements-of-ml">
-   Essential elements of ML
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#an-optimization-minimization-problem">
-   An optimization/minimization problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">
-   A Frequentist approach to data analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-a-good-model">
-   What is a good model?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-a-good-model-can-we-define-it">
-   What is a good model? Can we define it?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#software-and-needed-installations">
-   Software and needed installations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#python-installers">
-   Python installers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#useful-python-libraries">
-   Useful Python libraries
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#installing-r-c-cython-or-julia">
-   Installing R, C++, cython or Julia
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#installing-r-c-cython-numba-etc">
-   Installing R, C++, cython, Numba etc
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#numpy-examples-and-important-matrix-and-vector-handling-packages">
-   Numpy examples and Important Matrix and vector handling packages
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#numpy-and-arrays">
-   Numpy and arrays
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#matrices-in-python">
-   Matrices in Python
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-pandas">
-   Meet the Pandas
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">
-     Simple linear regression model using
-     <strong>
-      scikit-learn
-     </strong>
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
-     To our real data: nuclear binding energies. Brief reminder on masses and binding energies
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#organizing-our-data">
-     Organizing our data
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#and-what-about-using-neural-networks">
-     And what about using neural networks?
-    </a>
-   </li>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-first-summary">
-   A first summary
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family">
-   Why Linear Regression (aka Ordinary Least Squares and family)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-analysis-overarching-aims">
-   Regression analysis, overarching aims
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-analysis-overarching-aims-ii">
-   Regression analysis, overarching aims II
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#examples">
-   Examples
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#general-linear-models-and-linear-algebra">
-   General linear models and linear algebra
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem">
-   Rewriting the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">
-   Rewriting the fitting procedure as a linear algebra problem, more details
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem">
-   Generalizing the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Generalizing the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimizing-our-parameters">
-   Optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#our-model-for-the-nuclear-binding-energies">
-   Our model for the nuclear binding energies
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimizing-our-parameters-more-details">
-   Optimizing our parameters, more details
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">
-   Some useful matrix and vector expressions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id3">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">
-   Own code for Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">
-   Adding error analysis and training set up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-chi-2-function">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id4">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id5">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id6">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id7">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id8">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">
-   Fitting an Equation of State for Dense Nuclear Matter
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-code">
-   The code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercises">
-   Exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">
-   Exercise 1: Setting up various Python environments
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">
-   Exercise 2: making your own data and exploring scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">
-   Exercise 3: Split data in test and training data
-  </a>
- </li>
-</ul>
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+    <h1>Week 34: Introduction to the course, Logistics and Practicalities</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
+            
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#overview-of-first-week">Overview of first week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#schedule-first-week">Schedule first week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lectures-and-computerlab">Lectures and ComputerLab</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#communication-channels">Communication channels</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#course-format">Course Format</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#teachers">Teachers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deadlines-for-projects-tentative">Deadlines for projects (tentative)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#grading">Grading</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-material">Reading material</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#textbooks">Textbooks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-suggestions-week-34">Reading suggestions week 34</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites">Prerequisites</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">Topics covered in this course: Statistical analysis and optimization of data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#statistical-analysis-and-optimization-of-data">Statistical analysis and optimization of data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#machine-learning">Machine Learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extremely-useful-tools-strongly-recommended">Extremely useful tools, strongly recommended</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio">Other courses on Data science and Machine Learning  at UiO</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn">Other courses on Data science and Machine Learning  at UiO, contn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-outcomes">Learning outcomes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">AI/ML and some statements you may have heard (and what do they mean?)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-machine-learning">What is Machine Learning?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#types-of-machine-learning">Types of Machine Learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#essential-elements-of-ml">Essential elements of ML</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-optimization-minimization-problem">An optimization/minimization problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">A Frequentist approach to data analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model">What is a good model?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model-can-we-define-it">What is a good model? Can we define it?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#software-and-needed-installations">Software and needed installations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#python-installers">Python installers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#useful-python-libraries">Useful Python libraries</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#installing-r-c-cython-or-julia">Installing R, C++, cython or Julia</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#installing-r-c-cython-numba-etc">Installing R, C++, cython, Numba etc</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-examples-and-important-matrix-and-vector-handling-packages">Numpy examples and Important Matrix and vector handling packages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-and-arrays">Numpy and arrays</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#matrices-in-python">Matrices in Python</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-pandas">Meet the Pandas</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">Simple linear regression model using <strong>scikit-learn</strong></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#organizing-our-data">Organizing our data</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#and-what-about-using-neural-networks">And what about using neural networks?</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-first-summary">A first summary</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family">Why Linear Regression (aka Ordinary Least Squares and family)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-overarching-aims">Regression analysis, overarching aims</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-overarching-aims-ii">Regression analysis, overarching aims II</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples">Examples</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#general-linear-models-and-linear-algebra">General linear models and linear algebra</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem">Rewriting the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">Rewriting the fitting procedure as a linear algebra problem, more details</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem">Generalizing the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Generalizing the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-our-parameters">Optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#our-model-for-the-nuclear-binding-energies">Our model for the nuclear binding energies</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-our-parameters-more-details">Optimizing our parameters, more details</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">Some useful matrix and vector expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id3">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">Own code for Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">Adding error analysis and training set up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-chi-2-function">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id4">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id5">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id6">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id7">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id8">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">Fitting an Equation of State for Dense Nuclear Matter</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-code">The code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">Exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">Exercise 1: Setting up various Python environments</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">Exercise 2: making your own data and exploring scikit-learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">Exercise 3: Split data in test and training data</a></li>
+</ul>
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Week 34: Introduction to the course, Logistics and Practicalities</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#overview-of-first-week">
-   Overview of first week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#schedule-first-week">
-   Schedule first week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lectures-and-computerlab">
-   Lectures and ComputerLab
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#communication-channels">
-   Communication channels
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#course-format">
-   Course Format
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#teachers">
-   Teachers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deadlines-for-projects-tentative">
-   Deadlines for projects (tentative)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#grading">
-   Grading
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reading-material">
-   Reading material
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#textbooks">
-   Textbooks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reading-suggestions-week-34">
-   Reading suggestions week 34
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#prerequisites">
-   Prerequisites
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">
-   Topics covered in this course: Statistical analysis and optimization of data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#statistical-analysis-and-optimization-of-data">
-   Statistical analysis and optimization of data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#machine-learning">
-   Machine Learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extremely-useful-tools-strongly-recommended">
-   Extremely useful tools, strongly recommended
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio">
-   Other courses on Data science and Machine Learning  at UiO
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn">
-   Other courses on Data science and Machine Learning  at UiO, contn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#learning-outcomes">
-   Learning outcomes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introduction">
-   Introduction
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">
-   AI/ML and some statements you may have heard (and what do they mean?)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-machine-learning">
-   What is Machine Learning?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#types-of-machine-learning">
-   Types of Machine Learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#essential-elements-of-ml">
-   Essential elements of ML
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#an-optimization-minimization-problem">
-   An optimization/minimization problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">
-   A Frequentist approach to data analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-a-good-model">
-   What is a good model?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-is-a-good-model-can-we-define-it">
-   What is a good model? Can we define it?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#software-and-needed-installations">
-   Software and needed installations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#python-installers">
-   Python installers
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#useful-python-libraries">
-   Useful Python libraries
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#installing-r-c-cython-or-julia">
-   Installing R, C++, cython or Julia
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#installing-r-c-cython-numba-etc">
-   Installing R, C++, cython, Numba etc
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#numpy-examples-and-important-matrix-and-vector-handling-packages">
-   Numpy examples and Important Matrix and vector handling packages
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#numpy-and-arrays">
-   Numpy and arrays
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#matrices-in-python">
-   Matrices in Python
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-pandas">
-   Meet the Pandas
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">
-     Simple linear regression model using
-     <strong>
-      scikit-learn
-     </strong>
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
-     To our real data: nuclear binding energies. Brief reminder on masses and binding energies
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#organizing-our-data">
-     Organizing our data
-    </a>
-   </li>
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#and-what-about-using-neural-networks">
-     And what about using neural networks?
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-first-summary">
-   A first summary
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family">
-   Why Linear Regression (aka Ordinary Least Squares and family)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-analysis-overarching-aims">
-   Regression analysis, overarching aims
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#regression-analysis-overarching-aims-ii">
-   Regression analysis, overarching aims II
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#examples">
-   Examples
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#general-linear-models-and-linear-algebra">
-   General linear models and linear algebra
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem">
-   Rewriting the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">
-   Rewriting the fitting procedure as a linear algebra problem, more details
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem">
-   Generalizing the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Generalizing the fitting procedure as a linear algebra problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimizing-our-parameters">
-   Optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#our-model-for-the-nuclear-binding-energies">
-   Our model for the nuclear binding energies
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimizing-our-parameters-more-details">
-   Optimizing our parameters, more details
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">
-   Some useful matrix and vector expressions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id3">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">
-   Own code for Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">
-   Adding error analysis and training set up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-chi-2-function">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id4">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id5">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id6">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id7">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id8">
-   The
-   <span class="math notranslate nohighlight">
-    \(\chi^2\)
-   </span>
-   function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">
-   Fitting an Equation of State for Dense Nuclear Matter
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-code">
-   The code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercises">
-   Exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">
-   Exercise 1: Setting up various Python environments
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">
-   Exercise 2: making your own data and exploring scikit-learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">
-   Exercise 3: Split data in test and training data
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html week34.do.txt --no_mako -->
-<!-- dom:TITLE: Week 34: Introduction to the course, Logistics and Practicalities --><div class="tex2jax_ignore mathjax_ignore section" id="week-34-introduction-to-the-course-logistics-and-practicalities">
-<h1>Week 34: Introduction to the course, Logistics and Practicalities<a class="headerlink" href="#week-34-introduction-to-the-course-logistics-and-practicalities" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Week 34: Introduction to the course, Logistics and Practicalities --><section class="tex2jax_ignore mathjax_ignore" id="week-34-introduction-to-the-course-logistics-and-practicalities">
+<h1>Week 34: Introduction to the course, Logistics and Practicalities<a class="headerlink" href="#week-34-introduction-to-the-course-logistics-and-practicalities" title="Permalink to this heading">#</a></h1>
 <p><strong>Morten Hjorth-Jensen</strong>, Department of Physics and Center for Computing in Science Education, University of Oslo, Norway and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University, USA</p>
 <p>Date: <strong>Week 34, August 21-25, 2023</strong></p>
-<div class="section" id="overview-of-first-week">
-<h2>Overview of first week<a class="headerlink" href="#overview-of-first-week" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+<section id="overview-of-first-week">
+<h2>Overview of first week<a class="headerlink" href="#overview-of-first-week" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>The sessions on Tuesdays and Wednesdays last four hours for each group (four groups in total) and will include lectures in a flipped mode (promoting active learning) and work on exercices and projects.</p></li>
 <li><p>The sessions will begin with lectures, discussions, questions and answers about the material to be covered every week. Videos and teaching material will be announced in due time.</p></li>
 <li><p>There are four groups:</p></li>
@@ -1205,21 +504,21 @@ doconce format html week34.do.txt --no_mako -->
 <li><p>Tuesdays 815am-12pm and 1215pm-4pm</p></li>
 <li><p>Wednesdays 815am-12pm and 1215pm-4pm.</p></li>
 </ul>
-<ol class="simple">
+<ol class="arabic simple" start="4">
 <li><p>On Thursdays we have a regular lecture. These lectures start at 1215pm and end at 2pm and serve the aims of giving an overview over various topics. These lectures will also be recorded.</p></li>
 </ol>
 <p>The labs are also available till 6pm Tuesdays and Wednesdays. Videos and learning material with reading suggestions will be made available before each week starts.</p>
-</div>
-<div class="section" id="schedule-first-week">
-<h2>Schedule first week<a class="headerlink" href="#schedule-first-week" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="schedule-first-week">
+<h2>Schedule first week<a class="headerlink" href="#schedule-first-week" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>August 22: Presentation of the course, aims and content. Introduction to software and repetition of Python Programming, linear algebra and basic elements of statistics. Please select group.</p></li>
 <li><p>August 23: Presentation of the course, aims and content. Introduction to software and repetition of Python Programming, linear algebra and basic elements of statistics. Please select group.</p></li>
 <li><p>August 24: Lecture: Linear regression, examples and theory</p></li>
 </ul>
-</div>
-<div class="section" id="lectures-and-computerlab">
-<h2>Lectures and ComputerLab<a class="headerlink" href="#lectures-and-computerlab" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="lectures-and-computerlab">
+<h2>Lectures and ComputerLab<a class="headerlink" href="#lectures-and-computerlab" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>The sessions on Tuesdays and Wednesdays last four hours and will include partly lectures in a flipped mode (promoting active learning) and work on exercices and projects.</p></li>
 <li><p>Thursdays: regular lectures (12.15pm-2pm)</p></li>
@@ -1229,16 +528,16 @@ doconce format html week34.do.txt --no_mako -->
 <li><p>Weekly plans and all other information are on the official website. This info will also be conveyed via weekly emails.</p></li>
 <li><p>No final exam, three projects that are graded and have to be approved.</p></li>
 </ul>
-</div>
-<div class="section" id="communication-channels">
-<h2>Communication channels<a class="headerlink" href="#communication-channels" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="communication-channels">
+<h2>Communication channels<a class="headerlink" href="#communication-channels" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Chat and communications via &lt;<a class="reference external" href="http://canvas.uio.no">canvas.uio.no</a>&gt;</p></li>
 <li><p><strong>Discord</strong> channel will be added asap</p></li>
 </ul>
-</div>
-<div class="section" id="course-format">
-<h2>Course Format<a class="headerlink" href="#course-format" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="course-format">
+<h2>Course Format<a class="headerlink" href="#course-format" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Three compulsory projects. Electronic reports only using <a class="reference external" href="https://www.uio.no/english/services/it/education/canvas/">Canvas</a> to hand in projects and <a class="reference external" href="https://git-scm.com/">git</a> as version control software and <a class="reference external" href="https://github.com/">GitHub</a> for repository (or <a class="reference external" href="https://about.gitlab.com/">GitLab</a>) of all your material.</p></li>
 <li><p>Evaluation and grading: The three projects are graded and each counts 1/3 of the final mark. No final written or oral exam.</p></li>
@@ -1249,9 +548,9 @@ doconce format html week34.do.txt --no_mako -->
 <ul class="simple">
 <li><p>Python is the default programming language, but feel free to use C/C++, Julia and/or Fortran or other programming languages. All source codes discussed during the lectures can be found at the webpage and <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/tree/master/doc/Programs">github address</a> of the course.</p></li>
 </ul>
-</div>
-<div class="section" id="teachers">
-<h2>Teachers<a class="headerlink" href="#teachers" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="teachers">
+<h2>Teachers<a class="headerlink" href="#teachers" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Morten Hjorth-Jensen, <a class="reference external" href="mailto:morten&#46;hjorth-jensen&#37;&#52;&#48;fys&#46;uio&#46;no">morten<span>&#46;</span>hjorth-jensen<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p>
 <ul>
@@ -1267,18 +566,18 @@ doconce format html week34.do.txt --no_mako -->
 <li><p>Adam Jakobsen, <a class="reference external" href="mailto:adam&#46;jakobsen&#37;&#52;&#48;fys&#46;uio&#46;no">adam<span>&#46;</span>jakobsen<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
 <li><p>Daniel Haas Beccatini Lima, <a class="reference external" href="mailto:d&#46;h&#46;b&#46;lima&#37;&#52;&#48;fys&#46;uio&#46;no">d<span>&#46;</span>h<span>&#46;</span>b<span>&#46;</span>lima<span>&#64;</span>fys<span>&#46;</span>uio<span>&#46;</span>no</a></p></li>
 </ul>
-</div>
-<div class="section" id="deadlines-for-projects-tentative">
-<h2>Deadlines for projects (tentative)<a class="headerlink" href="#deadlines-for-projects-tentative" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="deadlines-for-projects-tentative">
+<h2>Deadlines for projects (tentative)<a class="headerlink" href="#deadlines-for-projects-tentative" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>Project 1: October 9 (available September 4) graded with feedback)</p></li>
 <li><p>Project 2: November 6 (available October 6, graded with feedback)</p></li>
 <li><p>Project 3: December 11  (available November 10, graded with feedback)</p></li>
 </ol>
 <p>Extra Credit (not mandatory),  weekly exercise assignments, 10 in total (due Friday same week), 10% additional score. The extra credit assignments are due each Friday and can be uploaed to <strong>Canvas</strong> in your preferred format (although we prefer jupyter-notebooks). First assignment is for week 35. Each weekly exercise set counts 1%.</p>
-</div>
-<div class="section" id="grading">
-<h2>Grading<a class="headerlink" href="#grading" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="grading">
+<h2>Grading<a class="headerlink" href="#grading" title="Permalink to this heading">#</a></h2>
 <p>Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. There are three projects which are graded and each project counts 1/3 of the final grade. The total score is thus the average from all three projects.</p>
 <p>The final number of points is based on the average of all projects and the grade follows the following table:</p>
 <ul class="simple">
@@ -1290,14 +589,14 @@ doconce format html week34.do.txt --no_mako -->
 <li><p>0-39 points: F-failed</p></li>
 </ul>
 <p>In addition you can get an extra 10% score for weekly assignments (10 in total and due each Friday). Each weekly assignment counts 1%.</p>
-</div>
-<div class="section" id="reading-material">
-<h2>Reading material<a class="headerlink" href="#reading-material" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reading-material">
+<h2>Reading material<a class="headerlink" href="#reading-material" title="Permalink to this heading">#</a></h2>
 <p>The lecture notes are collected as a jupyter-book at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html</a>.</p>
 <p>In addition to the lecture notes, we recommend the books of Bishop, Hastie et al, Murphy and Goodfellow et al. We will follow these texts closely and the weekly reading assignments refer to these texts. The text by Hastie et al is also widely used in the Machine Learning community. Finally, we also recommend the hands-on text by Geron, see next slide for links.</p>
-</div>
-<div class="section" id="textbooks">
-<h2>Textbooks<a class="headerlink" href="#textbooks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="textbooks">
+<h2>Textbooks<a class="headerlink" href="#textbooks" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><a class="reference external" href="https://www.deeplearningbook.org/">Goodfellow, Bengio, and Courville (GBC), Deep Learning</a></p></li>
 <li><p>Christopher M. Bishop (CB), Pattern Recognition and Machine Learning</p></li>
@@ -1305,13 +604,13 @@ doconce format html week34.do.txt --no_mako -->
 <li><p><a class="reference external" href="https://www.oreilly.com/library/view/hands-on-machine-learning/9781492032632/">Aurelien Geron (AG), Hands‑On Machine Learning with Scikit‑Learn and TensorFlow, O’Reilly</a>. This text is very useful since it contains many code examples and hands-on applications of all algorithms discussed in this course.</p></li>
 <li><p><a class="reference external" href="https://probml.github.io/pml-book/book1.html">Kevin Murphy (KM), Probabilistic Machine Learning, an Introduction</a></p></li>
 </ul>
-</div>
-<div class="section" id="reading-suggestions-week-34">
-<h2>Reading suggestions week 34<a class="headerlink" href="#reading-suggestions-week-34" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reading-suggestions-week-34">
+<h2>Reading suggestions week 34<a class="headerlink" href="#reading-suggestions-week-34" title="Permalink to this heading">#</a></h2>
 <p>This week: Refresh linear algebra, GBC chapters 1 and 2. HTF chapters 2 and 3. Install scikit-learn. See lecture notes for week 34 at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/web/course.html">https://compphysics.github.io/MachineLearning/doc/web/course.html</a> (these notes).</p>
-</div>
-<div class="section" id="prerequisites">
-<h2>Prerequisites<a class="headerlink" href="#prerequisites" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="prerequisites">
+<h2>Prerequisites<a class="headerlink" href="#prerequisites" title="Permalink to this heading">#</a></h2>
 <p>Basic knowledge in programming and mathematics, with an emphasis on
 linear algebra. Knowledge of Python or/and C++ as programming
 languages is strongly recommended and experience with Jupiter notebook
@@ -1321,18 +620,18 @@ of the corresponding computing and programming courses INF1000/INF1110
 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1100. Most universities
 offer nowadays a basic programming course (often compulsory) where
 Python is the recurring programming language.</p>
-</div>
-<div class="section" id="topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">
-<h2>Topics covered in this course: Statistical analysis and optimization of data<a class="headerlink" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">
+<h2>Topics covered in this course: Statistical analysis and optimization of data<a class="headerlink" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data" title="Permalink to this heading">#</a></h2>
 <p>The course has two central parts</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Statistical analysis and optimization of data</p></li>
 <li><p>Machine learning</p></li>
 </ol>
 <p>These topics will be scattered thorughout the course and may not  necessarily be taught separately. Rather, we will often take an approach (during the lectures and project/exercise sessions) where say elements from statistical data analysis are mixed with specific Machine Learning algorithms.</p>
-</div>
-<div class="section" id="statistical-analysis-and-optimization-of-data">
-<h2>Statistical analysis and optimization of data<a class="headerlink" href="#statistical-analysis-and-optimization-of-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="statistical-analysis-and-optimization-of-data">
+<h2>Statistical analysis and optimization of data<a class="headerlink" href="#statistical-analysis-and-optimization-of-data" title="Permalink to this heading">#</a></h2>
 <p>We plan to cover the following topics:</p>
 <ul class="simple">
 <li><p>Basic concepts, expectation values, variance, covariance, correlation functions and errors;</p></li>
@@ -1343,9 +642,9 @@ Python is the recurring programming language.</p>
 <li><p>Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;</p></li>
 <li><p>Principal Component Analysis (PCA) and its mathematical foundation;</p></li>
 </ul>
-</div>
-<div class="section" id="machine-learning">
-<h2>Machine Learning<a class="headerlink" href="#machine-learning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="machine-learning">
+<h2>Machine Learning<a class="headerlink" href="#machine-learning" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Pre deep-learning revolution (2008 approx)</p>
 <ul>
@@ -1367,17 +666,17 @@ Python is the recurring programming language.</p>
 </li>
 </ul>
 <p>Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics.</p>
-</div>
-<div class="section" id="extremely-useful-tools-strongly-recommended">
-<h2>Extremely useful tools, strongly recommended<a class="headerlink" href="#extremely-useful-tools-strongly-recommended" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="extremely-useful-tools-strongly-recommended">
+<h2>Extremely useful tools, strongly recommended<a class="headerlink" href="#extremely-useful-tools-strongly-recommended" title="Permalink to this heading">#</a></h2>
 <p><strong>and discussed at the lab sessions.</strong></p>
 <ul class="simple">
 <li><p>GIT for version control, and GitHub or GitLab as repositories, highly recommended. This will be discussed during the first exercise session</p></li>
 <li><p>Anaconda and other Python environments, see intro slides and links to programming resources at <a class="reference external" href="https://computationalscienceuio.github.io/RefreshProgrammingSkills/intro.html">https://computationalscienceuio.github.io/RefreshProgrammingSkills/intro.html</a></p></li>
 </ul>
-</div>
-<div class="section" id="other-courses-on-data-science-and-machine-learning-at-uio">
-<h2>Other courses on Data science and Machine Learning  at UiO<a class="headerlink" href="#other-courses-on-data-science-and-machine-learning-at-uio" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-courses-on-data-science-and-machine-learning-at-uio">
+<h2>Other courses on Data science and Machine Learning  at UiO<a class="headerlink" href="#other-courses-on-data-science-and-machine-learning-at-uio" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS5419/index-eng.html">FYS5419 Quantum Computing and Quantum Machine Learning</a></p></li>
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS5429/index-eng.html">FYS5429 Advanced Machine Learning for the Physical Sciences</a></p></li>
@@ -1386,18 +685,18 @@ Python is the recurring programming language.</p>
 <li><p><a class="reference external" href="http://www.uio.no/studier/emner/matnat/math/STK-INF3000/index-eng.html">STK-INF3000/4000 Selected Topics in Data Science</a>. The course provides insight into selected contemporary relevant topics within Data Science.</p></li>
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/ifi/IN4080/index.html">IN4080 Natural Language Processing</a>. Probabilistic and machine learning techniques applied to natural language processing.</p></li>
 </ul>
-</div>
-<div class="section" id="other-courses-on-data-science-and-machine-learning-at-uio-contn">
-<h2>Other courses on Data science and Machine Learning  at UiO, contn<a class="headerlink" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-courses-on-data-science-and-machine-learning-at-uio-contn">
+<h2>Other courses on Data science and Machine Learning  at UiO, contn<a class="headerlink" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/STK-IN4300/index-eng.html">STK-IN4300 Statistical learning methods in Data Science</a>. An advanced introduction to statistical and machine learning. For students with a good mathematics and statistics background.</p></li>
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/ifi/IN4310/index.html">IN3310/4310 Deep Learnig for Image Analysis</a></p></li>
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/STK4051/index-eng.html">STK4051 Computational Statistics</a></p></li>
 <li><p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/math/STK4021/index-eng.html">STK4021 Applied Bayesian Analysis and Numerical Methods</a></p></li>
 </ul>
-</div>
-<div class="section" id="learning-outcomes">
-<h2>Learning outcomes<a class="headerlink" href="#learning-outcomes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="learning-outcomes">
+<h2>Learning outcomes<a class="headerlink" href="#learning-outcomes" title="Permalink to this heading">#</a></h2>
 <p>This course aims at giving you insights and knowledge about many of
 the central algorithms used in Data Analysis and Machine Learning.
 The course is project based and through various numerical projects,
@@ -1423,9 +722,9 @@ specifically, after this course you will</p>
 <li><p>Generative models</p></li>
 <li><p>Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later) or Julia or other.</p></li>
 </ul>
-</div>
-<div class="section" id="introduction">
-<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this heading">#</a></h2>
 <p>Our emphasis throughout this series of lectures<br />
 is on understanding the mathematical aspects of
 different algorithms used in the fields of data analysis and machine learning.</p>
@@ -1455,19 +754,19 @@ Tensorflow with Keras (see below for links etc).  Moreover, the examples we
 introduce will serve as inputs to many of our discussions later, as
 well as allowing you to set up models and produce your own data and
 get started with programming.</p>
-</div>
-<div class="section" id="ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">
-<h2>AI/ML and some statements you may have heard (and what do they mean?)<a class="headerlink" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">
+<h2>AI/ML and some statements you may have heard (and what do they mean?)<a class="headerlink" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>Fei-Fei Li on ImageNet: <strong>map out the entire world of objects</strong> (<a class="reference external" href="https://cacm.acm.org/news/219702-the-data-that-transformed-ai-research-and-possibly-the-world/fulltext">The data that transformed AI research</a>)</p></li>
 <li><p>Russell and Norvig in their popular textbook: <strong>relevant to any intellectual task; it is truly a universal field</strong> (<a class="reference external" href="http://aima.cs.berkeley.edu/">Artificial Intelligence, A modern approach</a>)</p></li>
 <li><p>Woody Bledsoe puts it more bluntly: <strong>in the long run, AI is the only science</strong> (quoted in Pamilla McCorduck, <a class="reference external" href="https://www.pamelamccorduck.com/machines-who-think">Machines who think</a>)</p></li>
 </ol>
 <p>If you wish to have a critical read on AI/ML from a societal point of view, see <a class="reference external" href="https://www.katecrawford.net/">Kate Crawford’s recent text Atlas of AI</a></p>
 <p><strong>Here: with AI/ML we intend a collection of machine learning methods with an emphasis on statistical learning and data analysis</strong></p>
-</div>
-<div class="section" id="what-is-machine-learning">
-<h2>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-is-machine-learning">
+<h2>What is Machine Learning?<a class="headerlink" href="#what-is-machine-learning" title="Permalink to this heading">#</a></h2>
 <p>Statistics, data science and machine learning form important fields of
 research in modern science.  They describe how to learn and make
 predictions from data, as well as allowing us to extract important
@@ -1526,9 +825,9 @@ solid command of linear algebra, multivariate theory, probability
 theory, statistical data analysis, understanding errors and Monte
 Carlo methods are central elements in a proper understanding of many
 of algorithms and methods we will discuss.</p>
-</div>
-<div class="section" id="types-of-machine-learning">
-<h2>Types of Machine Learning<a class="headerlink" href="#types-of-machine-learning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="types-of-machine-learning">
+<h2>Types of Machine Learning<a class="headerlink" href="#types-of-machine-learning" title="Permalink to this heading">#</a></h2>
 <p>The approaches to machine learning are many, but are often split into
 two main categories.  In <em>supervised learning</em> we know the answer to a
 problem, and let the computer deduce the logic behind it. On the other
@@ -1545,9 +844,9 @@ desired output of a system.  Some of the most common tasks are:</p>
 <li><p>Regression: Finding a functional relationship between an input data set and a reference data set.   The goal is to construct a function that maps input data to continuous output values.</p></li>
 <li><p>Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand.  It is thus a form of unsupervised learning.</p></li>
 </ul>
-</div>
-<div class="section" id="essential-elements-of-ml">
-<h2>Essential elements of ML<a class="headerlink" href="#essential-elements-of-ml" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="essential-elements-of-ml">
+<h2>Essential elements of ML<a class="headerlink" href="#essential-elements-of-ml" title="Permalink to this heading">#</a></h2>
 <p>The methods we cover have three main topics in common, irrespective of
 whether we deal with supervised or unsupervised learning.</p>
 <ul class="simple">
@@ -1555,13 +854,13 @@ whether we deal with supervised or unsupervised learning.</p>
 <li><p>The second item is a model which is normally a function of some parameters.  The model reflects our knowledge of the system (or lack thereof). As an example, if we know that our data show a behavior similar to what would be predicted by a polynomial, fitting our data to a polynomial of some degree would then determin our model.</p></li>
 <li><p>The last ingredient is a so-called <strong>cost/loss</strong> function (or error or risk function) which allows us to present an estimate on how good our model is in reproducing the data it is supposed to train.</p></li>
 </ul>
-</div>
-<div class="section" id="an-optimization-minimization-problem">
-<h2>An optimization/minimization problem<a class="headerlink" href="#an-optimization-minimization-problem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="an-optimization-minimization-problem">
+<h2>An optimization/minimization problem<a class="headerlink" href="#an-optimization-minimization-problem" title="Permalink to this heading">#</a></h2>
 <p>At the heart of basically all Machine Learning algorithms we will encounter so-called minimization or optimization algorithms. A large family of such methods are so-called <strong>gradient methods</strong>.</p>
-</div>
-<div class="section" id="a-frequentist-approach-to-data-analysis">
-<h2>A Frequentist approach to data analysis<a class="headerlink" href="#a-frequentist-approach-to-data-analysis" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-frequentist-approach-to-data-analysis">
+<h2>A Frequentist approach to data analysis<a class="headerlink" href="#a-frequentist-approach-to-data-analysis" title="Permalink to this heading">#</a></h2>
 <p>When you hear phrases like <strong>predictions and estimations</strong> and
 <strong>correlations and causations</strong>, what do you think of?  May be you think
 of the difference between classifying new data points and generating
@@ -1584,9 +883,9 @@ where the aim is to make predictions and find correlations. We focus
 less on for example extracting a probability distribution function (PDF). The PDF can be
 used in turn to make estimations and find causations such as given <span class="math notranslate nohighlight">\(A\)</span>
 what is the likelihood of finding <span class="math notranslate nohighlight">\(B\)</span>.</p>
-</div>
-<div class="section" id="what-is-a-good-model">
-<h2>What is a good model?<a class="headerlink" href="#what-is-a-good-model" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-is-a-good-model">
+<h2>What is a good model?<a class="headerlink" href="#what-is-a-good-model" title="Permalink to this heading">#</a></h2>
 <p>In science and engineering we often end up in situations where we want to infer (or learn) a
 quantitative model <span class="math notranslate nohighlight">\(M\)</span> for a given set of sample points <span class="math notranslate nohighlight">\(\boldsymbol{X} \in [x_1, x_2,\dots x_N]\)</span>.</p>
 <p>As we will see repeatedely in these lectures, we could try to fit these data points to a model given by a
@@ -1602,9 +901,9 @@ us in making predictions about  future data samples.</p>
 for a given data set is an elusive, if not impossible, task. The fundamental difficulty
 is that if we are not specific about what we mean by a <em>correct</em> model, there
 could easily be many different models that fit the given data set <em>equally well</em>.</p>
-</div>
-<div class="section" id="what-is-a-good-model-can-we-define-it">
-<h2>What is a good model? Can we define it?<a class="headerlink" href="#what-is-a-good-model-can-we-define-it" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-is-a-good-model-can-we-define-it">
+<h2>What is a good model? Can we define it?<a class="headerlink" href="#what-is-a-good-model-can-we-define-it" title="Permalink to this heading">#</a></h2>
 <p>The central question is this: what leads us to say that a model is correct or
 optimal for a given data set? To make the model inference problem well posed, i.e.,
 to guarantee that there is a unique optimal model for the given data, we need to
@@ -1623,9 +922,9 @@ simplest class of models and increase the complexity of the models only when the
 simpler models become inadequate. For instance, if we work with a regression problem to fit a set of sample points, one
 may first try the simplest class of models, namely linear models, followed obviously by more complex models.</p>
 <p>How to evaluate which model fits best the data is something we will come back to over and over again in these sets of lectures.</p>
-</div>
-<div class="section" id="software-and-needed-installations">
-<h2>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="software-and-needed-installations">
+<h2>Software and needed installations<a class="headerlink" href="#software-and-needed-installations" title="Permalink to this heading">#</a></h2>
 <p>We will make extensive use of Python as programming language and its
 myriad of available libraries.  You will find
 Jupyter notebooks invaluable in your work.  You can run <strong>R</strong>
@@ -1636,25 +935,25 @@ on Python.</p>
 <p>If you have Python installed (we strongly recommend Python3) and you feel
 pretty familiar with installing different packages, we recommend that
 you install the following Python packages via <strong>pip</strong> as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow</p></li>
 </ol>
 <p>For Python3, replace <strong>pip</strong> with <strong>pip3</strong>.</p>
 <p>For OSX users we recommend, after having installed Xcode, to
 install <strong>brew</strong>. Brew allows for a seamless installation of additional
 software via for example</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>brew install python3</p></li>
 </ol>
 <p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
 you can use <strong>pip</strong> as well and simply install Python as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>sudo apt-get install python3  (or python for pyhton2.7)</p></li>
 </ol>
 <p>etc etc.</p>
-</div>
-<div class="section" id="python-installers">
-<h2>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="python-installers">
+<h2>Python installers<a class="headerlink" href="#python-installers" title="Permalink to this heading">#</a></h2>
 <p>If you don’t want to perform these operations separately and venture
 into the hassle of exploring how to set up dependencies and paths, we
 recommend two widely used distrubutions which set up all relevant
@@ -1676,9 +975,9 @@ analysis environment, available for free and under a commercial
 license.</p>
 <p>Furthermore, <a class="reference external" href="https://colab.research.google.com/notebooks/welcome.ipynb">Google’s Colab</a> is a free Jupyter notebook environment that requires
 no setup and runs entirely in the cloud. Try it out!</p>
-</div>
-<div class="section" id="useful-python-libraries">
-<h2>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="useful-python-libraries">
+<h2>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Permalink to this heading">#</a></h2>
 <p>Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)</p>
 <ul class="simple">
 <li><p><a class="reference external" href="https://www.numpy.org/">NumPy</a> is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays</p></li>
@@ -1694,9 +993,9 @@ no setup and runs entirely in the cloud. Try it out!</p>
 <li><p><a class="reference external" href="https://keras.io/">Keras</a> is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano</p></li>
 <li><p>And many more such as <a class="reference external" href="https://pytorch.org/">pytorch</a>,  <a class="reference external" href="https://pypi.org/project/Theano/">Theano</a> etc</p></li>
 </ul>
-</div>
-<div class="section" id="installing-r-c-cython-or-julia">
-<h2>Installing R, C++, cython or Julia<a class="headerlink" href="#installing-r-c-cython-or-julia" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="installing-r-c-cython-or-julia">
+<h2>Installing R, C++, cython or Julia<a class="headerlink" href="#installing-r-c-cython-or-julia" title="Permalink to this heading">#</a></h2>
 <p>You will also find it convenient to utilize <strong>R</strong>. We will mainly
 use Python during our lectures and in various projects and exercises.
 Those of you
@@ -1709,9 +1008,9 @@ and allows for an easy usage of the tools and algorithms we will discuss in thes
 lectures.</p>
 <p>To install <strong>R</strong> with Jupyter notebook
 <a class="reference external" href="https://mpacer.org/maths/r-kernel-for-ipython-notebook">follow the link here</a></p>
-</div>
-<div class="section" id="installing-r-c-cython-numba-etc">
-<h2>Installing R, C++, cython, Numba etc<a class="headerlink" href="#installing-r-c-cython-numba-etc" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="installing-r-c-cython-numba-etc">
+<h2>Installing R, C++, cython, Numba etc<a class="headerlink" href="#installing-r-c-cython-numba-etc" title="Permalink to this heading">#</a></h2>
 <p>For the C++ aficionados, Jupyter/IPython notebook allows you also to
 install C++ and run codes written in this language interactively in
 the browser. Since we will emphasize writing many of the algorithms
@@ -1732,9 +1031,9 @@ further processing. For example, convert to latex as</p>
 </div>
 <p>And to add more versatility, the Python package <a class="reference external" href="http://www.sympy.org/en/index.html">SymPy</a> is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS)  and is entirely written in Python.</p>
 <p>Finally, we recommend strongly using Autograd or JAX for automatic differentiation.</p>
-</div>
-<div class="section" id="numpy-examples-and-important-matrix-and-vector-handling-packages">
-<h2>Numpy examples and Important Matrix and vector handling packages<a class="headerlink" href="#numpy-examples-and-important-matrix-and-vector-handling-packages" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="numpy-examples-and-important-matrix-and-vector-handling-packages">
+<h2>Numpy examples and Important Matrix and vector handling packages<a class="headerlink" href="#numpy-examples-and-important-matrix-and-vector-handling-packages" title="Permalink to this heading">#</a></h2>
 <p>There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
 popular ones have been wrapped into ofter software packages like those from the widely used text <strong>Numerical Recipes</strong>. The original source codes in many of the available packages are often taken from the widely used
 software package LAPACK, which follows two other popular packages
@@ -1744,9 +1043,9 @@ developed in the 1970s, namely EISPACK and LINPACK.  We describe them shortly he
 <li><p>LAPACK:package for solving symmetric, unsymmetric and generalized eigenvalue problems. From LAPACK’s website <a class="reference external" href="http://www.netlib.org">http://www.netlib.org</a> it is possible to download for free all source codes from this library. Both C/C++ and Fortran versions are available.</p></li>
 <li><p>BLAS (I, II and III): (Basic Linear Algebra Subprograms) are routines that provide standard building blocks for performing basic vector and matrix operations. Blas I is vector operations, II vector-matrix operations and III matrix-matrix operations. Highly parallelized and efficient codes, all available for download from <a class="reference external" href="http://www.netlib.org">http://www.netlib.org</a>.</p></li>
 </ul>
-</div>
-<div class="section" id="numpy-and-arrays">
-<h2>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="numpy-and-arrays">
+<h2>Numpy and arrays<a class="headerlink" href="#numpy-and-arrays" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="http://www.numpy.org/">Numpy</a> provides an easy way to handle arrays in Python. The standard way to import this library is as</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1765,8 +1064,8 @@ developed in the 1970s, namely EISPACK and LINPACK.  We describe them shortly he
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[-1.79544237 -0.19322111  0.14623399  0.65045925 -0.73133982 -1.90092179
-  0.45359479  1.04800573 -1.16171326  1.30577095]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 0.90148776 -0.63784548  0.61907743 -0.95073282  0.3897131   0.88123172
+  0.68407077  1.02936353 -0.85538578 -1.44188631]
 </pre></div>
 </div>
 </div>
@@ -1873,9 +1172,9 @@ The attentive reader will also notice that the output is <span class="math notra
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="matrices-in-python">
-<h2>Matrices in Python<a class="headerlink" href="#matrices-in-python" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="matrices-in-python">
+<h2>Matrices in Python<a class="headerlink" href="#matrices-in-python" title="Permalink to this heading">#</a></h2>
 <p>Having defined vectors, we are now ready to try out matrices. We can
 define a <span class="math notranslate nohighlight">\(3 \times 3 \)</span> real matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> as (recall that we user
 lowercase letters for vectors and uppercase letters for matrices)</p>
@@ -1991,26 +1290,36 @@ lowercase letters for vectors and uppercase letters for matrices)</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[0.79725436 0.93166184 0.53462883 0.92250132 0.79313278 0.4185877
-  0.21601417 0.21037404 0.98496212 0.89482188]
- [0.15696119 0.72299619 0.71846708 0.7506246  0.74409239 0.1280756
-  0.5316382  0.91236018 0.24479698 0.3435384 ]
- [0.5342745  0.2369833  0.47356208 0.16499193 0.60378214 0.9920084
-  0.80788856 0.36452684 0.23309661 0.33829607]
- [0.7803076  0.17074761 0.15484848 0.82187419 0.69965466 0.85754328
-  0.35700089 0.70856363 0.44993812 0.48802709]
- [0.06875458 0.23106527 0.28230186 0.40805354 0.54632096 0.11033412
-  0.51220693 0.07752967 0.58908017 0.78263078]
- [0.62686358 0.14793475 0.11341291 0.46164895 0.32542732 0.42090072
-  0.25033968 0.33199489 0.25137033 0.17009925]
- [0.74260356 0.49932184 0.99035178 0.5146617  0.9859105  0.8990231
-  0.38098948 0.10635754 0.21186069 0.07687896]
- [0.92173899 0.87556429 0.04674926 0.70911476 0.43975616 0.37622356
-  0.79994469 0.22524236 0.10951119 0.04316854]
- [0.3521478  0.25186426 0.59164202 0.44214614 0.09497154 0.97558913
-  0.40837841 0.56953559 0.36074377 0.95539206]
- [0.33113182 0.3702755  0.31816439 0.83303886 0.51013506 0.6257439
-  0.89881026 0.55805262 0.79700882 0.14010994]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[9.01367154e-01 4.99358923e-02 8.62083431e-02 4.87662496e-01
+  4.35268384e-01 4.95778501e-01 8.47259540e-01 8.19492614e-01
+  7.48029002e-01 6.23905282e-01]
+ [1.27137716e-01 2.21803999e-01 7.73335363e-01 8.12636533e-01
+  9.98254070e-01 5.73014312e-01 2.20054803e-01 3.32763666e-01
+  9.06059481e-01 8.89711757e-01]
+ [8.96925518e-02 7.63406517e-01 6.37309895e-01 7.34414668e-01
+  5.05136701e-01 8.15223640e-04 8.94612568e-01 4.58800064e-01
+  7.05353991e-01 1.57603741e-01]
+ [8.12532842e-01 9.31595458e-01 3.53618097e-01 9.13032740e-02
+  7.90877850e-01 7.77836912e-01 2.21341535e-01 4.30426390e-01
+  3.37060503e-01 8.73565723e-01]
+ [9.00991648e-01 5.91377887e-01 1.24999213e-01 8.88127749e-02
+  7.49811765e-01 2.74541956e-01 6.70054572e-01 6.20486376e-01
+  3.12715695e-01 9.93767143e-01]
+ [1.07972608e-01 9.20716385e-01 8.20068837e-01 5.64069531e-02
+  1.06786283e-01 2.76784740e-01 7.16634263e-01 7.86140930e-01
+  4.32839766e-01 9.78922154e-01]
+ [4.56496194e-02 9.39925712e-01 4.16339920e-01 8.51501448e-01
+  6.50094775e-01 2.69132527e-01 9.01148802e-01 3.82213353e-01
+  8.63686244e-02 4.94507958e-01]
+ [4.44878750e-01 5.09959399e-01 8.90303141e-01 1.35897374e-01
+  2.21820632e-01 2.18969262e-01 6.93515781e-01 6.38299113e-01
+  2.08291478e-01 4.53609787e-01]
+ [5.28044814e-01 3.39354674e-01 7.73240597e-02 3.69972328e-01
+  4.52291156e-01 2.34048640e-01 7.34023583e-01 2.86689196e-01
+  4.68794083e-01 9.14515024e-01]
+ [2.35728987e-01 5.58997922e-01 1.81586331e-01 7.01875673e-02
+  4.86286714e-01 1.91892059e-02 1.99830074e-01 1.38493791e-01
+  5.80880777e-01 9.24801038e-01]]
 </pre></div>
 </div>
 </div>
@@ -2065,13 +1374,13 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>-0.13314597157635316
-3.42745728579187
--0.1549258803307933
-[[ 1.0457893   3.16754123  2.39769983]
- [ 3.16754123 10.50453066  7.29238177]
- [ 2.39769983  7.29238177  8.3431023 ]]
-[17.73772319  0.07333967  2.0823594 ]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.19672699443907488
+4.695047732333614
+0.5139271024913812
+[[0.9118261  2.86708608 1.95090925]
+ [2.86708608 9.97030515 6.26396287]
+ [1.95090925 6.26396287 6.36590624]]
+[15.50830953  0.07327648  1.66645148]
 </pre></div>
 </div>
 </div>
@@ -2095,22 +1404,60 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[1. 0. 0. 0.]
- [0. 1. 0. 0.]
- [0. 0. 1. 0.]
- [0. 0. 0. 1.]]
-  (0, 0)	1.0
-  (1, 1)	1.0
-  (2, 2)	1.0
-  (3, 3)	1.0
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">16</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
-<img alt="_images/week34_74_1.png" src="_images/week34_74_1.png" />
 </div>
 </div>
-</div>
-<div class="section" id="meet-the-pandas">
-<h2>Meet the Pandas<a class="headerlink" href="#meet-the-pandas" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="meet-the-pandas">
+<h2>Meet the Pandas<a class="headerlink" href="#meet-the-pandas" title="Permalink to this heading">#</a></h2>
 <!-- dom:FIGURE: [fig/pandas.jpg, width=600 frac=0.8] -->
 <!-- begin figure -->
 <p><img src="fig/pandas.jpg" width="600"><p style="font-size: 0.9em"><i>Figure 1: </i></p></p>
@@ -2136,63 +1483,6 @@ analysis tools for Python. <strong>pandas</strong> stands for panel data, a term
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>First Name</th>
-      <th>Last Name</th>
-      <th>Place of birth</th>
-      <th>Date of Birth T.A.</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>Frodo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2968</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>Bilbo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2890</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>Aragorn II</td>
-      <td>Elessar</td>
-      <td>Eriador</td>
-      <td>2931</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>Samwise</td>
-      <td>Gamgee</td>
-      <td>Shire</td>
-      <td>2980</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>In the above we have imported <strong>pandas</strong> with the shorthand <strong>pd</strong>, the latter has become the standard way we import <strong>pandas</strong>. We make then a list of various variables
 and reorganize the aboves lists into a <strong>DataFrame</strong> and then print out  a neat table with specific column labels as <em>Name</em>, <em>place of birth</em> and <em>date of birth</em>.
@@ -2205,63 +1495,6 @@ Displaying these results, we see that the indices are given by the default numbe
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>First Name</th>
-      <th>Last Name</th>
-      <th>Place of birth</th>
-      <th>Date of Birth T.A.</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>Frodo</th>
-      <td>Frodo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2968</td>
-    </tr>
-    <tr>
-      <th>Bilbo</th>
-      <td>Bilbo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2890</td>
-    </tr>
-    <tr>
-      <th>Aragorn</th>
-      <td>Aragorn II</td>
-      <td>Elessar</td>
-      <td>Eriador</td>
-      <td>2931</td>
-    </tr>
-    <tr>
-      <th>Sam</th>
-      <td>Samwise</td>
-      <td>Gamgee</td>
-      <td>Shire</td>
-      <td>2980</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>Thereafter we display the content of the row which begins with the index <strong>Aragorn</strong></p>
 <div class="cell docutils container">
@@ -2270,15 +1503,6 @@ Displaying these results, we see that the indices are given by the default numbe
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>First Name            Aragorn II
-Last Name                Elessar
-Place of birth           Eriador
-Date of Birth T.A.          2931
-Name: Aragorn, dtype: object
-</pre></div>
-</div>
-</div>
 </div>
 <p>We can easily append data to this, for example</p>
 <div class="cell docutils container">
@@ -2293,74 +1517,6 @@ Name: Aragorn, dtype: object
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7752/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
-  data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=[&#39;Pippin&#39;]))
-</pre></div>
-</div>
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>First Name</th>
-      <th>Last Name</th>
-      <th>Place of birth</th>
-      <th>Date of Birth T.A.</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>Frodo</th>
-      <td>Frodo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2968</td>
-    </tr>
-    <tr>
-      <th>Bilbo</th>
-      <td>Bilbo</td>
-      <td>Baggins</td>
-      <td>Shire</td>
-      <td>2890</td>
-    </tr>
-    <tr>
-      <th>Aragorn</th>
-      <td>Aragorn II</td>
-      <td>Elessar</td>
-      <td>Eriador</td>
-      <td>2931</td>
-    </tr>
-    <tr>
-      <th>Sam</th>
-      <td>Samwise</td>
-      <td>Gamgee</td>
-      <td>Shire</td>
-      <td>2980</td>
-    </tr>
-    <tr>
-      <th>Pippin</th>
-      <td>Peregrin</td>
-      <td>Took</td>
-      <td>Shire</td>
-      <td>2990</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>Here are other examples where we use the <strong>DataFrame</strong> functionality to handle arrays, now with more interesting features for us, namely numbers. We set up a matrix
 of dimensionality <span class="math notranslate nohighlight">\(10\times 5\)</span> and compute the mean value and standard deviation of each column. Similarly, we can perform mathematial operations like squaring the matrix elements and many other operations.</p>
@@ -2382,238 +1538,6 @@ of dimensionality <span class="math notranslate nohighlight">\(10\times 5\)</spa
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>0</th>
-      <th>1</th>
-      <th>2</th>
-      <th>3</th>
-      <th>4</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>-1.749765</td>
-      <td>0.342680</td>
-      <td>1.153036</td>
-      <td>-0.252436</td>
-      <td>0.981321</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.514219</td>
-      <td>0.221180</td>
-      <td>-1.070043</td>
-      <td>-0.189496</td>
-      <td>0.255001</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>-0.458027</td>
-      <td>0.435163</td>
-      <td>-0.583595</td>
-      <td>0.816847</td>
-      <td>0.672721</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.104411</td>
-      <td>-0.531280</td>
-      <td>1.029733</td>
-      <td>-0.438136</td>
-      <td>-1.118318</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>1.618982</td>
-      <td>1.541605</td>
-      <td>-0.251879</td>
-      <td>-0.842436</td>
-      <td>0.184519</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>0.937082</td>
-      <td>0.731000</td>
-      <td>1.361556</td>
-      <td>-0.326238</td>
-      <td>0.055676</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.222400</td>
-      <td>-1.443217</td>
-      <td>-0.756352</td>
-      <td>0.816454</td>
-      <td>0.750445</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>-0.455947</td>
-      <td>1.189622</td>
-      <td>-1.690617</td>
-      <td>-1.356399</td>
-      <td>-1.232435</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>-0.544439</td>
-      <td>-0.668172</td>
-      <td>0.007315</td>
-      <td>-0.612939</td>
-      <td>1.299748</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>-1.733096</td>
-      <td>-0.983310</td>
-      <td>0.357508</td>
-      <td>-1.613579</td>
-      <td>1.470714</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0   -0.175300
-1    0.083527
-2   -0.044334
-3   -0.399836
-4    0.331939
-dtype: float64
-0    1.069584
-1    0.965548
-2    1.018232
-3    0.793167
-4    0.918992
-dtype: float64
-</pre></div>
-</div>
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>0</th>
-      <th>1</th>
-      <th>2</th>
-      <th>3</th>
-      <th>4</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>3.061679</td>
-      <td>0.117430</td>
-      <td>1.329492</td>
-      <td>0.063724</td>
-      <td>0.962990</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.264421</td>
-      <td>0.048920</td>
-      <td>1.144993</td>
-      <td>0.035909</td>
-      <td>0.065026</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>0.209789</td>
-      <td>0.189367</td>
-      <td>0.340583</td>
-      <td>0.667239</td>
-      <td>0.452553</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>0.010902</td>
-      <td>0.282259</td>
-      <td>1.060349</td>
-      <td>0.191963</td>
-      <td>1.250636</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>2.621102</td>
-      <td>2.376547</td>
-      <td>0.063443</td>
-      <td>0.709698</td>
-      <td>0.034047</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>0.878123</td>
-      <td>0.534362</td>
-      <td>1.853835</td>
-      <td>0.106431</td>
-      <td>0.003100</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.049462</td>
-      <td>2.082875</td>
-      <td>0.572069</td>
-      <td>0.666597</td>
-      <td>0.563167</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>0.207888</td>
-      <td>1.415201</td>
-      <td>2.858185</td>
-      <td>1.839818</td>
-      <td>1.518895</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>0.296414</td>
-      <td>0.446453</td>
-      <td>0.000054</td>
-      <td>0.375694</td>
-      <td>1.689345</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>3.003620</td>
-      <td>0.966899</td>
-      <td>0.127812</td>
-      <td>2.603636</td>
-      <td>2.162999</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>Thereafter we can select specific columns only and plot final results</p>
 <div class="cell docutils container">
@@ -2639,143 +1563,6 @@ dtype: float64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>First</th>
-      <th>Second</th>
-      <th>Third</th>
-      <th>Fourth</th>
-      <th>Fifth</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>-1.749765</td>
-      <td>0.342680</td>
-      <td>1.153036</td>
-      <td>-0.252436</td>
-      <td>0.981321</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.514219</td>
-      <td>0.221180</td>
-      <td>-1.070043</td>
-      <td>-0.189496</td>
-      <td>0.255001</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>-0.458027</td>
-      <td>0.435163</td>
-      <td>-0.583595</td>
-      <td>0.816847</td>
-      <td>0.672721</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.104411</td>
-      <td>-0.531280</td>
-      <td>1.029733</td>
-      <td>-0.438136</td>
-      <td>-1.118318</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>1.618982</td>
-      <td>1.541605</td>
-      <td>-0.251879</td>
-      <td>-0.842436</td>
-      <td>0.184519</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>0.937082</td>
-      <td>0.731000</td>
-      <td>1.361556</td>
-      <td>-0.326238</td>
-      <td>0.055676</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.222400</td>
-      <td>-1.443217</td>
-      <td>-0.756352</td>
-      <td>0.816454</td>
-      <td>0.750445</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>-0.455947</td>
-      <td>1.189622</td>
-      <td>-1.690617</td>
-      <td>-1.356399</td>
-      <td>-1.232435</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>-0.544439</td>
-      <td>-0.668172</td>
-      <td>0.007315</td>
-      <td>-0.612939</td>
-      <td>1.299748</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>-1.733096</td>
-      <td>-0.983310</td>
-      <td>0.357508</td>
-      <td>-1.613579</td>
-      <td>1.470714</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08352721390288316
-&lt;class &#39;pandas.core.frame.DataFrame&#39;&gt;
-Int64Index: 10 entries, 0 to 9
-Data columns (total 5 columns):
- #   Column  Non-Null Count  Dtype  
----  ------  --------------  -----  
- 0   First   10 non-null     float64
- 1   Second  10 non-null     float64
- 2   Third   10 non-null     float64
- 3   Fourth  10 non-null     float64
- 4   Fifth   10 non-null     float64
-dtypes: float64(5)
-memory usage: 480.0 bytes
-None
-           First     Second      Third     Fourth      Fifth
-count  10.000000  10.000000  10.000000  10.000000  10.000000
-mean   -0.175300   0.083527  -0.044334  -0.399836   0.331939
-std     1.069584   0.965548   1.018232   0.793167   0.918992
-min    -1.749765  -1.443217  -1.690617  -1.613579  -1.232435
-25%    -0.522836  -0.633949  -0.713163  -0.785061   0.087887
-50%    -0.280179   0.281930  -0.122282  -0.382187   0.463861
-75%     0.441264   0.657041   0.861676  -0.205231   0.923602
-max     1.618982   1.541605   1.361556   0.816847   1.470714
-</pre></div>
-</div>
-<img alt="_images/week34_86_2.png" src="_images/week34_86_2.png" />
-<img alt="_images/week34_86_3.png" src="_images/week34_86_3.png" />
-</div>
 </div>
 <p>We can produce a <span class="math notranslate nohighlight">\(4\times 4\)</span> matrix</p>
 <div class="cell docutils container">
@@ -2787,19 +1574,6 @@ max     1.618982   1.541605   1.361556   0.816847   1.470714
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 0  1  2  3]
- [ 4  5  6  7]
- [ 8  9 10 11]
- [12 13 14 15]]
-    0   1   2   3
-0   0   1   2   3
-1   4   5   6   7
-2   8   9  10  11
-3  12  13  14  15
-</pre></div>
-</div>
-</div>
 </div>
 <p>and many other operations.</p>
 <p>The <strong>Series</strong> class is another important class included in
@@ -2808,8 +1582,8 @@ we have just a single column of data. It shares many of the same features as <st
 most operations are vectorized, achieving thereby a high performance when dealing with computations of arrays, in particular labeled arrays.
 As we will see below it leads also to a very concice code close to the mathematical operations we may be interested in.
 For multidimensional arrays, we recommend strongly <a class="reference external" href="http://xarray.pydata.org/en/stable/">xarray</a>. <strong>xarray</strong> has much of the same flexibility as <strong>pandas</strong>, but allows for the extension to higher dimensions than two. We will see examples later of the usage of both <strong>pandas</strong> and <strong>xarray</strong>.</p>
-<div class="section" id="simple-linear-regression-model-using-scikit-learn">
-<h3>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this headline">¶</a></h3>
+<section id="simple-linear-regression-model-using-scikit-learn">
+<h3>Simple linear regression model using <strong>scikit-learn</strong><a class="headerlink" href="#simple-linear-regression-model-using-scikit-learn" title="Permalink to this heading">#</a></h3>
 <p>We start with perhaps our simplest possible example, using <strong>Scikit-Learn</strong> to perform linear regression analysis on a data set produced by us.</p>
 <p>What follows is a simple Python code where we have defined a function
 <span class="math notranslate nohighlight">\(y\)</span> in terms of the variable <span class="math notranslate nohighlight">\(x\)</span>. Both are defined as vectors with  <span class="math notranslate nohighlight">\(100\)</span> entries.
@@ -2872,9 +1646,6 @@ data with a straight line.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week34_93_0.png" src="_images/week34_93_0.png" />
-</div>
 </div>
 <p>This example serves several aims. It allows us to demonstrate several
 aspects of data analysis and later machine learning algorithms. The
@@ -2956,9 +1727,6 @@ to be dominated by outliers.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week34_101_0.png" src="_images/week34_101_0.png" />
-</div>
 </div>
 <p>Depending on the parameter in front of the normal distribution, we may
 have a small or larger relative error. Try to play around with
@@ -3002,19 +1770,6 @@ example of the functionality of <strong>Scikit-Learn</strong>.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The intercept alpha: 
- [2.18780801]
-Coefficient beta : 
- [[4.72228205]]
-Mean squared error: 0.37
-Variance score: 0.83
-Mean squared log error: 0.01
-Mean absolute error: 0.47
-</pre></div>
-</div>
-<img alt="_images/week34_103_1.png" src="_images/week34_103_1.png" />
-</div>
 </div>
 <p>The function <strong>coef</strong> gives us the parameter <span class="math notranslate nohighlight">\(\beta\)</span> of our fit while <strong>intercept</strong> yields
 <span class="math notranslate nohighlight">\(\alpha\)</span>. Depending on the constant in front of the normal distribution, we get values near or far from <span class="math notranslate nohighlight">\(\alpha =2\)</span> and <span class="math notranslate nohighlight">\(\beta =5\)</span>. Try to play around with different parameters in front of the normal distribution. The function <strong>meansquarederror</strong> gives us the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error or loss defined as</p>
@@ -3072,9 +1827,9 @@ H_{\delta}(\boldsymbol{a})=\left\{\begin{array}{cc}\frac{1}{2} \boldsymbol{a}^{2
 <p>Here <span class="math notranslate nohighlight">\(\boldsymbol{a}=\boldsymbol{y} - \boldsymbol{\tilde{y}}\)</span>.</p>
 <p>We will discuss in more detail these and other functions in the
 various lectures and lab sessions.</p>
-</div>
-<div class="section" id="to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
-<h3>To our real data: nuclear binding energies. Brief reminder on masses and binding energies<a class="headerlink" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">
+<h3>To our real data: nuclear binding energies. Brief reminder on masses and binding energies<a class="headerlink" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" title="Permalink to this heading">#</a></h3>
 <p>Let us now dive into  nuclear physics and remind ourselves briefly about some basic features about binding
 energies.  A basic quantity which can be measured for the ground
 states of nuclei is the atomic mass <span class="math notranslate nohighlight">\(M(N, Z)\)</span> of the neutral atom with
@@ -3135,9 +1890,9 @@ to the experimental data.</p>
 <p>We could also add a so-called pairing term, which is a correction term that
 arises from the tendency of proton pairs and neutron pairs to
 occur. An even number of particles is more stable than an odd number.</p>
-</div>
-<div class="section" id="organizing-our-data">
-<h3>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="organizing-our-data">
+<h3>Organizing our data<a class="headerlink" href="#organizing-our-data" title="Permalink to this heading">#</a></h3>
 <p>Let us start with reading and organizing our data.
 We start with the compilation of masses and binding energies from 2016.
 After having downloaded this file to our own computer, we are now ready to read the file and start structuring our data.</p>
@@ -3220,11 +1975,6 @@ data) to actually open the file and simply take a look at it!</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&#39;                                                                                                                         \nThis is taken from the data file of the mass 2016 evaluation.                                                               \nAll files are 3436 lines long with 124 character per line.                                                                  \n       Headers are 39 lines long.                                                                                           \n   col 1     :  Fortran character control: 1 = page feed  0 = line feed                                                     \n   format    :  a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5                     \n   These formats are reflected in the pandas widths variable below, see the statement                                       \n   widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),                                                            \n   Pandas has also a variable header, with length 39 in this case.                                                          \n&#39;
-</pre></div>
-</div>
-</div>
 </div>
 <p>The data we are interested in are in columns 2, 3, 4 and 11, giving us
 the number of neutrons, protons, mass numbers and binding energies,
@@ -3253,40 +2003,6 @@ covert them into the <strong>pandas</strong> DataFrame structure.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">ValueError</span><span class="g g-Whitespace">                                </span>Traceback (most recent call last)
-<span class="nn">Input In [30],</span> in <span class="ni">&lt;cell line: 2&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="c1"># Read the experimental data with Pandas</span>
-<span class="ne">----&gt; </span><span class="mi">2</span> <span class="n">Masses</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_fwf</span><span class="p">(</span><span class="n">infile</span><span class="p">,</span> <span class="n">usecols</span><span class="o">=</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">11</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">3</span>               <span class="n">names</span><span class="o">=</span><span class="p">(</span><span class="s1">&#39;N&#39;</span><span class="p">,</span> <span class="s1">&#39;Z&#39;</span><span class="p">,</span> <span class="s1">&#39;A&#39;</span><span class="p">,</span> <span class="s1">&#39;Element&#39;</span><span class="p">,</span> <span class="s1">&#39;Ebinding&#39;</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">4</span>               <span class="n">widths</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">13</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">12</span><span class="p">,</span><span class="mi">11</span><span class="p">,</span><span class="mi">1</span><span class="p">),</span>
-<span class="g g-Whitespace">      </span><span class="mi">5</span>               <span class="n">header</span><span class="o">=</span><span class="mi">39</span><span class="p">,</span>
-<span class="g g-Whitespace">      </span><span class="mi">6</span>               <span class="n">index_col</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
-<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="c1"># Extrapolated values are indicated by &#39;#&#39; in place of the decimal place, so</span>
-<span class="g g-Whitespace">      </span><span class="mi">9</span> <span class="c1"># the Ebinding column won&#39;t be numeric. Coerce to float and drop these entries.</span>
-<span class="g g-Whitespace">     </span><span class="mi">10</span> <span class="n">Masses</span><span class="p">[</span><span class="s1">&#39;Ebinding&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">to_numeric</span><span class="p">(</span><span class="n">Masses</span><span class="p">[</span><span class="s1">&#39;Ebinding&#39;</span><span class="p">],</span> <span class="n">errors</span><span class="o">=</span><span class="s1">&#39;coerce&#39;</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/util/_decorators.py:311,</span> in <span class="ni">deprecate_nonkeyword_arguments.&lt;locals&gt;.decorate.&lt;locals&gt;.wrapper</span><span class="nt">(*args, **kwargs)</span>
-<span class="g g-Whitespace">    </span><span class="mi">305</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">args</span><span class="p">)</span> <span class="o">&gt;</span> <span class="n">num_allow_args</span><span class="p">:</span>
-<span class="g g-Whitespace">    </span><span class="mi">306</span>     <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span>
-<span class="g g-Whitespace">    </span><span class="mi">307</span>         <span class="n">msg</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">arguments</span><span class="o">=</span><span class="n">arguments</span><span class="p">),</span>
-<span class="g g-Whitespace">    </span><span class="mi">308</span>         <span class="ne">FutureWarning</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">309</span>         <span class="n">stacklevel</span><span class="o">=</span><span class="n">stacklevel</span><span class="p">,</span>
-<span class="g g-Whitespace">    </span><span class="mi">310</span>     <span class="p">)</span>
-<span class="ne">--&gt; </span><span class="mi">311</span> <span class="k">return</span> <span class="n">func</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/io/parsers/readers.py:871,</span> in <span class="ni">read_fwf</span><span class="nt">(filepath_or_buffer, colspecs, widths, infer_nrows, **kwds)</span>
-<span class="g g-Whitespace">    </span><span class="mi">869</span>                     <span class="n">len_index</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">index_col</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">870</span>         <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">names</span><span class="p">)</span> <span class="o">+</span> <span class="n">len_index</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">colspecs</span><span class="p">):</span>
-<span class="ne">--&gt; </span><span class="mi">871</span>             <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">&quot;Length of colspecs must match length of names&quot;</span><span class="p">)</span>
-<span class="g g-Whitespace">    </span><span class="mi">873</span> <span class="n">kwds</span><span class="p">[</span><span class="s2">&quot;colspecs&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">colspecs</span>
-<span class="g g-Whitespace">    </span><span class="mi">874</span> <span class="n">kwds</span><span class="p">[</span><span class="s2">&quot;infer_nrows&quot;</span><span class="p">]</span> <span class="o">=</span> <span class="n">infer_nrows</span>
-
-<span class="ne">ValueError</span>: Length of colspecs must match length of names
-</pre></div>
-</div>
-</div>
 </div>
 <p>We have now read in the data, grouped them according to the variables we are interested in.
 We see how easy it is to reorganize the data using <strong>pandas</strong>. If we
@@ -3361,9 +2077,9 @@ Now we can print measures of how our fit is doing, the coefficients from the fit
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="and-what-about-using-neural-networks">
-<h3>And what about using neural networks?<a class="headerlink" href="#and-what-about-using-neural-networks" title="Permalink to this headline">¶</a></h3>
+</section>
+<section id="and-what-about-using-neural-networks">
+<h3>And what about using neural networks?<a class="headerlink" href="#and-what-about-using-neural-networks" title="Permalink to this heading">#</a></h3>
 <p>The <strong>seaborn</strong> package allows us to visualize data in an efficient way. Note that we use <strong>scikit-learn</strong>’s multi-layer perceptron (or feed forward neural network)
 functionality.</p>
 <div class="cell docutils container">
@@ -3401,10 +2117,10 @@ functionality.</p>
 </div>
 </div>
 </div>
-</div>
-</div>
-<div class="section" id="a-first-summary">
-<h2>A first summary<a class="headerlink" href="#a-first-summary" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="a-first-summary">
+<h2>A first summary<a class="headerlink" href="#a-first-summary" title="Permalink to this heading">#</a></h2>
 <p>The aim behind these introductory words was to present to you various
 Python libraries and their functionalities, in particular libraries like
 <strong>numpy</strong>, <strong>pandas</strong>, <strong>xarray</strong> and <strong>matplotlib</strong> and other that make our life much easier
@@ -3413,9 +2129,9 @@ in handling various data sets and visualizing data.</p>
 <strong>Scikit-Learn</strong> allows us with few lines of code to implement popular
 Machine Learning algorithms for supervised learning. Later we will meet <strong>Tensorflow</strong>, a powerful library for deep learning.
 Now it is time to dive more into the details of various methods. We will start with linear regression and try to take a deeper look at what it entails.</p>
-</div>
-<div class="section" id="why-linear-regression-aka-ordinary-least-squares-and-family">
-<h2>Why Linear Regression (aka Ordinary Least Squares and family)<a class="headerlink" href="#why-linear-regression-aka-ordinary-least-squares-and-family" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="why-linear-regression-aka-ordinary-least-squares-and-family">
+<h2>Why Linear Regression (aka Ordinary Least Squares and family)<a class="headerlink" href="#why-linear-regression-aka-ordinary-least-squares-and-family" title="Permalink to this heading">#</a></h2>
 <p>Fitting a continuous function with linear parameterization in terms of the parameters  <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.</p>
 <ul class="simple">
 <li><p>Method of choice for fitting a continuous function!</p></li>
@@ -3430,9 +2146,9 @@ Now it is time to dive more into the details of various methods. We will start w
 </ul>
 <p>For more discussions of Ridge and Lasso regression, <a class="reference external" href="https://arxiv.org/abs/1509.09169">Wessel van Wieringen’s</a> article is highly recommended.
 Similarly, <a class="reference external" href="https://arxiv.org/abs/1803.08823">Mehta et al’s article</a> is also recommended.</p>
-</div>
-<div class="section" id="regression-analysis-overarching-aims">
-<h2>Regression analysis, overarching aims<a class="headerlink" href="#regression-analysis-overarching-aims" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="regression-analysis-overarching-aims">
+<h2>Regression analysis, overarching aims<a class="headerlink" href="#regression-analysis-overarching-aims" title="Permalink to this heading">#</a></h2>
 <p>Regression modeling deals with the description of  the sampling distribution of a given random variable <span class="math notranslate nohighlight">\(y\)</span> and how it varies as function of another variable or a set of such variables <span class="math notranslate nohighlight">\(\boldsymbol{x} =[x_0, x_1,\dots, x_{n-1}]^T\)</span>.
 The first variable is called the <strong>dependent</strong>, the <strong>outcome</strong> or the <strong>response</strong> variable while the set of variables <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> is called the independent variable, or the predictor variable or the explanatory variable, or simply just the <strong>inputs</strong>.</p>
 <p>A regression model aims at finding a likelihood function <span class="math notranslate nohighlight">\(p(\boldsymbol{y}\vert \boldsymbol{x})\)</span> or in the more traditional sense a function <span class="math notranslate nohighlight">\(\boldsymbol{y}(\boldsymbol{x})\)</span>, that is the conditional distribution for <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> with a given <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span>. The estimation of  <span class="math notranslate nohighlight">\(p(\boldsymbol{y}\vert \boldsymbol{x})\)</span> is made using a data set with</p>
@@ -3442,9 +2158,9 @@ The first variable is called the <strong>dependent</strong>, the <strong>outcome
 <li><p><span class="math notranslate nohighlight">\(p\)</span> so-called explanatory (independent or predictor or feature) variables <span class="math notranslate nohighlight">\(\boldsymbol{x}_i=[x_{i0}, x_{i1}, \dots, x_{ip-1}]\)</span> with <span class="math notranslate nohighlight">\(i = 0, 1, 2, \dots, n-1\)</span> and explanatory variables running from <span class="math notranslate nohighlight">\(0\)</span> to <span class="math notranslate nohighlight">\(p-1\)</span>. See below for more explicit examples.</p></li>
 </ul>
 <p>The goal of the regression analysis is to extract/exploit relationship between <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> in order to infer specific dependencies, approximations to the likelihood functions, functional relationships and to make predictions, making fits and many other things.</p>
-</div>
-<div class="section" id="regression-analysis-overarching-aims-ii">
-<h2>Regression analysis, overarching aims II<a class="headerlink" href="#regression-analysis-overarching-aims-ii" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="regression-analysis-overarching-aims-ii">
+<h2>Regression analysis, overarching aims II<a class="headerlink" href="#regression-analysis-overarching-aims-ii" title="Permalink to this heading">#</a></h2>
 <p>Consider an experiment in which <span class="math notranslate nohighlight">\(p\)</span> characteristics/features of <span class="math notranslate nohighlight">\(n\)</span> samples are
 measured. The data from this experiment, for various explanatory variables <span class="math notranslate nohighlight">\(p\)</span> are normally represented by a matrix<br />
 <span class="math notranslate nohighlight">\(\mathbf{X}\)</span>.</p>
@@ -3460,9 +2176,9 @@ between <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> and
 the <em>linear regression model</em> where <span class="math notranslate nohighlight">\(\boldsymbol{\beta} = [\beta_0, \ldots,
 \beta_{p-1}]^{T}\)</span> are the <em>regression parameters</em>.</p>
 <p>Linear regression gives us a set of analytical equations for the parameters <span class="math notranslate nohighlight">\(\beta_j\)</span>.</p>
-</div>
-<div class="section" id="examples">
-<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="examples">
+<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this heading">#</a></h2>
 <p>In order to understand the relation among the predictors (or features or properties) <span class="math notranslate nohighlight">\(p\)</span>, the set of data <span class="math notranslate nohighlight">\(n\)</span> and the target (outcome, output etc) <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span>,
 consider the model we discussed for describing nuclear binding energies.</p>
 <p>There we assumed that we could parametrize the data using a polynomial approximation based on the liquid drop model.
@@ -3476,9 +2192,9 @@ This gives <span class="math notranslate nohighlight">\(p=0,1,2,3,4\)</span>. Fu
 <span class="math notranslate nohighlight">\(p\times n\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
 <p>Here the predictors are based on a model we have made. A popular data set which is widely encountered in ML applications is the
 so-called <a class="reference external" href="https://www.sciencedirect.com/science/article/pii/S0957417407006719?via%3Dihub">credit card default data from Taiwan</a>. The data set contains data on <span class="math notranslate nohighlight">\(n=30000\)</span> credit card holders with predictors like gender, marital status, age, profession, education, etc. In total there are <span class="math notranslate nohighlight">\(24\)</span> such predictors or attributes leading to a design matrix of dimensionality <span class="math notranslate nohighlight">\(24 \times 30000\)</span>. This is however a classification problem and we will come back to it when we discuss Logistic Regression.</p>
-</div>
-<div class="section" id="general-linear-models-and-linear-algebra">
-<h2>General linear models and linear algebra<a class="headerlink" href="#general-linear-models-and-linear-algebra" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="general-linear-models-and-linear-algebra">
+<h2>General linear models and linear algebra<a class="headerlink" href="#general-linear-models-and-linear-algebra" title="Permalink to this heading">#</a></h2>
 <p>Before we proceed let us study a case where we aim at fitting a set of data <span class="math notranslate nohighlight">\(\boldsymbol{y}=[y_0,y_1,\dots,y_{n-1}]\)</span>. We could think of these data as a result of an experiment or a complicated numerical experiment. These data are functions of a series of variables <span class="math notranslate nohighlight">\(\boldsymbol{x}=[x_0,x_1,\dots,x_{n-1}]\)</span>, that is <span class="math notranslate nohighlight">\(y_i = y(x_i)\)</span> with <span class="math notranslate nohighlight">\(i=0,1,2,\dots,n-1\)</span>. The variables <span class="math notranslate nohighlight">\(x_i\)</span> could represent physical quantities like time, temperature, position etc. We assume that <span class="math notranslate nohighlight">\(y(x)\)</span> is a smooth function.</p>
 <p>Since obtaining these data points may not be trivial, we want to use these data to fit a function which can allow us to make predictions for values of <span class="math notranslate nohighlight">\(y\)</span> which are not in the present set. The perhaps simplest approach is to assume we can parametrize our function in terms of a polynomial of degree <span class="math notranslate nohighlight">\(n-1\)</span> with <span class="math notranslate nohighlight">\(n\)</span> points, that is</p>
 <div class="math notranslate nohighlight">
@@ -3486,9 +2202,9 @@ so-called <a class="reference external" href="https://www.sciencedirect.com/scie
 y=y(x) \rightarrow y(x_i)=\tilde{y}_i+\epsilon_i=\sum_{j=0}^{n-1} \beta_j x_i^j+\epsilon_i,
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\epsilon_i\)</span> is the error in our approximation.</p>
-</div>
-<div class="section" id="rewriting-the-fitting-procedure-as-a-linear-algebra-problem">
-<h2>Rewriting the fitting procedure as a linear algebra problem<a class="headerlink" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="rewriting-the-fitting-procedure-as-a-linear-algebra-problem">
+<h2>Rewriting the fitting procedure as a linear algebra problem<a class="headerlink" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" title="Permalink to this heading">#</a></h2>
 <p>For every set of values <span class="math notranslate nohighlight">\(y_i,x_i\)</span> we have thus the corresponding set of equations</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -3500,9 +2216,9 @@ y_2&amp;=\beta_0+\beta_1x_2^1+\beta_2x_2^2+\dots+\beta_{n-1}x_2^{n-1}+\epsilon_2
 y_{n-1}&amp;=\beta_0+\beta_1x_{n-1}^1+\beta_2x_{n-1}^2+\dots+\beta_{n-1}x_{n-1}^{n-1}+\epsilon_{n-1}.\\
 \end{align*}
 \end{split}\]</div>
-</div>
-<div class="section" id="rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">
-<h2>Rewriting the fitting procedure as a linear algebra problem, more details<a class="headerlink" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">
+<h2>Rewriting the fitting procedure as a linear algebra problem, more details<a class="headerlink" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" title="Permalink to this heading">#</a></h2>
 <p>Defining the vectors</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3536,9 +2252,9 @@ y_{n-1}&amp;=\beta_0+\beta_1x_{n-1}^1+\beta_2x_{n-1}^2+\dots+\beta_{n-1}x_{n-1}^
 \boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{\epsilon}.
 \]</div>
 <p>The above design matrix is called a <a class="reference external" href="https://en.wikipedia.org/wiki/Vandermonde_matrix">Vandermonde matrix</a>.</p>
-</div>
-<div class="section" id="generalizing-the-fitting-procedure-as-a-linear-algebra-problem">
-<h2>Generalizing the fitting procedure as a linear algebra problem<a class="headerlink" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="generalizing-the-fitting-procedure-as-a-linear-algebra-problem">
+<h2>Generalizing the fitting procedure as a linear algebra problem<a class="headerlink" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" title="Permalink to this heading">#</a></h2>
 <p>We are obviously not limited to the above polynomial expansions.  We
 could replace the various powers of <span class="math notranslate nohighlight">\(x\)</span> with elements of Fourier
 series or instead of <span class="math notranslate nohighlight">\(x_i^j\)</span> we could have <span class="math notranslate nohighlight">\(\cos{(j x_i)}\)</span> or <span class="math notranslate nohighlight">\(\sin{(j
@@ -3557,9 +2273,9 @@ y_{n-1}&amp;=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_{n-1
 \end{align*}
 \end{split}\]</div>
 <p><strong>Note that we have <span class="math notranslate nohighlight">\(p=n\)</span> here. The matrix is symmetric. This is generally not the case!</strong></p>
-</div>
-<div class="section" id="id1">
-<h2>Generalizing the fitting procedure as a linear algebra problem<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2>Generalizing the fitting procedure as a linear algebra problem<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>We redefine in turn the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> as</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -3578,9 +2294,9 @@ x_{n-1,0}&amp; x_{n-1,1} &amp;x_{n-1,2}&amp; \dots &amp; \dots &amp;x_{n-1,n-1}\
 \boldsymbol{y} = \boldsymbol{X}\boldsymbol{\beta}+\boldsymbol{\epsilon}.
 \]</div>
 <p>The left-hand side of this equation is kwown. Our error vector <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> and the parameter vector <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> are our unknow quantities. How can we obtain the optimal set of <span class="math notranslate nohighlight">\(\beta_i\)</span> values?</p>
-</div>
-<div class="section" id="optimizing-our-parameters">
-<h2>Optimizing our parameters<a class="headerlink" href="#optimizing-our-parameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="optimizing-our-parameters">
+<h2>Optimizing our parameters<a class="headerlink" href="#optimizing-our-parameters" title="Permalink to this heading">#</a></h2>
 <p>We have defined the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> via the equations</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -3597,9 +2313,9 @@ y_{n-1}&amp;=\beta_0x_{n-1,0}+\beta_1x_{n-1,2}+\beta_2x_{n-1,2}+\dots+\beta_{n-1
 <p>As we noted above, we stayed with a system with the design matrix
 <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times n}\)</span>, that is we have <span class="math notranslate nohighlight">\(p=n\)</span>. For reasons to come later (algorithmic arguments) we will hereafter define
 our matrix as <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\)</span>, with the predictors refering to the column numbers and the entries <span class="math notranslate nohighlight">\(n\)</span> being the row elements.</p>
-</div>
-<div class="section" id="our-model-for-the-nuclear-binding-energies">
-<h2>Our model for the nuclear binding energies<a class="headerlink" href="#our-model-for-the-nuclear-binding-energies" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="our-model-for-the-nuclear-binding-energies">
+<h2>Our model for the nuclear binding energies<a class="headerlink" href="#our-model-for-the-nuclear-binding-energies" title="Permalink to this heading">#</a></h2>
 <p>In our <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/How2ReadData/html/How2ReadData.html">introductory notes</a> we looked at the so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Semi-empirical_mass_formula">liquid drop model</a>. Let us remind ourselves about what we did by looking at the code.</p>
 <p>We restate the parts of the code we are most interested in.</p>
 <div class="cell docutils container">
@@ -3683,9 +2399,9 @@ our matrix as <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\m
 \boldsymbol{\tilde{y}}= \boldsymbol{X}\boldsymbol{\beta},
 \]</div>
 <p>throughout these lectures.</p>
-</div>
-<div class="section" id="optimizing-our-parameters-more-details">
-<h2>Optimizing our parameters, more details<a class="headerlink" href="#optimizing-our-parameters-more-details" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="optimizing-our-parameters-more-details">
+<h2>Optimizing our parameters, more details<a class="headerlink" href="#optimizing-our-parameters-more-details" title="Permalink to this heading">#</a></h2>
 <p>With the above we use the design matrix to define the approximation <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\)</span> via the unknown quantity <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3709,9 +2425,9 @@ the function <span class="math notranslate nohighlight">\(C\)</span> as</p>
 C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
 \]</div>
 <p>since when taking the first derivative with respect to the unknown parameters <span class="math notranslate nohighlight">\(\beta\)</span>, the factor of <span class="math notranslate nohighlight">\(2\)</span> cancels out.</p>
-</div>
-<div class="section" id="interpretations-and-optimizing-our-parameters">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#interpretations-and-optimizing-our-parameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpretations-and-optimizing-our-parameters">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#interpretations-and-optimizing-our-parameters" title="Permalink to this heading">#</a></h2>
 <p>The function</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3752,9 +2468,9 @@ will treat <span class="math notranslate nohighlight">\(y_i\)</span> as our exac
 \[
 \frac{\partial C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right).
 \]</div>
-</div>
-<div class="section" id="id2">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id2">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id2" title="Permalink to this heading">#</a></h2>
 <p>We can rewrite</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3781,14 +2497,14 @@ regression or support vector machines, exhibit dimensionalities which
 allow for the usage of direct linear algebra methods such as <strong>LU</strong> decomposition or <strong>Singular Value Decomposition</strong> (SVD) for finding the inverse of the matrix
 <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>.</p>
 <p><strong>Small question</strong>: Do you think the example we have at hand here (the nuclear binding energies) can lead to problems in inverting the matrix  <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>? What kind of problems can we expect?</p>
-</div>
-<div class="section" id="some-useful-matrix-and-vector-expressions">
-<h2>Some useful matrix and vector expressions<a class="headerlink" href="#some-useful-matrix-and-vector-expressions" title="Permalink to this headline">¶</a></h2>
-<p>See the handwritten notes at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesExercise5Week452022.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesExercise5Week452022.pdf</a></p>
+</section>
+<section id="some-useful-matrix-and-vector-expressions">
+<h2>Some useful matrix and vector expressions<a class="headerlink" href="#some-useful-matrix-and-vector-expressions" title="Permalink to this heading">#</a></h2>
+<p>See the handwritten notes at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2022/NotesExercise5Week452022.pdf">CompPhysics/MachineLearning</a></p>
 <p>These notes will be discussed during one of the lectures.</p>
-</div>
-<div class="section" id="id3">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id3" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id3">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id3" title="Permalink to this heading">#</a></h2>
 <p>The residuals <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> are in turn given by</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3806,9 +2522,9 @@ allow for the usage of direct linear algebra methods such as <strong>LU</strong>
 \]</div>
 <p>meaning that the solution for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> is the one which minimizes the residuals.  Later we will link this with the maximum likelihood approach.</p>
 <p>Let us now return to our nuclear binding energies and simply code the above equations.</p>
-</div>
-<div class="section" id="own-code-for-ordinary-least-squares">
-<h2>Own code for Ordinary Least Squares<a class="headerlink" href="#own-code-for-ordinary-least-squares" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="own-code-for-ordinary-least-squares">
+<h2>Own code for Ordinary Least Squares<a class="headerlink" href="#own-code-for-ordinary-least-squares" title="Permalink to this heading">#</a></h2>
 <p>It is rather straightforward to implement the matrix inversion and obtain the parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>. After having defined the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> we simply need to
 write</p>
 <div class="cell docutils container">
@@ -3849,9 +2565,9 @@ write</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="adding-error-analysis-and-training-set-up">
-<h2>Adding error analysis and training set up<a class="headerlink" href="#adding-error-analysis-and-training-set-up" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="adding-error-analysis-and-training-set-up">
+<h2>Adding error analysis and training set up<a class="headerlink" href="#adding-error-analysis-and-training-set-up" title="Permalink to this heading">#</a></h2>
 <p>We can easily test our fit by computing the <span class="math notranslate nohighlight">\(R2\)</span> score that we discussed in connection with the functionality of <strong>Scikit-Learn</strong> in the introductory slides.
 Since we are not using <strong>Scikit-Learn</strong> here we can define our own <span class="math notranslate nohighlight">\(R2\)</span> function as</p>
 <div class="cell docutils container">
@@ -3892,9 +2608,9 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="the-chi-2-function">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#the-chi-2-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-chi-2-function">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#the-chi-2-function" title="Permalink to this heading">#</a></h2>
 <p>Normally, the response (dependent or outcome) variable <span class="math notranslate nohighlight">\(y_i\)</span> is the
 outcome of a numerical experiment or another type of experiment and is
 thus only an approximation to the true value. It is then always
@@ -3910,9 +2626,9 @@ as</p>
 \chi^2(\boldsymbol{\beta})=\frac{1}{n}\sum_{i=0}^{n-1}\frac{\left(y_i-\tilde{y}_i\right)^2}{\sigma_i^2}=\frac{1}{n}\left\{\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)^T\frac{1}{\boldsymbol{\Sigma^2}}\left(\boldsymbol{y}-\boldsymbol{\tilde{y}}\right)\right\},
 \]</div>
 <p>where the matrix <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> is a diagonal matrix with <span class="math notranslate nohighlight">\(\sigma_i\)</span> as matrix elements.</p>
-</div>
-<div class="section" id="id4">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id4" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id4">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id4" title="Permalink to this heading">#</a></h2>
 <p>In order to find the parameters <span class="math notranslate nohighlight">\(\beta_i\)</span> we will then minimize the spread of <span class="math notranslate nohighlight">\(\chi^2(\boldsymbol{\beta})\)</span> by requiring</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3929,9 +2645,9 @@ as</p>
 \frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = 0 = \boldsymbol{A}^T\left( \boldsymbol{b}-\boldsymbol{A}\boldsymbol{\beta}\right).
 \]</div>
 <p>where we have defined the matrix <span class="math notranslate nohighlight">\(\boldsymbol{A} =\boldsymbol{X}/\boldsymbol{\Sigma}\)</span> with matrix elements <span class="math notranslate nohighlight">\(a_{ij} = x_{ij}/\sigma_i\)</span> and the vector <span class="math notranslate nohighlight">\(\boldsymbol{b}\)</span> with elements <span class="math notranslate nohighlight">\(b_i = y_i/\sigma_i\)</span>.</p>
-</div>
-<div class="section" id="id5">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id5" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id5">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id5" title="Permalink to this heading">#</a></h2>
 <p>We can rewrite</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3947,9 +2663,9 @@ as</p>
 \[
 \boldsymbol{\beta} =\left(\boldsymbol{A}^T\boldsymbol{A}\right)^{-1}\boldsymbol{A}^T\boldsymbol{b}.
 \]</div>
-</div>
-<div class="section" id="id6">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id6" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id6">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id6" title="Permalink to this heading">#</a></h2>
 <p>If we then introduce the matrix</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3970,9 +2686,9 @@ as</p>
 \[
 \sigma^2(\beta_j) = \left(\sum_{k=0}^{p-1}h_{jk}\sum_{i=0}^{n-1}a_{ik}\right)\left(\sum_{l=0}^{p-1}h_{jl}\sum_{m=0}^{n-1}a_{ml}\right) = h_{jj}!
 \]</div>
-</div>
-<div class="section" id="id7">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id7" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id7">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id7" title="Permalink to this heading">#</a></h2>
 <p>The first step here is to approximate the function <span class="math notranslate nohighlight">\(y\)</span> with a first-order polynomial, that is we write</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3988,9 +2704,9 @@ y=y(x) \rightarrow y(x_i) \approx \beta_0+\beta_1 x_i.
 \[
 \frac{\partial \chi^2(\boldsymbol{\beta})}{\partial \beta_1} = -\frac{2}{n}\left[ \sum_{i=0}^{n-1}x_i\left(\frac{y_i-\beta_0-\beta_1x_{i}}{\sigma_i^2}\right)\right]=0.
 \]</div>
-</div>
-<div class="section" id="id8">
-<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id8" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id8">
+<h2>The <span class="math notranslate nohighlight">\(\chi^2\)</span> function<a class="headerlink" href="#id8" title="Permalink to this heading">#</a></h2>
 <p>For a linear fit (a first-order polynomial) we don’t need to invert a matrix!!<br />
 Defining</p>
 <div class="math notranslate nohighlight">
@@ -4026,9 +2742,9 @@ Defining</p>
 often from both being underdetermined and overdetermined in the
 unknown coefficients <span class="math notranslate nohighlight">\(\beta_i\)</span>.  A better approach is to use the
 Singular Value Decomposition (SVD) method discussed next week.</p>
-</div>
-<div class="section" id="fitting-an-equation-of-state-for-dense-nuclear-matter">
-<h2>Fitting an Equation of State for Dense Nuclear Matter<a class="headerlink" href="#fitting-an-equation-of-state-for-dense-nuclear-matter" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="fitting-an-equation-of-state-for-dense-nuclear-matter">
+<h2>Fitting an Equation of State for Dense Nuclear Matter<a class="headerlink" href="#fitting-an-equation-of-state-for-dense-nuclear-matter" title="Permalink to this heading">#</a></h2>
 <p>Before we continue, let us introduce yet another example. We are going to fit the
 nuclear equation of state using results from many-body calculations.
 The equation of state we have made available here, as function of
@@ -4043,9 +2759,9 @@ before, with the same initializations and declarations. We use also
 instead of our own matrix inversion implementation. Furthermore, we
 sneak in <strong>Ridge</strong> regression (to be discussed below) which includes a
 hyperparameter <span class="math notranslate nohighlight">\(\lambda\)</span>, also to be explained below.</p>
-</div>
-<div class="section" id="the-code">
-<h2>The code<a class="headerlink" href="#the-code" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-code">
+<h2>The code<a class="headerlink" href="#the-code" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Common imports</span>
@@ -4142,9 +2858,9 @@ to the data.</p>
 <p>We note also that there is a small deviation between the
 standard OLS and the Ridge regression at higher densities. We discuss this in more detail
 below.</p>
-</div>
-<div class="section" id="splitting-our-data-in-training-and-test-data">
-<h2>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="splitting-our-data-in-training-and-test-data">
+<h2>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this heading">#</a></h2>
 <p>It is normal in essentially all Machine Learning studies to split the
 data in a training set and a test set (sometimes also an additional
 validation set).  <strong>Scikit-Learn</strong> has an own function for this. There
@@ -4225,13 +2941,13 @@ but now splitting the data into a training set and a test set.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="exercises">
-<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercises">
+<h2>Exercises<a class="headerlink" href="#exercises" title="Permalink to this heading">#</a></h2>
 <p>Here are three possible exercises for week 34</p>
-</div>
-<div class="section" id="exercise-1-setting-up-various-python-environments">
-<h2>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-1-setting-up-various-python-environments">
+<h2>Exercise 1: Setting up various Python environments<a class="headerlink" href="#exercise-1-setting-up-various-python-environments" title="Permalink to this heading">#</a></h2>
 <p>The first exercise here is of a mere technical art. We want you to have</p>
 <ul class="simple">
 <li><p>git as a version control software and to establish a user account on a provider like GitHub. Other providers like GitLab etc are equally fine. You can also use the University of Oslo <a class="reference external" href="https://www.uio.no/tjenester/it/maskin/filer/versjonskontroll/github.html">GitHub facilities</a>.</p></li>
@@ -4247,7 +2963,7 @@ on Python.</p>
 <p>If you have Python installed (we recommend Python3) and you feel
 pretty familiar with installing different packages, we recommend that
 you install the following Python packages via <strong>pip</strong> as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>pip install numpy scipy matplotlib ipython scikit-learn sympy pandas pillow</p></li>
 </ol>
 <p>For <strong>Tensorflow</strong>, we recommend following the instructions in the text of
@@ -4257,12 +2973,12 @@ you install the following Python packages via <strong>pip</strong> as</p>
 <p>For OSX users we recommend, after having installed Xcode, to
 install <strong>brew</strong>. Brew allows for a seamless installation of additional
 software via for example</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>brew install python3</p></li>
 </ol>
 <p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
 you can use <strong>pip</strong> as well and simply install Python as</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>sudo apt-get install python3  (or python for Python2.7)</p></li>
 </ol>
 <p>If you don’t want to perform these operations separately and venture
@@ -4285,9 +3001,9 @@ distribution for scientific and analytic computing distribution and
 analysis environment, available for free and under a commercial
 license.</p>
 <p>We recommend using <strong>Anaconda</strong> if you are not too familiar with setting paths in a terminal environment.</p>
-</div>
-<div class="section" id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
-<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-2-making-your-own-data-and-exploring-scikit-learn">
+<h2>Exercise 2: making your own data and exploring scikit-learn<a class="headerlink" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>We will generate our own dataset for a function <span class="math notranslate nohighlight">\(y(x)\)</span> where <span class="math notranslate nohighlight">\(x \in [0,1]\)</span> and defined by random numbers computed with the uniform distribution. The function <span class="math notranslate nohighlight">\(y\)</span> is a quadratic polynomial in <span class="math notranslate nohighlight">\(x\)</span> with added stochastic noise according to the normal distribution <span class="math notranslate nohighlight">\(\cal {N}(0,1)\)</span>.
 The following simple Python instructions define our <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> values (with 100 data points).</p>
 <div class="cell docutils container">
@@ -4298,7 +3014,7 @@ The following simple Python instructions define our <span class="math notranslat
 </div>
 </div>
 </div>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Write your own code (following the examples under the <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter1.html">regression notes</a>) for computing the parametrization of the data set fitting a second-order polynomial.</p></li>
 <li><p>Use thereafter <strong>scikit-learn</strong> (see again the examples in the regression slides) and compare with your own code.</p></li>
 <li><p>Using scikit-learn, compute also the mean square error, a risk metric corresponding to the expected value of the squared (quadratic) error defined as</p></li>
@@ -4321,9 +3037,9 @@ R^2(\boldsymbol{y}, \tilde{\boldsymbol{y}}) = 1 - \frac{\sum_{i=0}^{n - 1} (y_i
 \]</div>
 <p>You can use the functionality included in scikit-learn. If you feel for it, you can use your own program and define functions which compute the above two functions.
 Discuss the meaning of these results. Try also to vary the coefficient in front of the added stochastic noise term and discuss the quality of the fits.</p>
-</div>
-<div class="section" id="exercise-3-split-data-in-test-and-training-data">
-<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="exercise-3-split-data-in-test-and-training-data">
+<h2>Exercise 3: Split data in test and training data<a class="headerlink" href="#exercise-3-split-data-in-test-and-training-data" title="Permalink to this heading">#</a></h2>
 <p>In this exercise we want you to to compute the MSE for the training
 data and the test data as function of the complexity of a polynomial,
 that is the degree of a given polynomial.</p>
@@ -4348,8 +3064,8 @@ Write thereafter (using either <strong>scikit-learn</strong> or your matrix inve
 and perform an ordinary least squares fitting and compute the mean squared error for the training data and the test data. These calculations should apply to a model given by a fifth-order polynomial.</p>
 <p><strong>c)</strong>
 Add now a model which allows you to make polynomials up to degree <span class="math notranslate nohighlight">\(15\)</span>.  Perform a standard OLS fitting of the training data and compute the MSE for the training and test data and plot both test and training data MSE as functions of the polynomial degree. Compare what you see with Figure 2.11 of Hastie et al. Comment your results. For which polynomial degree do you find an optimal MSE (smallest value)?</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -4363,7 +3079,7 @@ Add now a model which allows you to make polynomials up to degree <span class="m
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -4371,44 +3087,175 @@ Add now a model which allows you to make polynomials up to degree <span class="m
     </script>
     <script>kernelName = 'python3'</script>
 
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+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#overview-of-first-week">Overview of first week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#schedule-first-week">Schedule first week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lectures-and-computerlab">Lectures and ComputerLab</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#communication-channels">Communication channels</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#course-format">Course Format</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#teachers">Teachers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deadlines-for-projects-tentative">Deadlines for projects (tentative)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#grading">Grading</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-material">Reading material</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#textbooks">Textbooks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-suggestions-week-34">Reading suggestions week 34</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites">Prerequisites</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">Topics covered in this course: Statistical analysis and optimization of data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#statistical-analysis-and-optimization-of-data">Statistical analysis and optimization of data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#machine-learning">Machine Learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extremely-useful-tools-strongly-recommended">Extremely useful tools, strongly recommended</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio">Other courses on Data science and Machine Learning  at UiO</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-courses-on-data-science-and-machine-learning-at-uio-contn">Other courses on Data science and Machine Learning  at UiO, contn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-outcomes">Learning outcomes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ai-ml-and-some-statements-you-may-have-heard-and-what-do-they-mean">AI/ML and some statements you may have heard (and what do they mean?)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-machine-learning">What is Machine Learning?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#types-of-machine-learning">Types of Machine Learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#essential-elements-of-ml">Essential elements of ML</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#an-optimization-minimization-problem">An optimization/minimization problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-frequentist-approach-to-data-analysis">A Frequentist approach to data analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model">What is a good model?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-is-a-good-model-can-we-define-it">What is a good model? Can we define it?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#software-and-needed-installations">Software and needed installations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#python-installers">Python installers</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#useful-python-libraries">Useful Python libraries</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#installing-r-c-cython-or-julia">Installing R, C++, cython or Julia</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#installing-r-c-cython-numba-etc">Installing R, C++, cython, Numba etc</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-examples-and-important-matrix-and-vector-handling-packages">Numpy examples and Important Matrix and vector handling packages</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#numpy-and-arrays">Numpy and arrays</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#matrices-in-python">Matrices in Python</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-pandas">Meet the Pandas</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-linear-regression-model-using-scikit-learn">Simple linear regression model using <strong>scikit-learn</strong></a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies">To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#organizing-our-data">Organizing our data</a></li>
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#and-what-about-using-neural-networks">And what about using neural networks?</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-first-summary">A first summary</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family">Why Linear Regression (aka Ordinary Least Squares and family)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-overarching-aims">Regression analysis, overarching aims</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#regression-analysis-overarching-aims-ii">Regression analysis, overarching aims II</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples">Examples</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#general-linear-models-and-linear-algebra">General linear models and linear algebra</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem">Rewriting the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details">Rewriting the fitting procedure as a linear algebra problem, more details</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#generalizing-the-fitting-procedure-as-a-linear-algebra-problem">Generalizing the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Generalizing the fitting procedure as a linear algebra problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-our-parameters">Optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#our-model-for-the-nuclear-binding-energies">Our model for the nuclear binding energies</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimizing-our-parameters-more-details">Optimizing our parameters, more details</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">Some useful matrix and vector expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id3">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">Own code for Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">Adding error analysis and training set up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-chi-2-function">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id4">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id5">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id6">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id7">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id8">The <span class="math notranslate nohighlight">\(\chi^2\)</span> function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fitting-an-equation-of-state-for-dense-nuclear-matter">Fitting an Equation of State for Dense Nuclear Matter</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-code">The code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercises">Exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-1-setting-up-various-python-environments">Exercise 1: Setting up various Python environments</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-2-making-your-own-data-and-exploring-scikit-learn">Exercise 2: making your own data and exploring scikit-learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#exercise-3-split-data-in-test-and-training-data">Exercise 3: Split data in test and training data</a></li>
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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 </ul>
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- <span class="caption-text">
-  Dimensionality Reduction
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-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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-   Exercises week 34
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-   Week 34: Introduction to the course, Logistics and Practicalities
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-   Exercises week 35
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-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-35">
-   Plans for week 35
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#reading-recommendations">
-     Reading recommendations:
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+      
   </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">
-   Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations-for-ordinary-least-squares">
-   The equations for ordinary least squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cost-loss-function">
-   The cost/loss function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">
-   Some useful matrix and vector expressions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-jacobian">
-   The Jacobian
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#derivatives-example-1">
-   Derivatives, example 1
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-2">
-   Example 2
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-3">
-   Example 3
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-4">
-   Example 4
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-mean-squared-error-and-its-derivative">
-   The mean squared error and its derivative
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-useful-relations">
-   Other useful relations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-hessian-matrix">
-   Meet the Hessian Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-relevant-for-the-exercises">
-   Example relevant for the exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">
-   Own code for Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">
-   Adding error analysis and training set up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-complete-code-with-a-simple-data-set">
-   The complete code with a simple data set
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#making-your-own-test-train-splitting">
-   Making your own test-train splitting
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">
-   Reducing the number of degrees of freedom, overarching view
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#preprocessing-our-data">
-   Preprocessing our data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#functionality-in-scikit-learn">
-   Functionality in Scikit-Learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-preprocessing">
-   More preprocessing
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#frequently-used-scaling-functions">
-   Frequently used scaling functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-own-standard-scaling">
-   Example of own Standard scaling
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#min-max-scaling">
-   Min-Max Scaling
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">
-   Testing the Means Squared Error as function of Complexity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function">
-   More preprocessing examples, two-dimensional example, the Franke function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#to-think-about-first-part">
-   To think about, first part
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-thinking">
-   More thinking
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#still-thinking">
-   Still thinking
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically">
-   What does centering (subtracting the mean values) mean mathematically?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-manipulations">
-   Further Manipulations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wrapping-it-up">
-   Wrapping it up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-code-intercept-handling-first">
-   Linear Regression code, Intercept handling first
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-boston-housing-data-example">
-   The Boston housing data example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#housing-data-the-code">
-   Housing data, the code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-august-31">
-   Material for lecture Thursday, August 31
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">
-   Mathematical Interpretation of Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#residual-error">
-   Residual Error
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-case">
-   Simple case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-singular-value-decomposition">
-   The singular value decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-problems">
-   Linear Regression Problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fixing-the-singularity">
-   Fixing the singularity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basic-math-of-the-svd">
-   Basic math of the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-svd-a-fantastic-algorithm">
-   The SVD, a Fantastic Algorithm
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#economy-size-svd">
-   Economy-size SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#codes-for-the-svd">
-   Codes for the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#note-about-svd-calculations">
-   Note about SVD Calculations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">
-   Mathematics of the SVD and implications
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-matrix">
-   Example Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#setting-up-the-matrix-to-be-inverted">
-   Setting up the Matrix to be inverted
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">
-   Further properties (important for our analyses later)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-covariance-matrix">
-   Meet the Covariance Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
-   Introducing the Covariance and Correlation functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#covariance-and-correlation-matrix">
-   Covariance and Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-function-and-design-feature-matrix">
-   Correlation Function and Design/Feature Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#covariance-matrix-examples">
-   Covariance Matrix Examples
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix">
-   Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix-with-pandas">
-   Correlation Matrix with Pandas
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix-with-pandas-and-the-franke-function">
-   Correlation Matrix with Pandas and the Franke function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-covariance-and-or-correlation-matrix">
-   Rewriting the Covariance and/or Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-with-the-svd">
-   Linking with the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-it-mean">
-   What does it mean?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">
-   And finally
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{X}\boldsymbol{X}^T\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-lasso-regression">
-   Ridge and LASSO Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">
-   Deriving the  Ridge Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpreting-the-ridge-results">
-   Interpreting the Ridge results
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-interpretations">
-   More interpretations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">
-   Deriving the  Lasso Regression Equations
-  </a>
- </li>
-</ul>
+</div>
 
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+<div id="jb-print-docs-body" class="onlyprint">
+    <h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
+            
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-35">Plans for week 35</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-recommendations">Reading recommendations:</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-for-ordinary-least-squares">The equations for ordinary least squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cost-loss-function">The cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">Some useful matrix and vector expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-jacobian">The Jacobian</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#derivatives-example-1">Derivatives, example 1</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-2">Example 2</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-3">Example 3</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-4">Example 4</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-mean-squared-error-and-its-derivative">The mean squared error and its derivative</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-useful-relations">Other useful relations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-hessian-matrix">Meet the Hessian Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-relevant-for-the-exercises">Example relevant for the exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">Own code for Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">Adding error analysis and training set up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-complete-code-with-a-simple-data-set">The complete code with a simple data set</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#making-your-own-test-train-splitting">Making your own test-train splitting</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">Reducing the number of degrees of freedom, overarching view</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#preprocessing-our-data">Preprocessing our data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#functionality-in-scikit-learn">Functionality in Scikit-Learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-preprocessing">More preprocessing</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#frequently-used-scaling-functions">Frequently used scaling functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-own-standard-scaling">Example of own Standard scaling</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#min-max-scaling">Min-Max Scaling</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">Testing the Means Squared Error as function of Complexity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function">More preprocessing examples, two-dimensional example, the Franke function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#to-think-about-first-part">To think about, first part</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-thinking">More thinking</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#still-thinking">Still thinking</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically">What does centering (subtracting the mean values) mean mathematically?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-manipulations">Further Manipulations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wrapping-it-up">Wrapping it up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-code-intercept-handling-first">Linear Regression code, Intercept handling first</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-boston-housing-data-example">The Boston housing data example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#housing-data-the-code">Housing data, the code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-august-31">Material for lecture Thursday, August 31</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">Mathematical Interpretation of Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#residual-error">Residual Error</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-case">Simple case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-singular-value-decomposition">The singular value decomposition</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-problems">Linear Regression Problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fixing-the-singularity">Fixing the singularity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-math-of-the-svd">Basic math of the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-svd-a-fantastic-algorithm">The SVD, a Fantastic Algorithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#economy-size-svd">Economy-size SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#codes-for-the-svd">Codes for the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#note-about-svd-calculations">Note about SVD Calculations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">Mathematics of the SVD and implications</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-matrix">Example Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#setting-up-the-matrix-to-be-inverted">Setting up the Matrix to be inverted</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">Further properties (important for our analyses later)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance-matrix">Meet the Covariance Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">Introducing the Covariance and Correlation functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#covariance-and-correlation-matrix">Covariance and Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-function-and-design-feature-matrix">Correlation Function and Design/Feature Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#covariance-matrix-examples">Covariance Matrix Examples</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix">Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix-with-pandas">Correlation Matrix with Pandas</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix-with-pandas-and-the-franke-function">Correlation Matrix with Pandas and the Franke function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-covariance-and-or-correlation-matrix">Rewriting the Covariance and/or Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-with-the-svd">Linking with the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-it-mean">What does it mean?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-lasso-regression">Ridge and LASSO Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">Deriving the  Ridge Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpreting-the-ridge-results">Interpreting the Ridge results</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-interpretations">More interpretations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">Deriving the  Lasso Regression Equations</a></li>
+</ul>
             </nav>
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-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-35">
-   Plans for week 35
-  </a>
-  <ul class="nav section-nav flex-column">
-   <li class="toc-h3 nav-item toc-entry">
-    <a class="reference internal nav-link" href="#reading-recommendations">
-     Reading recommendations:
-    </a>
-   </li>
-  </ul>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">
-   Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations-for-ordinary-least-squares">
-   The equations for ordinary least squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cost-loss-function">
-   The cost/loss function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">
-   Some useful matrix and vector expressions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-jacobian">
-   The Jacobian
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#derivatives-example-1">
-   Derivatives, example 1
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-2">
-   Example 2
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-3">
-   Example 3
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-4">
-   Example 4
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-mean-squared-error-and-its-derivative">
-   The mean squared error and its derivative
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-useful-relations">
-   Other useful relations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-hessian-matrix">
-   Meet the Hessian Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Interpretations and optimizing our parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-relevant-for-the-exercises">
-   Example relevant for the exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">
-   Own code for Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">
-   Adding error analysis and training set up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">
-   Splitting our Data in Training and Test data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-complete-code-with-a-simple-data-set">
-   The complete code with a simple data set
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#making-your-own-test-train-splitting">
-   Making your own test-train splitting
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">
-   Reducing the number of degrees of freedom, overarching view
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#preprocessing-our-data">
-   Preprocessing our data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#functionality-in-scikit-learn">
-   Functionality in Scikit-Learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-preprocessing">
-   More preprocessing
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#frequently-used-scaling-functions">
-   Frequently used scaling functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-own-standard-scaling">
-   Example of own Standard scaling
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#min-max-scaling">
-   Min-Max Scaling
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">
-   Testing the Means Squared Error as function of Complexity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function">
-   More preprocessing examples, two-dimensional example, the Franke function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#to-think-about-first-part">
-   To think about, first part
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-thinking">
-   More thinking
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#still-thinking">
-   Still thinking
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically">
-   What does centering (subtracting the mean values) mean mathematically?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-manipulations">
-   Further Manipulations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wrapping-it-up">
-   Wrapping it up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-code-intercept-handling-first">
-   Linear Regression code, Intercept handling first
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-boston-housing-data-example">
-   The Boston housing data example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#housing-data-the-code">
-   Housing data, the code
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-august-31">
-   Material for lecture Thursday, August 31
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">
-   Mathematical Interpretation of Ordinary Least Squares
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#residual-error">
-   Residual Error
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-case">
-   Simple case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-singular-value-decomposition">
-   The singular value decomposition
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-problems">
-   Linear Regression Problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#fixing-the-singularity">
-   Fixing the singularity
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basic-math-of-the-svd">
-   Basic math of the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-svd-a-fantastic-algorithm">
-   The SVD, a Fantastic Algorithm
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#economy-size-svd">
-   Economy-size SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#codes-for-the-svd">
-   Codes for the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#note-about-svd-calculations">
-   Note about SVD Calculations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">
-   Mathematics of the SVD and implications
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-matrix">
-   Example Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#setting-up-the-matrix-to-be-inverted">
-   Setting up the Matrix to be inverted
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">
-   Further properties (important for our analyses later)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#meet-the-covariance-matrix">
-   Meet the Covariance Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
-   Introducing the Covariance and Correlation functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#covariance-and-correlation-matrix">
-   Covariance and Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-function-and-design-feature-matrix">
-   Correlation Function and Design/Feature Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#covariance-matrix-examples">
-   Covariance Matrix Examples
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix">
-   Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix-with-pandas">
-   Correlation Matrix with Pandas
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#correlation-matrix-with-pandas-and-the-franke-function">
-   Correlation Matrix with Pandas and the Franke function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-covariance-and-or-correlation-matrix">
-   Rewriting the Covariance and/or Correlation Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-with-the-svd">
-   Linking with the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-it-mean">
-   What does it mean?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">
-   And finally
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{X}\boldsymbol{X}^T\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-lasso-regression">
-   Ridge and LASSO Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">
-   Deriving the  Ridge Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpreting-the-ridge-results">
-   Interpreting the Ridge results
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-interpretations">
-   More interpretations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">
-   Deriving the  Lasso Regression Equations
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html week35.do.txt --no_mako -->
-<!-- dom:TITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression --><div class="tex2jax_ignore mathjax_ignore section" id="week-35-from-ordinary-linear-regression-to-ridge-and-lasso-regression">
-<h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression<a class="headerlink" href="#week-35-from-ordinary-linear-regression-to-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression --><section class="tex2jax_ignore mathjax_ignore" id="week-35-from-ordinary-linear-regression-to-ridge-and-lasso-regression">
+<h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression<a class="headerlink" href="#week-35-from-ordinary-linear-regression-to-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h1>
 <p><strong>Morten Hjorth-Jensen</strong>, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</p>
 <p>Date: <strong>August 28-September 1</strong></p>
-<div class="section" id="plans-for-week-35">
-<h2>Plans for week 35<a class="headerlink" href="#plans-for-week-35" title="Permalink to this headline">¶</a></h2>
+<section id="plans-for-week-35">
+<h2>Plans for week 35<a class="headerlink" href="#plans-for-week-35" title="Permalink to this heading">#</a></h2>
 <p>The main topics are:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Brief repetition from last week</p></li>
 <li><p>Derivation of the equations for ordinary least squares</p></li>
 <li><p>Discussion on how to prepare data and examples of applications of linear regression</p></li>
@@ -1168,17 +506,17 @@ doconce format html week35.do.txt --no_mako -->
 <li><p><a class="reference external" href="https://youtu.be/qBNm-HGSxL4">Video of lecture</a></p></li>
 <li><p><a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesAug31.pdf">Whiteboard notes</a></p></li>
 </ol>
-<div class="section" id="reading-recommendations">
-<h3>Reading recommendations:<a class="headerlink" href="#reading-recommendations" title="Permalink to this headline">¶</a></h3>
-<ol class="simple">
+<section id="reading-recommendations">
+<h3>Reading recommendations:<a class="headerlink" href="#reading-recommendations" title="Permalink to this heading">#</a></h3>
+<ol class="arabic simple">
 <li><p>See lecture notes for week 35 at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/web/course.html">https://compphysics.github.io/MachineLearning/doc/web/course.html</a></p></li>
 <li><p>Goodfellow, Bengio and Courville, Deep Learning, chapter 2 on linear algebra and sections 3.1-3.10 on elements of statistics (background)</p></li>
 <li><p>Hastie, Tibshirani and Friedman, The elements of statistical learning, sections 3.1-3.4 (on relevance for the discussion of linear regression).</p></li>
 </ol>
-</div>
-</div>
-<div class="section" id="why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">
-<h2>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week<a class="headerlink" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" title="Permalink to this headline">¶</a></h2>
+</section>
+</section>
+<section id="why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">
+<h2>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week<a class="headerlink" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" title="Permalink to this heading">#</a></h2>
 <p>We need first a reminder from last week about linear regression.</p>
 <p>Fitting a continuous function with linear parameterization in terms of the parameters  <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.</p>
 <ul class="simple">
@@ -1194,9 +532,9 @@ doconce format html week35.do.txt --no_mako -->
 </ul>
 <p>For more discussions of Ridge and Lasso regression, <a class="reference external" href="https://arxiv.org/abs/1509.09169">Wessel van Wieringen’s</a> article is highly recommended.
 Similarly, <a class="reference external" href="https://arxiv.org/abs/1803.08823">Mehta et al’s article</a> is also recommended.</p>
-</div>
-<div class="section" id="the-equations-for-ordinary-least-squares">
-<h2>The equations for ordinary least squares<a class="headerlink" href="#the-equations-for-ordinary-least-squares" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-equations-for-ordinary-least-squares">
+<h2>The equations for ordinary least squares<a class="headerlink" href="#the-equations-for-ordinary-least-squares" title="Permalink to this heading">#</a></h2>
 <p>Our data which we want to apply a machine learning method on, consist
 of a set of inputs <span class="math notranslate nohighlight">\(\boldsymbol{x}^T=[x_0,x_1,x_2,\dots,x_{n-1}]\)</span> and the
 outputs we want to model <span class="math notranslate nohighlight">\(\boldsymbol{y}^T=[y_0,y_1,y_2,\dots,y_{n-1}]\)</span>.
@@ -1229,9 +567,9 @@ the approximation <span class="math notranslate nohighlight">\(\boldsymbol{\tild
 gives a measure of the spread between the values <span class="math notranslate nohighlight">\(y_i\)</span> (which
 represent the output values we want to reproduce) and the parametrized
 values <span class="math notranslate nohighlight">\(\tilde{y}_i\)</span>, namely the so-called cost/loss function.</p>
-</div>
-<div class="section" id="the-cost-loss-function">
-<h2>The cost/loss function<a class="headerlink" href="#the-cost-loss-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-cost-loss-function">
+<h2>The cost/loss function<a class="headerlink" href="#the-cost-loss-function" title="Permalink to this heading">#</a></h2>
 <p>We used the mean squared error to define the way we measure the quality of our model</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1250,9 +588,9 @@ the function <span class="math notranslate nohighlight">\(C\)</span> as</p>
 C(\boldsymbol{\beta})=\frac{1}{2n}\sum_{i=0}^{n-1}\left(y_i-\tilde{y}_i\right)^2,
 \]</div>
 <p>since when taking the first derivative with respect to the unknown parameters <span class="math notranslate nohighlight">\(\beta\)</span>, the factor of <span class="math notranslate nohighlight">\(2\)</span> cancels out.</p>
-</div>
-<div class="section" id="interpretations-and-optimizing-our-parameters">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#interpretations-and-optimizing-our-parameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpretations-and-optimizing-our-parameters">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#interpretations-and-optimizing-our-parameters" title="Permalink to this heading">#</a></h2>
 <p>The function</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1293,9 +631,9 @@ will treat <span class="math notranslate nohighlight">\(y_i\)</span> as our exac
 \[
 \frac{\partial C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T} = 0 = \boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right).
 \]</div>
-</div>
-<div class="section" id="id1">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>We can rewrite, see the derivations below,</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1321,9 +659,9 @@ regression or support vector machines, exhibit dimensionalities which
 allow for the usage of direct linear algebra methods such as <strong>LU</strong> decomposition or <strong>Singular Value Decomposition</strong> (SVD) for finding the inverse of the matrix
 <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>.  This is discussed on Thursday this week.</p>
 <p><strong>Small question</strong>: Do you think the example we have at hand here (the nuclear binding energies) can lead to problems in inverting the matrix  <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>? What kind of problems can we expect?</p>
-</div>
-<div class="section" id="some-useful-matrix-and-vector-expressions">
-<h2>Some useful matrix and vector expressions<a class="headerlink" href="#some-useful-matrix-and-vector-expressions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="some-useful-matrix-and-vector-expressions">
+<h2>Some useful matrix and vector expressions<a class="headerlink" href="#some-useful-matrix-and-vector-expressions" title="Permalink to this heading">#</a></h2>
 <p>The following matrix and vector relation will be useful here and for
 the rest of the course. Vectors are always written as boldfaced lower
 case letters and matrices as upper case boldfaced letters.  In the
@@ -1342,9 +680,9 @@ given function <span class="math notranslate nohighlight">\(f\)</span></p>
 \[
 \boldsymbol{y}=f(\boldsymbol{x}).
 \]</div>
-</div>
-<div class="section" id="the-jacobian">
-<h2>The Jacobian<a class="headerlink" href="#the-jacobian" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-jacobian">
+<h2>The Jacobian<a class="headerlink" href="#the-jacobian" title="Permalink to this heading">#</a></h2>
 <p>We define the partial derivatives of the various components of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> as functions of <span class="math notranslate nohighlight">\(x_i\)</span> in terms of the so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant">Jacobian matrix</a></p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -1362,9 +700,9 @@ on the other hand <span class="math notranslate nohighlight">\(\boldsymbol{y}\)<
 determinant. Both the matrix and (if <span class="math notranslate nohighlight">\(m=n\)</span>) the determinant are
 often referred to simply as the Jacobian. The Jacobian matrix represents the differential of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> at every point where the
 vector is differentiable.</p>
-</div>
-<div class="section" id="derivatives-example-1">
-<h2>Derivatives, example 1<a class="headerlink" href="#derivatives-example-1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="derivatives-example-1">
+<h2>Derivatives, example 1<a class="headerlink" href="#derivatives-example-1" title="Permalink to this heading">#</a></h2>
 <p>Let now <span class="math notranslate nohighlight">\(\boldsymbol{y}=\boldsymbol{A}\boldsymbol{x}\)</span>, where <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> is an <span class="math notranslate nohighlight">\(m\times n\)</span> matrix and the matrix does not depend on <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span>. If we write out the vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> compoment by component we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1381,9 +719,9 @@ It follows that the partial derivatives of <span class="math notranslate nohighl
 \[
 \frac{\partial \boldsymbol{y} }{\partial \boldsymbol{x}}= \boldsymbol{A}.
 \]</div>
-</div>
-<div class="section" id="example-2">
-<h2>Example 2<a class="headerlink" href="#example-2" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-2">
+<h2>Example 2<a class="headerlink" href="#example-2" title="Permalink to this heading">#</a></h2>
 <p>We define a scalar (our cost/loss functions are in general also scalars,
 just think of the mean squared error) as the result of some matrix vector
 multiplications</p>
@@ -1409,9 +747,9 @@ In order to find the derivative of <span class="math notranslate nohighlight">\(
 \[
 \frac{\partial \alpha}{\partial \boldsymbol{y}} = \boldsymbol{z}^T=\boldsymbol{x}^T\boldsymbol{A}^T.
 \]</div>
-</div>
-<div class="section" id="example-3">
-<h2>Example 3<a class="headerlink" href="#example-3" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-3">
+<h2>Example 3<a class="headerlink" href="#example-3" title="Permalink to this heading">#</a></h2>
 <p>We start with a new scalar but where now the vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> is
 replaced by a vector <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> and the matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> is a square
 matrix with dimension <span class="math notranslate nohighlight">\(n\times n\)</span>.</p>
@@ -1440,9 +778,9 @@ matrix with dimension <span class="math notranslate nohighlight">\(n\times n\)</
 \[
 \frac{\partial \alpha}{\partial \boldsymbol{x}}  = 2\boldsymbol{x}^T\boldsymbol{A}.
 \]</div>
-</div>
-<div class="section" id="example-4">
-<h2>Example 4<a class="headerlink" href="#example-4" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-4">
+<h2>Example 4<a class="headerlink" href="#example-4" title="Permalink to this heading">#</a></h2>
 <p>We let the scalar <span class="math notranslate nohighlight">\(\alpha\)</span> be defined by</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1473,9 +811,9 @@ inner product that defines <span class="math notranslate nohighlight">\(\alpha\)
 \[
 \frac{\partial \alpha}{\partial \boldsymbol{z}}  = 2\boldsymbol{x}^T\frac{\partial \boldsymbol{x}}{\partial \boldsymbol{z}}.
 \]</div>
-</div>
-<div class="section" id="the-mean-squared-error-and-its-derivative">
-<h2>The mean squared error and its derivative<a class="headerlink" href="#the-mean-squared-error-and-its-derivative" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-mean-squared-error-and-its-derivative">
+<h2>The mean squared error and its derivative<a class="headerlink" href="#the-mean-squared-error-and-its-derivative" title="Permalink to this heading">#</a></h2>
 <p>We defined earlier a possible cost function using the mean squared error</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1518,9 +856,9 @@ C(\boldsymbol{\beta})=\frac{1}{n}\boldsymbol{w}^T\boldsymbol{w},
 \[
 \frac{\partial C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T}=-\frac{2}{n}\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right).
 \]</div>
-</div>
-<div class="section" id="other-useful-relations">
-<h2>Other useful relations<a class="headerlink" href="#other-useful-relations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-useful-relations">
+<h2>Other useful relations<a class="headerlink" href="#other-useful-relations" title="Permalink to this heading">#</a></h2>
 <p>We list here some other useful relations we may encounter (recall that vectors are defined by boldfaced low-key letters)</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1534,9 +872,9 @@ C(\boldsymbol{\beta})=\frac{1}{n}\boldsymbol{w}^T\boldsymbol{w},
 \[
 \frac{\partial \log{\vert\boldsymbol{A}\vert}}{\partial \boldsymbol{A}} = (\boldsymbol{A}^{-1})^T.
 \]</div>
-</div>
-<div class="section" id="meet-the-hessian-matrix">
-<h2>Meet the Hessian Matrix<a class="headerlink" href="#meet-the-hessian-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="meet-the-hessian-matrix">
+<h2>Meet the Hessian Matrix<a class="headerlink" href="#meet-the-hessian-matrix" title="Permalink to this heading">#</a></h2>
 <p>A very important matrix we will meet again and again in machine
 learning is the Hessian.  It is given by the second derivative of the
 cost function with respect to the parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>. Using the above
@@ -1559,9 +897,9 @@ important role in optmization algorithms and Principal Component
 Analysis as a way to reduce the dimensionality of a machine learning/data analysis
 problem.</p>
 <p><strong>Linear algebra question:</strong>  Can we use the Hessian matrix to say something about properties of the cost function (our optmization  problem)? (hint: think about convex or concave problems and how to relate these to a matrix!).</p>
-</div>
-<div class="section" id="id2">
-<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id2">
+<h2>Interpretations and optimizing our parameters<a class="headerlink" href="#id2" title="Permalink to this heading">#</a></h2>
 <p>The residuals <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> are in turn given by</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1578,9 +916,9 @@ problem.</p>
 \boldsymbol{X}^T\boldsymbol{\epsilon}=\boldsymbol{X}^T\left( \boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta}\right)= 0,
 \]</div>
 <p>meaning that the solution for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> is the one which minimizes the residuals.</p>
-</div>
-<div class="section" id="example-relevant-for-the-exercises">
-<h2>Example relevant for the exercises<a class="headerlink" href="#example-relevant-for-the-exercises" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-relevant-for-the-exercises">
+<h2>Example relevant for the exercises<a class="headerlink" href="#example-relevant-for-the-exercises" title="Permalink to this heading">#</a></h2>
 <p>In order to understand the relation among the predictors <span class="math notranslate nohighlight">\(p\)</span>, the set of data <span class="math notranslate nohighlight">\(n\)</span> and the target (outcome, output etc) <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span>,
 we condiser a simple polynomial fit.
 We assume our data can represented by a fourth-order polynomial. For the <span class="math notranslate nohighlight">\(i\)</span>th component we have</p>
@@ -1590,9 +928,9 @@ We assume our data can represented by a fourth-order polynomial. For the <span c
 \]</div>
 <p>we have five predictors/features. The first is the intercept <span class="math notranslate nohighlight">\(\beta_0\)</span>. The other terms are <span class="math notranslate nohighlight">\(\beta_i\)</span> with <span class="math notranslate nohighlight">\(i=1,2,3,4\)</span>. Furthermore we have <span class="math notranslate nohighlight">\(n\)</span> entries for each predictor. It means that our design matrix is an
 <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="own-code-for-ordinary-least-squares">
-<h2>Own code for Ordinary Least Squares<a class="headerlink" href="#own-code-for-ordinary-least-squares" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="own-code-for-ordinary-least-squares">
+<h2>Own code for Ordinary Least Squares<a class="headerlink" href="#own-code-for-ordinary-least-squares" title="Permalink to this heading">#</a></h2>
 <p>It is rather straightforward to implement the matrix inversion and obtain the parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>. After having defined the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> and the outputs <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> we have</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1625,9 +963,9 @@ We assume our data can represented by a fourth-order polynomial. For the <span c
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="adding-error-analysis-and-training-set-up">
-<h2>Adding error analysis and training set up<a class="headerlink" href="#adding-error-analysis-and-training-set-up" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="adding-error-analysis-and-training-set-up">
+<h2>Adding error analysis and training set up<a class="headerlink" href="#adding-error-analysis-and-training-set-up" title="Permalink to this heading">#</a></h2>
 <p>We can easily test our fit by computing the <span class="math notranslate nohighlight">\(R2\)</span> score that we discussed in connection with the functionality of <strong>Scikit-Learn</strong> in the introductory slides.
 Since we are not using <strong>Scikit-Learn</strong> here we can define our own <span class="math notranslate nohighlight">\(R2\)</span> function as</p>
 <div class="cell docutils container">
@@ -1646,7 +984,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9952714635635723
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.9947950318641428
 </pre></div>
 </div>
 </div>
@@ -1663,7 +1001,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.009039197557276654
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.010272505059533654
 </pre></div>
 </div>
 </div>
@@ -1678,38 +1016,30 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[6.11430166e-02 7.59428035e-03 7.64295978e-03 5.34442654e-02
- 2.53861506e-02 7.46543658e-02 2.79339933e-02 1.32946226e-02
- 3.80320028e-03 2.40474117e-02 4.36028477e-02 3.24382528e-02
- 1.26022420e-02 5.06848116e-03 1.96793569e-02 1.04826413e-04
- 9.25580178e-03 1.80413812e-02 1.22519792e-02 1.01505087e-02
- 2.67180442e-02 6.71316703e-02 7.68415876e-03 3.33174939e-02
- 1.43570786e-02 8.43459933e-03 4.11046407e-03 9.10453697e-04
- 4.33142087e-03 7.64507671e-02 2.19696497e-02 1.18460525e-02
- 4.35665906e-02 3.62818572e-02 1.61018347e-03 3.78738205e-02
- 4.57031517e-03 3.11279984e-02 1.07745809e-02 7.09848429e-03
- 2.30006341e-03 4.62535124e-02 6.70493970e-02 6.26624267e-03
- 4.23399553e-02 1.88690267e-02 7.46184816e-03 1.75934097e-02
- 3.60820168e-02 1.09322328e-02 3.16749353e-02 2.30626515e-02
- 5.76196895e-04 1.51000420e-02 1.95456434e-03 1.22138768e-02
- 2.52945186e-03 2.12804129e-03 3.32695433e-03 1.90886410e-02
- 1.84291049e-02 1.78104004e-02 6.34498455e-02 1.50032818e-02
- 3.43525003e-02 1.52033394e-03 3.95921014e-02 7.67148008e-02
- 2.40893740e-02 6.75638425e-02 1.22105472e-02 7.72706640e-03
- 3.00721135e-02 8.77081499e-02 1.40684484e-02 4.57081718e-02
- 3.51190686e-02 7.42092776e-02 4.03105744e-02 1.08994018e-02
- 1.37071826e-02 3.69106251e-02 1.94966662e-03 1.71112140e-02
- 3.12669602e-03 3.01610677e-02 1.72139847e-02 2.75703556e-02
- 2.23333773e-02 2.76892410e-03 8.05886306e-02 1.15545946e-01
- 4.88029792e-02 4.59648068e-02 1.98750794e-02 2.69178261e-03
- 1.07925220e-02 1.13151043e-03 5.00620642e-03 3.69871367e-03]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.01027068 0.05313438 0.04538489 0.01836177 0.02080937 0.01800647
+ 0.01875198 0.00467902 0.00753502 0.02005707 0.00232645 0.01531078
+ 0.03829802 0.00785147 0.04770861 0.04729106 0.01202626 0.05597075
+ 0.00759075 0.01536802 0.02241641 0.00274849 0.0097933  0.01440849
+ 0.05803407 0.03087398 0.0131244  0.0291341  0.03955471 0.04581495
+ 0.0096887  0.02838502 0.00331854 0.00917575 0.02232857 0.01026639
+ 0.01719879 0.04680163 0.03691034 0.05657464 0.01277062 0.02319192
+ 0.03410211 0.0114457  0.03498633 0.0345711  0.00908896 0.05115386
+ 0.01253218 0.00362237 0.03169296 0.06165423 0.0072295  0.00869224
+ 0.03849245 0.05269447 0.01539813 0.04350167 0.05006792 0.00862396
+ 0.02270315 0.0141736  0.00537237 0.02931659 0.02817395 0.025761
+ 0.05417012 0.01227    0.00370021 0.02342548 0.00361816 0.0400444
+ 0.02198873 0.00914991 0.01461902 0.04424899 0.00910613 0.0099676
+ 0.02701179 0.03971778 0.04524779 0.05279081 0.01519497 0.00134839
+ 0.04233422 0.01660753 0.05817493 0.0167955  0.01299388 0.00265975
+ 0.02189559 0.04726103 0.01705804 0.10695767 0.06613465 0.04663936
+ 0.00250484 0.02495131 0.01816794 0.01905766]
 </pre></div>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="splitting-our-data-in-training-and-test-data">
-<h2>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="splitting-our-data-in-training-and-test-data">
+<h2>Splitting our Data in Training and Test data<a class="headerlink" href="#splitting-our-data-in-training-and-test-data" title="Permalink to this heading">#</a></h2>
 <p>It is normal in essentially all Machine Learning studies to split the
 data in a training set and a test set (sometimes also an additional
 validation set).  <strong>Scikit-Learn</strong> has an own function for this. There
@@ -1720,9 +1050,9 @@ postpone a discussion of this splitting to the end of these notes and
 our discussion of the so-called <strong>bias-variance</strong> tradeoff. Here we
 limit ourselves to repeat the above equation of state fitting example
 but now splitting the data into a training set and a test set.</p>
-</div>
-<div class="section" id="the-complete-code-with-a-simple-data-set">
-<h2>The complete code with a simple data set<a class="headerlink" href="#the-complete-code-with-a-simple-data-set" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-complete-code-with-a-simple-data-set">
+<h2>The complete code with a simple data set<a class="headerlink" href="#the-complete-code-with-a-simple-data-set" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
@@ -1771,22 +1101,60 @@ but now splitting the data into a training set and a test set.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[ 2.04038959 -0.81343612  7.94304103 -3.83770135  1.70073443]
-Training R2
-0.9954441212986554
-Training MSE
-0.008653750612762521
-Test R2
-0.99255249100346
-Test MSE
-0.016970019460234076
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">7</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">os</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="making-your-own-test-train-splitting">
-<h2>Making your own test-train splitting<a class="headerlink" href="#making-your-own-test-train-splitting" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="making-your-own-test-train-splitting">
+<h2>Making your own test-train splitting<a class="headerlink" href="#making-your-own-test-train-splitting" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># equivalently in numpy</span>
@@ -1810,9 +1178,9 @@ Test MSE
 <p>But since <strong>scikit-learn</strong> has its own function for doing this and since
 it interfaces easily with <strong>tensorflow</strong> and other libraries, we
 normally recommend using the latter functionality.</p>
-</div>
-<div class="section" id="reducing-the-number-of-degrees-of-freedom-overarching-view">
-<h2>Reducing the number of degrees of freedom, overarching view<a class="headerlink" href="#reducing-the-number-of-degrees-of-freedom-overarching-view" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="reducing-the-number-of-degrees-of-freedom-overarching-view">
+<h2>Reducing the number of degrees of freedom, overarching view<a class="headerlink" href="#reducing-the-number-of-degrees-of-freedom-overarching-view" title="Permalink to this heading">#</a></h2>
 <p>Many Machine Learning problems involve thousands or even millions of
 features for each training instance. Not only does this make training
 extremely slow, it can also make it much harder to find a good
@@ -1829,9 +1197,9 @@ subspace</a> to a set of of
 data points in a high-dimensional space. With its family of methods it
 is one of the most used tools in data modeling, compression and
 visualization.</p>
-</div>
-<div class="section" id="preprocessing-our-data">
-<h2>Preprocessing our data<a class="headerlink" href="#preprocessing-our-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="preprocessing-our-data">
+<h2>Preprocessing our data<a class="headerlink" href="#preprocessing-our-data" title="Permalink to this heading">#</a></h2>
 <p>Before we proceed however, we will discuss how to preprocess our
 data. Till now and in connection with our previous examples we have
 not met so many cases where we are too sensitive to the scaling of our
@@ -1845,9 +1213,9 @@ features such as <strong>age</strong> in the range <span class="math notranslate
 Many machine learning methods sensitive to the scales of the features and may perform poorly if they
 are very different scales. Therefore, it is typical to scale
 the features in a way to avoid such outlier values.</p>
-</div>
-<div class="section" id="functionality-in-scikit-learn">
-<h2>Functionality in Scikit-Learn<a class="headerlink" href="#functionality-in-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="functionality-in-scikit-learn">
+<h2>Functionality in Scikit-Learn<a class="headerlink" href="#functionality-in-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p><strong>Scikit-Learn</strong> has several functions which allow us to rescale the
 data, normally resulting in much better results in terms of various
 accuracy scores.  The <strong>StandardScaler</strong> function in <strong>Scikit-Learn</strong>
@@ -1857,9 +1225,9 @@ matrix).  This scaling has the drawback that it does not ensure that
 we have a particular maximum or minimum in our data set. Another
 function included in <strong>Scikit-Learn</strong> is the <strong>MinMaxScaler</strong> which
 ensures that all features are exactly between <span class="math notranslate nohighlight">\(0\)</span> and <span class="math notranslate nohighlight">\(1\)</span>. The</p>
-</div>
-<div class="section" id="more-preprocessing">
-<h2>More preprocessing<a class="headerlink" href="#more-preprocessing" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-preprocessing">
+<h2>More preprocessing<a class="headerlink" href="#more-preprocessing" title="Permalink to this heading">#</a></h2>
 <p>The <strong>Normalizer</strong> scales each data
 point such that the feature vector has a euclidean length of one. In other words, it
 projects a data point on the circle (or sphere in the case of higher dimensions) with a
@@ -1875,9 +1243,9 @@ RobustScaler ignore data points that are very different from the rest
 (like measurement errors). These odd data points are also called
 outliers, and might often lead to trouble for other scaling
 techniques.</p>
-</div>
-<div class="section" id="frequently-used-scaling-functions">
-<h2>Frequently used scaling functions<a class="headerlink" href="#frequently-used-scaling-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="frequently-used-scaling-functions">
+<h2>Frequently used scaling functions<a class="headerlink" href="#frequently-used-scaling-functions" title="Permalink to this heading">#</a></h2>
 <p>Many features are often scaled using standardization to improve performance. In <strong>Scikit-Learn</strong> this is given by the <strong>StandardScaler</strong> function as discussed above. It is easy however to write your own.
 Mathematically, this involves subtracting the mean and divide by the standard deviation over the data set, for each feature:</p>
 <div class="math notranslate nohighlight">
@@ -1886,9 +1254,9 @@ x_j^{(i)} \rightarrow \frac{x_j^{(i)} - \overline{x}_j}{\sigma(x_j)},
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\overline{x}_j\)</span> and <span class="math notranslate nohighlight">\(\sigma(x_j)\)</span> are the mean and standard deviation, respectively,  of the feature <span class="math notranslate nohighlight">\(x_j\)</span>.
 This ensures that each feature has zero mean and unit standard deviation.  For data sets where  we do not have the standard deviation or don’t wish to calculate it,  it is then common to simply set it to one.</p>
-</div>
-<div class="section" id="example-of-own-standard-scaling">
-<h2>Example of own Standard scaling<a class="headerlink" href="#example-of-own-standard-scaling" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-of-own-standard-scaling">
+<h2>Example of own Standard scaling<a class="headerlink" href="#example-of-own-standard-scaling" title="Permalink to this heading">#</a></h2>
 <p>Let us consider the following vanilla example where we use both
 <strong>Scikit-Learn</strong> and write our own function as well.  We produce a
 simple test design matrix with random numbers. Each column could then
@@ -1921,351 +1289,11 @@ represent a specific feature whose mean value is subracted.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
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-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>0</th>
-      <th>1</th>
-      <th>2</th>
-      <th>3</th>
-      <th>4</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>-1.749765</td>
-      <td>0.342680</td>
-      <td>1.153036</td>
-      <td>-0.252436</td>
-      <td>0.981321</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.514219</td>
-      <td>0.221180</td>
-      <td>-1.070043</td>
-      <td>-0.189496</td>
-      <td>0.255001</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>-0.458027</td>
-      <td>0.435163</td>
-      <td>-0.583595</td>
-      <td>0.816847</td>
-      <td>0.672721</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>-0.104411</td>
-      <td>-0.531280</td>
-      <td>1.029733</td>
-      <td>-0.438136</td>
-      <td>-1.118318</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>1.618982</td>
-      <td>1.541605</td>
-      <td>-0.251879</td>
-      <td>-0.842436</td>
-      <td>0.184519</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>0.937082</td>
-      <td>0.731000</td>
-      <td>1.361556</td>
-      <td>-0.326238</td>
-      <td>0.055676</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.222400</td>
-      <td>-1.443217</td>
-      <td>-0.756352</td>
-      <td>0.816454</td>
-      <td>0.750445</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>-0.455947</td>
-      <td>1.189622</td>
-      <td>-1.690617</td>
-      <td>-1.356399</td>
-      <td>-1.232435</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>-0.544439</td>
-      <td>-0.668172</td>
-      <td>0.007315</td>
-      <td>-0.612939</td>
-      <td>1.299748</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>-1.733096</td>
-      <td>-0.983310</td>
-      <td>0.357508</td>
-      <td>-1.613579</td>
-      <td>1.470714</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0   -0.175300
-1    0.083527
-2   -0.044334
-3   -0.399836
-4    0.331939
-dtype: float64
-0    1.069584
-1    0.965548
-2    1.018232
-3    0.793167
-4    0.918992
-dtype: float64
-</pre></div>
-</div>
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>0</th>
-      <th>1</th>
-      <th>2</th>
-      <th>3</th>
-      <th>4</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>-1.574465</td>
-      <td>0.259153</td>
-      <td>1.197370</td>
-      <td>0.147400</td>
-      <td>0.649382</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.689519</td>
-      <td>0.137652</td>
-      <td>-1.025709</td>
-      <td>0.210340</td>
-      <td>-0.076938</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>-0.282727</td>
-      <td>0.351636</td>
-      <td>-0.539261</td>
-      <td>1.216683</td>
-      <td>0.340782</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>0.070889</td>
-      <td>-0.614808</td>
-      <td>1.074067</td>
-      <td>-0.038300</td>
-      <td>-1.450257</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>1.794282</td>
-      <td>1.458078</td>
-      <td>-0.207545</td>
-      <td>-0.442600</td>
-      <td>-0.147420</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>1.112383</td>
-      <td>0.647473</td>
-      <td>1.405890</td>
-      <td>0.073598</td>
-      <td>-0.276263</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.397700</td>
-      <td>-1.526744</td>
-      <td>-0.712018</td>
-      <td>1.216290</td>
-      <td>0.418506</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>-0.280647</td>
-      <td>1.106095</td>
-      <td>-1.646283</td>
-      <td>-0.956563</td>
-      <td>-1.564374</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>-0.369139</td>
-      <td>-0.751699</td>
-      <td>0.051649</td>
-      <td>-0.213103</td>
-      <td>0.967809</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>-1.557795</td>
-      <td>-1.066837</td>
-      <td>0.401842</td>
-      <td>-1.213743</td>
-      <td>1.138775</td>
-    </tr>
-  </tbody>
-</table>
-</div></div><div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
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-    }
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-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>0</th>
-      <th>1</th>
-      <th>2</th>
-      <th>3</th>
-      <th>4</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>5</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>6</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>7</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>8</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-    <tr>
-      <th>9</th>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-      <td>0.0</td>
-    </tr>
-  </tbody>
-</table>
-</div></div></div>
 </div>
 <p>Small exercise: perform the standard scaling by including the standard deviation and compare with what Scikit-Learn gives.</p>
-</div>
-<div class="section" id="min-max-scaling">
-<h2>Min-Max Scaling<a class="headerlink" href="#min-max-scaling" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="min-max-scaling">
+<h2>Min-Max Scaling<a class="headerlink" href="#min-max-scaling" title="Permalink to this heading">#</a></h2>
 <p>Another commonly used scaling method is min-max scaling. This is very
 useful for when we want the features to lie in a certain interval. To
 scale the feature <span class="math notranslate nohighlight">\(x_j\)</span> to the interval <span class="math notranslate nohighlight">\([a, b]\)</span>, we can apply the
@@ -2275,9 +1303,9 @@ transformation</p>
 x_j^{(i)} \rightarrow (b-a)\frac{x_j^{(i)} - \min(x_j)}{\max(x_j) - \min(x_j)} - a
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\min(x_j)\)</span> and <span class="math notranslate nohighlight">\(\max(x_j)\)</span> return the minimum and maximum value of <span class="math notranslate nohighlight">\(x_j\)</span> over the data set, respectively.</p>
-</div>
-<div class="section" id="testing-the-means-squared-error-as-function-of-complexity">
-<h2>Testing the Means Squared Error as function of Complexity<a class="headerlink" href="#testing-the-means-squared-error-as-function-of-complexity" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="testing-the-means-squared-error-as-function-of-complexity">
+<h2>Testing the Means Squared Error as function of Complexity<a class="headerlink" href="#testing-the-means-squared-error-as-function-of-complexity" title="Permalink to this heading">#</a></h2>
 <p>One of
 the aims is to reproduce Figure 2.11 of <a class="reference external" href="https://github.com/CompPhysics/MLErasmus/blob/master/doc/Textbooks/elementsstat.pdf">Hastie et al</a>.</p>
 <p>Our data is defined by <span class="math notranslate nohighlight">\(x\in [-3,3]\)</span> with a total of for example <span class="math notranslate nohighlight">\(100\)</span> data points.</p>
@@ -2336,13 +1364,10 @@ the aims is to reproduce Figure 2.11 of <a class="reference external" href="http
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week35_146_0.png" src="_images/week35_146_0.png" />
 </div>
-</div>
-</div>
-<div class="section" id="more-preprocessing-examples-two-dimensional-example-the-franke-function">
-<h2>More preprocessing examples, two-dimensional example, the Franke function<a class="headerlink" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-preprocessing-examples-two-dimensional-example-the-franke-function">
+<h2>More preprocessing examples, two-dimensional example, the Franke function<a class="headerlink" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Common imports</span>
@@ -2440,40 +1465,10 @@ the aims is to reproduce Figure 2.11 of <a class="reference external" href="http
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>MSE before scaling: 0.00
-R2 score before scaling 1.00
-Feature min values before scaling:
- [1.00000000e+00 6.97906022e-03 2.43639284e-03 4.87072815e-05
- 1.70037324e-05 5.93601008e-06 3.39931051e-07 1.18670072e-07
- 4.14277718e-08 1.44624525e-08 2.37239927e-09 8.28205578e-10
- 2.89126914e-10 1.00934327e-10 3.52362157e-11 1.65571174e-11
- 5.78009660e-12 2.01783414e-12 7.04426744e-13 2.45915671e-13
- 8.58492636e-14]
-Feature max values before scaling:
- [1.         0.99970894 0.99978365 0.99941797 0.99949266 0.99956735
- 0.99912709 0.99920175 0.99927642 0.9993511  0.99883628 0.99891093
- 0.99898558 0.99906023 0.99913489 0.99854557 0.99862019 0.99869482
- 0.99876945 0.99884409 0.99891873]
-Feature min values after scaling:
- [ 0.         -1.71761101 -1.75770568 -1.12330033 -1.12591227 -1.12871842
- -0.88613493 -0.884669   -0.88323026 -0.88182591 -0.75269037 -0.75050135
- -0.74829661 -0.74607851 -0.74384949 -0.6652177  -0.66294408 -0.66064822
- -0.65833132 -0.65599456 -0.6536392 ]
-Feature max values after scaling:
- [0.         1.71737253 1.75576555 2.20916295 2.23971032 2.26995402
- 2.60543038 2.63162342 2.65743689 2.68286725 2.94273542 2.96631321
- 2.98947894 3.01222822 3.034557   3.24159785 3.26297455 3.28391978
- 3.30442964 3.32450054 3.34412923]
-MSE after  scaling: 0.00
-R2 score for  scaled data: 1.00
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="to-think-about-first-part">
-<h2>To think about, first part<a class="headerlink" href="#to-think-about-first-part" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="to-think-about-first-part">
+<h2>To think about, first part<a class="headerlink" href="#to-think-about-first-part" title="Permalink to this heading">#</a></h2>
 <p>When you are comparing your own code with for example <strong>Scikit-Learn</strong>’s
 library, there are some technicalities to keep in mind.  The examples
 here demonstrate some of these aspects with potential pitfalls.</p>
@@ -2489,9 +1484,9 @@ Furthermore, in for example Ridge and Lasso regression (to be discussed in moe d
 from the library <strong>Scikit-Learn</strong> (when not shrinking <span class="math notranslate nohighlight">\(\beta_0\)</span>) for the unknown parameters
 <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>, are derived under the assumption that both <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> and
 <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> are zero centered, that is we subtract the mean values.</p>
-</div>
-<div class="section" id="more-thinking">
-<h2>More thinking<a class="headerlink" href="#more-thinking" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-thinking">
+<h2>More thinking<a class="headerlink" href="#more-thinking" title="Permalink to this heading">#</a></h2>
 <p>If our predictors represent different scales, then it is important to
 standardize the design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> by subtracting the mean of each
 column from the corresponding column and dividing the column with its
@@ -2513,9 +1508,9 @@ kilometers. If measured in kilometers, a standard linear regression
 model with this predictor would probably give a much bigger
 coefficient term, than if measured in millimeters.
 This can clearly lead to problems in evaluating the cost/loss functions.</p>
-</div>
-<div class="section" id="still-thinking">
-<h2>Still thinking<a class="headerlink" href="#still-thinking" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="still-thinking">
+<h2>Still thinking<a class="headerlink" href="#still-thinking" title="Permalink to this heading">#</a></h2>
 <p>Keep in mind that when you transform your data set before training a model, the same transformation needs to be done
 on your eventual new data set  before making a prediction. If we translate this into a Python code, it would could be implemented as follows
 (note that the lines are commented since the model function has not been defined)</p>
@@ -2539,9 +1534,9 @@ on your eventual new data set  before making a prediction. If we translate this
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="what-does-centering-subtracting-the-mean-values-mean-mathematically">
-<h2>What does centering (subtracting the mean values) mean mathematically?<a class="headerlink" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-does-centering-subtracting-the-mean-values-mean-mathematically">
+<h2>What does centering (subtracting the mean values) mean mathematically?<a class="headerlink" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically" title="Permalink to this heading">#</a></h2>
 <p>Let us try to understand what this may imply mathematically when we
 subtract the mean values, also known as <em>zero centering</em>. For
 simplicity, we will focus on  ordinary regression, as done in the above example.</p>
@@ -2569,9 +1564,9 @@ When we take the derivative with respect to <span class="math notranslate nohigh
 \[
 \sum_{i=0}^{n-1} \beta_0 = \sum_{i=0}^{n-1}y_i - \sum_{i=0}^{n-1} \sum_{j=1}^{p-1} X_{ij} \beta_j.
 \]</div>
-</div>
-<div class="section" id="further-manipulations">
-<h2>Further Manipulations<a class="headerlink" href="#further-manipulations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="further-manipulations">
+<h2>Further Manipulations<a class="headerlink" href="#further-manipulations" title="Permalink to this heading">#</a></h2>
 <p>Let us special first to the case where we have only two parameters <span class="math notranslate nohighlight">\(\beta_0\)</span> and <span class="math notranslate nohighlight">\(\beta_1\)</span>.
 Our result for <span class="math notranslate nohighlight">\(\beta_0\)</span> simplifies then to</p>
 <div class="math notranslate nohighlight">
@@ -2608,9 +1603,9 @@ n\beta_0 = \sum_{i=0}^{n-1}y_i - \sum_{i=0}^{n-1} X_{i1} \beta_1.
 \[
 C(\boldsymbol{\beta}) = (\boldsymbol{\tilde{y}} - \tilde{X}\boldsymbol{\beta})^T(\boldsymbol{\tilde{y}} - \tilde{X}\boldsymbol{\beta}).
 \]</div>
-</div>
-<div class="section" id="wrapping-it-up">
-<h2>Wrapping it up<a class="headerlink" href="#wrapping-it-up" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="wrapping-it-up">
+<h2>Wrapping it up<a class="headerlink" href="#wrapping-it-up" title="Permalink to this heading">#</a></h2>
 <p>If we minimize with respect to <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> we have then</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2624,9 +1619,9 @@ and <span class="math notranslate nohighlight">\(\tilde{X}_{ij} = X_{ij} - \frac
 \hat{\boldsymbol{\beta}} = (\tilde{X}^T\tilde{X} + \lambda I)^{-1}\tilde{X}^T\boldsymbol{\tilde{y}}.
 \]</div>
 <p>What does this mean? And why do we insist on all this? Let us look at some examples.</p>
-</div>
-<div class="section" id="linear-regression-code-intercept-handling-first">
-<h2>Linear Regression code, Intercept handling first<a class="headerlink" href="#linear-regression-code-intercept-handling-first" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linear-regression-code-intercept-handling-first">
+<h2>Linear Regression code, Intercept handling first<a class="headerlink" href="#linear-regression-code-intercept-handling-first" title="Permalink to this heading">#</a></h2>
 <p>This code shows a simple first-order fit to a data set using the above transformed data, where we consider the role of the intercept first, by either excluding it or including it (<em>code example thanks to  Øyvind Sigmundson Schøyen</em>). Here our scaling of the data is done by subtracting the mean values only.
 Note also that we do not split the data into training and test.</p>
 <div class="cell docutils container">
@@ -2720,26 +1715,6 @@ Note also that we do not split the data into training and test.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>True beta: [2, 0.5, 3.7]
-Fitted beta: [2.08376632 0.19569961 3.97898392]
-Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]
-MSE with intercept column
-0.004113634617443139
-MSE with intercept column from SKL
-0.004113634617443147
-Manual intercept: 2.083766322923899
-Fitted beta (wiothout intercept): [0.19569961 3.97898392]
-Sklearn intercept: 2.0837663229239043
-Sklearn fitted beta (without intercept): [0.19569961 3.97898392]
-MSE with Manual intercept
-0.00411363461744314
-MSE with Sklearn intercept
-0.004113634617443131
-</pre></div>
-</div>
-<img alt="_images/week35_181_1.png" src="_images/week35_181_1.png" />
-</div>
 </div>
 <p>The intercept is the value of our output/target variable
 when all our features are zero and our function crosses the <span class="math notranslate nohighlight">\(y\)</span>-axis (for a one-dimensional case).</p>
@@ -2772,9 +1747,9 @@ since it focuses only on the remaining quantities. If we however bring
 back the intercept, we will get an MSE which then contains the
 intercept. This becomes more important when we discuss Ridge and Lasso
 regression next week.</p>
-</div>
-<div class="section" id="the-boston-housing-data-example">
-<h2>The Boston housing data example<a class="headerlink" href="#the-boston-housing-data-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-boston-housing-data-example">
+<h2>The Boston housing data example<a class="headerlink" href="#the-boston-housing-data-example" title="Permalink to this heading">#</a></h2>
 <p>The Boston housing<br />
 data set was originally a part of UCI Machine Learning Repository
 and has been removed now. The data set is now included in <strong>Scikit-Learn</strong>’s
@@ -2782,7 +1757,7 @@ library.  There are 506 samples and 13 feature (predictor) variables
 in this data set. The objective is to predict the value of prices of
 the house using the features (predictors) listed here.</p>
 <p>The features/predictors are</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>CRIM: Per capita crime rate by town</p></li>
 <li><p>ZN: Proportion of residential land zoned for lots over 25000 square feet</p></li>
 <li><p>INDUS: Proportion of non-retail business acres per town</p></li>
@@ -2797,9 +1772,9 @@ the house using the features (predictors) listed here.</p>
 <li><p>LSTAT: Percentage of lower status of the population</p></li>
 <li><p>MEDV: Median value of owner-occupied homes in USD 1000s</p></li>
 </ol>
-</div>
-<div class="section" id="housing-data-the-code">
-<h2>Housing data, the code<a class="headerlink" href="#housing-data-the-code" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="housing-data-the-code">
+<h2>Housing data, the code<a class="headerlink" href="#housing-data-the-code" title="Permalink to this heading">#</a></h2>
 <p>We start by importing the libraries</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2825,49 +1800,6 @@ the house using the features (predictors) listed here.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.
-
-    The Boston housing prices dataset has an ethical problem. You can refer to
-    the documentation of this function for further details.
-
-    The scikit-learn maintainers therefore strongly discourage the use of this
-    dataset unless the purpose of the code is to study and educate about
-    ethical issues in data science and machine learning.
-
-    In this special case, you can fetch the dataset from the original
-    source::
-
-        import pandas as pd
-        import numpy as np
-
-
-        data_url = &quot;http://lib.stat.cmu.edu/datasets/boston&quot;
-        raw_df = pd.read_csv(data_url, sep=&quot;\s+&quot;, skiprows=22, header=None)
-        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])
-        target = raw_df.values[1::2, 2]
-
-    Alternative datasets include the California housing dataset (i.e.
-    :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing
-    dataset. You can load the datasets as follows::
-
-        from sklearn.datasets import fetch_california_housing
-        housing = fetch_california_housing()
-
-    for the California housing dataset and::
-
-        from sklearn.datasets import fetch_openml
-        housing = fetch_openml(name=&quot;house_prices&quot;, as_frame=True)
-
-    for the Ames housing dataset.
-    
-  warnings.warn(msg, category=FutureWarning)
-</pre></div>
-</div>
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>dict_keys([&#39;data&#39;, &#39;target&#39;, &#39;feature_names&#39;, &#39;DESCR&#39;, &#39;filename&#39;, &#39;data_module&#39;])
-</pre></div>
-</div>
-</div>
 </div>
 <p>Then we invoke Pandas</p>
 <div class="cell docutils container">
@@ -2887,25 +1819,6 @@ the house using the features (predictors) listed here.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>CRIM       0
-ZN         0
-INDUS      0
-CHAS       0
-NOX        0
-RM         0
-AGE        0
-DIS        0
-RAD        0
-TAX        0
-PTRATIO    0
-B          0
-LSTAT      0
-MEDV       0
-dtype: int64
-</pre></div>
-</div>
-</div>
 </div>
 <p>We can then visualize the data</p>
 <div class="cell docutils container">
@@ -2919,13 +1832,6 @@ dtype: int64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).
-  warnings.warn(msg, FutureWarning)
-</pre></div>
-</div>
-<img alt="_images/week35_199_1.png" src="_images/week35_199_1.png" />
-</div>
 </div>
 <p>It is now useful to look at the correlation matrix</p>
 <div class="cell docutils container">
@@ -2938,12 +1844,6 @@ dtype: int64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_plain highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>&lt;AxesSubplot:&gt;
-</pre></div>
-</div>
-<img alt="_images/week35_201_1.png" src="_images/week35_201_1.png" />
-</div>
 </div>
 <p>From the above coorelation plot we can see that <strong>MEDV</strong> is strongly correlated to <strong>LSTAT</strong> and  <strong>RM</strong>. We see also that <strong>RAD</strong> and <strong>TAX</strong> are stronly correlated, but we don’t include this in our features together to avoid multi-colinearity</p>
 <div class="cell docutils container">
@@ -2964,9 +1864,6 @@ dtype: int64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week35_203_0.png" src="_images/week35_203_0.png" />
-</div>
 </div>
 <p>Now we start training our model</p>
 <div class="cell docutils container">
@@ -2992,14 +1889,6 @@ dtype: int64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(404, 2)
-(102, 2)
-(404,)
-(102,)
-</pre></div>
-</div>
-</div>
 </div>
 <p>Then we use the linear regression functionality from <strong>Scikit-Learn</strong></p>
 <div class="cell docutils container">
@@ -3038,20 +1927,6 @@ dtype: int64
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>The model performance for training set
---------------------------------------
-RMSE is 5.637129335071195
-R2 score is 0.6300745149331701
-
-
-The model performance for testing set
---------------------------------------
-RMSE is 5.137400784702911
-R2 score is 0.6628996975186953
-</pre></div>
-</div>
-</div>
 </div>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -3062,16 +1937,13 @@ R2 score is 0.6628996975186953
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week35_210_0.png" src="_images/week35_210_0.png" />
 </div>
-</div>
-</div>
-<div class="section" id="material-for-lecture-thursday-august-31">
-<h2>Material for lecture Thursday, August 31<a class="headerlink" href="#material-for-lecture-thursday-august-31" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="mathematical-interpretation-of-ordinary-least-squares">
-<h2>Mathematical Interpretation of Ordinary Least Squares<a class="headerlink" href="#mathematical-interpretation-of-ordinary-least-squares" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-for-lecture-thursday-august-31">
+<h2>Material for lecture Thursday, August 31<a class="headerlink" href="#material-for-lecture-thursday-august-31" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="mathematical-interpretation-of-ordinary-least-squares">
+<h2>Mathematical Interpretation of Ordinary Least Squares<a class="headerlink" href="#mathematical-interpretation-of-ordinary-least-squares" title="Permalink to this heading">#</a></h2>
 <p>What is presented here is a mathematical analysis of various regression algorithms (ordinary least  squares, Ridge and Lasso Regression). The analysis is based on an important algorithm in linear algebra, the so-called Singular Value Decomposition (SVD).</p>
 <p>We have shown that in ordinary least squares the optimal parameters <span class="math notranslate nohighlight">\(\beta\)</span> are given by</p>
 <div class="math notranslate nohighlight">
@@ -3096,18 +1968,18 @@ R2 score is 0.6628996975186953
 \]</div>
 <p>The matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> has the important property that <span class="math notranslate nohighlight">\(\boldsymbol{A}^2=\boldsymbol{A}\)</span>. This is the definition of a projection matrix.
 We can then interpret our optimal model <span class="math notranslate nohighlight">\(\tilde{\boldsymbol{y}}\)</span> as being represented  by an orthogonal  projection of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> onto a space defined by the column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.  In our case here the matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> is a square matrix. If it is a general rectangular matrix we have an oblique projection matrix.</p>
-</div>
-<div class="section" id="residual-error">
-<h2>Residual Error<a class="headerlink" href="#residual-error" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="residual-error">
+<h2>Residual Error<a class="headerlink" href="#residual-error" title="Permalink to this heading">#</a></h2>
 <p>We have defined the residual error as</p>
 <div class="math notranslate nohighlight">
 \[
 \boldsymbol{\epsilon}=\boldsymbol{y}-\tilde{\boldsymbol{y}}=\left[\boldsymbol{I}-\boldsymbol{X}\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\right]\boldsymbol{y}.
 \]</div>
 <p>The residual errors are then the projections of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> onto the orthogonal component of the space defined by the column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="simple-case">
-<h2>Simple case<a class="headerlink" href="#simple-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-case">
+<h2>Simple case<a class="headerlink" href="#simple-case" title="Permalink to this heading">#</a></h2>
 <p>If the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is an orthogonal (or unitary in case of complex values) matrix, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3124,9 +1996,9 @@ We can then interpret our optimal model <span class="math notranslate nohighligh
 \boldsymbol{\epsilon}=\boldsymbol{y}-\tilde{\boldsymbol{y}}=0.
 \]</div>
 <p>This serves also as a useful test of our codes.</p>
-</div>
-<div class="section" id="the-singular-value-decomposition">
-<h2>The singular value decomposition<a class="headerlink" href="#the-singular-value-decomposition" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-singular-value-decomposition">
+<h2>The singular value decomposition<a class="headerlink" href="#the-singular-value-decomposition" title="Permalink to this heading">#</a></h2>
 <p>The examples we have looked at so far are cases where we normally can
 invert the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>. Using a polynomial expansion where we fit of various functions leads to
 row vectors of the design matrix which are essentially orthogonal due
@@ -3152,9 +2024,9 @@ to the covariance matrix (and thereby the correlation matrix) and in
 turn the variance of a given quantity. It plays also an important role
 in the principal component analysis where high-dimensional data can be
 reduced to the statistically relevant features.</p>
-</div>
-<div class="section" id="linear-regression-problems">
-<h2>Linear Regression Problems<a class="headerlink" href="#linear-regression-problems" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linear-regression-problems">
+<h2>Linear Regression Problems<a class="headerlink" href="#linear-regression-problems" title="Permalink to this heading">#</a></h2>
 <p>One of the typical problems we encounter with linear regression, in particular
 when the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> (our so-called design matrix) is high-dimensional,
 are problems with near singular or singular matrices. The column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>
@@ -3196,9 +2068,9 @@ that the inverse of the matrix <span class="math notranslate nohighlight">\(\bol
 \end{split}\]</div>
 <p>We see easily that  <span class="math notranslate nohighlight">\(\mbox{det}(\boldsymbol{X}) = x_{11} x_{22} - x_{12} x_{21} = 1 \times (-1) - 1 \times (-1) = 0\)</span>. Hence, <span class="math notranslate nohighlight">\(\mathbf{X}\)</span> is singular and its inverse is undefined.
 This is equivalent to saying that the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> has at least an eigenvalue which is zero.</p>
-</div>
-<div class="section" id="fixing-the-singularity">
-<h2>Fixing the singularity<a class="headerlink" href="#fixing-the-singularity" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="fixing-the-singularity">
+<h2>Fixing the singularity<a class="headerlink" href="#fixing-the-singularity" title="Permalink to this heading">#</a></h2>
 <p>If our design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> which enters the linear regression problem</p>
 <!-- Equation labels as ordinary links -->
 <div id="_auto1"></div>
@@ -3220,9 +2092,9 @@ the regression parameters <span class="math notranslate nohighlight">\(\beta_i\)
 \boldsymbol{X}^{T} \boldsymbol{X} \rightarrow \boldsymbol{X}^{T} \boldsymbol{X}+\lambda \boldsymbol{I},
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> is the identity matrix.  When we discuss <strong>Ridge</strong> regression this is actually what we end up evaluating. The parameter <span class="math notranslate nohighlight">\(\lambda\)</span> is called a hyperparameter. More about this later.</p>
-</div>
-<div class="section" id="basic-math-of-the-svd">
-<h2>Basic math of the SVD<a class="headerlink" href="#basic-math-of-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="basic-math-of-the-svd">
+<h2>Basic math of the SVD<a class="headerlink" href="#basic-math-of-the-svd" title="Permalink to this heading">#</a></h2>
 <p>From standard linear algebra we know that a square matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> can be diagonalized if and only it is
 a so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Normal_matrix">normal matrix</a>, that is if <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times n}\)</span>
 we have <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}\)</span> or if <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{C}}^{n\times n}\)</span> we have <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^{\dagger}=\boldsymbol{X}^{\dagger}\boldsymbol{X}\)</span>.
@@ -3252,9 +2124,9 @@ The matrix has then a set of eigenpairs</p>
 \end{split}\]</div>
 <p>is not diagonalizable, it is a so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Defective_matrix">defective matrix</a>. It is easy to see that the condition
 <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T=\boldsymbol{X}^T\boldsymbol{X}\)</span> is not fulfilled.</p>
-</div>
-<div class="section" id="the-svd-a-fantastic-algorithm">
-<h2>The SVD, a Fantastic Algorithm<a class="headerlink" href="#the-svd-a-fantastic-algorithm" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-svd-a-fantastic-algorithm">
+<h2>The SVD, a Fantastic Algorithm<a class="headerlink" href="#the-svd-a-fantastic-algorithm" title="Permalink to this heading">#</a></h2>
 <p>However, and this is the strength of the SVD algorithm, any general
 matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> can be decomposed in terms of a diagonal matrix and
 two orthogonal/unitary matrices.  The <a class="reference external" href="https://en.wikipedia.org/wiki/Singular_value_decomposition">Singular Value Decompostion
@@ -3290,9 +2162,9 @@ masses and the equation of state this is indeed the case, while for
 the Ising model we have <span class="math notranslate nohighlight">\(p &gt; n\)</span>. These are often cases that lead to
 near singular or singular matrices.</p>
 <p>The columns of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> are called the left singular vectors while the columns of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span> are the right singular vectors.</p>
-</div>
-<div class="section" id="economy-size-svd">
-<h2>Economy-size SVD<a class="headerlink" href="#economy-size-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="economy-size-svd">
+<h2>Economy-size SVD<a class="headerlink" href="#economy-size-svd" title="Permalink to this heading">#</a></h2>
 <p>If we assume that <span class="math notranslate nohighlight">\(n &gt; p\)</span>, then our matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> has dimension <span class="math notranslate nohighlight">\(n
 \times n\)</span>. The last <span class="math notranslate nohighlight">\(n-p\)</span> columns of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> become however
 irrelevant in our calculations since they are multiplied with the
@@ -3307,15 +2179,15 @@ the decomposition.</p>
 If <span class="math notranslate nohighlight">\(p &gt; n\)</span>, then only the first <span class="math notranslate nohighlight">\(n\)</span> columns of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span> are computed and <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> has dimension <span class="math notranslate nohighlight">\(n\times n\)</span>.
 The <span class="math notranslate nohighlight">\(n=p\)</span> case is obvious, we retain the full SVD.
 In general the economy-size SVD leads to less FLOPS and still conserving the desired accuracy.</p>
-</div>
-<div class="section" id="codes-for-the-svd">
-<h2>Codes for the SVD<a class="headerlink" href="#codes-for-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="codes-for-the-svd">
+<h2>Codes for the SVD<a class="headerlink" href="#codes-for-the-svd" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="c1"># SVD inversion</span>
 <span class="k">def</span> <span class="nf">SVD</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
+<span class="w">    </span><span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
 <span class="sd">    SVD is numerically more stable than the inversion algorithms provided by</span>
 <span class="sd">    numpy and scipy.linalg at the cost of being slower.</span>
 <span class="sd">    &#39;&#39;&#39;</span>
@@ -3344,25 +2216,6 @@ In general the economy-size SVD leads to less FLOPS and still conserving the des
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 1. -1.]
- [ 1. -1.]]
-test U
-[[0. 0.]
- [0. 0.]]
-test VT
-[[0. 0.]
- [0. 0.]]
-[[-0.70710678 -0.70710678]
- [-0.70710678  0.70710678]]
-[2.00000000e+00 3.35470445e-17]
-[[-0.70710678  0.70710678]
- [ 0.70710678  0.70710678]]
-[[-3.33066907e-16  4.44089210e-16]
- [ 0.00000000e+00  2.22044605e-16]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>The matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> has columns that are linearly dependent. The first
 column is the row-wise sum of the other two columns. The rank of a
@@ -3372,9 +2225,9 @@ independent columns, in this case just <span class="math notranslate nohighlight
 singular values when running the above code. Running the standard
 inversion algorithm for matrix inversion with <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> results
 in the program terminating due to a singular matrix.</p>
-</div>
-<div class="section" id="note-about-svd-calculations">
-<h2>Note about SVD Calculations<a class="headerlink" href="#note-about-svd-calculations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="note-about-svd-calculations">
+<h2>Note about SVD Calculations<a class="headerlink" href="#note-about-svd-calculations" title="Permalink to this heading">#</a></h2>
 <p>The <span class="math notranslate nohighlight">\(U\)</span>, <span class="math notranslate nohighlight">\(S\)</span>, and <span class="math notranslate nohighlight">\(V\)</span> matrices returned from the <strong>svd()</strong> function
 cannot be multiplied directly.</p>
 <p>As you can see from the code, the <span class="math notranslate nohighlight">\(S\)</span> vector must be converted into a
@@ -3385,9 +2238,9 @@ matrix.</p>
 <p>If you wish to include the zero singular values, you will need to
 resize the matrices and set up a diagonal matrix as done in the above
 example</p>
-</div>
-<div class="section" id="mathematics-of-the-svd-and-implications">
-<h2>Mathematics of the SVD and implications<a class="headerlink" href="#mathematics-of-the-svd-and-implications" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="mathematics-of-the-svd-and-implications">
+<h2>Mathematics of the SVD and implications<a class="headerlink" href="#mathematics-of-the-svd-and-implications" title="Permalink to this heading">#</a></h2>
 <p>Let us take a closer look at the mathematics of the SVD and the various implications for machine learning studies.</p>
 <p>Our starting point is our design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> of dimension <span class="math notranslate nohighlight">\(n\times p\)</span></p>
 <div class="math notranslate nohighlight">
@@ -3414,9 +2267,9 @@ x_{n-1,0} &amp; x_{n-1,1} &amp; x_{n-1,2}&amp; \dots &amp; \dots x_{n-1,p-1}\\
 \sigma_0 &gt; \sigma_1 &gt; \sigma_2 &gt; \dots &gt; \sigma_{p-1} &gt; 0.
 \]</div>
 <p>All values beyond <span class="math notranslate nohighlight">\(p-1\)</span> are all zero.</p>
-</div>
-<div class="section" id="example-matrix">
-<h2>Example Matrix<a class="headerlink" href="#example-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-matrix">
+<h2>Example Matrix<a class="headerlink" href="#example-matrix" title="Permalink to this heading">#</a></h2>
 <p>As an example, consider the following <span class="math notranslate nohighlight">\(3\times 2\)</span> example for the matrix <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span></p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -3467,9 +2320,9 @@ x_{n-1,0} &amp; x_{n-1,1} &amp; x_{n-1,2}&amp; \dots &amp; \dots x_{n-1,p-1}\\
 <p>is a <span class="math notranslate nohighlight">\(3\times 3 \)</span> matrix. The last row and column of this last matrix
 contain only zeros. This will have important consequences for our SVD
 decomposition of the design matrix.</p>
-</div>
-<div class="section" id="setting-up-the-matrix-to-be-inverted">
-<h2>Setting up the Matrix to be inverted<a class="headerlink" href="#setting-up-the-matrix-to-be-inverted" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="setting-up-the-matrix-to-be-inverted">
+<h2>Setting up the Matrix to be inverted<a class="headerlink" href="#setting-up-the-matrix-to-be-inverted" title="Permalink to this heading">#</a></h2>
 <p>The matrix that may cause problems for us is <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>. Using the SVD we can rewrite this matrix as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3503,9 +2356,9 @@ vectors of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U
 <span class="math notranslate nohighlight">\(p-1\)</span>, that is <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\ne \boldsymbol{y}\)</span>. We can thus not use the
 orthogonality relation for the matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span>. This can already be
 when we multiply the matrices <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}^T\boldsymbol{U}^T\)</span>.</p>
-</div>
-<div class="section" id="further-properties-important-for-our-analyses-later">
-<h2>Further properties (important for our analyses later)<a class="headerlink" href="#further-properties-important-for-our-analyses-later" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="further-properties-important-for-our-analyses-later">
+<h2>Further properties (important for our analyses later)<a class="headerlink" href="#further-properties-important-for-our-analyses-later" title="Permalink to this heading">#</a></h2>
 <p>Let us study again <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> in terms of our SVD,</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3546,9 +2399,9 @@ always refer to the number of features in our data set, while the
 number of rows represents the number of data inputs. Note that in
 other texts you may find the opposite notation. This has consequences
 for the definition of for example the covariance matrix and its relation to the SVD.</p>
-</div>
-<div class="section" id="meet-the-covariance-matrix">
-<h2>Meet the Covariance Matrix<a class="headerlink" href="#meet-the-covariance-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="meet-the-covariance-matrix">
+<h2>Meet the Covariance Matrix<a class="headerlink" href="#meet-the-covariance-matrix" title="Permalink to this heading">#</a></h2>
 <p>Before we move on to a discussion of Ridge and Lasso regression, we want to show an important example of the above.</p>
 <p>We have already noted that the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> in ordinary
 least squares is proportional to the second derivative of the cost
@@ -3567,9 +2420,9 @@ function, that is we have</p>
 the covariance matrix. This means also that we can use the SVD to find
 the eigenvalues of the covariance matrix and the Hessian matrix in
 terms of the singular values.   Let us develop these arguments, as they will play an important role in our machine learning studies.</p>
-</div>
-<div class="section" id="introducing-the-covariance-and-correlation-functions">
-<h2>Introducing the Covariance and Correlation functions<a class="headerlink" href="#introducing-the-covariance-and-correlation-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="introducing-the-covariance-and-correlation-functions">
+<h2>Introducing the Covariance and Correlation functions<a class="headerlink" href="#introducing-the-covariance-and-correlation-functions" title="Permalink to this heading">#</a></h2>
 <p>Before we discuss the link between for example Ridge regression and the singular value decomposition, we need to remind ourselves about
 the definition of the covariance and the correlation function. These are quantities that play a central role in machine learning methods.</p>
 <p>Suppose we have defined two vectors
@@ -3605,9 +2458,9 @@ and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
 <strong>Scikit-Learn</strong> or <strong>nunmpy’s</strong> function to calculate the covariance, this
 quantity will be computed with a factor <span class="math notranslate nohighlight">\(1/(n-1)\)</span>.</p>
-</div>
-<div class="section" id="covariance-and-correlation-matrix">
-<h2>Covariance and Correlation Matrix<a class="headerlink" href="#covariance-and-correlation-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="covariance-and-correlation-matrix">
+<h2>Covariance and Correlation Matrix<a class="headerlink" href="#covariance-and-correlation-matrix" title="Permalink to this heading">#</a></h2>
 <p>The covariance takes values between zero and infinity and may thus
 lead to problems with loss of numerical precision for particularly
 large values. It is common to scale the covariance matrix by
@@ -3628,9 +2481,9 @@ and <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> as</p>
              \end{bmatrix},
 \end{split}\]</div>
 <p>In the above example this is the function we constructed using <strong>pandas</strong>.</p>
-</div>
-<div class="section" id="correlation-function-and-design-feature-matrix">
-<h2>Correlation Function and Design/Feature Matrix<a class="headerlink" href="#correlation-function-and-design-feature-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="correlation-function-and-design-feature-matrix">
+<h2>Correlation Function and Design/Feature Matrix<a class="headerlink" href="#correlation-function-and-design-feature-matrix" title="Permalink to this heading">#</a></h2>
 <p>In our derivation of the various regression algorithms like <strong>Ordinary Least Squares</strong> or <strong>Ridge regression</strong>
 we defined the design/feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> as</p>
 <div class="math notranslate nohighlight">
@@ -3683,9 +2536,9 @@ covariance matrix for the vectors <span class="math notranslate nohighlight">\(\
 \mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_0]   &amp; \mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_1] &amp; \mathrm{corr}[\boldsymbol{x}_{p-1},\boldsymbol{x}_{2}]  &amp; \dots &amp; \dots  &amp; 1\\
 \end{bmatrix},
 \end{split}\]</div>
-</div>
-<div class="section" id="covariance-matrix-examples">
-<h2>Covariance Matrix Examples<a class="headerlink" href="#covariance-matrix-examples" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="covariance-matrix-examples">
+<h2>Covariance Matrix Examples<a class="headerlink" href="#covariance-matrix-examples" title="Permalink to this heading">#</a></h2>
 <p>The Numpy function <strong>np.cov</strong> calculates the covariance elements using
 the factor <span class="math notranslate nohighlight">\(1/(n-1)\)</span> instead of <span class="math notranslate nohighlight">\(1/n\)</span> since it assumes we do not have
 the exact mean values.  The following simple function uses the
@@ -3718,18 +2571,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.10790125813226321
-4.340071371496255
-[[ 1.04193203  3.08165104]
- [ 3.08165104 10.18383522]]
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="correlation-matrix">
-<h2>Correlation Matrix<a class="headerlink" href="#correlation-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="correlation-matrix">
+<h2>Correlation Matrix<a class="headerlink" href="#correlation-matrix" title="Permalink to this heading">#</a></h2>
 <p>The previous example can be converted into the correlation matrix by
 simply scaling the matrix elements with the variances.  We should also
 subtract the mean values for each column. This leads to the following
@@ -3761,22 +2606,14 @@ a more brute force way. Here we scale the mean values for each column of the des
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08881497884574564
-1.7086067479626619
-[[1.         0.66080313]
- [0.66080313 1.        ]]
-</pre></div>
-</div>
-</div>
 </div>
 <p>We see that the matrix elements along the diagonal are one as they
 should be and that the matrix is symmetric. Furthermore, diagonalizing
 this matrix we easily see that it is a positive definite matrix.</p>
 <p>The above procedure with <strong>numpy</strong> can be made more compact if we use <strong>pandas</strong>.</p>
-</div>
-<div class="section" id="correlation-matrix-with-pandas">
-<h2>Correlation Matrix with Pandas<a class="headerlink" href="#correlation-matrix-with-pandas" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="correlation-matrix-with-pandas">
+<h2>Correlation Matrix with Pandas<a class="headerlink" href="#correlation-matrix-with-pandas" title="Permalink to this heading">#</a></h2>
 <p>We whow here how we can set up the correlation matrix using <strong>pandas</strong>, as done in this simple code</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -3797,39 +2634,11 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.40620066 -2.01265755]
- [ 0.01458611  0.37737221]
- [-1.0895387  -3.65442354]
- [ 0.2338675   1.12044974]
- [ 0.4676059   1.54393936]
- [-0.65891389 -3.16304863]
- [-0.1715252   0.39197698]
- [ 0.71142161  2.95511792]
- [ 0.39214397  0.13069442]
- [ 0.50655336  2.3105791 ]]
-          0         1
-0 -0.406201 -2.012658
-1  0.014586  0.377372
-2 -1.089539 -3.654424
-3  0.233868  1.120450
-4  0.467606  1.543939
-5 -0.658914 -3.163049
-6 -0.171525  0.391977
-7  0.711422  2.955118
-8  0.392144  0.130694
-9  0.506553  2.310579
-          0         1
-0  1.000000  0.952387
-1  0.952387  1.000000
-</pre></div>
-</div>
-</div>
 </div>
 <p>We expand this model to the Franke function discussed above.</p>
-</div>
-<div class="section" id="correlation-matrix-with-pandas-and-the-franke-function">
-<h2>Correlation Matrix with Pandas and the Franke function<a class="headerlink" href="#correlation-matrix-with-pandas-and-the-franke-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="correlation-matrix-with-pandas-and-the-franke-function">
+<h2>Correlation Matrix with Pandas and the Franke function<a class="headerlink" href="#correlation-matrix-with-pandas-and-the-franke-function" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Common imports</span>
@@ -3878,43 +2687,6 @@ this matrix we easily see that it is a positive definite matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>     0         1         2         3         4         5         6         7   \
-0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   
-1   0.0  0.078974  0.081276  0.075889  0.077168  0.078540  0.065410  0.066474   
-2   0.0  0.081276  0.084076  0.078336  0.079946  0.081655  0.067707  0.069028   
-3   0.0  0.075889  0.078336  0.077460  0.078986  0.080616  0.069452  0.070737   
-4   0.0  0.077168  0.079946  0.078986  0.080764  0.082653  0.070986  0.072476   
-5   0.0  0.078540  0.081655  0.080616  0.082653  0.084809  0.072621  0.074323   
-6   0.0  0.065410  0.067707  0.069452  0.070986  0.072621  0.064074  0.065378   
-7   0.0  0.066474  0.069028  0.070737  0.072476  0.074323  0.065378  0.066854   
-8   0.0  0.067637  0.070457  0.072132  0.074084  0.076150  0.066787  0.068441   
-9   0.0  0.068906  0.072000  0.073644  0.075816  0.078110  0.068307  0.070146   
-10  0.0  0.055734  0.057835  0.060872  0.062337  0.063894  0.057393  0.058645   
-11  0.0  0.056683  0.058996  0.062016  0.063653  0.065390  0.058552  0.059951   
-12  0.0  0.057722  0.060254  0.063260  0.065077  0.066999  0.059807  0.061359   
-13  0.0  0.058854  0.061614  0.064609  0.066612  0.068727  0.061163  0.062874   
-14  0.0  0.060083  0.063080  0.066066  0.068264  0.070582  0.062624  0.064501   
-
-          8         9         10        11        12        13        14  
-0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  
-1   0.067637  0.068906  0.055734  0.056683  0.057722  0.058854  0.060083  
-2   0.070457  0.072000  0.057835  0.058996  0.060254  0.061614  0.063080  
-3   0.072132  0.073644  0.060872  0.062016  0.063260  0.064609  0.066066  
-4   0.074084  0.075816  0.062337  0.063653  0.065077  0.066612  0.068264  
-5   0.076150  0.078110  0.063894  0.065390  0.066999  0.068727  0.070582  
-6   0.066787  0.068307  0.057393  0.058552  0.059807  0.061163  0.062624  
-7   0.068441  0.070146  0.058645  0.059951  0.061359  0.062874  0.064501  
-8   0.070213  0.072111  0.059993  0.061452  0.063019  0.064699  0.066500  
-9   0.072111  0.074210  0.061443  0.063061  0.064793  0.066647  0.068629  
-10  0.059993  0.061443  0.052305  0.053417  0.054617  0.055910  0.057300  
-11  0.061452  0.063061  0.053417  0.054655  0.055987  0.057418  0.058952  
-12  0.063019  0.064793  0.054617  0.055987  0.057457  0.059031  0.060716  
-13  0.064699  0.066647  0.055910  0.057418  0.059031  0.060756  0.062599  
-14  0.066500  0.068629  0.057300  0.058952  0.060716  0.062599  0.064606  
-</pre></div>
-</div>
-</div>
 </div>
 <p>We note here that the covariance is zero for the first rows and
 columns since all matrix elements in the design matrix were set to one
@@ -3923,9 +2695,9 @@ columns since all matrix elements in the design matrix were set to one
 cause problems when we set up the correlation matrix.  We can simply
 drop these elements and construct a correlation
 matrix without these elements.</p>
-</div>
-<div class="section" id="rewriting-the-covariance-and-or-correlation-matrix">
-<h2>Rewriting the Covariance and/or Correlation Matrix<a class="headerlink" href="#rewriting-the-covariance-and-or-correlation-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="rewriting-the-covariance-and-or-correlation-matrix">
+<h2>Rewriting the Covariance and/or Correlation Matrix<a class="headerlink" href="#rewriting-the-covariance-and-or-correlation-matrix" title="Permalink to this heading">#</a></h2>
 <p>We can rewrite the covariance matrix in a more compact form in terms of the design/feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3958,9 +2730,9 @@ x_{01}x_{00}+x_{11}x_{10} &amp; x_{01}^2+x_{11}^2\\
 \end{split}\]</div>
 <p>where we wrote $<span class="math notranslate nohighlight">\(\boldsymbol{C}[\boldsymbol{x}_0,\boldsymbol{x}_1] = \boldsymbol{C}[\boldsymbol{x}]\)</span><span class="math notranslate nohighlight">\( to indicate that this is the covariance of the vectors \)</span>\boldsymbol{x}<span class="math notranslate nohighlight">\( of the design/feature matrix \)</span>\boldsymbol{X}$.</p>
 <p>It is easy to generalize this to a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\in {\mathbb{R}}^{n\times p}\)</span>.</p>
-</div>
-<div class="section" id="linking-with-the-svd">
-<h2>Linking with the SVD<a class="headerlink" href="#linking-with-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linking-with-the-svd">
+<h2>Linking with the SVD<a class="headerlink" href="#linking-with-the-svd" title="Permalink to this heading">#</a></h2>
 <p>We saw earlier that</p>
 <div class="math notranslate nohighlight">
 \[
@@ -3991,9 +2763,9 @@ x_{01}x_{00}+x_{11}x_{10} &amp; x_{01}^2+x_{11}^2\\
 \[
 \left(\boldsymbol{X}^T\boldsymbol{X}\right)\boldsymbol{V}=\boldsymbol{V}\tilde{\boldsymbol{\Sigma}}^2.
 \]</div>
-</div>
-<div class="section" id="what-does-it-mean">
-<h2>What does it mean?<a class="headerlink" href="#what-does-it-mean" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-does-it-mean">
+<h2>What does it mean?<a class="headerlink" href="#what-does-it-mean" title="Permalink to this heading">#</a></h2>
 <p>This means the vectors <span class="math notranslate nohighlight">\(\boldsymbol{v}_i\)</span> of the orthogonal matrix <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>
 are the eigenvectors of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> with eigenvalues
 given by the singular values squared, that is</p>
@@ -4022,9 +2794,9 @@ matrix. Every singular value of <span class="math notranslate nohighlight">\(\bo
 root of an eigenvalue of <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>. If the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is
 self-adjoint, the singular values of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> are equal to the
 absolute value of the eigenvalues of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="and-finally-boldsymbol-x-boldsymbol-x-t">
-<h2>And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span><a class="headerlink" href="#and-finally-boldsymbol-x-boldsymbol-x-t" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="and-finally-boldsymbol-x-boldsymbol-x-t">
+<h2>And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span><a class="headerlink" href="#and-finally-boldsymbol-x-boldsymbol-x-t" title="Permalink to this heading">#</a></h2>
 <p>For <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span> we found</p>
 <div class="math notranslate nohighlight">
 \[
@@ -4052,9 +2824,9 @@ measure how much correlations are contained in the rows of <span class="math not
 <p>Since we will mainly be interested in the correlations among the features
 of our data (the columns of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>, the quantity of interest for us are the non-zero singular
 values and the column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>.</p>
-</div>
-<div class="section" id="ridge-and-lasso-regression">
-<h2>Ridge and LASSO Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="ridge-and-lasso-regression">
+<h2>Ridge and LASSO Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Let us remind ourselves about the expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is
 our optimization problem is</p>
 <div class="math notranslate nohighlight">
@@ -4100,9 +2872,9 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\vert\vert \boldsymbol{y}-\bolds
 \[
 \vert\vert \boldsymbol{x}\vert\vert_1 = \sum_i \vert x_i\vert.
 \]</div>
-</div>
-<div class="section" id="deriving-the-ridge-regression-equations">
-<h2>Deriving the  Ridge Regression Equations<a class="headerlink" href="#deriving-the-ridge-regression-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-the-ridge-regression-equations">
+<h2>Deriving the  Ridge Regression Equations<a class="headerlink" href="#deriving-the-ridge-regression-equations" title="Permalink to this heading">#</a></h2>
 <p>Using the matrix-vector expression for Ridge regression and dropping the parameter <span class="math notranslate nohighlight">\(1/n\)</span> in front of the standard means squared error equation, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -4152,9 +2924,9 @@ We have already analyzed the OLS solutions in terms of the eigenvectors (the col
 \tilde{\boldsymbol{y}}_{\mathrm{Ridge}}=\boldsymbol{X}\boldsymbol{\beta}_{\mathrm{Ridge}} = \boldsymbol{U\Sigma V^T}\left(\boldsymbol{V}\boldsymbol{\Sigma}^2\boldsymbol{V}^T+\lambda\boldsymbol{I} \right)^{-1}(\boldsymbol{U\Sigma V^T})^T\boldsymbol{y}=\sum_{j=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\frac{\sigma_j^2}{\sigma_j^2+\lambda}\boldsymbol{y},
 \]</div>
 <p>with the vectors <span class="math notranslate nohighlight">\(\boldsymbol{u}_j\)</span> being the columns of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> from the SVD of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="interpreting-the-ridge-results">
-<h2>Interpreting the Ridge results<a class="headerlink" href="#interpreting-the-ridge-results" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpreting-the-ridge-results">
+<h2>Interpreting the Ridge results<a class="headerlink" href="#interpreting-the-ridge-results" title="Permalink to this heading">#</a></h2>
 <p>Since <span class="math notranslate nohighlight">\(\lambda \geq 0\)</span>, it means that compared to OLS, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -4166,9 +2938,9 @@ orthonormal basis <span class="math notranslate nohighlight">\(\boldsymbol{U}\)<
 eigenvalues ordered in a descending way, that is <span class="math notranslate nohighlight">\(\sigma_i \geq
 \sigma_{i+1}\)</span>.</p>
 <p>For small eigenvalues <span class="math notranslate nohighlight">\(\sigma_i\)</span> it means that their contributions become less important, a fact which can be used to reduce the number of degrees of freedom. More about this when we have covered the material on a statistical interpretation of various linear regression methods.</p>
-</div>
-<div class="section" id="more-interpretations">
-<h2>More interpretations<a class="headerlink" href="#more-interpretations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-interpretations">
+<h2>More interpretations<a class="headerlink" href="#more-interpretations" title="Permalink to this heading">#</a></h2>
 <p>For the sake of simplicity, let us assume that the design matrix is orthonormal, that is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -4190,9 +2962,9 @@ infinity.</p>
 <p>We will come back to more interpreations after we have gone through some of the statistical analysis part.</p>
 <p>For more discussions of Ridge and Lasso regression, <a class="reference external" href="https://arxiv.org/abs/1509.09169">Wessel van Wieringen’s</a> article is highly recommended.
 Similarly, <a class="reference external" href="https://arxiv.org/abs/1803.08823">Mehta et al’s article</a> is also recommended.</p>
-</div>
-<div class="section" id="deriving-the-lasso-regression-equations">
-<h2>Deriving the  Lasso Regression Equations<a class="headerlink" href="#deriving-the-lasso-regression-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-the-lasso-regression-equations">
+<h2>Deriving the  Lasso Regression Equations<a class="headerlink" href="#deriving-the-lasso-regression-equations" title="Permalink to this heading">#</a></h2>
 <p>Using the matrix-vector expression for Lasso regression, we have the following <strong>cost</strong> function</p>
 <div class="math notranslate nohighlight">
 \[
@@ -4219,8 +2991,8 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\left\{(\boldsymbol{y}-\boldsymb
 \boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=2\boldsymbol{X}^T\boldsymbol{y}.
 \]</div>
 <p>This equation does not lead to a nice analytical equation as in either Ridge regression or ordinary least squares. This equation can however be solved by using standard convex optimization algorithms using for example the Python package <a class="reference external" href="https://cvxopt.org/">CVXOPT</a>. We will discuss this later.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -4234,7 +3006,7 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\left\{(\boldsymbol{y}-\boldsymb
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -4242,44 +3014,176 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\left\{(\boldsymbol{y}-\boldsymb
     </script>
     <script>kernelName = 'python3'</script>
 
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+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-35">Plans for week 35</a><ul class="nav section-nav flex-column">
+<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#reading-recommendations">Reading recommendations:</a></li>
+</ul>
+</li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week">Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-for-ordinary-least-squares">The equations for ordinary least squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cost-loss-function">The cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-and-optimizing-our-parameters">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-useful-matrix-and-vector-expressions">Some useful matrix and vector expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-jacobian">The Jacobian</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#derivatives-example-1">Derivatives, example 1</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-2">Example 2</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-3">Example 3</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-4">Example 4</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-mean-squared-error-and-its-derivative">The mean squared error and its derivative</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-useful-relations">Other useful relations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-hessian-matrix">Meet the Hessian Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Interpretations and optimizing our parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-relevant-for-the-exercises">Example relevant for the exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#own-code-for-ordinary-least-squares">Own code for Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adding-error-analysis-and-training-set-up">Adding error analysis and training set up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#splitting-our-data-in-training-and-test-data">Splitting our Data in Training and Test data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-complete-code-with-a-simple-data-set">The complete code with a simple data set</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#making-your-own-test-train-splitting">Making your own test-train splitting</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#reducing-the-number-of-degrees-of-freedom-overarching-view">Reducing the number of degrees of freedom, overarching view</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#preprocessing-our-data">Preprocessing our data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#functionality-in-scikit-learn">Functionality in Scikit-Learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-preprocessing">More preprocessing</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#frequently-used-scaling-functions">Frequently used scaling functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-own-standard-scaling">Example of own Standard scaling</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#min-max-scaling">Min-Max Scaling</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#testing-the-means-squared-error-as-function-of-complexity">Testing the Means Squared Error as function of Complexity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-preprocessing-examples-two-dimensional-example-the-franke-function">More preprocessing examples, two-dimensional example, the Franke function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#to-think-about-first-part">To think about, first part</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-thinking">More thinking</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#still-thinking">Still thinking</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-centering-subtracting-the-mean-values-mean-mathematically">What does centering (subtracting the mean values) mean mathematically?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-manipulations">Further Manipulations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wrapping-it-up">Wrapping it up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-code-intercept-handling-first">Linear Regression code, Intercept handling first</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-boston-housing-data-example">The Boston housing data example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#housing-data-the-code">Housing data, the code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-august-31">Material for lecture Thursday, August 31</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematical-interpretation-of-ordinary-least-squares">Mathematical Interpretation of Ordinary Least Squares</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#residual-error">Residual Error</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-case">Simple case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-singular-value-decomposition">The singular value decomposition</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-problems">Linear Regression Problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#fixing-the-singularity">Fixing the singularity</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basic-math-of-the-svd">Basic math of the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-svd-a-fantastic-algorithm">The SVD, a Fantastic Algorithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#economy-size-svd">Economy-size SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#codes-for-the-svd">Codes for the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#note-about-svd-calculations">Note about SVD Calculations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#mathematics-of-the-svd-and-implications">Mathematics of the SVD and implications</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-matrix">Example Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#setting-up-the-matrix-to-be-inverted">Setting up the Matrix to be inverted</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#further-properties-important-for-our-analyses-later">Further properties (important for our analyses later)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#meet-the-covariance-matrix">Meet the Covariance Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">Introducing the Covariance and Correlation functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#covariance-and-correlation-matrix">Covariance and Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-function-and-design-feature-matrix">Correlation Function and Design/Feature Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#covariance-matrix-examples">Covariance Matrix Examples</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix">Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix-with-pandas">Correlation Matrix with Pandas</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#correlation-matrix-with-pandas-and-the-franke-function">Correlation Matrix with Pandas and the Franke function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-covariance-and-or-correlation-matrix">Rewriting the Covariance and/or Correlation Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-with-the-svd">Linking with the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-it-mean">What does it mean?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-lasso-regression">Ridge and LASSO Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">Deriving the  Ridge Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpreting-the-ridge-results">Interpreting the Ridge results</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-interpretations">More interpretations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">Deriving the  Lasso Regression Equations</a></li>
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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-   2. Linear Algebra, Handling of Arrays and more Python Features
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+<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  From Regression to Support Vector Machines
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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-   4. Ridge and Lasso Regression
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-   5. Resampling Methods
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-   6. Logistic Regression
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+<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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-   12. Clustering and Unsupervised Learning
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+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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-   14. Building a Feed Forward Neural Network
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-   15. Solving Differential Equations  with Deep Learning
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-   16. Convolutional Neural Networks
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-   17. Recurrent neural networks: Overarching view
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+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-<p aria-level="2" class="caption" role="heading">
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-  Weekly material, notes and exercises
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-   Exercises week 35
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
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-   Exercises week 37
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-   Week 37: Statitsitcal interpretations and Resampling Methods
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
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+    <h1>Week 36: Statistical interpretation of Linear Regression and Resampling techniques</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
             
-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-36">
-   Plans for week 36
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday">
-   Material for the active learning sessions Tuesday and Wednesday
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-and-the-svd">
-   Linear Regression and  the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-it-mean">
-   What does it mean?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">
-   And finally
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{X}\boldsymbol{X}^T\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">
-   Code for SVD and Inversion of Matrices
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#inverse-of-rectangular-matrix">
-   Inverse of Rectangular Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-lasso-regression">
-   Ridge and LASSO Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#from-ols-to-ridge-and-lasso">
-   From OLS to Ridge and Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">
-   Deriving the  Ridge Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#note-on-scikit-learn">
-   Note on Scikit-Learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#comparison-with-ols">
-   Comparison with OLS
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#svd-analysis">
-   SVD analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpreting-the-ridge-results">
-   Interpreting the Ridge results
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-interpretations">
-   More interpretations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">
-   Deriving the  Lasso Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">
-   Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-regression">
-   Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-regression">
-   Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#yet-another-example">
-   Yet another Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ols-case">
-   The OLS case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ridge-case">
-   The Ridge case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#writing-the-cost-function">
-   Writing the Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-case">
-   Lasso case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-first-case">
-   The first Case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-code-for-solving-the-above-problem">
-   Simple code for solving the above problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#with-lasso-regression">
-   With Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#another-example-now-with-a-polynomial-fit">
-   Another Example, now with a polynomial fit
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-7">
-   Material for lecture Thursday September 7
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#important-technicalities-more-on-rescaling-data">
-   Important technicalities: More on Rescaling data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#test-function-for-what-happens-with-ols-ridge-and-lasso">
-   Test Function for what happens with OLS, Ridge and Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#assumptions-made">
-   Assumptions made
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance">
-   Expectation value and variance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">
-   Expectation value and variance for
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{\beta}\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">
-   Independent and Identically Distrubuted (iid)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">
-   Maximum Likelihood Estimation (MLE)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-new-cost-function">
-   A new Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">
-   More basic Statistics and Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#marginal-probability">
-   Marginal Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditional-probability">
-   Conditional  Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem">
-   Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">
-   Interpretations of Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">
-   Example of Usage of Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#doing-it-correctly">
-   Doing it correctly
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-bayes">
-   Ridge and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-and-bayes">
-   Lasso and Bayes
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-36">Plans for week 36</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday">Material for the active learning sessions Tuesday and Wednesday</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-and-the-svd">Linear Regression and  the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-it-mean">What does it mean?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">Code for SVD and Inversion of Matrices</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#inverse-of-rectangular-matrix">Inverse of Rectangular Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-lasso-regression">Ridge and LASSO Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#from-ols-to-ridge-and-lasso">From OLS to Ridge and Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">Deriving the  Ridge Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#note-on-scikit-learn">Note on Scikit-Learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#comparison-with-ols">Comparison with OLS</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#svd-analysis">SVD analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpreting-the-ridge-results">Interpreting the Ridge results</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-interpretations">More interpretations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">Deriving the  Lasso Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-regression">Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-regression">Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#yet-another-example">Yet another Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ols-case">The OLS case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ridge-case">The Ridge case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-the-cost-function">Writing the Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-case">Lasso case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-first-case">The first Case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-code-for-solving-the-above-problem">Simple code for solving the above problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#with-lasso-regression">With Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-now-with-a-polynomial-fit">Another Example, now with a polynomial fit</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-7">Material for lecture Thursday September 7</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#important-technicalities-more-on-rescaling-data">Important technicalities: More on Rescaling data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#test-function-for-what-happens-with-ols-ridge-and-lasso">Test Function for what happens with OLS, Ridge and Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#assumptions-made">Assumptions made</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance">Expectation value and variance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">Independent and Identically Distrubuted (iid)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">Maximum Likelihood Estimation (MLE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-new-cost-function">A new Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">More basic Statistics and Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#marginal-probability">Marginal Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditional-probability">Conditional  Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem">Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">Interpretations of Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">Example of Usage of Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#doing-it-correctly">Doing it correctly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-bayes">Ridge and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-and-bayes">Lasso and Bayes</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Week 36: Statistical interpretation of Linear Regression and Resampling techniques</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-36">
-   Plans for week 36
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday">
-   Material for the active learning sessions Tuesday and Wednesday
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-regression-and-the-svd">
-   Linear Regression and  the SVD
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#what-does-it-mean">
-   What does it mean?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">
-   And finally
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{X}\boldsymbol{X}^T\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">
-   Code for SVD and Inversion of Matrices
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#inverse-of-rectangular-matrix">
-   Inverse of Rectangular Matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-lasso-regression">
-   Ridge and LASSO Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#from-ols-to-ridge-and-lasso">
-   From OLS to Ridge and Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">
-   Deriving the  Ridge Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#note-on-scikit-learn">
-   Note on Scikit-Learn
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#comparison-with-ols">
-   Comparison with OLS
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#svd-analysis">
-   SVD analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpreting-the-ridge-results">
-   Interpreting the Ridge results
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-interpretations">
-   More interpretations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">
-   Deriving the  Lasso Regression Equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">
-   Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-regression">
-   Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-regression">
-   Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#yet-another-example">
-   Yet another Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ols-case">
-   The OLS case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ridge-case">
-   The Ridge case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#writing-the-cost-function">
-   Writing the Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-case">
-   Lasso case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-first-case">
-   The first Case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-code-for-solving-the-above-problem">
-   Simple code for solving the above problem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#with-lasso-regression">
-   With Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#another-example-now-with-a-polynomial-fit">
-   Another Example, now with a polynomial fit
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-7">
-   Material for lecture Thursday September 7
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#important-technicalities-more-on-rescaling-data">
-   Important technicalities: More on Rescaling data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#test-function-for-what-happens-with-ols-ridge-and-lasso">
-   Test Function for what happens with OLS, Ridge and Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#assumptions-made">
-   Assumptions made
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance">
-   Expectation value and variance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">
-   Expectation value and variance for
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{\beta}\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">
-   Independent and Identically Distrubuted (iid)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">
-   Maximum Likelihood Estimation (MLE)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-new-cost-function">
-   A new Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">
-   More basic Statistics and Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#marginal-probability">
-   Marginal Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditional-probability">
-   Conditional  Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem">
-   Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">
-   Interpretations of Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">
-   Example of Usage of Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#doing-it-correctly">
-   Doing it correctly
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-bayes">
-   Ridge and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-and-bayes">
-   Lasso and Bayes
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html week36.do.txt --no_mako -->
-<!-- dom:TITLE: Week 36: Statistical interpretation of Linear Regression and Resampling techniques --><div class="tex2jax_ignore mathjax_ignore section" id="week-36-statistical-interpretation-of-linear-regression-and-resampling-techniques">
-<h1>Week 36: Statistical interpretation of Linear Regression and Resampling techniques<a class="headerlink" href="#week-36-statistical-interpretation-of-linear-regression-and-resampling-techniques" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Week 36: Statistical interpretation of Linear Regression and Resampling techniques --><section class="tex2jax_ignore mathjax_ignore" id="week-36-statistical-interpretation-of-linear-regression-and-resampling-techniques">
+<h1>Week 36: Statistical interpretation of Linear Regression and Resampling techniques<a class="headerlink" href="#week-36-statistical-interpretation-of-linear-regression-and-resampling-techniques" title="Permalink to this heading">#</a></h1>
 <p><strong>Morten Hjorth-Jensen</strong>, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</p>
 <p>Date: <strong>September 4-8, 2023</strong></p>
-<div class="section" id="plans-for-week-36">
-<h2>Plans for week 36<a class="headerlink" href="#plans-for-week-36" title="Permalink to this headline">¶</a></h2>
+<section id="plans-for-week-36">
+<h2>Plans for week 36<a class="headerlink" href="#plans-for-week-36" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Material for the active learning sessions on Tuesday and Wednesday</p>
 <ul>
@@ -929,13 +488,13 @@ doconce format html week36.do.txt --no_mako -->
 </ul>
 </li>
 </ul>
-</div>
-<div class="section" id="material-for-the-active-learning-sessions-tuesday-and-wednesday">
-<h2>Material for the active learning sessions Tuesday and Wednesday<a class="headerlink" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-for-the-active-learning-sessions-tuesday-and-wednesday">
+<h2>Material for the active learning sessions Tuesday and Wednesday<a class="headerlink" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday" title="Permalink to this heading">#</a></h2>
 <p>The material here contains a summary from last week and discussion of SVD, Ridge and Lasso regression with examples</p>
-</div>
-<div class="section" id="linear-regression-and-the-svd">
-<h2>Linear Regression and  the SVD<a class="headerlink" href="#linear-regression-and-the-svd" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linear-regression-and-the-svd">
+<h2>Linear Regression and  the SVD<a class="headerlink" href="#linear-regression-and-the-svd" title="Permalink to this heading">#</a></h2>
 <p>We used the SVD to analyse the matrix to invert in ordinary lineat regression</p>
 <div class="math notranslate nohighlight">
 \[
@@ -966,9 +525,9 @@ doconce format html week36.do.txt --no_mako -->
 \[
 \left(\boldsymbol{X}^T\boldsymbol{X}\right)\boldsymbol{V}=\boldsymbol{V}\tilde{\boldsymbol{\Sigma}}^2.
 \]</div>
-</div>
-<div class="section" id="what-does-it-mean">
-<h2>What does it mean?<a class="headerlink" href="#what-does-it-mean" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="what-does-it-mean">
+<h2>What does it mean?<a class="headerlink" href="#what-does-it-mean" title="Permalink to this heading">#</a></h2>
 <p>This means the vectors <span class="math notranslate nohighlight">\(\boldsymbol{v}_i\)</span> of the orthogonal matrix <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>
 are the eigenvectors of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> with eigenvalues
 given by the singular values squared, that is</p>
@@ -997,9 +556,9 @@ matrix. Every singular value of <span class="math notranslate nohighlight">\(\bo
 root of an eigenvalue of <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span>. If the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is
 self-adjoint, the singular values of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> are equal to the
 absolute value of the eigenvalues of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="and-finally-boldsymbol-x-boldsymbol-x-t">
-<h2>And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span><a class="headerlink" href="#and-finally-boldsymbol-x-boldsymbol-x-t" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="and-finally-boldsymbol-x-boldsymbol-x-t">
+<h2>And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span><a class="headerlink" href="#and-finally-boldsymbol-x-boldsymbol-x-t" title="Permalink to this heading">#</a></h2>
 <p>For <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span> we found</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1027,9 +586,9 @@ measure how much correlations are contained in the rows of <span class="math not
 <p>Since we will mainly be interested in the correlations among the features
 of our data (the columns of <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>, the quantity of interest for us are the non-zero singular
 values and the column vectors of <span class="math notranslate nohighlight">\(\boldsymbol{V}\)</span>.</p>
-</div>
-<div class="section" id="code-for-svd-and-inversion-of-matrices">
-<h2>Code for SVD and Inversion of Matrices<a class="headerlink" href="#code-for-svd-and-inversion-of-matrices" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="code-for-svd-and-inversion-of-matrices">
+<h2>Code for SVD and Inversion of Matrices<a class="headerlink" href="#code-for-svd-and-inversion-of-matrices" title="Permalink to this heading">#</a></h2>
 <p>How do we use the SVD to invert a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^\boldsymbol{X}\)</span> which is singular or near singular?
 The simple answer is to use the linear algebra function for the computation of the pseudoinverse of a given matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>, that is</p>
 <div class="cell docutils container">
@@ -1043,12 +602,12 @@ The simple answer is to use the linear algebra function for the computation of t
 <div class="cell_output docutils container">
 <div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
 <span class="ne">AttributeError</span><span class="g g-Whitespace">                            </span>Traceback (most recent call last)
-<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 3&gt;</span><span class="nt">()</span>
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">3</span>
 <span class="g g-Whitespace">      </span><span class="mi">1</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span> <span class="p">[</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],[</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]])</span>
 <span class="ne">----&gt; </span><span class="mi">3</span> <span class="n">Xinv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linlag</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
 
-<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/__init__.py:313,</span> in <span class="ni">__getattr__</span><span class="nt">(attr)</span>
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/numpy/__init__.py:313,</span> in <span class="ni">__getattr__</span><span class="nt">(attr)</span>
 <span class="g g-Whitespace">    </span><span class="mi">310</span>     <span class="kn">from</span> <span class="nn">.testing</span> <span class="kn">import</span> <span class="n">Tester</span>
 <span class="g g-Whitespace">    </span><span class="mi">311</span>     <span class="k">return</span> <span class="n">Tester</span>
 <span class="ne">--&gt; </span><span class="mi">313</span> <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">&quot;module </span><span class="si">{!r}</span><span class="s2"> has no attribute &quot;</span>
@@ -1065,7 +624,7 @@ The simple answer is to use the linear algebra function for the computation of t
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="c1"># SVD inversion</span>
 <span class="k">def</span> <span class="nf">SVDinv</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
-    <span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
+<span class="w">    </span><span class="sd">&#39;&#39;&#39; Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
 <span class="sd">    SVD is numerically more stable than the inversion algorithms provided by</span>
 <span class="sd">    numpy and scipy.linalg at the cost of being slower.</span>
 <span class="sd">    &#39;&#39;&#39;</span>
@@ -1095,9 +654,9 @@ The simple answer is to use the linear algebra function for the computation of t
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="inverse-of-rectangular-matrix">
-<h2>Inverse of Rectangular Matrix<a class="headerlink" href="#inverse-of-rectangular-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="inverse-of-rectangular-matrix">
+<h2>Inverse of Rectangular Matrix<a class="headerlink" href="#inverse-of-rectangular-matrix" title="Permalink to this heading">#</a></h2>
 <p>Although our matrix to invert <span class="math notranslate nohighlight">\(\boldsymbol{X}^T\boldsymbol{X}\)</span> is a square matrix, our matrix may be singular.</p>
 <p>The pseudoinverse is the generalization of the matrix inverse for square matrices to
 rectangular matrices where the number of rows and columns are not equal.</p>
@@ -1139,9 +698,9 @@ It is used for the calculation of the inverse for singular or near singular matr
 </div>
 </div>
 <p>As you can see from this example, our own decomposition based on the SVD agrees with  the pseudoinverse algorithm provided by <strong>Numpy</strong>.</p>
-</div>
-<div class="section" id="ridge-and-lasso-regression">
-<h2>Ridge and LASSO Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="ridge-and-lasso-regression">
+<h2>Ridge and LASSO Regression<a class="headerlink" href="#ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Let us remind ourselves about the expression for the standard Mean Squared Error (MSE) which we used to define our cost function and the equations for the ordinary least squares (OLS) method, that is
 our optimization problem is</p>
 <div class="math notranslate nohighlight">
@@ -1159,9 +718,9 @@ our optimization problem is</p>
 \[
 \vert\vert \boldsymbol{x}\vert\vert_2 = \sqrt{\sum_i x_i^2}.
 \]</div>
-</div>
-<div class="section" id="from-ols-to-ridge-and-lasso">
-<h2>From OLS to Ridge and Lasso<a class="headerlink" href="#from-ols-to-ridge-and-lasso" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="from-ols-to-ridge-and-lasso">
+<h2>From OLS to Ridge and Lasso<a class="headerlink" href="#from-ols-to-ridge-and-lasso" title="Permalink to this heading">#</a></h2>
 <p>By minimizing the above equation with respect to the parameters
 <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> we could then obtain an analytical expression for the
 parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.  We can add a regularization parameter <span class="math notranslate nohighlight">\(\lambda\)</span> by
@@ -1191,9 +750,9 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\vert\vert \boldsymbol{y}-\bolds
 \[
 \vert\vert \boldsymbol{x}\vert\vert_1 = \sum_i \vert x_i\vert.
 \]</div>
-</div>
-<div class="section" id="deriving-the-ridge-regression-equations">
-<h2>Deriving the  Ridge Regression Equations<a class="headerlink" href="#deriving-the-ridge-regression-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-the-ridge-regression-equations">
+<h2>Deriving the  Ridge Regression Equations<a class="headerlink" href="#deriving-the-ridge-regression-equations" title="Permalink to this heading">#</a></h2>
 <p>Using the matrix-vector expression for Ridge regression and dropping the parameter <span class="math notranslate nohighlight">\(1/n\)</span> in front of the standard means squared error equation, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1214,18 +773,18 @@ the optimal parameters</p>
 \sum_{i=0}^{p-1} \beta_i^2 \leq t,
 \]</div>
 <p>with <span class="math notranslate nohighlight">\(t\)</span> a finite positive number.</p>
-</div>
-<div class="section" id="note-on-scikit-learn">
-<h2>Note on Scikit-Learn<a class="headerlink" href="#note-on-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="note-on-scikit-learn">
+<h2>Note on Scikit-Learn<a class="headerlink" href="#note-on-scikit-learn" title="Permalink to this heading">#</a></h2>
 <p>Note well that a library like <strong>Scikit-Learn</strong> does not include the <span class="math notranslate nohighlight">\(1/n\)</span> factor in the expression for the mean-squared error. If you include it, the optimal parameter <span class="math notranslate nohighlight">\(\beta\)</span> becomes</p>
 <div class="math notranslate nohighlight">
 \[
 \hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \left(\boldsymbol{X}^T\boldsymbol{X}+n\lambda\boldsymbol{I}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}.
 \]</div>
 <p>In our codes where we compare our own codes with <strong>Scikit-Learn</strong>, we do thus not include the <span class="math notranslate nohighlight">\(1/n\)</span> factor in the cost function.</p>
-</div>
-<div class="section" id="comparison-with-ols">
-<h2>Comparison with OLS<a class="headerlink" href="#comparison-with-ols" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="comparison-with-ols">
+<h2>Comparison with OLS<a class="headerlink" href="#comparison-with-ols" title="Permalink to this heading">#</a></h2>
 <p>When we compare this with the ordinary least squares result we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1237,9 +796,9 @@ modified diagonal term added to <span class="math notranslate nohighlight">\(\bo
 particular for our discussion of the bias-variance tradeoff are rather
 interesting. We will see that for specific values of <span class="math notranslate nohighlight">\(\lambda\)</span>, we may
 even reduce the variance of the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>. These topics and other related ones, will be discussed after the more linear algebra oriented analysis here.</p>
-</div>
-<div class="section" id="svd-analysis">
-<h2>SVD analysis<a class="headerlink" href="#svd-analysis" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="svd-analysis">
+<h2>SVD analysis<a class="headerlink" href="#svd-analysis" title="Permalink to this heading">#</a></h2>
 <p>Using our insights about the SVD of the design matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>
 We have already analyzed the OLS solutions in terms of the eigenvectors (the columns) of the right singular value matrix <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> as</p>
 <div class="math notranslate nohighlight">
@@ -1252,9 +811,9 @@ We have already analyzed the OLS solutions in terms of the eigenvectors (the col
 \tilde{\boldsymbol{y}}_{\mathrm{Ridge}}=\boldsymbol{X}\boldsymbol{\beta}_{\mathrm{Ridge}} = \boldsymbol{U\Sigma V^T}\left(\boldsymbol{V}\boldsymbol{\Sigma}^2\boldsymbol{V}^T+\lambda\boldsymbol{I} \right)^{-1}(\boldsymbol{U\Sigma V^T})^T\boldsymbol{y}=\sum_{j=0}^{p-1}\boldsymbol{u}_j\boldsymbol{u}_j^T\frac{\sigma_j^2}{\sigma_j^2+\lambda}\boldsymbol{y},
 \]</div>
 <p>with the vectors <span class="math notranslate nohighlight">\(\boldsymbol{u}_j\)</span> being the columns of <span class="math notranslate nohighlight">\(\boldsymbol{U}\)</span> from the SVD of the matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>.</p>
-</div>
-<div class="section" id="interpreting-the-ridge-results">
-<h2>Interpreting the Ridge results<a class="headerlink" href="#interpreting-the-ridge-results" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpreting-the-ridge-results">
+<h2>Interpreting the Ridge results<a class="headerlink" href="#interpreting-the-ridge-results" title="Permalink to this heading">#</a></h2>
 <p>Since <span class="math notranslate nohighlight">\(\lambda \geq 0\)</span>, it means that compared to OLS, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1266,9 +825,9 @@ orthonormal basis <span class="math notranslate nohighlight">\(\boldsymbol{U}\)<
 eigenvalues ordered in a descending way, that is <span class="math notranslate nohighlight">\(\sigma_i \geq
 \sigma_{i+1}\)</span>.</p>
 <p>For small eigenvalues <span class="math notranslate nohighlight">\(\sigma_i\)</span> it means that their contributions become less important, a fact which can be used to reduce the number of degrees of freedom. More about this when we have covered the material on a statistical interpretation of various linear regression methods.</p>
-</div>
-<div class="section" id="more-interpretations">
-<h2>More interpretations<a class="headerlink" href="#more-interpretations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-interpretations">
+<h2>More interpretations<a class="headerlink" href="#more-interpretations" title="Permalink to this heading">#</a></h2>
 <p>For the sake of simplicity, let us assume that the design matrix is orthonormal, that is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1290,9 +849,9 @@ infinity.</p>
 <p>We will come back to more interpreations after we have gone through some of the statistical analysis part.</p>
 <p>For more discussions of Ridge and Lasso regression, <a class="reference external" href="https://arxiv.org/abs/1509.09169">Wessel van Wieringen’s</a> article is highly recommended.
 Similarly, <a class="reference external" href="https://arxiv.org/abs/1803.08823">Mehta et al’s article</a> is also recommended.</p>
-</div>
-<div class="section" id="deriving-the-lasso-regression-equations">
-<h2>Deriving the  Lasso Regression Equations<a class="headerlink" href="#deriving-the-lasso-regression-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-the-lasso-regression-equations">
+<h2>Deriving the  Lasso Regression Equations<a class="headerlink" href="#deriving-the-lasso-regression-equations" title="Permalink to this heading">#</a></h2>
 <p>Using the matrix-vector expression for Lasso regression, we have the following <strong>cost</strong> function</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1314,9 +873,9 @@ C(\boldsymbol{X},\boldsymbol{\beta})=\frac{1}{n}\left\{(\boldsymbol{y}-\boldsymb
 \boldsymbol{X}^T\boldsymbol{X}\boldsymbol{\beta}+\lambda sgn(\boldsymbol{\beta})=\boldsymbol{X}^T\boldsymbol{y}.
 \]</div>
 <p>This equation does not lead to a nice analytical equation as in Ridge regression or ordinary least squares. We have absorbed the factor <span class="math notranslate nohighlight">\(2/n\)</span> in a redefinition of the parameter <span class="math notranslate nohighlight">\(\lambda\)</span>. We will solve this type of problems using libraries like <strong>scikit-learn</strong>.</p>
-</div>
-<div class="section" id="simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">
-<h2>Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression<a class="headerlink" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">
+<h2>Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression<a class="headerlink" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Let us assume that our design matrix is given by unit (identity) matrix, that is a square diagonal matrix with ones only along the
 diagonal. In this case we have an equal number of rows and columns <span class="math notranslate nohighlight">\(n=p\)</span>.</p>
 <p>Our model approximation is just <span class="math notranslate nohighlight">\(\tilde{\boldsymbol{y}}=\boldsymbol{\beta}\)</span> and the mean squared error and thereby the cost function for ordinary least sqquares (OLS) is then (we drop the term <span class="math notranslate nohighlight">\(1/n\)</span>)</p>
@@ -1329,9 +888,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2,
 \[
 \hat{\beta}_i^{\mathrm{OLS}} = y_i.
 \]</div>
-</div>
-<div class="section" id="ridge-regression">
-<h2>Ridge Regression<a class="headerlink" href="#ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="ridge-regression">
+<h2>Ridge Regression<a class="headerlink" href="#ridge-regression" title="Permalink to this heading">#</a></h2>
 <p>For Ridge regression our cost function is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1342,9 +901,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\be
 \[
 \hat{\beta}_i^{\mathrm{Ridge}} = \frac{y_i}{1+\lambda}.
 \]</div>
-</div>
-<div class="section" id="lasso-regression">
-<h2>Lasso Regression<a class="headerlink" href="#lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="lasso-regression">
+<h2>Lasso Regression<a class="headerlink" href="#lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>For Lasso regression our cost function is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1363,9 +922,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\ve
 							  0 &amp;\mathrm{if} &amp; \vert y_i\vert\le  \frac{\lambda}{2}\end{array}\right.\\.
 \end{split}\]</div>
 <p>Plotting these results shows clearly that Lasso regression suppresses (sets to zero) values of <span class="math notranslate nohighlight">\(\beta_i\)</span> for specific values of <span class="math notranslate nohighlight">\(\lambda\)</span>. Ridge regression reduces on the other hand the values of <span class="math notranslate nohighlight">\(\beta_i\)</span> as function of <span class="math notranslate nohighlight">\(\lambda\)</span>.</p>
-</div>
-<div class="section" id="yet-another-example">
-<h2>Yet another Example<a class="headerlink" href="#yet-another-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="yet-another-example">
+<h2>Yet another Example<a class="headerlink" href="#yet-another-example" title="Permalink to this heading">#</a></h2>
 <p>Let us assume we have a data set with outputs/targets given by the vector</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -1377,9 +936,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\ve
 \boldsymbol{X}=\begin{bmatrix}2 &amp; 0\\ 0 &amp; 1 \\ 0 &amp; 0\end{bmatrix},
 \end{split}\]</div>
 <p>meaning that we have two features and two unknown parameters <span class="math notranslate nohighlight">\(\beta_0\)</span> and <span class="math notranslate nohighlight">\(\beta_1\)</span> to be determined either by ordinary least squares, Ridge or Lasso regression.</p>
-</div>
-<div class="section" id="the-ols-case">
-<h2>The OLS case<a class="headerlink" href="#the-ols-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-ols-case">
+<h2>The OLS case<a class="headerlink" href="#the-ols-case" title="Permalink to this heading">#</a></h2>
 <p>For ordinary least squares (OLS) we know that the optimal solution is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1391,9 +950,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\ve
 \hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\begin{bmatrix}2 \\ 2\end{bmatrix},
 \end{split}\]</div>
 <p>The code which implements this simpler case is presented after the discussion of Ridge and Lasso.</p>
-</div>
-<div class="section" id="the-ridge-case">
-<h2>The Ridge case<a class="headerlink" href="#the-ridge-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-ridge-case">
+<h2>The Ridge case<a class="headerlink" href="#the-ridge-case" title="Permalink to this heading">#</a></h2>
 <p>For Ridge regression we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1407,9 +966,9 @@ C(\boldsymbol{\beta})=\sum_{i=0}^{p-1}(y_i-\beta_i)^2+\lambda\sum_{i=0}^{p-1}\ve
 <p>There is normally a constraint on the value of <span class="math notranslate nohighlight">\(\vert\vert \boldsymbol{\beta}\vert\vert_2\)</span> via the parameter <span class="math notranslate nohighlight">\(\lambda\)</span>.
 Let us for simplicity assume that <span class="math notranslate nohighlight">\(\beta_0^2+\beta_1^2=1\)</span> as constraint. This will allow us to find an expression for the optimal values of <span class="math notranslate nohighlight">\(\beta\)</span> and <span class="math notranslate nohighlight">\(\lambda\)</span>.</p>
 <p>To see this, let us write the cost function for Ridge regression.</p>
-</div>
-<div class="section" id="writing-the-cost-function">
-<h2>Writing the Cost Function<a class="headerlink" href="#writing-the-cost-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="writing-the-cost-function">
+<h2>Writing the Cost Function<a class="headerlink" href="#writing-the-cost-function" title="Permalink to this heading">#</a></h2>
 <p>We define the MSE without the <span class="math notranslate nohighlight">\(1/n\)</span> factor and have then, using that</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -1435,9 +994,9 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\beta_0^2+\beta_1^2),
 \left(\frac{8}{4+\lambda}\right)^2+\left(\frac{2}{1+\lambda}\right)^2=1,
 \]</div>
 <p>which gives <span class="math notranslate nohighlight">\(\lambda=4.571\)</span> and <span class="math notranslate nohighlight">\(\beta_0=0.933\)</span> and <span class="math notranslate nohighlight">\(\beta_1=0.359\)</span>.</p>
-</div>
-<div class="section" id="lasso-case">
-<h2>Lasso case<a class="headerlink" href="#lasso-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="lasso-case">
+<h2>Lasso case<a class="headerlink" href="#lasso-case" title="Permalink to this heading">#</a></h2>
 <p>For Lasso we need now, keeping a  constraint on <span class="math notranslate nohighlight">\(\vert\beta_0\vert+\vert\beta_1\vert=1\)</span>,  to take the derivative of the absolute values of <span class="math notranslate nohighlight">\(\beta_0\)</span>
 and <span class="math notranslate nohighlight">\(\beta_1\)</span>. This gives us the following derivatives of the cost function</p>
 <div class="math notranslate nohighlight">
@@ -1454,15 +1013,15 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 \frac{\partial C(\boldsymbol{\beta})}{\partial \beta_1}=-2(2-\beta_1)+\lambda\mathrm{sgn}(\beta_1)=0.
 \]</div>
 <p>We have now four cases to solve besides the trivial cases <span class="math notranslate nohighlight">\(\beta_0\)</span> and/or <span class="math notranslate nohighlight">\(\beta_1\)</span> are zero, namely</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &gt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &gt; 0\)</span>,</p></li>
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &gt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &lt; 0\)</span>,</p></li>
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &lt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &gt; 0\)</span>,</p></li>
 <li><p><span class="math notranslate nohighlight">\(\beta_0 &lt; 0\)</span> and <span class="math notranslate nohighlight">\(\beta_1 &lt; 0\)</span>.</p></li>
 </ol>
-</div>
-<div class="section" id="the-first-case">
-<h2>The first Case<a class="headerlink" href="#the-first-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-first-case">
+<h2>The first Case<a class="headerlink" href="#the-first-case" title="Permalink to this heading">#</a></h2>
 <p>If we consider the first case, we have then</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1484,9 +1043,9 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 \beta_1=\frac{4+\lambda}{2}.
 \]</div>
 <p>Using the constraint on <span class="math notranslate nohighlight">\(\beta_0\)</span> and <span class="math notranslate nohighlight">\(\beta_1\)</span> we can then find the optimal value of <span class="math notranslate nohighlight">\(\lambda\)</span> for the different cases. We leave this as an exercise to you.</p>
-</div>
-<div class="section" id="simple-code-for-solving-the-above-problem">
-<h2>Simple code for solving the above problem<a class="headerlink" href="#simple-code-for-solving-the-above-problem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-code-for-solving-the-above-problem">
+<h2>Simple code for solving the above problem<a class="headerlink" href="#simple-code-for-solving-the-above-problem" title="Permalink to this heading">#</a></h2>
 <p>Here we set up the OLS, Ridge and Lasso functionality in order to study the above example. Note that here we have opted for a set of values of <span class="math notranslate nohighlight">\(\lambda\)</span>, meaning that we need to perform a search in order to find the optimal values.</p>
 <p>First we study and compare the OLS and Ridge results.  The next code compares all three methods.</p>
 <div class="cell docutils container">
@@ -1547,9 +1106,9 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 </div>
 </div>
 <p>We see here that we reach a plateau. What is actually happening?</p>
-</div>
-<div class="section" id="with-lasso-regression">
-<h2>With Lasso Regression<a class="headerlink" href="#with-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="with-lasso-regression">
+<h2>With Lasso Regression<a class="headerlink" href="#with-lasso-regression" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">os</span>
@@ -1612,9 +1171,9 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="another-example-now-with-a-polynomial-fit">
-<h2>Another Example, now with a polynomial fit<a class="headerlink" href="#another-example-now-with-a-polynomial-fit" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="another-example-now-with-a-polynomial-fit">
+<h2>Another Example, now with a polynomial fit<a class="headerlink" href="#another-example-now-with-a-polynomial-fit" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">os</span>
@@ -1699,12 +1258,12 @@ C(\boldsymbol{\beta})=(4-2\beta_0)^2+(2-\beta_1)^2+\lambda(\vert\beta_0\vert+\ve
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="material-for-lecture-thursday-september-7">
-<h2>Material for lecture Thursday September 7<a class="headerlink" href="#material-for-lecture-thursday-september-7" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="important-technicalities-more-on-rescaling-data">
-<h2>Important technicalities: More on Rescaling data<a class="headerlink" href="#important-technicalities-more-on-rescaling-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-for-lecture-thursday-september-7">
+<h2>Material for lecture Thursday September 7<a class="headerlink" href="#material-for-lecture-thursday-september-7" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="important-technicalities-more-on-rescaling-data">
+<h2>Important technicalities: More on Rescaling data<a class="headerlink" href="#important-technicalities-more-on-rescaling-data" title="Permalink to this heading">#</a></h2>
 <p>When you are comparing your own code with for example <strong>Scikit-Learn</strong>’s
 library, there are some technicalities to keep in mind.  The examples
 here demonstrate some of these aspects with potential pitfalls.</p>
@@ -2144,9 +1703,9 @@ because the regularization term does not include the intercept value
 <span class="math notranslate nohighlight">\(\beta_0\)</span> in the fitting.  This applies to Lasso regularization as
 well.  It means that our optimization is now done only with the
 centered matrix and/or vector that enter the fitting procedure.</p>
-</div>
-<div class="section" id="test-function-for-what-happens-with-ols-ridge-and-lasso">
-<h2>Test Function for what happens with OLS, Ridge and Lasso<a class="headerlink" href="#test-function-for-what-happens-with-ols-ridge-and-lasso" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="test-function-for-what-happens-with-ols-ridge-and-lasso">
+<h2>Test Function for what happens with OLS, Ridge and Lasso<a class="headerlink" href="#test-function-for-what-happens-with-ols-ridge-and-lasso" title="Permalink to this heading">#</a></h2>
 <p>Hitherto we have discussed Ridge and Lasso regression in terms of a
 linear analysis. This may to many of you feel rather technical and
 perhaps not that intuitive. The question is whether we can develop a
@@ -2227,9 +1786,9 @@ polynomial fit and that for larger and larger polynomial degrees of freedom, the
 </div>
 </div>
 <p>How can we understand this?</p>
-</div>
-<div class="section" id="linking-the-regression-analysis-with-a-statistical-interpretation">
-<h2>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linking-the-regression-analysis-with-a-statistical-interpretation">
+<h2>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this heading">#</a></h2>
 <p>We will now couple the discussions of ordinary least squares, Ridge
 and Lasso regression with a statistical interpretation, that is we
 move from a linear algebra analysis to a statistical analysis. In
@@ -2263,9 +1822,9 @@ non-random scalar. To specify the parameters of the distribution of
 <p>Recall that <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is a matrix of dimensionality <span class="math notranslate nohighlight">\(n\times p\)</span>. The
 notation above <span class="math notranslate nohighlight">\(\mathbf{X}_{i,\ast}\)</span> means that we are looking at the
 row number <span class="math notranslate nohighlight">\(i\)</span> and perform a sum over all values <span class="math notranslate nohighlight">\(p\)</span>.</p>
-</div>
-<div class="section" id="assumptions-made">
-<h2>Assumptions made<a class="headerlink" href="#assumptions-made" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="assumptions-made">
+<h2>Assumptions made<a class="headerlink" href="#assumptions-made" title="Permalink to this heading">#</a></h2>
 <p>The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)
 that there exists a function <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and  a normal distributed error <span class="math notranslate nohighlight">\(\boldsymbol{\varepsilon}\sim \mathcal{N}(0, \sigma^2)\)</span>
 which describe our data</p>
@@ -2279,9 +1838,9 @@ function <span class="math notranslate nohighlight">\(f\)</span> is approximated
 \[
 \boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
 \]</div>
-</div>
-<div class="section" id="expectation-value-and-variance">
-<h2>Expectation value and variance<a class="headerlink" href="#expectation-value-and-variance" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="expectation-value-and-variance">
+<h2>Expectation value and variance<a class="headerlink" href="#expectation-value-and-variance" title="Permalink to this heading">#</a></h2>
 <p>We can calculate the expectation value of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> for a given element <span class="math notranslate nohighlight">\(i\)</span></p>
 <div class="math notranslate nohighlight">
 \[
@@ -2310,9 +1869,9 @@ its variance is</p>
 \end{split}\]</div>
 <p>Hence, <span class="math notranslate nohighlight">\(y_i \sim \mathcal{N}( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)\)</span>, that is <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> follows a normal distribution with
 mean value <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{\beta}\)</span> and variance <span class="math notranslate nohighlight">\(\sigma^2\)</span> (not be confused with the singular values of the SVD).</p>
-</div>
-<div class="section" id="expectation-value-and-variance-for-boldsymbol-beta">
-<h2>Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span><a class="headerlink" href="#expectation-value-and-variance-for-boldsymbol-beta" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="expectation-value-and-variance-for-boldsymbol-beta">
+<h2>Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span><a class="headerlink" href="#expectation-value-and-variance-for-boldsymbol-beta" title="Permalink to this heading">#</a></h2>
 <p>With the OLS expressions for the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\hat{\beta}}\)</span> we can evaluate the expectation value</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2375,9 +1934,9 @@ when we employ Ridge regression, allowing us again to define a confidence interv
 <p>The difference is non-negative definite since each component of the
 matrix product is non-negative definite.
 This means the variance we obtain with the standard OLS will always for <span class="math notranslate nohighlight">\(\lambda &gt; 0\)</span> be larger than the variance of <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.</p>
-</div>
-<div class="section" id="deriving-ols-from-a-probability-distribution">
-<h2>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="deriving-ols-from-a-probability-distribution">
+<h2>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this heading">#</a></h2>
 <p>Our basic assumption when we derived the OLS equations was to assume
 that our output is determined by a given continuous function
 <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and a random noise <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> given by the normal
@@ -2393,9 +1952,9 @@ single output <span class="math notranslate nohighlight">\(y_i\)</span> is given
 \[
 y_i\sim \mathcal{N}(\boldsymbol{X}_{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
 \]</div>
-</div>
-<div class="section" id="independent-and-identically-distrubuted-iid">
-<h2>Independent and Identically Distrubuted (iid)<a class="headerlink" href="#independent-and-identically-distrubuted-iid" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="independent-and-identically-distrubuted-iid">
+<h2>Independent and Identically Distrubuted (iid)<a class="headerlink" href="#independent-and-identically-distrubuted-iid" title="Permalink to this heading">#</a></h2>
 <p>We assume now that the various <span class="math notranslate nohighlight">\(y_i\)</span> values are stochastically distributed according to the above Gaussian distribution.
 We define this distribution as</p>
 <div class="math notranslate nohighlight">
@@ -2421,9 +1980,9 @@ We can now rewrite the above probability as</p>
 p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
 \]</div>
 <p>It is a conditional probability (see below) and reads as the likelihood of a domain of events <span class="math notranslate nohighlight">\(\boldsymbol{D}\)</span> given a set of parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.</p>
-</div>
-<div class="section" id="maximum-likelihood-estimation-mle">
-<h2>Maximum Likelihood Estimation (MLE)<a class="headerlink" href="#maximum-likelihood-estimation-mle" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="maximum-likelihood-estimation-mle">
+<h2>Maximum Likelihood Estimation (MLE)<a class="headerlink" href="#maximum-likelihood-estimation-mle" title="Permalink to this heading">#</a></h2>
 <p>In statistics, maximum likelihood estimation (MLE) is a method of
 estimating the parameters of an assumed probability distribution,
 given some observed data. This is achieved by maximizing a likelihood
@@ -2441,9 +2000,9 @@ negative of the logarithm since this is a monotonically decreasing
 function.</p>
 <p>Note also that maximization/minimization of the logarithm of the PDF
 is equivalent to the maximization/minimization of the function itself.</p>
-</div>
-<div class="section" id="a-new-cost-function">
-<h2>A new Cost Function<a class="headerlink" href="#a-new-cost-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-new-cost-function">
+<h2>A new Cost Function<a class="headerlink" href="#a-new-cost-function" title="Permalink to this heading">#</a></h2>
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2465,9 +2024,9 @@ C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol
 \hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
 \]</div>
 <p>Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics.</p>
-</div>
-<div class="section" id="more-basic-statistics-and-bayes-theorem">
-<h2>More basic Statistics and Bayes’ theorem<a class="headerlink" href="#more-basic-statistics-and-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-basic-statistics-and-bayes-theorem">
+<h2>More basic Statistics and Bayes’ theorem<a class="headerlink" href="#more-basic-statistics-and-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>A central theorem in statistics is Bayes’ theorem. This theorem plays a similar role as the good old Pythagoras’ theorem in geometry.
 Bayes’ theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.</p>
 <p>Assume we have two domains of events <span class="math notranslate nohighlight">\(X=[x_0,x_1,\dots,x_{n-1}]\)</span> and <span class="math notranslate nohighlight">\(Y=[y_0,y_1,\dots,y_{n-1}]\)</span>.</p>
@@ -2485,25 +2044,25 @@ p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
 \]</div>
 <p>where we read <span class="math notranslate nohighlight">\(p(X\vert Y)\)</span> as the likelihood of obtaining <span class="math notranslate nohighlight">\(X\)</span> given <span class="math notranslate nohighlight">\(Y\)</span>.</p>
 <p>If we have independent events then <span class="math notranslate nohighlight">\(p(X,Y)=p(X)p(Y)\)</span>.</p>
-</div>
-<div class="section" id="marginal-probability">
-<h2>Marginal Probability<a class="headerlink" href="#marginal-probability" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="marginal-probability">
+<h2>Marginal Probability<a class="headerlink" href="#marginal-probability" title="Permalink to this heading">#</a></h2>
 <p>The marginal probability is defined in terms of only one of the set of variables <span class="math notranslate nohighlight">\(X,Y\)</span>. For a discrete probability we have</p>
 <div class="math notranslate nohighlight">
 \[
 p(X)=\sum_{i=0}^{n-1}p(X,Y=y_i)=\sum_{i=0}^{n-1}p(X\vert Y=y_i)p(Y=y_i)=\sum_{i=0}^{n-1}p(X\vert y_i)p(y_i).
 \]</div>
-</div>
-<div class="section" id="conditional-probability">
-<h2>Conditional  Probability<a class="headerlink" href="#conditional-probability" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="conditional-probability">
+<h2>Conditional  Probability<a class="headerlink" href="#conditional-probability" title="Permalink to this heading">#</a></h2>
 <p>The conditional  probability, if <span class="math notranslate nohighlight">\(p(Y) &gt; 0\)</span>, is</p>
 <div class="math notranslate nohighlight">
 \[
 p(X\vert Y)= \frac{p(X,Y)}{p(Y)}=\frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}.
 \]</div>
-</div>
-<div class="section" id="bayes-theorem">
-<h2>Bayes’ Theorem<a class="headerlink" href="#bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bayes-theorem">
+<h2>Bayes’ Theorem<a class="headerlink" href="#bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>If we combine the conditional probability with the marginal probability and the standard product rule, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2515,18 +2074,18 @@ p(X\vert Y)= \frac{p(X,Y)}{p(Y)},
 p(X\vert Y)= \frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}=\frac{p(Y\vert X)p(X)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)},
 \]</div>
 <p>which is Bayes’ theorem. It allows us to evaluate the uncertainty in in <span class="math notranslate nohighlight">\(X\)</span> after we have observed <span class="math notranslate nohighlight">\(Y\)</span>. We can easily interchange <span class="math notranslate nohighlight">\(X\)</span> with <span class="math notranslate nohighlight">\(Y\)</span>.</p>
-</div>
-<div class="section" id="interpretations-of-bayes-theorem">
-<h2>Interpretations of Bayes’ Theorem<a class="headerlink" href="#interpretations-of-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpretations-of-bayes-theorem">
+<h2>Interpretations of Bayes’ Theorem<a class="headerlink" href="#interpretations-of-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>The quantity <span class="math notranslate nohighlight">\(p(Y\vert X)\)</span> on the right-hand side of the theorem is
 evaluated for the observed data <span class="math notranslate nohighlight">\(Y\)</span> and can be viewed as a function of
 the parameter space represented by <span class="math notranslate nohighlight">\(X\)</span>. This function is not
 necesseraly normalized and is normally called the likelihood function.</p>
 <p>The function <span class="math notranslate nohighlight">\(p(X)\)</span> on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.</p>
 <p>Let us try to illustrate Bayes’ theorem through an example.</p>
-</div>
-<div class="section" id="example-of-usage-of-bayes-theorem">
-<h2>Example of Usage of Bayes’ theorem<a class="headerlink" href="#example-of-usage-of-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-of-usage-of-bayes-theorem">
+<h2>Example of Usage of Bayes’ theorem<a class="headerlink" href="#example-of-usage-of-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>Let us suppose that you are undergoing a series of mammography scans in
 order to rule out possible breast cancer cases.  We define the
 sensitivity for a positive event by the variable <span class="math notranslate nohighlight">\(X\)</span>. It takes binary
@@ -2541,9 +2100,9 @@ p(X=1\vert Y=1) =0.8.
 \]</div>
 <p>This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of <span class="math notranslate nohighlight">\(80\%\)</span> for having cancer.
 It is however not correct, as the following Bayesian analysis shows.</p>
-</div>
-<div class="section" id="doing-it-correctly">
-<h2>Doing it correctly<a class="headerlink" href="#doing-it-correctly" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="doing-it-correctly">
+<h2>Doing it correctly<a class="headerlink" href="#doing-it-correctly" title="Permalink to this heading">#</a></h2>
 <p>If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.
 Let us assume that the prior probability in the population as a whole is</p>
 <div class="math notranslate nohighlight">
@@ -2561,9 +2120,9 @@ p(X=1\vert Y=0) =0.1.
 p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y=0)p(Y=0)}=\frac{0.8\times 0.004}{0.8\times 0.004+0.1\times 0.996}=0.031.
 \]</div>
 <p>That is, in case of a positive test, there is only a <span class="math notranslate nohighlight">\(3\%\)</span> chance of having breast cancer!</p>
-</div>
-<div class="section" id="bayes-theorem-and-ridge-and-lasso-regression">
-<h2>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bayes-theorem-and-ridge-and-lasso-regression">
+<h2>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Using Bayes’ theorem we can gain a better intuition about Ridge and Lasso regression.</p>
 <p>For ordinary least squares we postulated that the maximum likelihood for the doamin of events <span class="math notranslate nohighlight">\(\boldsymbol{D}\)</span> (one-dimensional case)</p>
 <div class="math notranslate nohighlight">
@@ -2586,9 +2145,9 @@ p(\boldsymbol{\beta}\vert\boldsymbol{D}).
 p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}).
 \]</div>
 <p>We have a model for <span class="math notranslate nohighlight">\(p(\boldsymbol{D}\vert\boldsymbol{\beta})\)</span> but need one for the <strong>prior</strong> <span class="math notranslate nohighlight">\(p(\boldsymbol{\beta}\)</span>!</p>
-</div>
-<div class="section" id="ridge-and-bayes">
-<h2>Ridge and Bayes<a class="headerlink" href="#ridge-and-bayes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="ridge-and-bayes">
+<h2>Ridge and Bayes<a class="headerlink" href="#ridge-and-bayes" title="Permalink to this heading">#</a></h2>
 <p>With the posterior probability defined by a likelihood which we have
 already modeled and an unknown prior, we are now ready to make
 additional models for the prior.</p>
@@ -2616,9 +2175,9 @@ C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol
 C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
 \]</div>
 <p>which is our Ridge cost function!  Nice, isn’t it?</p>
-</div>
-<div class="section" id="lasso-and-bayes">
-<h2>Lasso and Bayes<a class="headerlink" href="#lasso-and-bayes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="lasso-and-bayes">
+<h2>Lasso and Bayes<a class="headerlink" href="#lasso-and-bayes" title="Permalink to this heading">#</a></h2>
 <p>To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution (<a class="reference external" href="https://en.wikipedia.org/wiki/Laplace_distribution">Laplace in this case</a>) with zero mean value,  that is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2642,8 +2201,8 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
 C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
 \]</div>
 <p>which is our Lasso cost function!</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2657,7 +2216,7 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -2665,44 +2224,149 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
     </script>
     <script>kernelName = 'python3'</script>
 
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+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-36">Plans for week 36</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-the-active-learning-sessions-tuesday-and-wednesday">Material for the active learning sessions Tuesday and Wednesday</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-regression-and-the-svd">Linear Regression and  the SVD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#what-does-it-mean">What does it mean?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-boldsymbol-x-boldsymbol-x-t">And finally  <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{X}^T\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-for-svd-and-inversion-of-matrices">Code for SVD and Inversion of Matrices</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#inverse-of-rectangular-matrix">Inverse of Rectangular Matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-lasso-regression">Ridge and LASSO Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#from-ols-to-ridge-and-lasso">From OLS to Ridge and Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-ridge-regression-equations">Deriving the  Ridge Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#note-on-scikit-learn">Note on Scikit-Learn</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#comparison-with-ols">Comparison with OLS</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#svd-analysis">SVD analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpreting-the-ridge-results">Interpreting the Ridge results</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-interpretations">More interpretations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-the-lasso-regression-equations">Deriving the  Lasso Regression Equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression">Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-regression">Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-regression">Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#yet-another-example">Yet another Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ols-case">The OLS case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ridge-case">The Ridge case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#writing-the-cost-function">Writing the Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-case">Lasso case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-first-case">The first Case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-code-for-solving-the-above-problem">Simple code for solving the above problem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#with-lasso-regression">With Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-now-with-a-polynomial-fit">Another Example, now with a polynomial fit</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-7">Material for lecture Thursday September 7</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#important-technicalities-more-on-rescaling-data">Important technicalities: More on Rescaling data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#test-function-for-what-happens-with-ols-ridge-and-lasso">Test Function for what happens with OLS, Ridge and Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#assumptions-made">Assumptions made</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance">Expectation value and variance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">Independent and Identically Distrubuted (iid)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">Maximum Likelihood Estimation (MLE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-new-cost-function">A new Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">More basic Statistics and Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#marginal-probability">Marginal Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditional-probability">Conditional  Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem">Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">Interpretations of Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">Example of Usage of Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#doing-it-correctly">Doing it correctly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-bayes">Ridge and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-and-bayes">Lasso and Bayes</a></li>
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-  Review of Statistics with Resampling Techniques and Linear Algebra
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 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  From Regression to Support Vector Machines
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-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Dimensionality Reduction
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter8.html">
-   11. Basic ideas of the Principal Component Analysis (PCA)
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="clustering.html">
-   12. Clustering and Unsupervised Learning
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
+<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Deep Learning Methods
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
 <ul class="nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter9.html">
-   13. Neural networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter10.html">
-   14. Building a Feed Forward Neural Network
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter11.html">
-   15. Solving Differential Equations  with Deep Learning
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter12.html">
-   16. Convolutional Neural Networks
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="chapter13.html">
-   17. Recurrent neural networks: Overarching view
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations  with Deep Learning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Weekly material, notes and exercises
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
 <ul class="current nav bd-sidenav">
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek34.html">
-   Exercises week 34
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- </li>
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-  <a class="reference internal" href="week34.html">
-   Week 34: Introduction to the course, Logistics and Practicalities
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek35.html">
-   Exercises week 35
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week35.html">
-   Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toctree-l1">
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-   Exercises week 36
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-   Week 36: Statistical interpretation of Linear Regression and Resampling techniques
-  </a>
- </li>
- <li class="toctree-l1">
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-   Exercises week 37
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- <li class="toctree-l1 current active">
-  <a class="current reference internal" href="#">
-   Week 37: Statistical interpretations and Resampling Methods
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="exercisesweek38.html">
-   Exercises week 38
-  </a>
- </li>
- <li class="toctree-l1">
-  <a class="reference internal" href="week38.html">
-   Week38: Logistic Regression and Optimization
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
- <span class="caption-text">
-  Projects
- </span>
-</p>
+<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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- <li class="toctree-l1">
-  <a class="reference internal" href="project1.html">
-   Project 1 on Machine Learning, deadline October 9 (midnight), 2023
-  </a>
- </li>
+<li class="toctree-l1"><a class="reference internal" href="project1.html">Project 1 on Machine Learning, deadline October 9 (midnight), 2023</a></li>
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+    <h1>Week 37: Statistical interpretations and Resampling Methods</h1>
+    <!-- Table of contents -->
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-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-37">
-   Plans for week 37
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-weekly-exercises">
-   Material from last week and relevant for the weekly exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#assumptions-made">
-   Assumptions made
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance">
-   Expectation value and variance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">
-   Expectation value and variance for
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{\beta}\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-14">
-   Material for lecture Thursday September 14
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">
-   Independent and Identically Distrubuted (iid)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">
-   Maximum Likelihood Estimation (MLE)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-new-cost-function">
-   A new Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">
-   More basic Statistics and Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#marginal-probability">
-   Marginal Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditional-probability">
-   Conditional  Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem">
-   Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">
-   Interpretations of Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">
-   Example of Usage of Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#doing-it-correctly">
-   Doing it correctly
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-bayes">
-   Ridge and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-and-bayes">
-   Lasso and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-resampling-methods">
-   Why resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods">
-   Resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-approaches-can-be-computationally-expensive">
-   Resampling approaches can be computationally expensive
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Why resampling methods ?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#statistical-analysis">
-   Statistical analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap">
-   Resampling methods: Bootstrap
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-central-limit-theorem">
-   The Central Limit Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#finding-the-limit">
-   Finding the Limit
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-delta-function">
-   Rewriting the
-   <span class="math notranslate nohighlight">
-    \(\delta\)
-   </span>
-   -function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#identifying-terms">
-   Identifying Terms
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wrapping-it-up">
-   Wrapping it up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#confidence-intervals">
-   Confidence Intervals
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#standard-approach-based-on-the-normal-distribution">
-   Standard Approach based on the Normal Distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-background">
-   Resampling methods: Bootstrap background
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-more-bootstrap-background">
-   Resampling methods: More Bootstrap background
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-approach">
-   Resampling methods: Bootstrap approach
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-steps">
-   Resampling methods: Bootstrap steps
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-the-bootstrap-method">
-   Code example for the Bootstrap method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plotting-the-histogram">
-   Plotting the Histogram
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-bias-variance-tradeoff">
-   The bias-variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-way-to-read-the-bias-variance-tradeoff">
-   A way to Read the Bias-Variance Tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-code-for-bias-variance-tradeoff">
-   Example code for Bias-Variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#understanding-what-happens">
-   Understanding what happens
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#summing-up">
-   Summing up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#another-example-from-scikit-learn-s-repository">
-   Another Example from Scikit-Learn’s Repository
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#various-steps-in-cross-validation">
-   Various steps in cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation-in-brief">
-   Cross-validation in brief
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">
-   Code Example for Cross-validation and
-   <span class="math notranslate nohighlight">
-    \(k\)
-   </span>
-   -fold Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-examples-on-bootstrap-and-cross-validation-and-errors">
-   More examples on bootstrap and cross-validation and errors
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-same-example-but-now-with-cross-validation">
-   The same example but now with cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#notes-on-scaling-with-examples">
-   Notes on scaling with examples
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-37">Plans for week 37</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-weekly-exercises">Material from last week and relevant for the weekly exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#assumptions-made">Assumptions made</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance">Expectation value and variance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-14">Material for lecture Thursday September 14</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">Independent and Identically Distrubuted (iid)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">Maximum Likelihood Estimation (MLE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-new-cost-function">A new Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">More basic Statistics and Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#marginal-probability">Marginal Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditional-probability">Conditional  Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem">Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">Interpretations of Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">Example of Usage of Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#doing-it-correctly">Doing it correctly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-bayes">Ridge and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-and-bayes">Lasso and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-resampling-methods">Why resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods">Resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-approaches-can-be-computationally-expensive">Resampling approaches can be computationally expensive</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Why resampling methods ?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#statistical-analysis">Statistical analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap">Resampling methods: Bootstrap</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-central-limit-theorem">The Central Limit Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#finding-the-limit">Finding the Limit</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-delta-function">Rewriting the <span class="math notranslate nohighlight">\(\delta\)</span>-function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#identifying-terms">Identifying Terms</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wrapping-it-up">Wrapping it up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#confidence-intervals">Confidence Intervals</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-approach-based-on-the-normal-distribution">Standard Approach based on the Normal Distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-background">Resampling methods: Bootstrap background</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-more-bootstrap-background">Resampling methods: More Bootstrap background</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-approach">Resampling methods: Bootstrap approach</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-steps">Resampling methods: Bootstrap steps</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-the-bootstrap-method">Code example for the Bootstrap method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plotting-the-histogram">Plotting the Histogram</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-bias-variance-tradeoff">The bias-variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-way-to-read-the-bias-variance-tradeoff">A way to Read the Bias-Variance Tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-code-for-bias-variance-tradeoff">Example code for Bias-Variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#understanding-what-happens">Understanding what happens</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#summing-up">Summing up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-from-scikit-learn-s-repository">Another Example from Scikit-Learn’s Repository</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#various-steps-in-cross-validation">Various steps in cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation-in-brief">Cross-validation in brief</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-examples-on-bootstrap-and-cross-validation-and-errors">More examples on bootstrap and cross-validation and errors</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-same-example-but-now-with-cross-validation">The same example but now with cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#notes-on-scaling-with-examples">Notes on scaling with examples</a></li>
 </ul>
-
             </nav>
         </div>
     </div>
 </div>
-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Week 37: Statistical interpretations and Resampling Methods</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-37">
-   Plans for week 37
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-weekly-exercises">
-   Material from last week and relevant for the weekly exercises
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">
-   Linking the regression analysis with a statistical interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#assumptions-made">
-   Assumptions made
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance">
-   Expectation value and variance
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">
-   Expectation value and variance for
-   <span class="math notranslate nohighlight">
-    \(\boldsymbol{\beta}\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-14">
-   Material for lecture Thursday September 14
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">
-   Deriving OLS from a probability distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">
-   Independent and Identically Distrubuted (iid)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">
-   Maximum Likelihood Estimation (MLE)
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-new-cost-function">
-   A new Cost Function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">
-   More basic Statistics and Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#marginal-probability">
-   Marginal Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditional-probability">
-   Conditional  Probability
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem">
-   Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">
-   Interpretations of Bayes’ Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">
-   Example of Usage of Bayes’ theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#doing-it-correctly">
-   Doing it correctly
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">
-   Bayes’ Theorem and Ridge and Lasso Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#ridge-and-bayes">
-   Ridge and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#lasso-and-bayes">
-   Lasso and Bayes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#why-resampling-methods">
-   Why resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods">
-   Resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-approaches-can-be-computationally-expensive">
-   Resampling approaches can be computationally expensive
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Why resampling methods ?
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#statistical-analysis">
-   Statistical analysis
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id2">
-   Resampling methods
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap">
-   Resampling methods: Bootstrap
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-central-limit-theorem">
-   The Central Limit Theorem
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#finding-the-limit">
-   Finding the Limit
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#rewriting-the-delta-function">
-   Rewriting the
-   <span class="math notranslate nohighlight">
-    \(\delta\)
-   </span>
-   -function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#identifying-terms">
-   Identifying Terms
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wrapping-it-up">
-   Wrapping it up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#confidence-intervals">
-   Confidence Intervals
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#standard-approach-based-on-the-normal-distribution">
-   Standard Approach based on the Normal Distribution
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-background">
-   Resampling methods: Bootstrap background
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-more-bootstrap-background">
-   Resampling methods: More Bootstrap background
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-approach">
-   Resampling methods: Bootstrap approach
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#resampling-methods-bootstrap-steps">
-   Resampling methods: Bootstrap steps
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-the-bootstrap-method">
-   Code example for the Bootstrap method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plotting-the-histogram">
-   Plotting the Histogram
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-bias-variance-tradeoff">
-   The bias-variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-way-to-read-the-bias-variance-tradeoff">
-   A way to Read the Bias-Variance Tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#example-code-for-bias-variance-tradeoff">
-   Example code for Bias-Variance tradeoff
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#understanding-what-happens">
-   Understanding what happens
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#summing-up">
-   Summing up
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#another-example-from-scikit-learn-s-repository">
-   Another Example from Scikit-Learn’s Repository
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#various-steps-in-cross-validation">
-   Various steps in cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation-in-brief">
-   Cross-validation in brief
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">
-   Code Example for Cross-validation and
-   <span class="math notranslate nohighlight">
-    \(k\)
-   </span>
-   -fold Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-examples-on-bootstrap-and-cross-validation-and-errors">
-   More examples on bootstrap and cross-validation and errors
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-same-example-but-now-with-cross-validation">
-   The same example but now with cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#notes-on-scaling-with-examples">
-   Notes on scaling with examples
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html week37.do.txt --no_mako -->
-<!-- dom:TITLE: Week 37: Statistical interpretations and Resampling Methods --><div class="tex2jax_ignore mathjax_ignore section" id="week-37-statistical-interpretations-and-resampling-methods">
-<h1>Week 37: Statistical interpretations and Resampling Methods<a class="headerlink" href="#week-37-statistical-interpretations-and-resampling-methods" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Week 37: Statistical interpretations and Resampling Methods --><section class="tex2jax_ignore mathjax_ignore" id="week-37-statistical-interpretations-and-resampling-methods">
+<h1>Week 37: Statistical interpretations and Resampling Methods<a class="headerlink" href="#week-37-statistical-interpretations-and-resampling-methods" title="Permalink to this heading">#</a></h1>
 <p><strong>Morten Hjorth-Jensen</strong>, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</p>
 <p>Date: <strong>Sep 18, 2023</strong></p>
 <p>Copyright 1999-2023, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license</p>
-<!-- todo add link to videos and add link to Van Wieringens notes --><div class="section" id="plans-for-week-37">
-<h2>Plans for week 37<a class="headerlink" href="#plans-for-week-37" title="Permalink to this headline">¶</a></h2>
+<!-- todo add link to videos and add link to Van Wieringens notes --><section id="plans-for-week-37">
+<h2>Plans for week 37<a class="headerlink" href="#plans-for-week-37" title="Permalink to this heading">#</a></h2>
 <p><strong>Material for the active learning sessions on Tuesday and Wednesday.</strong></p>
 <ul class="simple">
 <li><p>Lecture from last week on calculations of expectation values</p></li>
@@ -994,12 +497,12 @@ doconce format html week37.do.txt --no_mako -->
 </ul>
 </li>
 </ul>
-</div>
-<div class="section" id="material-from-last-week-and-relevant-for-the-weekly-exercises">
-<h2>Material from last week and relevant for the weekly exercises<a class="headerlink" href="#material-from-last-week-and-relevant-for-the-weekly-exercises" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="linking-the-regression-analysis-with-a-statistical-interpretation">
-<h2>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-from-last-week-and-relevant-for-the-weekly-exercises">
+<h2>Material from last week and relevant for the weekly exercises<a class="headerlink" href="#material-from-last-week-and-relevant-for-the-weekly-exercises" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="linking-the-regression-analysis-with-a-statistical-interpretation">
+<h2>Linking the regression analysis with a statistical interpretation<a class="headerlink" href="#linking-the-regression-analysis-with-a-statistical-interpretation" title="Permalink to this heading">#</a></h2>
 <p>We will now couple the discussions of ordinary least squares, Ridge
 and Lasso regression with a statistical interpretation, that is we
 move from a linear algebra analysis to a statistical analysis. In
@@ -1033,9 +536,9 @@ non-random scalar. To specify the parameters of the distribution of
 <p>Recall that <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is a matrix of dimensionality <span class="math notranslate nohighlight">\(n\times p\)</span>. The
 notation above <span class="math notranslate nohighlight">\(\mathbf{X}_{i,\ast}\)</span> means that we are looking at the
 row number <span class="math notranslate nohighlight">\(i\)</span> and perform a sum over all values <span class="math notranslate nohighlight">\(p\)</span>.</p>
-</div>
-<div class="section" id="assumptions-made">
-<h2>Assumptions made<a class="headerlink" href="#assumptions-made" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="assumptions-made">
+<h2>Assumptions made<a class="headerlink" href="#assumptions-made" title="Permalink to this heading">#</a></h2>
 <p>The assumption we have made here can be summarized as (and this is going to be useful when we discuss the bias-variance trade off)
 that there exists a function <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and  a normal distributed error <span class="math notranslate nohighlight">\(\boldsymbol{\varepsilon}\sim \mathcal{N}(0, \sigma^2)\)</span>
 which describe our data</p>
@@ -1049,9 +552,9 @@ function <span class="math notranslate nohighlight">\(f\)</span> is approximated
 \[
 \boldsymbol{\tilde{y}} = \boldsymbol{X}\boldsymbol{\beta}.
 \]</div>
-</div>
-<div class="section" id="expectation-value-and-variance">
-<h2>Expectation value and variance<a class="headerlink" href="#expectation-value-and-variance" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="expectation-value-and-variance">
+<h2>Expectation value and variance<a class="headerlink" href="#expectation-value-and-variance" title="Permalink to this heading">#</a></h2>
 <p>We can calculate the expectation value of <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> for a given element <span class="math notranslate nohighlight">\(i\)</span></p>
 <div class="math notranslate nohighlight">
 \[
@@ -1080,9 +583,9 @@ its variance is</p>
 \end{split}\]</div>
 <p>Hence, <span class="math notranslate nohighlight">\(y_i \sim \mathcal{N}( \mathbf{X}_{i, \ast} \, \boldsymbol{\beta}, \sigma^2)\)</span>, that is <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> follows a normal distribution with
 mean value <span class="math notranslate nohighlight">\(\boldsymbol{X}\boldsymbol{\beta}\)</span> and variance <span class="math notranslate nohighlight">\(\sigma^2\)</span> (not be confused with the singular values of the SVD).</p>
-</div>
-<div class="section" id="expectation-value-and-variance-for-boldsymbol-beta">
-<h2>Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span><a class="headerlink" href="#expectation-value-and-variance-for-boldsymbol-beta" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="expectation-value-and-variance-for-boldsymbol-beta">
+<h2>Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span><a class="headerlink" href="#expectation-value-and-variance-for-boldsymbol-beta" title="Permalink to this heading">#</a></h2>
 <p>With the OLS expressions for the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\hat{\beta}}\)</span> we can evaluate the expectation value</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1146,12 +649,12 @@ when we employ Ridge regression, allowing us again to define a confidence interv
 matrix product is non-negative definite.
 This means the variance we obtain with the standard OLS will always for <span class="math notranslate nohighlight">\(\lambda &gt; 0\)</span> be larger than the variance of <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> obtained with the Ridge estimator. This has interesting consequences when we discuss the so-called bias-variance trade-off below.</p>
 <p>For more discussions of Ridge regression and calculation of averages, <a class="reference external" href="https://arxiv.org/abs/1509.09169">Wessel van Wieringen’s</a> article is highly recommended.</p>
-</div>
-<div class="section" id="material-for-lecture-thursday-september-14">
-<h2>Material for lecture Thursday September 14<a class="headerlink" href="#material-for-lecture-thursday-september-14" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="deriving-ols-from-a-probability-distribution">
-<h2>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-for-lecture-thursday-september-14">
+<h2>Material for lecture Thursday September 14<a class="headerlink" href="#material-for-lecture-thursday-september-14" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="deriving-ols-from-a-probability-distribution">
+<h2>Deriving OLS from a probability distribution<a class="headerlink" href="#deriving-ols-from-a-probability-distribution" title="Permalink to this heading">#</a></h2>
 <p>Our basic assumption when we derived the OLS equations was to assume
 that our output is determined by a given continuous function
 <span class="math notranslate nohighlight">\(f(\boldsymbol{x})\)</span> and a random noise <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span> given by the normal
@@ -1167,9 +670,9 @@ single output <span class="math notranslate nohighlight">\(y_i\)</span> is given
 \[
 y_i\sim \mathcal{N}(\boldsymbol{X}_{i,*}\boldsymbol{\beta}, \sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
 \]</div>
-</div>
-<div class="section" id="independent-and-identically-distrubuted-iid">
-<h2>Independent and Identically Distrubuted (iid)<a class="headerlink" href="#independent-and-identically-distrubuted-iid" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="independent-and-identically-distrubuted-iid">
+<h2>Independent and Identically Distrubuted (iid)<a class="headerlink" href="#independent-and-identically-distrubuted-iid" title="Permalink to this heading">#</a></h2>
 <p>We assume now that the various <span class="math notranslate nohighlight">\(y_i\)</span> values are stochastically distributed according to the above Gaussian distribution.
 We define this distribution as</p>
 <div class="math notranslate nohighlight">
@@ -1195,9 +698,9 @@ We can now rewrite the above probability as</p>
 p(\boldsymbol{D}\vert\boldsymbol{\beta})=\prod_{i=0}^{n-1}\frac{1}{\sqrt{2\pi\sigma^2}}\exp{\left[-\frac{(y_i-\boldsymbol{X}_{i,*}\boldsymbol{\beta})^2}{2\sigma^2}\right]}.
 \]</div>
 <p>It is a conditional probability (see below) and reads as the likelihood of a domain of events <span class="math notranslate nohighlight">\(\boldsymbol{D}\)</span> given a set of parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span>.</p>
-</div>
-<div class="section" id="maximum-likelihood-estimation-mle">
-<h2>Maximum Likelihood Estimation (MLE)<a class="headerlink" href="#maximum-likelihood-estimation-mle" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="maximum-likelihood-estimation-mle">
+<h2>Maximum Likelihood Estimation (MLE)<a class="headerlink" href="#maximum-likelihood-estimation-mle" title="Permalink to this heading">#</a></h2>
 <p>In statistics, maximum likelihood estimation (MLE) is a method of
 estimating the parameters of an assumed probability distribution,
 given some observed data. This is achieved by maximizing a likelihood
@@ -1215,9 +718,9 @@ negative of the logarithm since this is a monotonically decreasing
 function.</p>
 <p>Note also that maximization/minimization of the logarithm of the PDF
 is equivalent to the maximization/minimization of the function itself.</p>
-</div>
-<div class="section" id="a-new-cost-function">
-<h2>A new Cost Function<a class="headerlink" href="#a-new-cost-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-new-cost-function">
+<h2>A new Cost Function<a class="headerlink" href="#a-new-cost-function" title="Permalink to this heading">#</a></h2>
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1239,9 +742,9 @@ C(\boldsymbol{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol
 \hat{\boldsymbol{\beta}}^{\mathrm{OLS}}=\left(\boldsymbol{X}^T\boldsymbol{X}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y}!
 \]</div>
 <p>Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics.</p>
-</div>
-<div class="section" id="more-basic-statistics-and-bayes-theorem">
-<h2>More basic Statistics and Bayes’ theorem<a class="headerlink" href="#more-basic-statistics-and-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-basic-statistics-and-bayes-theorem">
+<h2>More basic Statistics and Bayes’ theorem<a class="headerlink" href="#more-basic-statistics-and-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>A central theorem in statistics is Bayes’ theorem. This theorem plays a similar role as the good old Pythagoras’ theorem in geometry.
 Bayes’ theorem is extremely simple to derive. But to do so we need some basic axioms from statistics.</p>
 <p>Assume we have two domains of events <span class="math notranslate nohighlight">\(X=[x_0,x_1,\dots,x_{n-1}]\)</span> and <span class="math notranslate nohighlight">\(Y=[y_0,y_1,\dots,y_{n-1}]\)</span>.</p>
@@ -1259,25 +762,25 @@ p(X \cup Y)= p(X,Y)= p(X\vert Y)p(Y)=p(Y\vert X)p(X),
 \]</div>
 <p>where we read <span class="math notranslate nohighlight">\(p(X\vert Y)\)</span> as the likelihood of obtaining <span class="math notranslate nohighlight">\(X\)</span> given <span class="math notranslate nohighlight">\(Y\)</span>.</p>
 <p>If we have independent events then <span class="math notranslate nohighlight">\(p(X,Y)=p(X)p(Y)\)</span>.</p>
-</div>
-<div class="section" id="marginal-probability">
-<h2>Marginal Probability<a class="headerlink" href="#marginal-probability" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="marginal-probability">
+<h2>Marginal Probability<a class="headerlink" href="#marginal-probability" title="Permalink to this heading">#</a></h2>
 <p>The marginal probability is defined in terms of only one of the set of variables <span class="math notranslate nohighlight">\(X,Y\)</span>. For a discrete probability we have</p>
 <div class="math notranslate nohighlight">
 \[
 p(X)=\sum_{i=0}^{n-1}p(X,Y=y_i)=\sum_{i=0}^{n-1}p(X\vert Y=y_i)p(Y=y_i)=\sum_{i=0}^{n-1}p(X\vert y_i)p(y_i).
 \]</div>
-</div>
-<div class="section" id="conditional-probability">
-<h2>Conditional  Probability<a class="headerlink" href="#conditional-probability" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="conditional-probability">
+<h2>Conditional  Probability<a class="headerlink" href="#conditional-probability" title="Permalink to this heading">#</a></h2>
 <p>The conditional  probability, if <span class="math notranslate nohighlight">\(p(Y) &gt; 0\)</span>, is</p>
 <div class="math notranslate nohighlight">
 \[
 p(X\vert Y)= \frac{p(X,Y)}{p(Y)}=\frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}.
 \]</div>
-</div>
-<div class="section" id="bayes-theorem">
-<h2>Bayes’ Theorem<a class="headerlink" href="#bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bayes-theorem">
+<h2>Bayes’ Theorem<a class="headerlink" href="#bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>If we combine the conditional probability with the marginal probability and the standard product rule, we have</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1289,18 +792,18 @@ p(X\vert Y)= \frac{p(X,Y)}{p(Y)},
 p(X\vert Y)= \frac{p(X,Y)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)}=\frac{p(Y\vert X)p(X)}{\sum_{i=0}^{n-1}p(Y\vert X=x_i)p(x_i)},
 \]</div>
 <p>which is Bayes’ theorem. It allows us to evaluate the uncertainty in in <span class="math notranslate nohighlight">\(X\)</span> after we have observed <span class="math notranslate nohighlight">\(Y\)</span>. We can easily interchange <span class="math notranslate nohighlight">\(X\)</span> with <span class="math notranslate nohighlight">\(Y\)</span>.</p>
-</div>
-<div class="section" id="interpretations-of-bayes-theorem">
-<h2>Interpretations of Bayes’ Theorem<a class="headerlink" href="#interpretations-of-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="interpretations-of-bayes-theorem">
+<h2>Interpretations of Bayes’ Theorem<a class="headerlink" href="#interpretations-of-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>The quantity <span class="math notranslate nohighlight">\(p(Y\vert X)\)</span> on the right-hand side of the theorem is
 evaluated for the observed data <span class="math notranslate nohighlight">\(Y\)</span> and can be viewed as a function of
 the parameter space represented by <span class="math notranslate nohighlight">\(X\)</span>. This function is not
 necesseraly normalized and is normally called the likelihood function.</p>
 <p>The function <span class="math notranslate nohighlight">\(p(X)\)</span> on the right hand side is called the prior while the function on the left hand side is the called the posterior probability. The denominator on the right hand side serves as a normalization factor for the posterior distribution.</p>
 <p>Let us try to illustrate Bayes’ theorem through an example.</p>
-</div>
-<div class="section" id="example-of-usage-of-bayes-theorem">
-<h2>Example of Usage of Bayes’ theorem<a class="headerlink" href="#example-of-usage-of-bayes-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="example-of-usage-of-bayes-theorem">
+<h2>Example of Usage of Bayes’ theorem<a class="headerlink" href="#example-of-usage-of-bayes-theorem" title="Permalink to this heading">#</a></h2>
 <p>Let us suppose that you are undergoing a series of mammography scans in
 order to rule out possible breast cancer cases.  We define the
 sensitivity for a positive event by the variable <span class="math notranslate nohighlight">\(X\)</span>. It takes binary
@@ -1315,9 +818,9 @@ p(X=1\vert Y=1) =0.8.
 \]</div>
 <p>This obviously sounds  scary since many would conclude that if the test is positive, there is a likelihood of <span class="math notranslate nohighlight">\(80\%\)</span> for having cancer.
 It is however not correct, as the following Bayesian analysis shows.</p>
-</div>
-<div class="section" id="doing-it-correctly">
-<h2>Doing it correctly<a class="headerlink" href="#doing-it-correctly" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="doing-it-correctly">
+<h2>Doing it correctly<a class="headerlink" href="#doing-it-correctly" title="Permalink to this heading">#</a></h2>
 <p>If we look at various national surveys on breast cancer, the general likelihood of developing breast cancer is a very small number.
 Let us assume that the prior probability in the population as a whole is</p>
 <div class="math notranslate nohighlight">
@@ -1335,9 +838,9 @@ p(X=1\vert Y=0) =0.1.
 p(Y=1\vert X=1)=\frac{p(X=1\vert Y=1)p(Y=1)}{p(X=1\vert Y=1)p(Y=1)+p(X=1\vert Y=0)p(Y=0)}=\frac{0.8\times 0.004}{0.8\times 0.004+0.1\times 0.996}=0.031.
 \]</div>
 <p>That is, in case of a positive test, there is only a <span class="math notranslate nohighlight">\(3\%\)</span> chance of having breast cancer!</p>
-</div>
-<div class="section" id="bayes-theorem-and-ridge-and-lasso-regression">
-<h2>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="bayes-theorem-and-ridge-and-lasso-regression">
+<h2>Bayes’ Theorem and Ridge and Lasso Regression<a class="headerlink" href="#bayes-theorem-and-ridge-and-lasso-regression" title="Permalink to this heading">#</a></h2>
 <p>Using Bayes’ theorem we can gain a better intuition about Ridge and Lasso regression.</p>
 <p>For ordinary least squares we postulated that the maximum likelihood for the doamin of events <span class="math notranslate nohighlight">\(\boldsymbol{D}\)</span> (one-dimensional case)</p>
 <div class="math notranslate nohighlight">
@@ -1360,9 +863,9 @@ p(\boldsymbol{\beta}\vert\boldsymbol{D}).
 p(\boldsymbol{\beta}\vert\boldsymbol{D})\propto p(\boldsymbol{D}\vert\boldsymbol{\beta})p(\boldsymbol{\beta}).
 \]</div>
 <p>We have a model for <span class="math notranslate nohighlight">\(p(\boldsymbol{D}\vert\boldsymbol{\beta})\)</span> but need one for the <strong>prior</strong> <span class="math notranslate nohighlight">\(p(\boldsymbol{\beta}\)</span>!</p>
-</div>
-<div class="section" id="ridge-and-bayes">
-<h2>Ridge and Bayes<a class="headerlink" href="#ridge-and-bayes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="ridge-and-bayes">
+<h2>Ridge and Bayes<a class="headerlink" href="#ridge-and-bayes" title="Permalink to this heading">#</a></h2>
 <p>With the posterior probability defined by a likelihood which we have
 already modeled and an unknown prior, we are now ready to make
 additional models for the prior.</p>
@@ -1390,9 +893,9 @@ C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol
 C(\boldsymbol{\beta})=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_2^2,
 \]</div>
 <p>which is our Ridge cost function!  Nice, isn’t it?</p>
-</div>
-<div class="section" id="lasso-and-bayes">
-<h2>Lasso and Bayes<a class="headerlink" href="#lasso-and-bayes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="lasso-and-bayes">
+<h2>Lasso and Bayes<a class="headerlink" href="#lasso-and-bayes" title="Permalink to this heading">#</a></h2>
 <p>To derive the Lasso cost function, we simply replace the Gaussian prior with an exponential distribution (<a class="reference external" href="https://en.wikipedia.org/wiki/Laplace_distribution">Laplace in this case</a>) with zero mean value,  that is</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1416,20 +919,20 @@ C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{
 C(\boldsymbol{\beta}=\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\beta})\vert\vert_2^2}{2\sigma^2}+\lambda\vert\vert\boldsymbol{\beta}\vert\vert_1,
 \]</div>
 <p>which is our Lasso cost function!</p>
-</div>
-<div class="section" id="why-resampling-methods">
-<h2>Why resampling methods<a class="headerlink" href="#why-resampling-methods" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="why-resampling-methods">
+<h2>Why resampling methods<a class="headerlink" href="#why-resampling-methods" title="Permalink to this heading">#</a></h2>
 <p>Before we proceed, we need to rethink what we have been doing. In our
 eager to fit the data, we have omitted several important elements in
 our regression analysis. In what follows we will</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>look at statistical properties, including a discussion of mean values, variance and the so-called bias-variance tradeoff</p></li>
 <li><p>introduce resampling techniques like cross-validation, bootstrapping and jackknife and more</p></li>
 </ol>
 <p>and discuss how to select a given model (one of the difficult parts in machine learning).</p>
-</div>
-<div class="section" id="resampling-methods">
-<h2>Resampling methods<a class="headerlink" href="#resampling-methods" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods">
+<h2>Resampling methods<a class="headerlink" href="#resampling-methods" title="Permalink to this heading">#</a></h2>
 <p>Resampling methods are an indispensable tool in modern
 statistics. They involve repeatedly drawing samples from a training
 set and refitting a model of interest on each sample in order to
@@ -1441,15 +944,15 @@ the resulting fits differ. Such an approach may allow us to obtain
 information that would not be available from fitting the model only
 once using the original training sample.</p>
 <p>Two resampling methods are often used in Machine Learning analyses,</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>The <strong>bootstrap method</strong></p></li>
 <li><p>and <strong>Cross-Validation</strong></p></li>
 </ol>
 <p>In addition there are several other methods such as the Jackknife and the Blocking methods. We will discuss in particular
 cross-validation and the bootstrap method.</p>
-</div>
-<div class="section" id="resampling-approaches-can-be-computationally-expensive">
-<h2>Resampling approaches can be computationally expensive<a class="headerlink" href="#resampling-approaches-can-be-computationally-expensive" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-approaches-can-be-computationally-expensive">
+<h2>Resampling approaches can be computationally expensive<a class="headerlink" href="#resampling-approaches-can-be-computationally-expensive" title="Permalink to this heading">#</a></h2>
 <p>Resampling approaches can be computationally expensive, because they
 involve fitting the same statistical method multiple times using
 different subsets of the training data. However, due to recent
@@ -1465,18 +968,18 @@ of flexibility. The process of evaluating a model’s performance is
 known as model assessment, whereas the process of selecting the proper
 level of flexibility for a model is known as model selection. The
 bootstrap is widely used.</p>
-</div>
-<div class="section" id="id1">
-<h2>Why resampling methods ?<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2>Why resampling methods ?<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p><strong>Statistical analysis.</strong></p>
 <ul class="simple">
 <li><p>Our simulations can be treated as <em>computer experiments</em>. This is particularly the case for Monte Carlo methods which are widely used in statistical analyses.</p></li>
 <li><p>The results can be analysed with the same statistical tools as we would use when analysing experimental data.</p></li>
 <li><p>As in all experiments, we are looking for expectation values and an estimate of how accurate they are, i.e., possible sources for errors.</p></li>
 </ul>
-</div>
-<div class="section" id="statistical-analysis">
-<h2>Statistical analysis<a class="headerlink" href="#statistical-analysis" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="statistical-analysis">
+<h2>Statistical analysis<a class="headerlink" href="#statistical-analysis" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>As in other experiments, many numerical  experiments have two classes of errors:</p>
 <ul>
@@ -1487,9 +990,9 @@ bootstrap is widely used.</p>
 <li><p>Statistical errors can be estimated using standard tools from statistics</p></li>
 <li><p>Systematical errors are method specific and must be treated differently from case to case.</p></li>
 </ul>
-</div>
-<div class="section" id="id2">
-<h2>Resampling methods<a class="headerlink" href="#id2" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id2">
+<h2>Resampling methods<a class="headerlink" href="#id2" title="Permalink to this heading">#</a></h2>
 <p>With all these analytical equations for both the OLS and Ridge
 regression, we will now outline how to assess a given model. This will
 lead to a discussion of the so-called bias-variance tradeoff (see
@@ -1499,21 +1002,21 @@ the mean-squared error (MSE), mainly used for fitting of continuous
 functions. Another choice is the absolute error.</p>
 <p>In the discussions below we will focus on the MSE and in particular since we will split the data into test and training data,
 we discuss the</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>prediction error or simply the <strong>test error</strong> <span class="math notranslate nohighlight">\(\mathrm{Err_{Test}}\)</span>, where we have a fixed training set and the test error is the MSE arising from the data reserved for testing. We discuss also the</p></li>
 <li><p>training error <span class="math notranslate nohighlight">\(\mathrm{Err_{Train}}\)</span>, which is the average loss over the training data.</p></li>
 </ol>
 <p>As our model becomes more and more complex, more of the training data tends to  used. The training may thence adapt to more complicated structures in the data. This may lead to a decrease in the bias (see below for code example) and a slight increase of the variance for the test error.
 For a certain level of complexity the test error will reach minimum, before starting to increase again. The
 training error reaches a saturation.</p>
-</div>
-<div class="section" id="resampling-methods-bootstrap">
-<h2>Resampling methods: Bootstrap<a class="headerlink" href="#resampling-methods-bootstrap" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods-bootstrap">
+<h2>Resampling methods: Bootstrap<a class="headerlink" href="#resampling-methods-bootstrap" title="Permalink to this heading">#</a></h2>
 <p>Bootstrapping is a <a class="reference external" href="https://en.wikipedia.org/wiki/Nonparametric_statistics">non-parametric approach</a> to statistical inference
 that substitutes computation for more traditional distributional
 assumptions and asymptotic results. Bootstrapping offers a number of
 advantages:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>The bootstrap is quite general, although there are some cases in which it fails.</p></li>
 <li><p>Because it does not require distributional assumptions (such as normally distributed errors), the bootstrap can provide more accurate inferences when the data are not well behaved or when the sample size is small.</p></li>
 <li><p>It is possible to apply the bootstrap to statistics with sampling distributions that are difficult to derive, even asymptotically.</p></li>
@@ -1521,9 +1024,9 @@ advantages:</p>
 </ol>
 <p>The textbook by <a class="reference external" href="https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A">Davison on the Bootstrap Methods and their Applications</a> provides many more insights and proofs. In this course we will take a more practical approach and use the results and theorems provided in the literature. For those interested in reading more about the bootstrap methods, we recommend the above text and the one by <a class="reference external" href="https://www.routledge.com/An-Introduction-to-the-Bootstrap/Efron-Tibshirani/p/book/9780412042317">Efron and Tibshirani</a>.</p>
 <p>Before we proceed however, we need to remind ourselves about a central theorem in statistics, namely the so-called <strong>central limit theorem</strong>.</p>
-</div>
-<div class="section" id="the-central-limit-theorem">
-<h2>The Central Limit Theorem<a class="headerlink" href="#the-central-limit-theorem" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-central-limit-theorem">
+<h2>The Central Limit Theorem<a class="headerlink" href="#the-central-limit-theorem" title="Permalink to this heading">#</a></h2>
 <p>Suppose we have a PDF <span class="math notranslate nohighlight">\(p(x)\)</span> from which we generate  a series <span class="math notranslate nohighlight">\(N\)</span>
 of averages <span class="math notranslate nohighlight">\(\mathbb{E}[x_i]\)</span>. Each mean value <span class="math notranslate nohighlight">\(\mathbb{E}[x_i]\)</span>
 is viewed as the average of a specific measurement, e.g., throwing
@@ -1537,9 +1040,9 @@ which follows. We do the same for <span class="math notranslate nohighlight">\(\
 z=\frac{x_1+x_2+\dots+x_m}{m},
 \]</div>
 <p>the question we pose is which is the PDF of the new variable <span class="math notranslate nohighlight">\(z\)</span>.</p>
-</div>
-<div class="section" id="finding-the-limit">
-<h2>Finding the Limit<a class="headerlink" href="#finding-the-limit" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="finding-the-limit">
+<h2>Finding the Limit<a class="headerlink" href="#finding-the-limit" title="Permalink to this heading">#</a></h2>
 <p>The probability of obtaining an average value <span class="math notranslate nohighlight">\(z\)</span> is the product of the
 probabilities of obtaining arbitrary individual mean values <span class="math notranslate nohighlight">\(x_i\)</span>,
 but with the constraint that the average is <span class="math notranslate nohighlight">\(z\)</span>. We can express this through
@@ -1553,9 +1056,9 @@ the following expression</p>
 All measurements that lead to each individual <span class="math notranslate nohighlight">\(x_i\)</span> are expected to
 be independent, which in turn means that we can express <span class="math notranslate nohighlight">\(\tilde{p}\)</span> as the
 product of individual <span class="math notranslate nohighlight">\(p(x_i)\)</span>.  The independence assumption is important in the derivation of the central limit theorem.</p>
-</div>
-<div class="section" id="rewriting-the-delta-function">
-<h2>Rewriting the <span class="math notranslate nohighlight">\(\delta\)</span>-function<a class="headerlink" href="#rewriting-the-delta-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="rewriting-the-delta-function">
+<h2>Rewriting the <span class="math notranslate nohighlight">\(\delta\)</span>-function<a class="headerlink" href="#rewriting-the-delta-function" title="Permalink to this heading">#</a></h2>
 <p>If we use the integral expression for the <span class="math notranslate nohighlight">\(\delta\)</span>-function</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1577,9 +1080,9 @@ we arrive at</p>
   \int_{-\infty}^{\infty}dxp(x)
    \left[1+\frac{iq(\mu-x)}{m}-\frac{q^2(\mu-x)^2}{2m^2}+\dots\right].
 \]</div>
-</div>
-<div class="section" id="identifying-terms">
-<h2>Identifying Terms<a class="headerlink" href="#identifying-terms" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="identifying-terms">
+<h2>Identifying Terms<a class="headerlink" href="#identifying-terms" title="Permalink to this heading">#</a></h2>
 <p>The second term on the rhs disappears since this is just the mean and
 employing the definition of <span class="math notranslate nohighlight">\(\sigma^2\)</span> we have</p>
 <div class="math notranslate nohighlight">
@@ -1602,9 +1105,9 @@ employing the definition of <span class="math notranslate nohighlight">\(\sigma^
 <p>which is the normal distribution with variance
 <span class="math notranslate nohighlight">\(\sigma^2_m=\sigma^2/m\)</span>, where <span class="math notranslate nohighlight">\(\sigma\)</span> is the variance of the PDF <span class="math notranslate nohighlight">\(p(x)\)</span>
 and <span class="math notranslate nohighlight">\(\mu\)</span> is also the mean of the PDF <span class="math notranslate nohighlight">\(p(x)\)</span>.</p>
-</div>
-<div class="section" id="wrapping-it-up">
-<h2>Wrapping it up<a class="headerlink" href="#wrapping-it-up" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="wrapping-it-up">
+<h2>Wrapping it up<a class="headerlink" href="#wrapping-it-up" title="Permalink to this heading">#</a></h2>
 <p>Thus, the central limit theorem states that the PDF <span class="math notranslate nohighlight">\(\tilde{p}(z)\)</span> of
 the average of <span class="math notranslate nohighlight">\(m\)</span> random values corresponding to a PDF <span class="math notranslate nohighlight">\(p(x)\)</span>
 is a normal distribution whose mean is the
@@ -1635,9 +1138,9 @@ correlations.</p>
 <p>The theorem is satisfied by a large class of PDFs. Note however that for a
 finite <span class="math notranslate nohighlight">\(m\)</span>, it is not always possible to find a closed form /analytic expression for
 <span class="math notranslate nohighlight">\(\tilde{p}(x)\)</span>.</p>
-</div>
-<div class="section" id="confidence-intervals">
-<h2>Confidence Intervals<a class="headerlink" href="#confidence-intervals" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="confidence-intervals">
+<h2>Confidence Intervals<a class="headerlink" href="#confidence-intervals" title="Permalink to this heading">#</a></h2>
 <p>Confidence intervals are used in statistics and represent a type of estimate
 computed from the observed data. This gives a range of values for an
 unknown parameter such as the parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> from linear regression.</p>
@@ -1647,9 +1150,9 @@ unknown parameter such as the parameters <span class="math notranslate nohighlig
 <span class="math notranslate nohighlight">\(\boldsymbol{\sigma}^2 (\boldsymbol{\beta}_j ) = \boldsymbol{\sigma}^2 [(\mathbf{X}^{T} \mathbf{X})^{-1}]_{jj} \)</span>.</p>
 <p>This quantity will be used to
 construct a confidence interval for the estimates.</p>
-</div>
-<div class="section" id="standard-approach-based-on-the-normal-distribution">
-<h2>Standard Approach based on the Normal Distribution<a class="headerlink" href="#standard-approach-based-on-the-normal-distribution" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="standard-approach-based-on-the-normal-distribution">
+<h2>Standard Approach based on the Normal Distribution<a class="headerlink" href="#standard-approach-based-on-the-normal-distribution" title="Permalink to this heading">#</a></h2>
 <p>We will assume that the parameters <span class="math notranslate nohighlight">\(\beta\)</span> follow a normal
 distribution.  We can then define the confidence interval.  Here we will be using as
 shorthands <span class="math notranslate nohighlight">\(\mu_{\beta}\)</span> for the above mean value and <span class="math notranslate nohighlight">\(\sigma_{\beta}\)</span>
@@ -1667,9 +1170,9 @@ approximate <span class="math notranslate nohighlight">\(z\approx 2\)</span>.</p
 <p>For more discussions of confidence intervals (and in particular linked with a discussion of the bootstrap method), see chapter 5 of the textbook by <a class="reference external" href="https://www.cambridge.org/core/books/bootstrap-methods-and-their-application/ED2FD043579F27952363566DC09CBD6A">Davison on the Bootstrap Methods and their Applications</a></p>
 <p>In this text you will also find an in-depth discussion of the
 Bootstrap method, why it works and various theorems related to it.</p>
-</div>
-<div class="section" id="resampling-methods-bootstrap-background">
-<h2>Resampling methods: Bootstrap background<a class="headerlink" href="#resampling-methods-bootstrap-background" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods-bootstrap-background">
+<h2>Resampling methods: Bootstrap background<a class="headerlink" href="#resampling-methods-bootstrap-background" title="Permalink to this heading">#</a></h2>
 <p>Since <span class="math notranslate nohighlight">\(\widehat{\beta} = \widehat{\beta}(\boldsymbol{X})\)</span> is a function of random variables,
 <span class="math notranslate nohighlight">\(\widehat{\beta}\)</span> itself must be a random variable. Thus it has
 a pdf, call this function <span class="math notranslate nohighlight">\(p(\boldsymbol{t})\)</span>. The aim of the bootstrap is to
@@ -1679,15 +1182,15 @@ in the place of <span class="math notranslate nohighlight">\(p(\boldsymbol{t})\)
 resembles <span class="math notranslate nohighlight">\(p(\vec{t})\)</span>, then using numerics, it is straight forward to
 estimate all the interesting parameters of <span class="math notranslate nohighlight">\(p(\boldsymbol{t})\)</span> using point
 estimators.</p>
-</div>
-<div class="section" id="resampling-methods-more-bootstrap-background">
-<h2>Resampling methods: More Bootstrap background<a class="headerlink" href="#resampling-methods-more-bootstrap-background" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods-more-bootstrap-background">
+<h2>Resampling methods: More Bootstrap background<a class="headerlink" href="#resampling-methods-more-bootstrap-background" title="Permalink to this heading">#</a></h2>
 <p>In the case that <span class="math notranslate nohighlight">\(\widehat{\beta}\)</span> has
 more than one component, and the components are independent, we use the
 same estimator on each component separately.  If the probability
 density function of <span class="math notranslate nohighlight">\(X_i\)</span>, <span class="math notranslate nohighlight">\(p(x)\)</span>, had been known, then it would have
 been straightforward to do this by:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Drawing lots of numbers from <span class="math notranslate nohighlight">\(p(x)\)</span>, suppose we call one such set of numbers <span class="math notranslate nohighlight">\((X_1^*, X_2^*, \cdots, X_n^*)\)</span>.</p></li>
 <li><p>Then using these numbers, we could compute a replica of <span class="math notranslate nohighlight">\(\widehat{\beta}\)</span> called <span class="math notranslate nohighlight">\(\widehat{\beta}^*\)</span>.</p></li>
 </ol>
@@ -1695,9 +1198,9 @@ been straightforward to do this by:</p>
 estimates of <span class="math notranslate nohighlight">\(\widehat{\beta}\)</span> can  be obtained. The
 idea is to use the relative frequency of <span class="math notranslate nohighlight">\(\widehat{\beta}^*\)</span>
 (think of a histogram) as an estimate of <span class="math notranslate nohighlight">\(p(\boldsymbol{t})\)</span>.</p>
-</div>
-<div class="section" id="resampling-methods-bootstrap-approach">
-<h2>Resampling methods: Bootstrap approach<a class="headerlink" href="#resampling-methods-bootstrap-approach" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods-bootstrap-approach">
+<h2>Resampling methods: Bootstrap approach<a class="headerlink" href="#resampling-methods-bootstrap-approach" title="Permalink to this heading">#</a></h2>
 <p>But
 unless there is enough information available about the process that
 generated <span class="math notranslate nohighlight">\(X_1,X_2,\cdots,X_n\)</span>, <span class="math notranslate nohighlight">\(p(x)\)</span> is in general
@@ -1707,11 +1210,11 @@ of the observation <span class="math notranslate nohighlight">\(X_i\)</span>?</p
 <p>If we draw observations in accordance with
 the relative frequency of the observations, will we obtain the same
 result in some asymptotic sense? The answer is yes.</p>
-</div>
-<div class="section" id="resampling-methods-bootstrap-steps">
-<h2>Resampling methods: Bootstrap steps<a class="headerlink" href="#resampling-methods-bootstrap-steps" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="resampling-methods-bootstrap-steps">
+<h2>Resampling methods: Bootstrap steps<a class="headerlink" href="#resampling-methods-bootstrap-steps" title="Permalink to this heading">#</a></h2>
 <p>The independent bootstrap works like this:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>Draw with replacement <span class="math notranslate nohighlight">\(n\)</span> numbers for the observed variables <span class="math notranslate nohighlight">\(\boldsymbol{x} = (x_1,x_2,\cdots,x_n)\)</span>.</p></li>
 <li><p>Define a vector <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span> containing the values which were drawn from <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span>.</p></li>
 <li><p>Using the vector <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span> compute <span class="math notranslate nohighlight">\(\widehat{\beta}^*\)</span> by evaluating <span class="math notranslate nohighlight">\(\widehat \beta\)</span> under the observations <span class="math notranslate nohighlight">\(\boldsymbol{x}^*\)</span>.</p></li>
@@ -1726,9 +1229,9 @@ you use the estimators corresponding to the statistic of interest. For
 example, if you are interested in estimating the variance of <span class="math notranslate nohighlight">\(\widehat
 \beta\)</span>, apply the etsimator <span class="math notranslate nohighlight">\(\widehat \sigma^2\)</span> to the values
 <span class="math notranslate nohighlight">\(\widehat \beta^*\)</span>.</p>
-</div>
-<div class="section" id="code-example-for-the-bootstrap-method">
-<h2>Code example for the Bootstrap method<a class="headerlink" href="#code-example-for-the-bootstrap-method" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="code-example-for-the-bootstrap-method">
+<h2>Code example for the Bootstrap method<a class="headerlink" href="#code-example-for-the-bootstrap-method" title="Permalink to this heading">#</a></h2>
 <p>The following code starts with a Gaussian distribution with mean value
 <span class="math notranslate nohighlight">\(\mu =100\)</span> and variance <span class="math notranslate nohighlight">\(\sigma=15\)</span>. We use this to generate the data
 used in the bootstrap analysis. The bootstrap analysis returns a data
@@ -1775,17 +1278,61 @@ theorem.</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Bootstrap Statistics :
-original           bias      std. error
-  99.971  15.2789        99.9715        0.152907
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">from</span> <span class="nn">time</span> <span class="kn">import</span> <span class="n">time</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
 </pre></div>
 </div>
 </div>
 </div>
 <p>We see that our new variance and from that the standard deviation, agrees with the central limit theorem.</p>
-</div>
-<div class="section" id="plotting-the-histogram">
-<h2>Plotting the Histogram<a class="headerlink" href="#plotting-the-histogram" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="plotting-the-histogram">
+<h2>Plotting the Histogram<a class="headerlink" href="#plotting-the-histogram" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># the histogram of the bootstrapped data (normalized data if density = True)</span>
@@ -1800,13 +1347,10 @@ original           bias      std. error
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week37_144_0.png" src="_images/week37_144_0.png" />
 </div>
-</div>
-</div>
-<div class="section" id="the-bias-variance-tradeoff">
-<h2>The bias-variance tradeoff<a class="headerlink" href="#the-bias-variance-tradeoff" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-bias-variance-tradeoff">
+<h2>The bias-variance tradeoff<a class="headerlink" href="#the-bias-variance-tradeoff" title="Permalink to this heading">#</a></h2>
 <p>We will discuss the bias-variance tradeoff in the context of
 continuous predictions such as regression. However, many of the
 intuitions and ideas discussed here also carry over to classification
@@ -1854,15 +1398,15 @@ We use a more compact notation in terms of the expectation value</p>
 \mathbb{E}\left[(\boldsymbol{y}-\boldsymbol{\tilde{y}})^2\right]=\mathbb{E}\left[(\boldsymbol{y}-\mathbb{E}\left[\boldsymbol{\tilde{y}}\right])^2\right]+\mathrm{Var}\left[\boldsymbol{\tilde{y}}\right]+\sigma^2,
 \]</div>
 <p>that is the rewriting in terms of the so-called bias, the variance of the model <span class="math notranslate nohighlight">\(\boldsymbol{\tilde{y}}\)</span> and the variance of <span class="math notranslate nohighlight">\(\boldsymbol{\epsilon}\)</span>.</p>
-</div>
-<div class="section" id="a-way-to-read-the-bias-variance-tradeoff">
-<h2>A way to Read the Bias-Variance Tradeoff<a class="headerlink" href="#a-way-to-read-the-bias-variance-tradeoff" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-way-to-read-the-bias-variance-tradeoff">
+<h2>A way to Read the Bias-Variance Tradeoff<a class="headerlink" href="#a-way-to-read-the-bias-variance-tradeoff" title="Permalink to this heading">#</a></h2>
 <!-- dom:FIGURE: [figures/BiasVariance.png, width=600 frac=0.9] -->
 <!-- begin figure -->
 <p><img src="figures/BiasVariance.png" width="600"><p style="font-size: 0.9em"><i>Figure 1: </i></p></p>
-<!-- end figure --></div>
-<div class="section" id="example-code-for-bias-variance-tradeoff">
-<h2>Example code for Bias-Variance tradeoff<a class="headerlink" href="#example-code-for-bias-variance-tradeoff" title="Permalink to this headline">¶</a></h2>
+<!-- end figure --></section>
+<section id="example-code-for-bias-variance-tradeoff">
+<h2>Example code for Bias-Variance tradeoff<a class="headerlink" href="#example-code-for-bias-variance-tradeoff" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1922,19 +1466,10 @@ We use a more compact notation in terms of the expectation value</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Error: 0.013121574062587286
-Bias^2: 0.012073649469946107
-Var: 0.0010479245926411787
-0.013121574062587286 &gt;= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286
-</pre></div>
 </div>
-<img alt="_images/week37_160_1.png" src="_images/week37_160_1.png" />
-</div>
-</div>
-</div>
-<div class="section" id="understanding-what-happens">
-<h2>Understanding what happens<a class="headerlink" href="#understanding-what-happens" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="understanding-what-happens">
+<h2>Understanding what happens<a class="headerlink" href="#understanding-what-happens" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -1986,89 +1521,10 @@ Var: 0.0010479245926411787
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 0
-Error: 0.32149601703519115
-Bias^2: 0.3123314713548606
-Var: 0.009164545680330616
-0.32149601703519115 &gt;= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912
-Polynomial degree: 1
-Error: 0.08426840630693412
-Bias^2: 0.0796891867672603
-Var: 0.004579219539673834
-0.08426840630693412 &gt;= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413
-Polynomial degree: 2
-Error: 0.10398646080125037
-Bias^2: 0.10077114273548984
-Var: 0.0032153180657605116
-0.10398646080125037 &gt;= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036
-Polynomial degree: 3
-Error: 0.06547790180152352
-Bias^2: 0.062082386342319454
-Var: 0.0033955154592040923
-0.06547790180152352 &gt;= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355
-Polynomial degree: 4
-Error: 0.06844519414009445
-Bias^2: 0.06453579006728322
-Var: 0.003909404072811221
-0.06844519414009445 &gt;= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444
-Polynomial degree: 5
-Error: 0.05227921801205679
-Bias^2: 0.04818727730430286
-Var: 0.004091940707753925
-0.05227921801205679 &gt;= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679
-</pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 6
-Error: 0.03781367141738902
-Bias^2: 0.03365768507152769
-Var: 0.0041559863458613296
-0.03781367141738902 &gt;= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902
-Polynomial degree: 7
-Error: 0.027609773491022394
-Bias^2: 0.022999498260366198
-Var: 0.004610275230656182
-0.027609773491022394 &gt;= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238
-Polynomial degree: 8
-Error: 0.017355848195593312
-Bias^2: 0.010331721306655165
-Var: 0.007024126888938144
-0.017355848195593312 &gt;= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331
-Polynomial degree: 9
-Error: 0.026605727637184558
-Bias^2: 0.010018312644139219
-Var: 0.016587414993045335
-0.026605727637184558 &gt;= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Polynomial degree: 10
-Error: 0.021592704588021178
-Bias^2: 0.010516485576646504
-Var: 0.01107621901137467
-0.021592704588021178 &gt;= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174
-Polynomial degree: 11
-Error: 0.07160048164232538
-Bias^2: 0.014436800088896381
-Var: 0.05716368155342902
-0.07160048164232538 &gt;= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254
-Polynomial degree: 12
-Error: 0.11547777218876518
-Bias^2: 0.016285782696017142
-Var: 0.09919198949274803
-0.11547777218876518 &gt;= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518
-Polynomial degree: 13
-Error: 0.2284246870217162
-Bias^2: 0.01975416527168255
-Var: 0.20867052175003364
-0.2284246870217162 &gt;= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162
-</pre></div>
-</div>
-<img alt="_images/week37_162_3.png" src="_images/week37_162_3.png" />
-</div>
-</div>
-</div>
-<div class="section" id="summing-up">
-<h2>Summing up<a class="headerlink" href="#summing-up" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="summing-up">
+<h2>Summing up<a class="headerlink" href="#summing-up" title="Permalink to this heading">#</a></h2>
 <p>The bias-variance tradeoff summarizes the fundamental tension in
 machine learning, particularly supervised learning, between the
 complexity of a model and the amount of training data needed to train
@@ -2093,9 +1549,9 @@ sets. However, if a method has high variance  then small changes in
 the training data can result in large changes in the model. In general, more
 flexible statistical methods have higher variance.</p>
 <p>You may also find this recent <a class="reference external" href="https://www.pnas.org/content/116/32/15849">article</a> of interest.</p>
-</div>
-<div class="section" id="another-example-from-scikit-learn-s-repository">
-<h2>Another Example from Scikit-Learn’s Repository<a class="headerlink" href="#another-example-from-scikit-learn-s-repository" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="another-example-from-scikit-learn-s-repository">
+<h2>Another Example from Scikit-Learn’s Repository<a class="headerlink" href="#another-example-from-scikit-learn-s-repository" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="sd">&quot;&quot;&quot;</span>
@@ -2172,34 +1628,10 @@ flexible statistical methods have higher variance.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>============================
-Underfitting vs. Overfitting
-============================
-
-This example demonstrates the problems of underfitting and overfitting and
-how we can use linear regression with polynomial features to approximate
-nonlinear functions. The plot shows the function that we want to approximate,
-which is a part of the cosine function. In addition, the samples from the
-real function and the approximations of different models are displayed. The
-models have polynomial features of different degrees. We can see that a
-linear function (polynomial with degree 1) is not sufficient to fit the
-training samples. This is called **underfitting**. A polynomial of degree 4
-approximates the true function almost perfectly. However, for higher degrees
-the model will **overfit** the training data, i.e. it learns the noise of the
-training data.
-We evaluate quantitatively **overfitting** / **underfitting** by using
-cross-validation. We calculate the mean squared error (MSE) on the validation
-set, the higher, the less likely the model generalizes correctly from the
-training data.
-</pre></div>
 </div>
-<img alt="_images/week37_165_1.png" src="_images/week37_165_1.png" />
-</div>
-</div>
-</div>
-<div class="section" id="various-steps-in-cross-validation">
-<h2>Various steps in cross-validation<a class="headerlink" href="#various-steps-in-cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="various-steps-in-cross-validation">
+<h2>Various steps in cross-validation<a class="headerlink" href="#various-steps-in-cross-validation" title="Permalink to this heading">#</a></h2>
 <p>When the repetitive splitting of the data set is done randomly,
 samples may accidently end up in a fast majority of the splits in
 either training or test set. Such samples may have an unbalanced
@@ -2214,11 +1646,11 @@ test set over the splits. Still the division into the <span class="math notransl
 involves a degree of randomness. This may be fully excluded when
 choosing <span class="math notranslate nohighlight">\(k=n\)</span>. This particular case is referred to as leave-one-out
 cross-validation (LOOCV).</p>
-</div>
-<div class="section" id="cross-validation-in-brief">
-<h2>Cross-validation in brief<a class="headerlink" href="#cross-validation-in-brief" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="cross-validation-in-brief">
+<h2>Cross-validation in brief<a class="headerlink" href="#cross-validation-in-brief" title="Permalink to this heading">#</a></h2>
 <p>For the various values of <span class="math notranslate nohighlight">\(k\)</span></p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>shuffle the dataset randomly.</p></li>
 <li><p>Split the dataset into <span class="math notranslate nohighlight">\(k\)</span> groups.</p></li>
 <li><p>For each unique group:</p></li>
@@ -2227,12 +1659,12 @@ cross-validation (LOOCV).</p>
 <p>b. Take the remaining groups as a training data set</p>
 <p>c. Fit a model on the training set and evaluate it on the test set</p>
 <p>d. Retain the evaluation score and discard the model</p>
-<ol class="simple">
+<ol class="arabic simple" start="5">
 <li><p>Summarize the model using the sample of model evaluation scores</p></li>
 </ol>
-</div>
-<div class="section" id="code-example-for-cross-validation-and-k-fold-cross-validation">
-<h2>Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation<a class="headerlink" href="#code-example-for-cross-validation-and-k-fold-cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="code-example-for-cross-validation-and-k-fold-cross-validation">
+<h2>Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation<a class="headerlink" href="#code-example-for-cross-validation-and-k-fold-cross-validation" title="Permalink to this heading">#</a></h2>
 <p>The code here uses Ridge regression with cross-validation (CV)  resampling and <span class="math notranslate nohighlight">\(k\)</span>-fold CV in order to fit a specific polynomial.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2328,13 +1760,10 @@ cross-validation (LOOCV).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week37_169_0.png" src="_images/week37_169_0.png" />
 </div>
-</div>
-</div>
-<div class="section" id="more-examples-on-bootstrap-and-cross-validation-and-errors">
-<h2>More examples on bootstrap and cross-validation and errors<a class="headerlink" href="#more-examples-on-bootstrap-and-cross-validation-and-errors" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-examples-on-bootstrap-and-cross-validation-and-errors">
+<h2>More examples on bootstrap and cross-validation and errors<a class="headerlink" href="#more-examples-on-bootstrap-and-cross-validation-and-errors" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Common imports</span>
@@ -2418,117 +1847,11 @@ cross-validation (LOOCV).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:   1
-Mean squared error on training data: 446033.51374050
-Mean squared error on test data: 455173.80460179
-Degree of polynomial:   2
-Mean squared error on training data: 114550.54637219
-Mean squared error on test data: 129963.83146596
-Degree of polynomial:   3
-Mean squared error on training data: 9054.61775176
-Mean squared error on test data: 10572.87627342
-Degree of polynomial:   4
-Mean squared error on training data: 302.15313054
-Mean squared error on test data: 433.26292364
-Degree of polynomial:   5
-Mean squared error on training data: 3.64316192
-Mean squared error on test data: 7.23528337
-Degree of polynomial:   6
-Mean squared error on training data: 3.56589683
-Mean squared error on test data: 10.50427787
-Degree of polynomial:   7
-Mean squared error on training data: 0.47313680
-Mean squared error on test data: 1.53738247
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:   8
-Mean squared error on training data: 0.04926746
-Mean squared error on test data: 0.14629156
-Degree of polynomial:   9
-Mean squared error on training data: 0.02546675
-Mean squared error on test data: 0.11202337
-Degree of polynomial:  10
-Mean squared error on training data: 0.02424794
-Mean squared error on test data: 0.22467274
-Degree of polynomial:  11
-Mean squared error on training data: 0.01594452
-Mean squared error on test data: 1.07641937
-Degree of polynomial:  12
-Mean squared error on training data: 0.00805074
-Mean squared error on test data: 0.04295757
-Degree of polynomial:  13
-Mean squared error on training data: 0.00781918
-Mean squared error on test data: 0.56965674
-Degree of polynomial:  14
-Mean squared error on training data: 0.00465099
-Mean squared error on test data: 0.28443039
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  15
-Mean squared error on training data: 0.00420072
-Mean squared error on test data: 568.47202442
-Degree of polynomial:  16
-Mean squared error on training data: 0.00325450
-Mean squared error on test data: 48.97690235
-Degree of polynomial:  17
-Mean squared error on training data: 0.00242954
-Mean squared error on test data: 2.52775466
-Degree of polynomial:  18
-Mean squared error on training data: 0.00219194
-Mean squared error on test data: 429.23643365
-Degree of polynomial:  19
-Mean squared error on training data: 0.00154860
-Mean squared error on test data: 238.16356503
-Degree of polynomial:  20
-Mean squared error on training data: 0.00140849
-Mean squared error on test data: 1345.68592431
-Degree of polynomial:  21
-Mean squared error on training data: 0.00119699
-Mean squared error on test data: 1836.21110005
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  22
-Mean squared error on training data: 0.00092904
-Mean squared error on test data: 1182.64316482
-Degree of polynomial:  23
-Mean squared error on training data: 0.00089187
-Mean squared error on test data: 3886.35846425
-Degree of polynomial:  24
-Mean squared error on training data: 0.00083346
-Mean squared error on test data: 1346.92651068
-Degree of polynomial:  25
-Mean squared error on training data: 0.00079910
-Mean squared error on test data: 7697.35412147
-Degree of polynomial:  26
-Mean squared error on training data: 0.00075597
-Mean squared error on test data: 1078.81597834
-Degree of polynomial:  27
-Mean squared error on training data: 0.00068088
-Mean squared error on test data: 3189.20355156
-</pre></div>
-</div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Degree of polynomial:  28
-Mean squared error on training data: 0.00063364
-Mean squared error on test data: 692.24085321
-Degree of polynomial:  29
-Mean squared error on training data: 0.00063862
-Mean squared error on test data: 3073.63180447
-</pre></div>
-</div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/626635268.py:73: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(trainingerror), label=&#39;Training Error&#39;)
-/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/626635268.py:74: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(testerror), label=&#39;Test Error&#39;)
-</pre></div>
-</div>
-<img alt="_images/week37_171_6.png" src="_images/week37_171_6.png" />
-</div>
 </div>
 <p>Note that we kept the intercept column in the fitting here. This means that we need to set the <strong>intercept</strong> in the call to the <strong>Scikit-Learn</strong> function as <strong>False</strong>. Alternatively, we could have set up the design matrix <span class="math notranslate nohighlight">\(X\)</span> without the first column of ones.</p>
-</div>
-<div class="section" id="the-same-example-but-now-with-cross-validation">
-<h2>The same example but now with cross-validation<a class="headerlink" href="#the-same-example-but-now-with-cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-same-example-but-now-with-cross-validation">
+<h2>The same example but now with cross-validation<a class="headerlink" href="#the-same-example-but-now-with-cross-validation" title="Permalink to this heading">#</a></h2>
 <p>In this example we keep the intercept column again but add cross-validation in order to estimate the best possible value of the means squared error.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2602,17 +1925,10 @@ Mean squared error on test data: 3073.63180447
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10
-  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label=&#39;Test Error&#39;)
-</pre></div>
 </div>
-<img alt="_images/week37_174_1.png" src="_images/week37_174_1.png" />
-</div>
-</div>
-</div>
-<div class="section" id="notes-on-scaling-with-examples">
-<h2>Notes on scaling with examples<a class="headerlink" href="#notes-on-scaling-with-examples" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="notes-on-scaling-with-examples">
+<h2>Notes on scaling with examples<a class="headerlink" href="#notes-on-scaling-with-examples" title="Permalink to this heading">#</a></h2>
 <p>The programs here use both ordinrary least squares (OLS) and Ridge
 regression with one value only for the hyperparameter <span class="math notranslate nohighlight">\(\lambda\)</span>. The
 first example has no scaling and includes the intercept as well and we
@@ -2694,19 +2010,6 @@ we subtract the mean values).</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[1.79934087 0.47179152 5.01549939]
-[1.79909592 0.47176716 5.01550546]
-  
-test MSE of OLS:
-1.13943111290393
-  
-test MSE of Ridge
-1.1395235273363686
-</pre></div>
-</div>
-<img alt="_images/week37_176_1.png" src="_images/week37_176_1.png" />
-</div>
 </div>
 <p>In this example we do not include the intercept and we scale the data by subtracting the mean values. This follows the discussion in the <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/chapter3.html#more-on-rescaling-data">lecture material</a>.
 see also the weekly slides <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week36/html/._week36-bs029.html">for week 36</a>.
@@ -2867,21 +2170,6 @@ and <span class="math notranslate nohighlight">\(\tilde{X}_{ij} = X_{ij} - \frac
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[0.47179152 5.01549939]
-[0.47176783 5.01542292]
-1.7993408651198877
-1.7995707762668065
-  
-test MSE of OLS:
-1.1394311129039245
-  
-test MSE of Ridge
-1.1395084586525954
-</pre></div>
-</div>
-<img alt="_images/week37_208_1.png" src="_images/week37_208_1.png" />
-</div>
 </div>
 <p>Finally, instead of using our own function we repeat the same example
 using the <strong>standardscaler</strong> functionality of the library
@@ -2950,23 +2238,9 @@ using the <strong>standardscaler</strong> functionality of the library
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [11],</span> in <span class="ni">&lt;cell line: 34&gt;</span><span class="nt">()</span>
-<span class="g g-Whitespace">     </span><span class="mi">32</span> <span class="n">ypredictOLS</span> <span class="o">=</span> <span class="n">OLS</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">33</span> <span class="n">linear_model</span><span class="o">.</span><span class="n">Ridge</span><span class="p">(</span><span class="n">Lambda</span><span class="p">)</span>
-<span class="ne">---&gt; </span><span class="mi">34</span> <span class="n">RegRidge</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train_scaled</span><span class="p">,</span><span class="n">y_train_scaled</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">35</span> <span class="n">ypredictRidge</span> <span class="o">=</span> <span class="n">RegRidge</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test_scaled</span><span class="p">)</span>
-<span class="g g-Whitespace">     </span><span class="mi">36</span> <span class="n">betaOLS</span> <span class="o">=</span> <span class="n">OLS</span><span class="o">.</span><span class="n">coef_</span>
-
-<span class="ne">NameError</span>: name &#39;RegRidge&#39; is not defined
-</pre></div>
-</div>
-</div>
-</div>
-</div>
 </div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2980,7 +2254,7 @@ using the <strong>standardscaler</strong> functionality of the library
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -2988,44 +2262,153 @@ using the <strong>standardscaler</strong> functionality of the library
     </script>
     <script>kernelName = 'python3'</script>
 
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+  <div class="sidebar-secondary-item">
+  <div class="page-toc tocsection onthispage">
+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-37">Plans for week 37</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-weekly-exercises">Material from last week and relevant for the weekly exercises</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linking-the-regression-analysis-with-a-statistical-interpretation">Linking the regression analysis with a statistical interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#assumptions-made">Assumptions made</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance">Expectation value and variance</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#expectation-value-and-variance-for-boldsymbol-beta">Expectation value and variance for <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-14">Material for lecture Thursday September 14</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#deriving-ols-from-a-probability-distribution">Deriving OLS from a probability distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#independent-and-identically-distrubuted-iid">Independent and Identically Distrubuted (iid)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood-estimation-mle">Maximum Likelihood Estimation (MLE)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-new-cost-function">A new Cost Function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-basic-statistics-and-bayes-theorem">More basic Statistics and Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#marginal-probability">Marginal Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditional-probability">Conditional  Probability</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem">Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#interpretations-of-bayes-theorem">Interpretations of Bayes’ Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-of-usage-of-bayes-theorem">Example of Usage of Bayes’ theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#doing-it-correctly">Doing it correctly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#bayes-theorem-and-ridge-and-lasso-regression">Bayes’ Theorem and Ridge and Lasso Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#ridge-and-bayes">Ridge and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#lasso-and-bayes">Lasso and Bayes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#why-resampling-methods">Why resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods">Resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-approaches-can-be-computationally-expensive">Resampling approaches can be computationally expensive</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Why resampling methods ?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#statistical-analysis">Statistical analysis</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Resampling methods</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap">Resampling methods: Bootstrap</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-central-limit-theorem">The Central Limit Theorem</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#finding-the-limit">Finding the Limit</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rewriting-the-delta-function">Rewriting the <span class="math notranslate nohighlight">\(\delta\)</span>-function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#identifying-terms">Identifying Terms</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wrapping-it-up">Wrapping it up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#confidence-intervals">Confidence Intervals</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-approach-based-on-the-normal-distribution">Standard Approach based on the Normal Distribution</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-background">Resampling methods: Bootstrap background</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-more-bootstrap-background">Resampling methods: More Bootstrap background</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-approach">Resampling methods: Bootstrap approach</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#resampling-methods-bootstrap-steps">Resampling methods: Bootstrap steps</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-the-bootstrap-method">Code example for the Bootstrap method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plotting-the-histogram">Plotting the Histogram</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-bias-variance-tradeoff">The bias-variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-way-to-read-the-bias-variance-tradeoff">A way to Read the Bias-Variance Tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#example-code-for-bias-variance-tradeoff">Example code for Bias-Variance tradeoff</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#understanding-what-happens">Understanding what happens</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#summing-up">Summing up</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#another-example-from-scikit-learn-s-repository">Another Example from Scikit-Learn’s Repository</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#various-steps-in-cross-validation">Various steps in cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation-in-brief">Cross-validation in brief</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-examples-on-bootstrap-and-cross-validation-and-errors">More examples on bootstrap and cross-validation and errors</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-same-example-but-now-with-cross-validation">The same example but now with cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#notes-on-scaling-with-examples">Notes on scaling with examples</a></li>
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-<p aria-level="2" class="caption" role="heading">
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-  From Regression to Support Vector Machines
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+<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
 </ul>
-<p aria-level="2" class="caption" role="heading">
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-  Decision Trees, Ensemble Methods and Boosting
- </span>
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+<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
 </ul>
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- <span class="caption-text">
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+<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
+<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
+
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-  Weekly material, notes and exercises
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-   Week 38: Logistic Regression and Optimization
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Statistical interpretation of Linear Regression and Resampling techniques</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 38: Logistic Regression and Optimization</a></li>
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+    <h1>Week 38: Logistic Regression and Optimization</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
             
-            <div class="tocsection onthispage pt-5 pb-3">
-                <i class="fas fa-list"></i> Contents
+            <div>
+                <h2> Contents </h2>
             </div>
-            <nav id="bd-toc-nav" aria-label="Page">
+            <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-38">
-   Plans for week 38
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-first-project">
-   Material from last week and relevant for the first project
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#various-steps-in-cross-validation">
-   Various steps in cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">
-   How to set up the cross-validation for Ridge and/or Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation-in-brief">
-   Cross-validation in brief
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">
-   Code Example for Cross-validation and
-   <span class="math notranslate nohighlight">
-    \(k\)
-   </span>
-   -fold Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">
-   Material for lecture Thursday September 21
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#logistic-regression">
-   Logistic Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#classification-problems">
-   Classification problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimization-and-deep-learning">
-   Optimization and Deep learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basics">
-   Basics
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-classifier">
-   Linear classifier
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-selected-properties">
-   Some selected properties
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-example">
-   Simple example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plotting-the-mean-value-for-each-group">
-   Plotting the mean value for each group
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-logistic-function">
-   The logistic function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">
-   Examples of likelihood functions used in logistic regression and nueral networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#two-parameters">
-   Two parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood">
-   Maximum likelihood
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cost-function-rewritten">
-   The cost function rewritten
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#minimizing-the-cross-entropy">
-   Minimizing the cross entropy
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-more-compact-expression">
-   A more compact expression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extending-to-more-predictors">
-   Extending to more predictors
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#including-more-classes">
-   Including more classes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-classes">
-   More classes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#friday-september-23">
-   Friday September 23
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">
-   Searching for Optimal Regularization Parameters
-   <span class="math notranslate nohighlight">
-    \(\lambda\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#grid-search">
-   Grid Search
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#randomized-grid-search">
-   Randomized Grid Search
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wisconsin-cancer-data">
-   Wisconsin Cancer Data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-the-correlation-matrix">
-   Using the correlation matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#discussing-the-correlation-data">
-   Discussing the correlation data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-measures-in-classification-studies-cancer-data-again">
-   Other measures in classification studies: Cancer Data  again
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">
-   Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">
-   Revisiting our Logistic Regression case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations-to-solve">
-   The equations to solve
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">
-   Solving using Newton-Raphson’s method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">
-   Brief reminder on Newton-Raphson’s method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations">
-   The equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-geometric-interpretation">
-   Simple geometric interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extending-to-more-than-one-variable">
-   Extending to more than one variable
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#steepest-descent">
-   Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-steepest-descent">
-   More on Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ideal">
-   The ideal
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">
-   The sensitiveness of the gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-functions">
-   Convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-function">
-   Convex function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditions-on-convex-functions">
-   Conditions on convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-convex-functions">
-   More on convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-simple-problems">
-   Some simple problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-first-homework">
-   Revisiting our first homework
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent-example">
-   Gradient descent example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">
-   The derivative of the cost/loss function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-hessian-matrix">
-   The Hessian matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-program">
-   Simple program
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Gradient Descent Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">
-   And a corresponding example using
-   <strong>
-    scikit-learn
-   </strong>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent-and-ridge">
-   Gradient descent and Ridge
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">
-   The Hessian matrix for Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">
-   Program example for gradient descent with Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">
-   Using gradient descent methods, limitations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#challenge-yourself-the-coming-weekend">
-   Challenge yourself the coming weekend
-  </a>
- </li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-38">Plans for week 38</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-first-project">Material from last week and relevant for the first project</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#various-steps-in-cross-validation">Various steps in cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation-in-brief">Cross-validation in brief</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">Material for lecture Thursday September 21</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#logistic-regression">Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#classification-problems">Classification problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-and-deep-learning">Optimization and Deep learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics">Basics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-classifier">Linear classifier</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-selected-properties">Some selected properties</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example">Simple example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plotting-the-mean-value-for-each-group">Plotting the mean value for each group</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-logistic-function">The logistic function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#two-parameters">Two parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood">Maximum likelihood</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cost-function-rewritten">The cost function rewritten</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#minimizing-the-cross-entropy">Minimizing the cross entropy</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-more-compact-expression">A more compact expression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-predictors">Extending to more predictors</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-more-classes">Including more classes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-classes">More classes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#friday-september-23">Friday September 23</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">Searching for Optimal Regularization Parameters <span class="math notranslate nohighlight">\(\lambda\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#grid-search">Grid Search</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#randomized-grid-search">Randomized Grid Search</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wisconsin-cancer-data">Wisconsin Cancer Data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-the-correlation-matrix">Using the correlation matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#discussing-the-correlation-data">Discussing the correlation data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-measures-in-classification-studies-cancer-data-again">Other measures in classification studies: Cancer Data  again</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-to-solve">The equations to solve</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">Solving using Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations">The equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-geometric-interpretation">Simple geometric interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-than-one-variable">Extending to more than one variable</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-steepest-descent">More on Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ideal">The ideal</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">Convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-function">Convex function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditions-on-convex-functions">Conditions on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-convex-functions">More on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">Some simple problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-first-homework">Revisiting our first homework</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-example">Gradient descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix">The Hessian matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-program">Simple program</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Gradient Descent Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">And a corresponding example using <strong>scikit-learn</strong></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-and-ridge">Gradient descent and Ridge</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#challenge-yourself-the-coming-weekend">Challenge yourself the coming weekend</a></li>
 </ul>
-
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-    <div id="main-content" class="row">
-        <div class="col-12 col-md-9 pl-md-3 pr-md-0">
-            <!-- Table of contents that is only displayed when printing the page -->
-            <div id="jb-print-docs-body" class="onlyprint">
-                <h1>Week 38: Logistic Regression and Optimization</h1>
-                <!-- Table of contents -->
-                <div id="print-main-content">
-                    <div id="jb-print-toc">
-                        
-                        <div>
-                            <h2> Contents </h2>
-                        </div>
-                        <nav aria-label="Page">
-                            <ul class="visible nav section-nav flex-column">
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plans-for-week-38">
-   Plans for week 38
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-first-project">
-   Material from last week and relevant for the first project
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#various-steps-in-cross-validation">
-   Various steps in cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">
-   How to set up the cross-validation for Ridge and/or Lasso
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#cross-validation-in-brief">
-   Cross-validation in brief
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">
-   Code Example for Cross-validation and
-   <span class="math notranslate nohighlight">
-    \(k\)
-   </span>
-   -fold Cross-validation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">
-   Material for lecture Thursday September 21
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#logistic-regression">
-   Logistic Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#classification-problems">
-   Classification problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimization-and-deep-learning">
-   Optimization and Deep learning
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#basics">
-   Basics
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#linear-classifier">
-   Linear classifier
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-selected-properties">
-   Some selected properties
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-example">
-   Simple example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#plotting-the-mean-value-for-each-group">
-   Plotting the mean value for each group
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-logistic-function">
-   The logistic function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">
-   Examples of likelihood functions used in logistic regression and nueral networks
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#two-parameters">
-   Two parameters
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#maximum-likelihood">
-   Maximum likelihood
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-cost-function-rewritten">
-   The cost function rewritten
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#minimizing-the-cross-entropy">
-   Minimizing the cross entropy
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#a-more-compact-expression">
-   A more compact expression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extending-to-more-predictors">
-   Extending to more predictors
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#including-more-classes">
-   Including more classes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-classes">
-   More classes
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#friday-september-23">
-   Friday September 23
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">
-   Searching for Optimal Regularization Parameters
-   <span class="math notranslate nohighlight">
-    \(\lambda\)
-   </span>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#grid-search">
-   Grid Search
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#randomized-grid-search">
-   Randomized Grid Search
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#wisconsin-cancer-data">
-   Wisconsin Cancer Data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-the-correlation-matrix">
-   Using the correlation matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#discussing-the-correlation-data">
-   Discussing the correlation data
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#other-measures-in-classification-studies-cancer-data-again">
-   Other measures in classification studies: Cancer Data  again
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">
-   Optimization, the central part of any Machine Learning algortithm
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">
-   Revisiting our Logistic Regression case
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations-to-solve">
-   The equations to solve
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">
-   Solving using Newton-Raphson’s method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">
-   Brief reminder on Newton-Raphson’s method
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-equations">
-   The equations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-geometric-interpretation">
-   Simple geometric interpretation
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#extending-to-more-than-one-variable">
-   Extending to more than one variable
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#steepest-descent">
-   Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-steepest-descent">
-   More on Steepest descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-ideal">
-   The ideal
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">
-   The sensitiveness of the gradient descent
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-functions">
-   Convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#convex-function">
-   Convex function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#conditions-on-convex-functions">
-   Conditions on convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#more-on-convex-functions">
-   More on convex functions
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#some-simple-problems">
-   Some simple problems
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#revisiting-our-first-homework">
-   Revisiting our first homework
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent-example">
-   Gradient descent example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">
-   The derivative of the cost/loss function
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-hessian-matrix">
-   The Hessian matrix
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#simple-program">
-   Simple program
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#id1">
-   Gradient Descent Example
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">
-   And a corresponding example using
-   <strong>
-    scikit-learn
-   </strong>
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#gradient-descent-and-ridge">
-   Gradient descent and Ridge
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">
-   The Hessian matrix for Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">
-   Program example for gradient descent with Ridge Regression
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">
-   Using gradient descent methods, limitations
-  </a>
- </li>
- <li class="toc-h2 nav-item toc-entry">
-  <a class="reference internal nav-link" href="#challenge-yourself-the-coming-weekend">
-   Challenge yourself the coming weekend
-  </a>
- </li>
-</ul>
 
-                        </nav>
-                    </div>
-                </div>
-            </div>
-            
-              <div>
+              
                 
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
   <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
 doconce format html week38.do.txt --no_mako -->
-<!-- dom:TITLE: Week 38: Logistic Regression and Optimization --><div class="tex2jax_ignore mathjax_ignore section" id="week-38-logistic-regression-and-optimization">
-<h1>Week 38: Logistic Regression and Optimization<a class="headerlink" href="#week-38-logistic-regression-and-optimization" title="Permalink to this headline">¶</a></h1>
+<!-- dom:TITLE: Week 38: Logistic Regression and Optimization --><section class="tex2jax_ignore mathjax_ignore" id="week-38-logistic-regression-and-optimization">
+<h1>Week 38: Logistic Regression and Optimization<a class="headerlink" href="#week-38-logistic-regression-and-optimization" title="Permalink to this heading">#</a></h1>
 <p><strong>Morten Hjorth-Jensen</strong>, Department of Physics and Center for Computing in Science Education, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</p>
 <p>Date: <strong>September 18-22</strong></p>
-<div class="section" id="plans-for-week-38">
-<h2>Plans for week 38<a class="headerlink" href="#plans-for-week-38" title="Permalink to this headline">¶</a></h2>
+<section id="plans-for-week-38">
+<h2>Plans for week 38<a class="headerlink" href="#plans-for-week-38" title="Permalink to this heading">#</a></h2>
 <p><strong>Material for the active learning sessions on Tuesday and Wednesday.</strong></p>
 <ul class="simple">
 <li><p>Lecture from last week on the bias-variance tradeoff</p></li>
 <li><p>Resampling techniques, cross-validation examples included here, see also the lectures from last week on the bootstrap method</p></li>
-<li><p>Exercise for week 38, see also the whiteboard notes from week 37 at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf</a></p></li>
+<li><p>Exercise for week 38, see also the whiteboard notes from week 37 at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">CompPhysics/MachineLearning</a></p></li>
 <li><p>Work on project 1, in particular resampling methods like cross-validation and bootstrap.</p></li>
 </ul>
 <p><strong>Material for the lecture on Thursday September 21.</strong></p>
@@ -1073,19 +497,19 @@ doconce format html week38.do.txt --no_mako -->
 <ul>
 <li><p>Hastie et al 4.1, 4.2 and 4.3 on logistic regression</p></li>
 <li><p>For a good discussion on gradient methods, see Goodfellow et al section 4.3-4.5 and chapter 8. We will come back to the latter chapter in our discussion of Neural networks as well.</p></li>
-<li><p>See also the whiteboard notes from week 37 at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf</a> for a discussion and derivation of the bias-variance tradeoff.</p></li>
+<li><p>See also the whiteboard notes from week 37 at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep14.pdf">CompPhysics/MachineLearning</a> for a discussion and derivation of the bias-variance tradeoff.</p></li>
 <li><p><a class="reference external" href="https://www.youtube.com/watch?v=C5268D9t9Ak">Video on Logistic regression</a></p></li>
 <li><p><a class="reference external" href="https://www.youtube.com/watch?v=yIYKR4sgzI8">Yet another video on logistic regression</a></p></li>
 <li><p><a class="reference external" href="https://www.youtube.com/watch?v=sDv4f4s2SB8">Video on gradient descent</a></p></li>
 </ul>
 </li>
 </ul>
-</div>
-<div class="section" id="material-from-last-week-and-relevant-for-the-first-project">
-<h2>Material from last week and relevant for the first project<a class="headerlink" href="#material-from-last-week-and-relevant-for-the-first-project" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="various-steps-in-cross-validation">
-<h2>Various steps in cross-validation<a class="headerlink" href="#various-steps-in-cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-from-last-week-and-relevant-for-the-first-project">
+<h2>Material from last week and relevant for the first project<a class="headerlink" href="#material-from-last-week-and-relevant-for-the-first-project" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="various-steps-in-cross-validation">
+<h2>Various steps in cross-validation<a class="headerlink" href="#various-steps-in-cross-validation" title="Permalink to this heading">#</a></h2>
 <p>When the repetitive splitting of the data set is done randomly,
 samples may accidently end up in a fast majority of the splits in
 either training or test set. Such samples may have an unbalanced
@@ -1100,9 +524,9 @@ test set over the splits. Still the division into the <span class="math notransl
 involves a degree of randomness. This may be fully excluded when
 choosing <span class="math notranslate nohighlight">\(k=n\)</span>. This particular case is referred to as leave-one-out
 cross-validation (LOOCV).</p>
-</div>
-<div class="section" id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">
-<h2>How to set up the cross-validation for Ridge and/or Lasso<a class="headerlink" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">
+<h2>How to set up the cross-validation for Ridge and/or Lasso<a class="headerlink" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p>Define a range of interest for the penalty parameter.</p></li>
 <li><p>Divide the data set into training and test set comprising samples <span class="math notranslate nohighlight">\(\{1, \ldots, n\} \setminus i\)</span> and <span class="math notranslate nohighlight">\(\{ i \}\)</span>, respectively.</p></li>
@@ -1121,11 +545,11 @@ cross-validation (LOOCV).</p>
 <li><p>Repeat the first three steps  such that each sample plays the role of the test set once.</p></li>
 <li><p>Average the prediction performances of the test sets at each grid point of the penalty bias/parameter. It is an estimate of the prediction performance of the model corresponding to this value of the penalty parameter on novel data.</p></li>
 </ul>
-</div>
-<div class="section" id="cross-validation-in-brief">
-<h2>Cross-validation in brief<a class="headerlink" href="#cross-validation-in-brief" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="cross-validation-in-brief">
+<h2>Cross-validation in brief<a class="headerlink" href="#cross-validation-in-brief" title="Permalink to this heading">#</a></h2>
 <p>For the various values of <span class="math notranslate nohighlight">\(k\)</span></p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>shuffle the dataset randomly.</p></li>
 <li><p>Split the dataset into <span class="math notranslate nohighlight">\(k\)</span> groups.</p></li>
 <li><p>For each unique group:</p></li>
@@ -1134,12 +558,12 @@ cross-validation (LOOCV).</p>
 <p>b. Take the remaining groups as a training data set</p>
 <p>c. Fit a model on the training set and evaluate it on the test set</p>
 <p>d. Retain the evaluation score and discard the model</p>
-<ol class="simple">
+<ol class="arabic simple" start="5">
 <li><p>Summarize the model using the sample of model evaluation scores</p></li>
 </ol>
-</div>
-<div class="section" id="code-example-for-cross-validation-and-k-fold-cross-validation">
-<h2>Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation<a class="headerlink" href="#code-example-for-cross-validation-and-k-fold-cross-validation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="code-example-for-cross-validation-and-k-fold-cross-validation">
+<h2>Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation<a class="headerlink" href="#code-example-for-cross-validation-and-k-fold-cross-validation" title="Permalink to this heading">#</a></h2>
 <p>The code here uses Ridge regression with cross-validation (CV)  resampling and <span class="math notranslate nohighlight">\(k\)</span>-fold CV in order to fit a specific polynomial.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1238,15 +662,63 @@ cross-validation (LOOCV).</p>
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="_images/week38_10_0.png" src="_images/week38_10_0.png" />
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
 </div>
 </div>
 </div>
-<div class="section" id="material-for-lecture-thursday-september-21">
-<h2>Material for lecture Thursday September 21<a class="headerlink" href="#material-for-lecture-thursday-september-21" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="logistic-regression">
-<h2>Logistic Regression<a class="headerlink" href="#logistic-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="material-for-lecture-thursday-september-21">
+<h2>Material for lecture Thursday September 21<a class="headerlink" href="#material-for-lecture-thursday-september-21" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="logistic-regression">
+<h2>Logistic Regression<a class="headerlink" href="#logistic-regression" title="Permalink to this heading">#</a></h2>
 <p>In linear regression our main interest was centered on learning the
 coefficients of a functional fit (say a polynomial) in order to be
 able to predict the response of a continuous variable on some unseen
@@ -1258,9 +730,9 @@ ranging from the variance and thereby the confidence intervals of the
 parameters <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> to the mean squared error. If we can invert
 the product of the design matrices, linear regression gives then a
 simple recipe for fitting our data.</p>
-</div>
-<div class="section" id="classification-problems">
-<h2>Classification problems<a class="headerlink" href="#classification-problems" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="classification-problems">
+<h2>Classification problems<a class="headerlink" href="#classification-problems" title="Permalink to this heading">#</a></h2>
 <p>Classification problems, however, are concerned with outcomes taking
 the form of discrete variables (i.e. categories). We may for example,
 on the basis of DNA sequencing for a number of patients, like to find
@@ -1275,9 +747,9 @@ situations.</p>
 regression is that of two possible outcomes, normally denoted as a
 binary outcome, true or false, positive or negative, success or
 failure etc.</p>
-</div>
-<div class="section" id="optimization-and-deep-learning">
-<h2>Optimization and Deep learning<a class="headerlink" href="#optimization-and-deep-learning" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="optimization-and-deep-learning">
+<h2>Optimization and Deep learning<a class="headerlink" href="#optimization-and-deep-learning" title="Permalink to this heading">#</a></h2>
 <p>Logistic regression will also serve as our stepping stone towards
 neural network algorithms and supervised deep learning. For logistic
 learning, the minimization of the cost function leads to a non-linear
@@ -1290,9 +762,9 @@ of basically all modern machine learning algorithms.</p>
 <p>We note also that many of the topics discussed here on logistic
 regression are also commonly used in modern supervised Deep Learning
 models, as we will see later.</p>
-</div>
-<div class="section" id="basics">
-<h2>Basics<a class="headerlink" href="#basics" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="basics">
+<h2>Basics<a class="headerlink" href="#basics" title="Permalink to this heading">#</a></h2>
 <p>We consider the case where the dependent variables, also called the
 responses or the outcomes, <span class="math notranslate nohighlight">\(y_i\)</span> are discrete and only take values
 from <span class="math notranslate nohighlight">\(k=0,\dots,K-1\)</span> (i.e. <span class="math notranslate nohighlight">\(K\)</span> classes).</p>
@@ -1309,9 +781,9 @@ debt. That is</p>
 \[\begin{split}
 y_i = \begin{bmatrix} 0 &amp; \mathrm{no}\\  1 &amp; \mathrm{yes} \end{bmatrix}.
 \end{split}\]</div>
-</div>
-<div class="section" id="linear-classifier">
-<h2>Linear classifier<a class="headerlink" href="#linear-classifier" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="linear-classifier">
+<h2>Linear classifier<a class="headerlink" href="#linear-classifier" title="Permalink to this heading">#</a></h2>
 <p>Before moving to the logistic model, let us try to use our linear
 regression model to classify these two outcomes. We could for example
 fit a linear model to the default case if <span class="math notranslate nohighlight">\(y_i &gt; 0.5\)</span> and the no
@@ -1329,9 +801,9 @@ weighted linear combination, namely</p>
 \]</div>
 <p>where <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> is a vector representing the possible outcomes, <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> is our
 <span class="math notranslate nohighlight">\(n\times p\)</span> design matrix and <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> represents our estimators/predictors.</p>
-</div>
-<div class="section" id="some-selected-properties">
-<h2>Some selected properties<a class="headerlink" href="#some-selected-properties" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="some-selected-properties">
+<h2>Some selected properties<a class="headerlink" href="#some-selected-properties" title="Permalink to this heading">#</a></h2>
 <p>The main problem with our function is that it takes values on the
 entire real axis. In the case of logistic regression, however, the
 labels <span class="math notranslate nohighlight">\(y_i\)</span> are discrete variables. A typical example is the credit
@@ -1346,9 +818,9 @@ We will encounter this model in our first demonstration of neural networks.</p>
 literature. This model is extremely simple. However, in many cases it is more
 favorable to use a ``soft” classifier that outputs
 the probability of a given category. This leads us to the logistic function.</p>
-</div>
-<div class="section" id="simple-example">
-<h2>Simple example<a class="headerlink" href="#simple-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-example">
+<h2>Simple example<a class="headerlink" href="#simple-example" title="Permalink to this heading">#</a></h2>
 <p>The following example on data for coronary heart disease (CHD) as function of age may serve as an illustration. In the code here we read and plot whether a person has had CHD (output = 1) or not (output = 0). This ouput  is plotted the person’s against age. Clearly, the figure shows that attempting to make a standard linear regression fit may not be very meaningful.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1409,118 +881,10 @@ the probability of a given category. This leads us to the logistic function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output text_html"><div>
-<style scoped>
-    .dataframe tbody tr th:only-of-type {
-        vertical-align: middle;
-    }
-
-    .dataframe tbody tr th {
-        vertical-align: top;
-    }
-
-    .dataframe thead th {
-        text-align: right;
-    }
-</style>
-<table border="1" class="dataframe">
-  <thead>
-    <tr style="text-align: right;">
-      <th></th>
-      <th>ID</th>
-      <th>Age</th>
-      <th>Agegroup</th>
-      <th>CHD</th>
-    </tr>
-  </thead>
-  <tbody>
-    <tr>
-      <th>0</th>
-      <td>1</td>
-      <td>21</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>1</th>
-      <td>2</td>
-      <td>23</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>2</th>
-      <td>3</td>
-      <td>25</td>
-      <td>1</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>3</th>
-      <td>4</td>
-      <td>29</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>4</th>
-      <td>5</td>
-      <td>21</td>
-      <td>1</td>
-      <td>0</td>
-    </tr>
-    <tr>
-      <th>...</th>
-      <td>...</td>
-      <td>...</td>
-      <td>...</td>
-      <td>...</td>
-    </tr>
-    <tr>
-      <th>95</th>
-      <td>96</td>
-      <td>61</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>96</th>
-      <td>97</td>
-      <td>69</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>97</th>
-      <td>98</td>
-      <td>65</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>98</th>
-      <td>99</td>
-      <td>64</td>
-      <td>8</td>
-      <td>1</td>
-    </tr>
-    <tr>
-      <th>99</th>
-      <td>100</td>
-      <td>63</td>
-      <td>8</td>
-      <td>0</td>
-    </tr>
-  </tbody>
-</table>
-<p>100 rows × 4 columns</p>
-</div></div><img alt="_images/week38_22_1.png" src="_images/week38_22_1.png" />
 </div>
-</div>
-</div>
-<div class="section" id="plotting-the-mean-value-for-each-group">
-<h2>Plotting the mean value for each group<a class="headerlink" href="#plotting-the-mean-value-for-each-group" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="plotting-the-mean-value-for-each-group">
+<h2>Plotting the mean value for each group<a class="headerlink" href="#plotting-the-mean-value-for-each-group" title="Permalink to this heading">#</a></h2>
 <p>What we could attempt however is to plot the mean value for each group.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1535,9 +899,6 @@ the probability of a given category. This leads us to the logistic function.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week38_24_0.png" src="_images/week38_24_0.png" />
-</div>
 </div>
 <p>We are now trying to find a function <span class="math notranslate nohighlight">\(f(y\vert x)\)</span>, that is a function which gives us an expected value for the output <span class="math notranslate nohighlight">\(y\)</span> with a given input <span class="math notranslate nohighlight">\(x\)</span>.
 In standard linear regression with a linear dependence on <span class="math notranslate nohighlight">\(x\)</span>, we would write this in terms of our model</p>
@@ -1555,9 +916,9 @@ us to a very popular model for the function <span class="math notranslate nohigh
 Sigmoid function or logistic model. We will consider this function as
 representing the probability for finding a value of <span class="math notranslate nohighlight">\(y_i\)</span> with a given
 <span class="math notranslate nohighlight">\(x_i\)</span>.</p>
-</div>
-<div class="section" id="the-logistic-function">
-<h2>The logistic function<a class="headerlink" href="#the-logistic-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-logistic-function">
+<h2>The logistic function<a class="headerlink" href="#the-logistic-function" title="Permalink to this heading">#</a></h2>
 <p>Another widely studied model, is the so-called
 perceptron model, which is an example of a “hard classification” model. We
 will encounter this model when we discuss neural networks as
@@ -1574,9 +935,9 @@ belongs to a category <span class="math notranslate nohighlight">\(y_i=\{0,1\}\)
 p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
 \]</div>
 <p>Note that <span class="math notranslate nohighlight">\(1-p(t)= p(-t)\)</span>.</p>
-</div>
-<div class="section" id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">
-<h2>Examples of likelihood functions used in logistic regression and nueral networks<a class="headerlink" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">
+<h2>Examples of likelihood functions used in logistic regression and nueral networks<a class="headerlink" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks" title="Permalink to this heading">#</a></h2>
 <p>The following code plots the logistic function, the step function and other functions we will encounter from here and on.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -1637,15 +998,10 @@ p(t) = \frac{1}{1+\mathrm \exp{-t}}=\frac{\exp{t}}{1+\mathrm \exp{t}}.
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week38_32_0.png" src="_images/week38_32_0.png" />
-<img alt="_images/week38_32_1.png" src="_images/week38_32_1.png" />
-<img alt="_images/week38_32_2.png" src="_images/week38_32_2.png" />
 </div>
-</div>
-</div>
-<div class="section" id="two-parameters">
-<h2>Two parameters<a class="headerlink" href="#two-parameters" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="two-parameters">
+<h2>Two parameters<a class="headerlink" href="#two-parameters" title="Permalink to this heading">#</a></h2>
 <p>We assume now that we have two classes with <span class="math notranslate nohighlight">\(y_i\)</span> either <span class="math notranslate nohighlight">\(0\)</span> or <span class="math notranslate nohighlight">\(1\)</span>. Furthermore we assume also that we have only two parameters <span class="math notranslate nohighlight">\(\beta\)</span> in our fitting of the Sigmoid function, that is we define probabilities</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -1660,9 +1016,9 @@ p(y_i=0|x_i,\boldsymbol{\beta}) &amp;= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
 \[
 p(y_i=0\vert x_i, \boldsymbol{\beta}) = 1-p(y_i=1\vert x_i, \boldsymbol{\beta}).
 \]</div>
-</div>
-<div class="section" id="maximum-likelihood">
-<h2>Maximum likelihood<a class="headerlink" href="#maximum-likelihood" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="maximum-likelihood">
+<h2>Maximum likelihood<a class="headerlink" href="#maximum-likelihood" title="Permalink to this heading">#</a></h2>
 <p>In order to define the total likelihood for all possible outcomes from a<br />
 dataset <span class="math notranslate nohighlight">\(\mathcal{D}=\{(y_i,x_i)\}\)</span>, with the binary labels
 <span class="math notranslate nohighlight">\(y_i\in\{0,1\}\)</span> and where the data points are drawn independently, we use the so-called <a class="reference external" href="https://en.wikipedia.org/wiki/Maximum_likelihood_estimation">Maximum Likelihood Estimation</a> (MLE) principle.
@@ -1680,9 +1036,9 @@ P(\mathcal{D}|\boldsymbol{\beta})&amp; = \prod_{i=1}^n \left[p(y_i=1|x_i,\boldsy
 \[
 \mathcal{C}(\boldsymbol{\beta}) = \sum_{i=1}^n \left( y_i\log{p(y_i=1|x_i,\boldsymbol{\beta})} + (1-y_i)\log\left[1-p(y_i=1|x_i,\boldsymbol{\beta}))\right]\right).
 \]</div>
-</div>
-<div class="section" id="the-cost-function-rewritten">
-<h2>The cost function rewritten<a class="headerlink" href="#the-cost-function-rewritten" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-cost-function-rewritten">
+<h2>The cost function rewritten<a class="headerlink" href="#the-cost-function-rewritten" title="Permalink to this heading">#</a></h2>
 <p>Reordering the logarithms, we can rewrite the <strong>cost/loss</strong> function as</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1696,9 +1052,9 @@ Since the cost (error) function is just the negative log-likelihood, for logisti
 \]</div>
 <p>This equation is known in statistics as the <strong>cross entropy</strong>. Finally, we note that just as in linear regression,
 in practice we often supplement the cross-entropy with additional regularization terms, usually <span class="math notranslate nohighlight">\(L_1\)</span> and <span class="math notranslate nohighlight">\(L_2\)</span> regularization as we did for Ridge and Lasso regression.</p>
-</div>
-<div class="section" id="minimizing-the-cross-entropy">
-<h2>Minimizing the cross entropy<a class="headerlink" href="#minimizing-the-cross-entropy" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="minimizing-the-cross-entropy">
+<h2>Minimizing the cross entropy<a class="headerlink" href="#minimizing-the-cross-entropy" title="Permalink to this heading">#</a></h2>
 <p>The cross entropy is a convex function of the weights <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> and,
 therefore, any local minimizer is a global minimizer.</p>
 <p>Minimizing this
@@ -1712,9 +1068,9 @@ cost function with respect to the two parameters <span class="math notranslate n
 \[
 \frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \beta_1} = -\sum_{i=1}^n  \left(y_ix_i -x_i\frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}}\right).
 \]</div>
-</div>
-<div class="section" id="a-more-compact-expression">
-<h2>A more compact expression<a class="headerlink" href="#a-more-compact-expression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="a-more-compact-expression">
+<h2>A more compact expression<a class="headerlink" href="#a-more-compact-expression" title="Permalink to this heading">#</a></h2>
 <p>Let us now define a vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> with <span class="math notranslate nohighlight">\(n\)</span> elements <span class="math notranslate nohighlight">\(y_i\)</span>, an
 <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> which contains the <span class="math notranslate nohighlight">\(x_i\)</span> values and a
 vector <span class="math notranslate nohighlight">\(\boldsymbol{p}\)</span> of fitted probabilities <span class="math notranslate nohighlight">\(p(y_i\vert x_i,\boldsymbol{\beta})\)</span>. We can rewrite in a more compact form the first
@@ -1729,9 +1085,9 @@ derivative of cost function as</p>
 \[
 \frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
 \]</div>
-</div>
-<div class="section" id="extending-to-more-predictors">
-<h2>Extending to more predictors<a class="headerlink" href="#extending-to-more-predictors" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="extending-to-more-predictors">
+<h2>Extending to more predictors<a class="headerlink" href="#extending-to-more-predictors" title="Permalink to this heading">#</a></h2>
 <p>Within a binary classification problem, we can easily expand our model to include multiple predictors. Our ratio between likelihoods is then with <span class="math notranslate nohighlight">\(p\)</span> predictors</p>
 <div class="math notranslate nohighlight">
 \[
@@ -1742,9 +1098,9 @@ derivative of cost function as</p>
 \[
 p(\boldsymbol{\beta}\boldsymbol{x})=\frac{ \exp{(\beta_0+\beta_1x_1+\beta_2x_2+\dots+\beta_px_p)}}{1+\exp{(\beta_0+\beta_1x_1+\beta_2x_2+\dots+\beta_px_p)}}.
 \]</div>
-</div>
-<div class="section" id="including-more-classes">
-<h2>Including more classes<a class="headerlink" href="#including-more-classes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="including-more-classes">
+<h2>Including more classes<a class="headerlink" href="#including-more-classes" title="Permalink to this heading">#</a></h2>
 <p>Till now we have mainly focused on two classes, the so-called binary
 system. Suppose we wish to extend to <span class="math notranslate nohighlight">\(K\)</span> classes.  Let us for the sake
 of simplicity assume we have only two predictors. We have then following model</p>
@@ -1764,9 +1120,9 @@ of simplicity assume we have only two predictors. We have then following model</
 \]</div>
 <p>and the model is specified in term of <span class="math notranslate nohighlight">\(K-1\)</span> so-called log-odds or
 <strong>logit</strong> transformations.</p>
-</div>
-<div class="section" id="more-classes">
-<h2>More classes<a class="headerlink" href="#more-classes" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-classes">
+<h2>More classes<a class="headerlink" href="#more-classes" title="Permalink to this heading">#</a></h2>
 <p>In our discussion of neural networks we will encounter the above again
 in terms of a slightly modified function, the so-called <strong>Softmax</strong> function.</p>
 <p>The softmax function is used in various multiclass classification
@@ -1794,12 +1150,12 @@ what we derived earlier is compatible with these equations.</p>
 descent method.  Newton’s method and gradient descent methods are
 discussed in the material on <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html">optimization
 methods</a>.</p>
-</div>
-<div class="section" id="friday-september-23">
-<h2>Friday September 23<a class="headerlink" href="#friday-september-23" title="Permalink to this headline">¶</a></h2>
-</div>
-<div class="section" id="searching-for-optimal-regularization-parameters-lambda">
-<h2>Searching for Optimal Regularization Parameters <span class="math notranslate nohighlight">\(\lambda\)</span><a class="headerlink" href="#searching-for-optimal-regularization-parameters-lambda" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="friday-september-23">
+<h2>Friday September 23<a class="headerlink" href="#friday-september-23" title="Permalink to this heading">#</a></h2>
+</section>
+<section id="searching-for-optimal-regularization-parameters-lambda">
+<h2>Searching for Optimal Regularization Parameters <span class="math notranslate nohighlight">\(\lambda\)</span><a class="headerlink" href="#searching-for-optimal-regularization-parameters-lambda" title="Permalink to this heading">#</a></h2>
 <p>In project 1, when using Ridge and Lasso regression, we end up
 searching for the optimal parameter <span class="math notranslate nohighlight">\(\lambda\)</span> which minimizes our
 selected scores (MSE or <span class="math notranslate nohighlight">\(R2\)</span> values for example). The brute force
@@ -1856,16 +1212,13 @@ which results in optimal scores (for example the smallest MSE or an <span class=
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week38_72_0.png" src="_images/week38_72_0.png" />
-</div>
 </div>
 <p>Here we have performed a rather data greedy calculation as function of the regularization parameter <span class="math notranslate nohighlight">\(\lambda\)</span>. There is no resampling here. The latter can easily be added by employing the function <strong>RidgeCV</strong> instead of just calling the <strong>Ridge</strong> function. For <strong>RidgeCV</strong> we need to pass the array of <span class="math notranslate nohighlight">\(\lambda\)</span> values.
 By inspecting the figure we can in turn determine which is the optimal regularization parameter.
 This becomes however less functional in the long run.</p>
-</div>
-<div class="section" id="grid-search">
-<h2>Grid Search<a class="headerlink" href="#grid-search" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="grid-search">
+<h2>Grid Search<a class="headerlink" href="#grid-search" title="Permalink to this heading">#</a></h2>
 <p>An alternative is to use the so-called grid search functionality
 included with the library <strong>Scikit-Learn</strong>, as demonstrated for the same
 example here.</p>
@@ -1916,26 +1269,15 @@ example here.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>GridSearchCV(estimator=Ridge(),
-             param_grid={&#39;alpha&#39;: array([1.00000000e-04, 4.64158883e-04, 2.15443469e-03, 1.00000000e-02,
-       4.64158883e-02, 2.15443469e-01, 1.00000000e+00, 4.64158883e+00,
-       2.15443469e+01, 1.00000000e+02])})
-Best estimated lambda-value: 100.0
-MSE score: 1.0892144853354966
-R2 score: -0.0038332550504751595
-</pre></div>
-</div>
-</div>
 </div>
 <p>By default the grid search function includes cross validation with
 five folds. The <a class="reference external" href="https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV">Scikit-Learn
 documentation</a>
 contains more information on how to set the different parameters.</p>
 <p>If we take out the random noise, running the above codes results in <span class="math notranslate nohighlight">\(\lambda=0\)</span> yielding the best fit.</p>
-</div>
-<div class="section" id="randomized-grid-search">
-<h2>Randomized Grid Search<a class="headerlink" href="#randomized-grid-search" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="randomized-grid-search">
+<h2>Randomized Grid Search<a class="headerlink" href="#randomized-grid-search" title="Permalink to this heading">#</a></h2>
 <p>An alternative to the above manual grid set up, is to use a random
 search where the parameters are tuned from a random distribution
 (uniform below) for a fixed number of iterations. A model is
@@ -1992,19 +1334,10 @@ case under study.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>RandomizedSearchCV(estimator=Ridge(), n_iter=100,
-                   param_distributions={&#39;alpha&#39;: &lt;scipy.stats._distn_infrastructure.rv_frozen object at 0x1309f4ca0&gt;})
-Best estimated lambda-value: 0.9849967686928113
-MSE score: 1.0853136633465326
-R2 score: -0.0002382102844775691
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="section" id="wisconsin-cancer-data">
-<h2>Wisconsin Cancer Data<a class="headerlink" href="#wisconsin-cancer-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="wisconsin-cancer-data">
+<h2>Wisconsin Cancer Data<a class="headerlink" href="#wisconsin-cancer-data" title="Permalink to this heading">#</a></h2>
 <p>We show here how we can use a simple regression case on the breast
 cancer data using Logistic regression as our algorithm for
 classification.</p>
@@ -2029,27 +1362,10 @@ classification.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
-(143, 30)
-Test set accuracy with Logistic Regression: 0.94
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-<div class="section" id="using-the-correlation-matrix">
-<h2>Using the correlation matrix<a class="headerlink" href="#using-the-correlation-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="using-the-correlation-matrix">
+<h2>Using the correlation matrix<a class="headerlink" href="#using-the-correlation-matrix" title="Permalink to this heading">#</a></h2>
 <p>In addition to the above scores, we could also study the covariance (and the correlation matrix).
 We use <strong>Pandas</strong> to compute the correlation matrix.</p>
 <div class="cell docutils container">
@@ -2091,14 +1407,10 @@ We use <strong>Pandas</strong> to compute the correlation matrix.</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<img alt="_images/week38_82_0.png" src="_images/week38_82_0.png" />
-<img alt="_images/week38_82_1.png" src="_images/week38_82_1.png" />
 </div>
-</div>
-</div>
-<div class="section" id="discussing-the-correlation-data">
-<h2>Discussing the correlation data<a class="headerlink" href="#discussing-the-correlation-data" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="discussing-the-correlation-data">
+<h2>Discussing the correlation data<a class="headerlink" href="#discussing-the-correlation-data" title="Permalink to this heading">#</a></h2>
 <p>In the above example we note two things. In the first plot we display
 the overlap of benign and malignant tumors as functions of the various
 features in the Wisconsing breast cancer data set. We see that for
@@ -2129,9 +1441,9 @@ matrix.</p>
 features are of relevance and which are not. This leads  us to
 the classical Principal Component Analysis (PCA) theorem with
 applications. This will be discussed later this semester (<a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week43/html/week43-bs.html">week 43</a>).</p>
-</div>
-<div class="section" id="other-measures-in-classification-studies-cancer-data-again">
-<h2>Other measures in classification studies: Cancer Data  again<a class="headerlink" href="#other-measures-in-classification-studies-cancer-data-again" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="other-measures-in-classification-studies-cancer-data-again">
+<h2>Other measures in classification studies: Cancer Data  again<a class="headerlink" href="#other-measures-in-classification-studies-cancer-data-again" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
@@ -2169,112 +1481,10 @@ applications. This will be discussed later this semester (<a class="reference ex
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>(426, 30)
-(143, 30)
-[1.         0.86666667 1.         0.92857143 1.         0.85714286
- 1.         0.92857143 0.92857143 1.        ]
-Test set accuracy with Logistic Regression: 0.94
-</pre></div>
 </div>
-<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
-STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
-
-Increase the number of iterations (max_iter) or scale the data as shown in:
-    https://scikit-learn.org/stable/modules/preprocessing.html
-Please also refer to the documentation for alternative solver options:
-    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression
-  n_iter_i = _check_optimize_result(
-</pre></div>
-</div>
-<img alt="_images/week38_89_2.png" src="_images/week38_89_2.png" />
-<img alt="_images/week38_89_3.png" src="_images/week38_89_3.png" />
-<img alt="_images/week38_89_4.png" src="_images/week38_89_4.png" />
-</div>
-</div>
-</div>
-<div class="section" id="optimization-the-central-part-of-any-machine-learning-algortithm">
-<h2>Optimization, the central part of any Machine Learning algortithm<a class="headerlink" href="#optimization-the-central-part-of-any-machine-learning-algortithm" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="optimization-the-central-part-of-any-machine-learning-algortithm">
+<h2>Optimization, the central part of any Machine Learning algortithm<a class="headerlink" href="#optimization-the-central-part-of-any-machine-learning-algortithm" title="Permalink to this heading">#</a></h2>
 <p><a class="reference external" href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/OverarchingAimsWeek39.mp4?vrtx=view-as-webpage">Overview Video, why do we care about gradient methods?</a></p>
 <p>Almost every problem in machine learning and data science starts with
 a dataset <span class="math notranslate nohighlight">\(X\)</span>, a model <span class="math notranslate nohighlight">\(g(\beta)\)</span>, which is a function of the
@@ -2284,9 +1494,9 @@ us to judge how well the model <span class="math notranslate nohighlight">\(g(\b
 the cost function. Ideally we would be able to solve for <span class="math notranslate nohighlight">\(\beta\)</span>
 analytically, however this is not possible in general and we must use
 some approximative/numerical method to compute the minimum.</p>
-</div>
-<div class="section" id="revisiting-our-logistic-regression-case">
-<h2>Revisiting our Logistic Regression case<a class="headerlink" href="#revisiting-our-logistic-regression-case" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="revisiting-our-logistic-regression-case">
+<h2>Revisiting our Logistic Regression case<a class="headerlink" href="#revisiting-our-logistic-regression-case" title="Permalink to this heading">#</a></h2>
 <p>In our discussion on Logistic Regression we studied the
 case of
 two classes, with <span class="math notranslate nohighlight">\(y_i\)</span> either
@@ -2301,9 +1511,9 @@ p(y_i=0|x_i,\boldsymbol{\beta}) &amp;= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
 \end{align*}
 \end{split}\]</div>
 <p>where <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> are the weights we wish to extract from data, in our case <span class="math notranslate nohighlight">\(\beta_0\)</span> and <span class="math notranslate nohighlight">\(\beta_1\)</span>.</p>
-</div>
-<div class="section" id="the-equations-to-solve">
-<h2>The equations to solve<a class="headerlink" href="#the-equations-to-solve" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-equations-to-solve">
+<h2>The equations to solve<a class="headerlink" href="#the-equations-to-solve" title="Permalink to this heading">#</a></h2>
 <p>Our compact equations used a definition of a vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> with <span class="math notranslate nohighlight">\(n\)</span>
 elements <span class="math notranslate nohighlight">\(y_i\)</span>, an <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> which contains the
 <span class="math notranslate nohighlight">\(x_i\)</span> values and a vector <span class="math notranslate nohighlight">\(\boldsymbol{p}\)</span> of fitted probabilities
@@ -2320,9 +1530,9 @@ the first derivative of the cost function as</p>
 \frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
 \]</div>
 <p>This defines what is called  the Hessian matrix.</p>
-</div>
-<div class="section" id="solving-using-newton-raphson-s-method">
-<h2>Solving using Newton-Raphson’s method<a class="headerlink" href="#solving-using-newton-raphson-s-method" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="solving-using-newton-raphson-s-method">
+<h2>Solving using Newton-Raphson’s method<a class="headerlink" href="#solving-using-newton-raphson-s-method" title="Permalink to this heading">#</a></h2>
 <p>If we can set up these equations, Newton-Raphson’s iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives.</p>
 <p>Our iterative scheme is then given by</p>
 <div class="math notranslate nohighlight">
@@ -2336,9 +1546,9 @@ the first derivative of the cost function as</p>
 \]</div>
 <p>The right-hand side is computed with the old values of <span class="math notranslate nohighlight">\(\beta\)</span>.</p>
 <p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement.</p>
-</div>
-<div class="section" id="brief-reminder-on-newton-raphson-s-method">
-<h2>Brief reminder on Newton-Raphson’s method<a class="headerlink" href="#brief-reminder-on-newton-raphson-s-method" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="brief-reminder-on-newton-raphson-s-method">
+<h2>Brief reminder on Newton-Raphson’s method<a class="headerlink" href="#brief-reminder-on-newton-raphson-s-method" title="Permalink to this heading">#</a></h2>
 <p>Let us quickly remind ourselves how we derive the above method.</p>
 <p>Perhaps the most celebrated of all one-dimensional root-finding
 routines is Newton’s method, also called the Newton-Raphson
@@ -2347,9 +1557,9 @@ function <span class="math notranslate nohighlight">\(f\)</span> and its derivat
 If you can only calculate the derivative
 numerically and/or your function is not of the smooth type, we
 normally discourage the use of this method.</p>
-</div>
-<div class="section" id="the-equations">
-<h2>The equations<a class="headerlink" href="#the-equations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-equations">
+<h2>The equations<a class="headerlink" href="#the-equations" title="Permalink to this heading">#</a></h2>
 <p>The Newton-Raphson formula consists geometrically of extending the
 tangent line at a current point until it crosses zero, then setting
 the next guess to the abscissa of that zero-crossing.  The mathematics
@@ -2378,9 +1588,9 @@ s\approx x-\frac{f(x)}{f'(x)}.
 \[
 x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
 \]</div>
-</div>
-<div class="section" id="simple-geometric-interpretation">
-<h2>Simple geometric interpretation<a class="headerlink" href="#simple-geometric-interpretation" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-geometric-interpretation">
+<h2>Simple geometric interpretation<a class="headerlink" href="#simple-geometric-interpretation" title="Permalink to this heading">#</a></h2>
 <p>The above is Newton-Raphson’s method. It has a simple geometric
 interpretation, namely <span class="math notranslate nohighlight">\(x_{n+1}\)</span> is the point where the tangent from
 <span class="math notranslate nohighlight">\((x_n,f(x_n))\)</span> crosses the <span class="math notranslate nohighlight">\(x\)</span>-axis.  Close to the solution,
@@ -2392,9 +1602,9 @@ from the true root as to let the search interval include a local
 maximum or minimum of the function.  If an iteration places a trial
 guess near such a local extremum, so that the first derivative nearly
 vanishes, then Newton-Raphson may fail totally</p>
-</div>
-<div class="section" id="extending-to-more-than-one-variable">
-<h2>Extending to more than one variable<a class="headerlink" href="#extending-to-more-than-one-variable" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="extending-to-more-than-one-variable">
+<h2>Extending to more than one variable<a class="headerlink" href="#extending-to-more-than-one-variable" title="Permalink to this heading">#</a></h2>
 <p>Newton’s method can be generalized to systems of several non-linear equations
 and variables. Consider the case with two equations</p>
 <div class="math notranslate nohighlight">
@@ -2440,9 +1650,9 @@ is to understand that difficulties  may
 arise in case <span class="math notranslate nohighlight">\({\bf \boldsymbol{J}}\)</span> is nearly singular.</p>
 <p>It is rather straightforward to extend the above scheme to systems of
 more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.</p>
-</div>
-<div class="section" id="steepest-descent">
-<h2>Steepest descent<a class="headerlink" href="#steepest-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="steepest-descent">
+<h2>Steepest descent<a class="headerlink" href="#steepest-descent" title="Permalink to this heading">#</a></h2>
 <p>The basic idea of gradient descent is
 that a function <span class="math notranslate nohighlight">\(F(\mathbf{x})\)</span>,
 <span class="math notranslate nohighlight">\(\mathbf{x} \equiv (x_1,\cdots,x_n)\)</span>, decreases fastest if one goes from <span class="math notranslate nohighlight">\(\bf {x}\)</span> in the
@@ -2456,9 +1666,9 @@ direction of the negative gradient <span class="math notranslate nohighlight">\(
 <p>For <span class="math notranslate nohighlight">\(\gamma_k\)</span> small enough, then <span class="math notranslate nohighlight">\(F(\mathbf{x}_{k+1}) \leq
 F(\mathbf{x}_k)\)</span>. This means that for a sufficiently small <span class="math notranslate nohighlight">\(\gamma_k\)</span>
 we are always moving towards smaller function values, i.e a minimum.</p>
-</div>
-<div class="section" id="more-on-steepest-descent">
-<h2>More on Steepest descent<a class="headerlink" href="#more-on-steepest-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-on-steepest-descent">
+<h2>More on Steepest descent<a class="headerlink" href="#more-on-steepest-descent" title="Permalink to this heading">#</a></h2>
 <p>The previous observation is the basis of the method of steepest
 descent, which is also referred to as just gradient descent (GD). One
 starts with an initial guess <span class="math notranslate nohighlight">\(\mathbf{x}_0\)</span> for a minimum of <span class="math notranslate nohighlight">\(F\)</span> and
@@ -2469,9 +1679,9 @@ computes new approximations according to</p>
 \]</div>
 <p>The parameter <span class="math notranslate nohighlight">\(\gamma_k\)</span> is often referred to as the step length or
 the learning rate within the context of Machine Learning.</p>
-</div>
-<div class="section" id="the-ideal">
-<h2>The ideal<a class="headerlink" href="#the-ideal" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-ideal">
+<h2>The ideal<a class="headerlink" href="#the-ideal" title="Permalink to this heading">#</a></h2>
 <p>Ideally the sequence <span class="math notranslate nohighlight">\(\{\mathbf{x}_k \}_{k=0}\)</span> converges to a global
 minimum of the function <span class="math notranslate nohighlight">\(F\)</span>. In general we do not know if we are in a
 global or local minimum. In the special case when <span class="math notranslate nohighlight">\(F\)</span> is a convex
@@ -2487,9 +1697,9 @@ have a very good intial guess. This also implies that the scheme is
 sensitive to the chosen initial condition.</p>
 <p>Note that the gradient is a function of <span class="math notranslate nohighlight">\(\mathbf{x} =
 (x_1,\cdots,x_n)\)</span> which makes it expensive to compute numerically.</p>
-</div>
-<div class="section" id="the-sensitiveness-of-the-gradient-descent">
-<h2>The sensitiveness of the gradient descent<a class="headerlink" href="#the-sensitiveness-of-the-gradient-descent" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-sensitiveness-of-the-gradient-descent">
+<h2>The sensitiveness of the gradient descent<a class="headerlink" href="#the-sensitiveness-of-the-gradient-descent" title="Permalink to this heading">#</a></h2>
 <p>The gradient descent method
 is sensitive to the choice of learning rate <span class="math notranslate nohighlight">\(\gamma_k\)</span>. This is due
 to the fact that we are only guaranteed that <span class="math notranslate nohighlight">\(F(\mathbf{x}_{k+1}) \leq
@@ -2500,9 +1710,9 @@ large we can experience erratic behavior.</p>
 <p>Many of these shortcomings can be alleviated by introducing
 randomness. One such method is that of Stochastic Gradient Descent
 (SGD), to be discussed next week.</p>
-</div>
-<div class="section" id="convex-functions">
-<h2>Convex functions<a class="headerlink" href="#convex-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="convex-functions">
+<h2>Convex functions<a class="headerlink" href="#convex-functions" title="Permalink to this heading">#</a></h2>
 <p>Ideally we want our cost/loss function to be convex(concave).</p>
 <p>First we give the definition of a convex set: A set <span class="math notranslate nohighlight">\(C\)</span> in
 <span class="math notranslate nohighlight">\(\mathbb{R}^n\)</span> is said to be convex if, for all <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> in <span class="math notranslate nohighlight">\(C\)</span> and
@@ -2512,13 +1722,13 @@ connecting <span class="math notranslate nohighlight">\(x\)</span> and <span cla
 <p>The convex subsets of <span class="math notranslate nohighlight">\(\mathbb{R}\)</span> are the intervals of
 <span class="math notranslate nohighlight">\(\mathbb{R}\)</span>. Examples of convex sets of <span class="math notranslate nohighlight">\(\mathbb{R}^2\)</span> are the
 regular polygons (triangles, rectangles, pentagons, etc…).</p>
-</div>
-<div class="section" id="convex-function">
-<h2>Convex function<a class="headerlink" href="#convex-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="convex-function">
+<h2>Convex function<a class="headerlink" href="#convex-function" title="Permalink to this heading">#</a></h2>
 <p><strong>Convex function</strong>: Let <span class="math notranslate nohighlight">\(X \subset \mathbb{R}^n\)</span> be a convex set. Assume that the function <span class="math notranslate nohighlight">\(f: X \rightarrow \mathbb{R}\)</span> is continuous, then <span class="math notranslate nohighlight">\(f\)</span> is said to be convex if $<span class="math notranslate nohighlight">\(f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)</span><span class="math notranslate nohighlight">\( for all \)</span>x_1, x_2 \in X<span class="math notranslate nohighlight">\( and for all \)</span>t \in [0,1]<span class="math notranslate nohighlight">\(. If \)</span>\leq<span class="math notranslate nohighlight">\( is replaced with a strict inequaltiy in the definition, we demand \)</span>x_1 \neq x_2<span class="math notranslate nohighlight">\( and \)</span>t\in(0,1)<span class="math notranslate nohighlight">\( then \)</span>f<span class="math notranslate nohighlight">\( is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \)</span>f(x_1)<span class="math notranslate nohighlight">\( and \)</span>f(x_2)<span class="math notranslate nohighlight">\(, the value of the function on the interval \)</span>[x_1,x_2]$ is always below the line as illustrated below.</p>
-</div>
-<div class="section" id="conditions-on-convex-functions">
-<h2>Conditions on convex functions<a class="headerlink" href="#conditions-on-convex-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="conditions-on-convex-functions">
+<h2>Conditions on convex functions<a class="headerlink" href="#conditions-on-convex-functions" title="Permalink to this heading">#</a></h2>
 <p>In the following we state first and second-order conditions which
 ensures convexity of a function <span class="math notranslate nohighlight">\(f\)</span>. We write <span class="math notranslate nohighlight">\(D_f\)</span> to denote the
 domain of <span class="math notranslate nohighlight">\(f\)</span>, i.e the subset of <span class="math notranslate nohighlight">\(R^n\)</span> where <span class="math notranslate nohighlight">\(f\)</span> is defined. For more
@@ -2540,9 +1750,9 @@ Hessian is positive semi-definite for all <span class="math notranslate nohighli
 single-variable function this reduces to <span class="math notranslate nohighlight">\(f''(x) \geq 0\)</span>. Geometrically this means that <span class="math notranslate nohighlight">\(f\)</span> has nonnegative curvature
 everywhere.</p>
 <p>This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition.</p>
-</div>
-<div class="section" id="more-on-convex-functions">
-<h2>More on convex functions<a class="headerlink" href="#more-on-convex-functions" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="more-on-convex-functions">
+<h2>More on convex functions<a class="headerlink" href="#more-on-convex-functions" title="Permalink to this heading">#</a></h2>
 <p>The next result is of great importance to us and the reason why we are
 going on about convex functions. In machine learning we frequently
 have to minimize a loss/cost function in order to find the best
@@ -2556,10 +1766,10 @@ is convex the following result provides invaluable information:</p>
 is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is convex and differentiable. Then, any point
 <span class="math notranslate nohighlight">\(x^*\)</span> that satisfies <span class="math notranslate nohighlight">\(\nabla f(x^*) = 0\)</span> is a global minimum.</p>
 <p>This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.</p>
-</div>
-<div class="section" id="some-simple-problems">
-<h2>Some simple problems<a class="headerlink" href="#some-simple-problems" title="Permalink to this headline">¶</a></h2>
-<ol class="simple">
+</section>
+<section id="some-simple-problems">
+<h2>Some simple problems<a class="headerlink" href="#some-simple-problems" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
 <li><p>Show that <span class="math notranslate nohighlight">\(f(x)=x^2\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span> using the definition of convexity. Hint: If you re-write the definition, <span class="math notranslate nohighlight">\(f\)</span> is convex if the following holds for all <span class="math notranslate nohighlight">\(x,y \in D_f\)</span> and any <span class="math notranslate nohighlight">\(\lambda \in [0,1]\)</span> <span class="math notranslate nohighlight">\(\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0\)</span>.</p></li>
 <li><p>Using the second order condition show that the following functions are convex on the specified domain.</p></li>
 </ol>
@@ -2567,7 +1777,7 @@ is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is con
 <li><p><span class="math notranslate nohighlight">\(f(x) = e^x\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>.</p></li>
 <li><p><span class="math notranslate nohighlight">\(g(x) = -\ln(x)\)</span> is convex for <span class="math notranslate nohighlight">\(x \in (0,\infty)\)</span>.</p></li>
 </ul>
-<ol class="simple">
+<ol class="arabic simple" start="3">
 <li><p>Let <span class="math notranslate nohighlight">\(f(x) = x^2\)</span> and <span class="math notranslate nohighlight">\(g(x) = e^x\)</span>. Show that <span class="math notranslate nohighlight">\(f(g(x))\)</span> and <span class="math notranslate nohighlight">\(g(f(x))\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>. Also show that if <span class="math notranslate nohighlight">\(f(x)\)</span> is any convex function than <span class="math notranslate nohighlight">\(h(x) = e^{f(x)}\)</span> is convex.</p></li>
 <li><p>A norm is any function that satisfy the following properties</p></li>
 </ol>
@@ -2577,14 +1787,14 @@ is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is con
 <li><p><span class="math notranslate nohighlight">\(f(x) \leq 0\)</span> for all <span class="math notranslate nohighlight">\(x \in \mathbb{R}^n\)</span> with equality if and only if <span class="math notranslate nohighlight">\(x = 0\)</span></p></li>
 </ul>
 <p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
-</div>
-<div class="section" id="revisiting-our-first-homework">
-<h2>Revisiting our first homework<a class="headerlink" href="#revisiting-our-first-homework" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="revisiting-our-first-homework">
+<h2>Revisiting our first homework<a class="headerlink" href="#revisiting-our-first-homework" title="Permalink to this heading">#</a></h2>
 <p>We will use linear regression as a case study for the gradient descent
 methods. Linear regression is a great test case for the gradient
 descent methods discussed in the lectures since it has several
 desirable properties such as:</p>
-<ol class="simple">
+<ol class="arabic simple">
 <li><p>An analytical solution (recall homework set 1).</p></li>
 <li><p>The gradient can be computed analytically.</p></li>
 <li><p>The cost function is convex which guarantees that gradient descent converges for small enough learning rates</p></li>
@@ -2597,17 +1807,6 @@ desirable properties such as:</p>
 </pre></div>
 </div>
 </div>
-<div class="cell_output docutils container">
-<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
-<span class="ne">NameError</span><span class="g g-Whitespace">                                 </span>Traceback (most recent call last)
-<span class="nn">Input In [13],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
-<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
-<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
-
-<span class="ne">NameError</span>: name &#39;m&#39; is not defined
-</pre></div>
-</div>
-</div>
 </div>
 <p>with <span class="math notranslate nohighlight">\(x_i \in [0,1] \)</span> is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution <span class="math notranslate nohighlight">\(\cal {N}(0,1)\)</span>.
 The linear regression model is given by</p>
@@ -2620,9 +1819,9 @@ h_\beta(x) = \boldsymbol{y} = \beta_0 + \beta_1 x,
 \[
 \boldsymbol{y}_i = \beta_0 + \beta_1 x_i.
 \]</div>
-</div>
-<div class="section" id="gradient-descent-example">
-<h2>Gradient descent example<a class="headerlink" href="#gradient-descent-example" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-descent-example">
+<h2>Gradient descent example<a class="headerlink" href="#gradient-descent-example" title="Permalink to this heading">#</a></h2>
 <p>Let <span class="math notranslate nohighlight">\(\mathbf{y} = (y_1,\cdots,y_n)^T\)</span>, <span class="math notranslate nohighlight">\(\mathbf{\boldsymbol{y}} = (\boldsymbol{y}_1,\cdots,\boldsymbol{y}_n)^T\)</span> and <span class="math notranslate nohighlight">\(\beta = (\beta_0, \beta_1)^T\)</span></p>
 <p>It is convenient to write <span class="math notranslate nohighlight">\(\mathbf{\boldsymbol{y}} = X\beta\)</span> where <span class="math notranslate nohighlight">\(X \in \mathbb{R}^{100 \times 2} \)</span> is the design matrix given by (we keep the intercept here)</p>
 <div class="math notranslate nohighlight">
@@ -2639,9 +1838,9 @@ X \equiv \begin{bmatrix}
 C(\beta) = \frac{1}{n}||X\beta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2\right]
 \]</div>
 <p>and we want to find <span class="math notranslate nohighlight">\(\beta\)</span> such that <span class="math notranslate nohighlight">\(C(\beta)\)</span> is minimized.</p>
-</div>
-<div class="section" id="the-derivative-of-the-cost-loss-function">
-<h2>The derivative of the cost/loss function<a class="headerlink" href="#the-derivative-of-the-cost-loss-function" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-derivative-of-the-cost-loss-function">
+<h2>The derivative of the cost/loss function<a class="headerlink" href="#the-derivative-of-the-cost-loss-function" title="Permalink to this heading">#</a></h2>
 <p>Computing <span class="math notranslate nohighlight">\(\partial C(\beta) / \partial \beta_0\)</span> and <span class="math notranslate nohighlight">\(\partial C(\beta) / \partial \beta_1\)</span> we can show  that the gradient can be written as</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -2650,9 +1849,9 @@ C(\beta) = \frac{1}{n}||X\beta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100
 \end{bmatrix} = \frac{2}{n}X^T(X\beta - \mathbf{y}),
 \end{split}\]</div>
 <p>where <span class="math notranslate nohighlight">\(X\)</span> is the design matrix defined above.</p>
-</div>
-<div class="section" id="the-hessian-matrix">
-<h2>The Hessian matrix<a class="headerlink" href="#the-hessian-matrix" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-hessian-matrix">
+<h2>The Hessian matrix<a class="headerlink" href="#the-hessian-matrix" title="Permalink to this heading">#</a></h2>
 <p>The Hessian matrix of <span class="math notranslate nohighlight">\(C(\beta)\)</span> is given by</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -2662,9 +1861,9 @@ C(\beta) = \frac{1}{n}||X\beta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100
 \end{bmatrix} = \frac{2}{n}X^T X.
 \end{split}\]</div>
 <p>This result implies that <span class="math notranslate nohighlight">\(C(\beta)\)</span> is a convex function since the matrix <span class="math notranslate nohighlight">\(X^T X\)</span> always is positive semi-definite.</p>
-</div>
-<div class="section" id="simple-program">
-<h2>Simple program<a class="headerlink" href="#simple-program" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="simple-program">
+<h2>Simple program<a class="headerlink" href="#simple-program" title="Permalink to this heading">#</a></h2>
 <p>We can now write a program that minimizes <span class="math notranslate nohighlight">\(C(\beta)\)</span> using the gradient descent method with a constant learning rate <span class="math notranslate nohighlight">\(\gamma\)</span> according to</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2675,9 +1874,9 @@ C(\beta) = \frac{1}{n}||X\beta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100
 when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8}\)</span>. <strong>Note that the code below does not include the latter stop criterion</strong>.</p>
 <p>And finally we can compare our solution for <span class="math notranslate nohighlight">\(\beta\)</span> with the analytic result given by
 <span class="math notranslate nohighlight">\(\beta= (X^TX)^{-1} X^T \mathbf{y}\)</span>.</p>
-</div>
-<div class="section" id="id1">
-<h2>Gradient Descent Example<a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="id1">
+<h2>Gradient Descent Example<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
 <p>Here our simple example</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
@@ -2730,9 +1929,9 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="and-a-corresponding-example-using-scikit-learn">
-<h2>And a corresponding example using <strong>scikit-learn</strong><a class="headerlink" href="#and-a-corresponding-example-using-scikit-learn" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="and-a-corresponding-example-using-scikit-learn">
+<h2>And a corresponding example using <strong>scikit-learn</strong><a class="headerlink" href="#and-a-corresponding-example-using-scikit-learn" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Importing various packages</span>
@@ -2755,9 +1954,9 @@ when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="gradient-descent-and-ridge">
-<h2>Gradient descent and Ridge<a class="headerlink" href="#gradient-descent-and-ridge" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="gradient-descent-and-ridge">
+<h2>Gradient descent and Ridge<a class="headerlink" href="#gradient-descent-and-ridge" title="Permalink to this heading">#</a></h2>
 <p>We have also discussed Ridge regression where the loss function contains a regularized term given by the <span class="math notranslate nohighlight">\(L_2\)</span> norm of <span class="math notranslate nohighlight">\(\beta\)</span>,</p>
 <div class="math notranslate nohighlight">
 \[
@@ -2775,9 +1974,9 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
 \[
 \beta_{\text{ridge}} = \left(X^T X + n\lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y}.
 \]</div>
-</div>
-<div class="section" id="the-hessian-matrix-for-ridge-regression">
-<h2>The Hessian matrix for Ridge Regression<a class="headerlink" href="#the-hessian-matrix-for-ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="the-hessian-matrix-for-ridge-regression">
+<h2>The Hessian matrix for Ridge Regression<a class="headerlink" href="#the-hessian-matrix-for-ridge-regression" title="Permalink to this heading">#</a></h2>
 <p>The Hessian matrix of Ridge Regression for our simple example  is given by</p>
 <div class="math notranslate nohighlight">
 \[\begin{split}
@@ -2791,9 +1990,9 @@ minimum.
 Note that the Ridge cost function is convex being  a sum of two convex
 functions. Therefore, the stationary point is a global
 minimum of this function.</p>
-</div>
-<div class="section" id="program-example-for-gradient-descent-with-ridge-regression">
-<h2>Program example for gradient descent with Ridge Regression<a class="headerlink" href="#program-example-for-gradient-descent-with-ridge-regression" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="program-example-for-gradient-descent-with-ridge-regression">
+<h2>Program example for gradient descent with Ridge Regression<a class="headerlink" href="#program-example-for-gradient-descent-with-ridge-regression" title="Permalink to this heading">#</a></h2>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
 <div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
@@ -2850,9 +2049,9 @@ minimum of this function.</p>
 </div>
 </div>
 </div>
-</div>
-<div class="section" id="using-gradient-descent-methods-limitations">
-<h2>Using gradient descent methods, limitations<a class="headerlink" href="#using-gradient-descent-methods-limitations" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="using-gradient-descent-methods-limitations">
+<h2>Using gradient descent methods, limitations<a class="headerlink" href="#using-gradient-descent-methods-limitations" title="Permalink to this heading">#</a></h2>
 <ul class="simple">
 <li><p><strong>Gradient descent (GD) finds local minima of our function</strong>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</p></li>
 <li><p><strong>GD is sensitive to initial conditions</strong>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</p></li>
@@ -2861,12 +2060,12 @@ minimum of this function.</p>
 <li><p><strong>GD treats all directions in parameter space uniformly.</strong> Another major drawback of GD is that unlike Newton’s method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</p></li>
 <li><p>GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</p></li>
 </ul>
-</div>
-<div class="section" id="challenge-yourself-the-coming-weekend">
-<h2>Challenge yourself the coming weekend<a class="headerlink" href="#challenge-yourself-the-coming-weekend" title="Permalink to this headline">¶</a></h2>
+</section>
+<section id="challenge-yourself-the-coming-weekend">
+<h2>Challenge yourself the coming weekend<a class="headerlink" href="#challenge-yourself-the-coming-weekend" title="Permalink to this heading">#</a></h2>
 <p>Write a code which implements gradient descent for a logistic regression example.</p>
-</div>
-</div>
+</section>
+</section>
 
     <script type="text/x-thebe-config">
     {
@@ -2880,7 +2079,7 @@ minimum of this function.</p>
             mode: "python"
         },
         kernelOptions: {
-            kernelName: "python3",
+            name: "python3",
             path: "./."
         },
         predefinedOutput: true
@@ -2888,44 +2087,162 @@ minimum of this function.</p>
     </script>
     <script>kernelName = 'python3'</script>
 
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+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plans-for-week-38">Plans for week 38</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-from-last-week-and-relevant-for-the-first-project">Material from last week and relevant for the first project</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#various-steps-in-cross-validation">Various steps in cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#how-to-set-up-the-cross-validation-for-ridge-and-or-lasso">How to set up the cross-validation for Ridge and/or Lasso</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cross-validation-in-brief">Cross-validation in brief</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-example-for-cross-validation-and-k-fold-cross-validation">Code Example for Cross-validation and <span class="math notranslate nohighlight">\(k\)</span>-fold Cross-validation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#material-for-lecture-thursday-september-21">Material for lecture Thursday September 21</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#logistic-regression">Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#classification-problems">Classification problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-and-deep-learning">Optimization and Deep learning</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#basics">Basics</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#linear-classifier">Linear classifier</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-selected-properties">Some selected properties</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example">Simple example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plotting-the-mean-value-for-each-group">Plotting the mean value for each group</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-logistic-function">The logistic function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks">Examples of likelihood functions used in logistic regression and nueral networks</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#two-parameters">Two parameters</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#maximum-likelihood">Maximum likelihood</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-cost-function-rewritten">The cost function rewritten</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#minimizing-the-cross-entropy">Minimizing the cross entropy</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#a-more-compact-expression">A more compact expression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-predictors">Extending to more predictors</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-more-classes">Including more classes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-classes">More classes</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#friday-september-23">Friday September 23</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#searching-for-optimal-regularization-parameters-lambda">Searching for Optimal Regularization Parameters <span class="math notranslate nohighlight">\(\lambda\)</span></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#grid-search">Grid Search</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#randomized-grid-search">Randomized Grid Search</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#wisconsin-cancer-data">Wisconsin Cancer Data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-the-correlation-matrix">Using the correlation matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#discussing-the-correlation-data">Discussing the correlation data</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#other-measures-in-classification-studies-cancer-data-again">Other measures in classification studies: Cancer Data  again</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-to-solve">The equations to solve</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">Solving using Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations">The equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-geometric-interpretation">Simple geometric interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-than-one-variable">Extending to more than one variable</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-steepest-descent">More on Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ideal">The ideal</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">Convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-function">Convex function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditions-on-convex-functions">Conditions on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-convex-functions">More on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">Some simple problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-first-homework">Revisiting our first homework</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-example">Gradient descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix">The Hessian matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-program">Simple program</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Gradient Descent Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">And a corresponding example using <strong>scikit-learn</strong></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-and-ridge">Gradient descent and Ridge</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#challenge-yourself-the-coming-weekend">Challenge yourself the coming weekend</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
+<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
+<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 39: Optimization and  Gradient Methods</a></li>
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+    <h1>Week 39: Optimization and  Gradient Methods</h1>
+    <!-- Table of contents -->
+    <div id="print-main-content">
+        <div id="jb-print-toc">
+            
+            <div>
+                <h2> Contents </h2>
+            </div>
+            <nav aria-label="Page">
+                <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plan-for-week-39">Plan for week 39</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-to-solve">The equations to solve</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">Solving using Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations">The equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-geometric-interpretation">Simple geometric interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-than-one-variable">Extending to more than one variable</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-steepest-descent">More on Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ideal">The ideal</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">Convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-function">Convex function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditions-on-convex-functions">Conditions on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-convex-functions">More on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">Some simple problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-steepest-descent">Standard steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-method">Gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent-method">Steepest descent  method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Steepest descent  method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#final-expressions">Final expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent-example">Steepest descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id3">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id4">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id5">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id6">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id7">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-first-homework">Revisiting our first homework</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-example">Gradient descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix">The Hessian matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-program">Simple program</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id8">Gradient Descent Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">And a corresponding example using <strong>scikit-learn</strong></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-and-ridge">Gradient descent and Ridge</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#improving-gradient-descent-with-momentum">Improving gradient descent with momentum</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#overview-video-on-stochastic-gradient-descent">Overview video on Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#batches-and-mini-batches">Batches and mini-batches</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">Stochastic Gradient Descent (SGD)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent">Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#computation-of-gradients">Computation of gradients</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sgd-example">SGD example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-gradient-step">The gradient step</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example-code">Simple example code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#when-do-we-stop">When do we stop?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#slightly-different-approach">Slightly different approach</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#time-decay-rate">Time decay rate</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-with-a-number-of-minibatches-which-varies">Code with a Number of Minibatches which varies</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#replace-or-not">Replace or not</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-based-gd">Momentum based GD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-momentum-based-approaches">More on momentum based approaches</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-parameter">Momentum parameter</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#second-moment-of-the-gradient">Second moment of the gradient</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rms-prop">RMS prop</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adam-optimizer">ADAM optimizer</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#algorithms-and-codes-for-adagrad-rmsprop-and-adam">Algorithms and codes for Adagrad, RMSprop and Adam</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#practical-tips">Practical tips</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#automatic-differentiation">Automatic differentiation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd">Using autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#autograd-with-more-complicated-functions">Autograd with more complicated functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-complicated-functions-using-the-elements-of-their-arguments-directly">More complicated functions using the elements of their arguments directly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#functions-using-mathematical-functions-from-numpy">Functions using mathematical functions from Numpy</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-autograd">More autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-with-loops">And  with loops</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-recursion">Using recursion</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#unsupported-functions">Unsupported functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-syntax-a-dot-b-when-finding-the-dot-product">The syntax a.dot(b) when finding the dot product</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#recommended-to-avoid">Recommended to avoid</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd-with-ols">Using Autograd with OLS</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id9">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#but-noen-of-these-can-compete-with-newton-s-method">But noen of these can compete with Newton’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">Including Stochastic Gradient Descent with Autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id10">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">Similar (second order function now) problem but now with AdaGrad</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent">RMSprop for adaptive learning rate with Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-adam">And finally ADAM</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-logistic-regression">And Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-jax">Introducing JAX</a></li>
+</ul>
+            </nav>
+        </div>
+    </div>
+</div>
+
+              
+                
+<div id="searchbox"></div>
+                <article class="bd-article" role="main">
+                  
+  <!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
+doconce format html week39.do.txt --no_mako -->
+<!-- dom:TITLE: Week 39: Optimization and  Gradient Methods --><section class="tex2jax_ignore mathjax_ignore" id="week-39-optimization-and-gradient-methods">
+<h1>Week 39: Optimization and  Gradient Methods<a class="headerlink" href="#week-39-optimization-and-gradient-methods" title="Permalink to this heading">#</a></h1>
+<p><strong>Morten Hjorth-Jensen</strong>, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University</p>
+<p>Date: <strong>Week 39</strong></p>
+<section id="plan-for-week-39">
+<h2>Plan for week 39<a class="headerlink" href="#plan-for-week-39" title="Permalink to this heading">#</a></h2>
+<p><strong>Material for the active learning sessions on Tuesday and Wednesday.</strong></p>
+<ul class="simple">
+<li><p>Discussions on how to structure your report for the first project</p></li>
+<li><p>Exercise for week 39 on how to write the abstract and the introduction of the report and how to include references.</p></li>
+<li><p>Work on project 1, in particular resampling methods like cross-validation and bootstrap. <strong>For more discussions of project 1, chapter 5 of Goodfellow et al is a good read, in particular sections 5.1-5.5 and 5.7-5.11</strong>.</p></li>
+</ul>
+<p>These sections summarize neatly what we have done till now and point to what is coming with respect to deep learning.</p>
+<ul class="simple">
+<li><p>A general guideline can be found at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">CompPhysics/MachineLearning</a>.</p></li>
+</ul>
+<p><strong>Material for the lecture on Thursday September 28.</strong></p>
+<ul class="simple">
+<li><p>Repetition of Logistic regression equations and classification problems and discussion of Gradient methods. Examples on how to implement Logistic Regression and discussion of stochastic gradient descent</p></li>
+<li><p>Stochastic Gradient descent with examples and automatic differentiation</p></li>
+<li><p><a class="reference external" href="https://youtu.be/">Video of lecture</a></p></li>
+<li><p>Whiteboard notes TBA at <a class="github reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep28.pdf">CompPhysics/MachineLearning</a></p></li>
+<li><p>Readings and Videos:</p>
+<ul>
+<li><p>These lecture notes</p></li>
+<li><p>For a good discussion on gradient methods, we would like to recommend Goodfellow et al section 4.3-4.5 and sections 8.3-8.6. We will come back to the latter chapter in our discussion of Neural networks as well.</p></li>
+<li><p><a class="reference external" href="https://www.youtube.com/watch?v=sDv4f4s2SB8">Video on gradient descent</a></p></li>
+<li><p><a class="reference external" href="https://www.youtube.com/watch?v=vMh0zPT0tLI">Video on stochastic gradient descent</a></p></li>
+</ul>
+</li>
+</ul>
+</section>
+<section id="optimization-the-central-part-of-any-machine-learning-algortithm">
+<h2>Optimization, the central part of any Machine Learning algortithm<a class="headerlink" href="#optimization-the-central-part-of-any-machine-learning-algortithm" title="Permalink to this heading">#</a></h2>
+<p>The first few slides here are a repetition from last week.</p>
+<p>Almost every problem in machine learning and data science starts with
+a dataset <span class="math notranslate nohighlight">\(X\)</span>, a model <span class="math notranslate nohighlight">\(g(\beta)\)</span>, which is a function of the
+parameters <span class="math notranslate nohighlight">\(\beta\)</span> and a cost function <span class="math notranslate nohighlight">\(C(X, g(\beta))\)</span> that allows
+us to judge how well the model <span class="math notranslate nohighlight">\(g(\beta)\)</span> explains the observations
+<span class="math notranslate nohighlight">\(X\)</span>. The model is fit by finding the values of <span class="math notranslate nohighlight">\(\beta\)</span> that minimize
+the cost function. Ideally we would be able to solve for <span class="math notranslate nohighlight">\(\beta\)</span>
+analytically, however this is not possible in general and we must use
+some approximative/numerical method to compute the minimum.</p>
+</section>
+<section id="revisiting-our-logistic-regression-case">
+<h2>Revisiting our Logistic Regression case<a class="headerlink" href="#revisiting-our-logistic-regression-case" title="Permalink to this heading">#</a></h2>
+<p>In our discussion on Logistic Regression we studied the
+case of
+two classes, with <span class="math notranslate nohighlight">\(y_i\)</span> either
+<span class="math notranslate nohighlight">\(0\)</span> or <span class="math notranslate nohighlight">\(1\)</span>. Furthermore we assumed also that we have only two
+parameters <span class="math notranslate nohighlight">\(\beta\)</span> in our fitting, that is we
+defined probabilities</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\begin{align*}
+p(y_i=1|x_i,\boldsymbol{\beta}) &amp;= \frac{\exp{(\beta_0+\beta_1x_i)}}{1+\exp{(\beta_0+\beta_1x_i)}},\nonumber\\
+p(y_i=0|x_i,\boldsymbol{\beta}) &amp;= 1 - p(y_i=1|x_i,\boldsymbol{\beta}),
+\end{align*}
+\end{split}\]</div>
+<p>where <span class="math notranslate nohighlight">\(\boldsymbol{\beta}\)</span> are the weights we wish to extract from data, in our case <span class="math notranslate nohighlight">\(\beta_0\)</span> and <span class="math notranslate nohighlight">\(\beta_1\)</span>.</p>
+</section>
+<section id="the-equations-to-solve">
+<h2>The equations to solve<a class="headerlink" href="#the-equations-to-solve" title="Permalink to this heading">#</a></h2>
+<p>Our compact equations used a definition of a vector <span class="math notranslate nohighlight">\(\boldsymbol{y}\)</span> with <span class="math notranslate nohighlight">\(n\)</span>
+elements <span class="math notranslate nohighlight">\(y_i\)</span>, an <span class="math notranslate nohighlight">\(n\times p\)</span> matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> which contains the
+<span class="math notranslate nohighlight">\(x_i\)</span> values and a vector <span class="math notranslate nohighlight">\(\boldsymbol{p}\)</span> of fitted probabilities
+<span class="math notranslate nohighlight">\(p(y_i\vert x_i,\boldsymbol{\beta})\)</span>. We rewrote in a more compact form
+the first derivative of the cost function as</p>
+<div class="math notranslate nohighlight">
+\[
+\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}} = -\boldsymbol{X}^T\left(\boldsymbol{y}-\boldsymbol{p}\right).
+\]</div>
+<p>If we in addition define a diagonal matrix <span class="math notranslate nohighlight">\(\boldsymbol{W}\)</span> with elements
+<span class="math notranslate nohighlight">\(p(y_i\vert x_i,\boldsymbol{\beta})(1-p(y_i\vert x_i,\boldsymbol{\beta})\)</span>, we can obtain a compact expression of the second derivative as</p>
+<div class="math notranslate nohighlight">
+\[
+\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} = \boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X}.
+\]</div>
+<p>This defines what is called  the Hessian matrix.</p>
+</section>
+<section id="solving-using-newton-raphson-s-method">
+<h2>Solving using Newton-Raphson’s method<a class="headerlink" href="#solving-using-newton-raphson-s-method" title="Permalink to this heading">#</a></h2>
+<p>If we can set up these equations, Newton-Raphson’s iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives.</p>
+<p>Our iterative scheme is then given by</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\frac{\partial^2 \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T}\right)^{-1}_{\boldsymbol{\beta}^{\mathrm{old}}}\times \left(\frac{\partial \mathcal{C}(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}}\right)_{\boldsymbol{\beta}^{\mathrm{old}}},
+\]</div>
+<p>or in matrix form as</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\beta}^{\mathrm{new}} = \boldsymbol{\beta}^{\mathrm{old}}-\left(\boldsymbol{X}^T\boldsymbol{W}\boldsymbol{X} \right)^{-1}\times \left(-\boldsymbol{X}^T(\boldsymbol{y}-\boldsymbol{p}) \right)_{\boldsymbol{\beta}^{\mathrm{old}}}.
+\]</div>
+<p>The right-hand side is computed with the old values of <span class="math notranslate nohighlight">\(\beta\)</span>.</p>
+<p>If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement.</p>
+</section>
+<section id="brief-reminder-on-newton-raphson-s-method">
+<h2>Brief reminder on Newton-Raphson’s method<a class="headerlink" href="#brief-reminder-on-newton-raphson-s-method" title="Permalink to this heading">#</a></h2>
+<p>Let us quickly remind ourselves how we derive the above method.</p>
+<p>Perhaps the most celebrated of all one-dimensional root-finding
+routines is Newton’s method, also called the Newton-Raphson
+method. This method  requires the evaluation of both the
+function <span class="math notranslate nohighlight">\(f\)</span> and its derivative <span class="math notranslate nohighlight">\(f'\)</span> at arbitrary points.
+If you can only calculate the derivative
+numerically and/or your function is not of the smooth type, we
+normally discourage the use of this method.</p>
+</section>
+<section id="the-equations">
+<h2>The equations<a class="headerlink" href="#the-equations" title="Permalink to this heading">#</a></h2>
+<p>The Newton-Raphson formula consists geometrically of extending the
+tangent line at a current point until it crosses zero, then setting
+the next guess to the abscissa of that zero-crossing.  The mathematics
+behind this method is rather simple. Employing a Taylor expansion for
+<span class="math notranslate nohighlight">\(x\)</span> sufficiently close to the solution <span class="math notranslate nohighlight">\(s\)</span>, we have</p>
+<!-- Equation labels as ordinary links -->
+<div id="eq:taylornr"></div>
+<div class="math notranslate nohighlight">
+\[
+f(s)=0=f(x)+(s-x)f'(x)+\frac{(s-x)^2}{2}f''(x) +\dots.
+    \label{eq:taylornr} \tag{1}
+\]</div>
+<p>For small enough values of the function and for well-behaved
+functions, the terms beyond linear are unimportant, hence we obtain</p>
+<div class="math notranslate nohighlight">
+\[
+f(x)+(s-x)f'(x)\approx 0,
+\]</div>
+<p>yielding</p>
+<div class="math notranslate nohighlight">
+\[
+s\approx x-\frac{f(x)}{f'(x)}.
+\]</div>
+<p>Having in mind an iterative procedure, it is natural to start iterating with</p>
+<div class="math notranslate nohighlight">
+\[
+x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}.
+\]</div>
+</section>
+<section id="simple-geometric-interpretation">
+<h2>Simple geometric interpretation<a class="headerlink" href="#simple-geometric-interpretation" title="Permalink to this heading">#</a></h2>
+<p>The above is Newton-Raphson’s method. It has a simple geometric
+interpretation, namely <span class="math notranslate nohighlight">\(x_{n+1}\)</span> is the point where the tangent from
+<span class="math notranslate nohighlight">\((x_n,f(x_n))\)</span> crosses the <span class="math notranslate nohighlight">\(x\)</span>-axis.  Close to the solution,
+Newton-Raphson converges fast to the desired result. However, if we
+are far from a root, where the higher-order terms in the series are
+important, the Newton-Raphson formula can give grossly inaccurate
+results. For instance, the initial guess for the root might be so far
+from the true root as to let the search interval include a local
+maximum or minimum of the function.  If an iteration places a trial
+guess near such a local extremum, so that the first derivative nearly
+vanishes, then Newton-Raphson may fail totally</p>
+</section>
+<section id="extending-to-more-than-one-variable">
+<h2>Extending to more than one variable<a class="headerlink" href="#extending-to-more-than-one-variable" title="Permalink to this heading">#</a></h2>
+<p>Newton’s method can be generalized to systems of several non-linear equations
+and variables. Consider the case with two equations</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\begin{array}{cc} f_1(x_1,x_2) &amp;=0\\
+                     f_2(x_1,x_2) &amp;=0,\end{array}
+\end{split}\]</div>
+<p>which we Taylor expand to obtain</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&amp;f_1(x_1,x_2)+h_1
+                     \partial f_1/\partial x_1+h_2
+                     \partial f_1/\partial x_2+\dots\\
+                     0=f_2(x_1+h_1,x_2+h_2)=&amp;f_2(x_1,x_2)+h_1
+                     \partial f_2/\partial x_1+h_2
+                     \partial f_2/\partial x_2+\dots
+                       \end{array}.
+\end{split}\]</div>
+<p>Defining the Jacobian matrix <span class="math notranslate nohighlight">\({\bf \boldsymbol{J}}\)</span> we have</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+{\bf \boldsymbol{J}}=\left( \begin{array}{cc}
+                         \partial f_1/\partial x_1  &amp; \partial f_1/\partial x_2 \\
+                          \partial f_2/\partial x_1     &amp;\partial f_2/\partial x_2
+             \end{array} \right),
+\end{split}\]</div>
+<p>we can rephrase Newton’s method as</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\left(\begin{array}{c} x_1^{n+1} \\ x_2^{n+1} \end{array} \right)=
+\left(\begin{array}{c} x_1^{n} \\ x_2^{n} \end{array} \right)+
+\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right),
+\end{split}\]</div>
+<p>where we have defined</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\left(\begin{array}{c} h_1^{n} \\ h_2^{n} \end{array} \right)=
+   -{\bf \boldsymbol{J}}^{-1}
+   \left(\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\ f_2(x_1^{n},x_2^{n}) \end{array} \right).
+\end{split}\]</div>
+<p>We need thus to compute the inverse of the Jacobian matrix and it
+is to understand that difficulties  may
+arise in case <span class="math notranslate nohighlight">\({\bf \boldsymbol{J}}\)</span> is nearly singular.</p>
+<p>It is rather straightforward to extend the above scheme to systems of
+more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function.</p>
+</section>
+<section id="steepest-descent">
+<h2>Steepest descent<a class="headerlink" href="#steepest-descent" title="Permalink to this heading">#</a></h2>
+<p>The basic idea of gradient descent is
+that a function <span class="math notranslate nohighlight">\(F(\mathbf{x})\)</span>,
+<span class="math notranslate nohighlight">\(\mathbf{x} \equiv (x_1,\cdots,x_n)\)</span>, decreases fastest if one goes from <span class="math notranslate nohighlight">\(\bf {x}\)</span> in the
+direction of the negative gradient <span class="math notranslate nohighlight">\(-\nabla F(\mathbf{x})\)</span>.</p>
+<p>It can be shown that if</p>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k),
+\]</div>
+<p>with <span class="math notranslate nohighlight">\(\gamma_k &gt; 0\)</span>.</p>
+<p>For <span class="math notranslate nohighlight">\(\gamma_k\)</span> small enough, then <span class="math notranslate nohighlight">\(F(\mathbf{x}_{k+1}) \leq
+F(\mathbf{x}_k)\)</span>. This means that for a sufficiently small <span class="math notranslate nohighlight">\(\gamma_k\)</span>
+we are always moving towards smaller function values, i.e a minimum.</p>
+</section>
+<section id="more-on-steepest-descent">
+<h2>More on Steepest descent<a class="headerlink" href="#more-on-steepest-descent" title="Permalink to this heading">#</a></h2>
+<p>The previous observation is the basis of the method of steepest
+descent, which is also referred to as just gradient descent (GD). One
+starts with an initial guess <span class="math notranslate nohighlight">\(\mathbf{x}_0\)</span> for a minimum of <span class="math notranslate nohighlight">\(F\)</span> and
+computes new approximations according to</p>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{x}_{k+1} = \mathbf{x}_k - \gamma_k \nabla F(\mathbf{x}_k), \ \ k \geq 0.
+\]</div>
+<p>The parameter <span class="math notranslate nohighlight">\(\gamma_k\)</span> is often referred to as the step length or
+the learning rate within the context of Machine Learning.</p>
+</section>
+<section id="the-ideal">
+<h2>The ideal<a class="headerlink" href="#the-ideal" title="Permalink to this heading">#</a></h2>
+<p>Ideally the sequence <span class="math notranslate nohighlight">\(\{\mathbf{x}_k \}_{k=0}\)</span> converges to a global
+minimum of the function <span class="math notranslate nohighlight">\(F\)</span>. In general we do not know if we are in a
+global or local minimum. In the special case when <span class="math notranslate nohighlight">\(F\)</span> is a convex
+function, all local minima are also global minima, so in this case
+gradient descent can converge to the global solution. The advantage of
+this scheme is that it is conceptually simple and straightforward to
+implement. However the method in this form has some severe
+limitations:</p>
+<p>In machine learing we are often faced with non-convex high dimensional
+cost functions with many local minima. Since GD is deterministic we
+will get stuck in a local minimum, if the method converges, unless we
+have a very good intial guess. This also implies that the scheme is
+sensitive to the chosen initial condition.</p>
+<p>Note that the gradient is a function of <span class="math notranslate nohighlight">\(\mathbf{x} =
+(x_1,\cdots,x_n)\)</span> which makes it expensive to compute numerically.</p>
+</section>
+<section id="the-sensitiveness-of-the-gradient-descent">
+<h2>The sensitiveness of the gradient descent<a class="headerlink" href="#the-sensitiveness-of-the-gradient-descent" title="Permalink to this heading">#</a></h2>
+<p>The gradient descent method
+is sensitive to the choice of learning rate <span class="math notranslate nohighlight">\(\gamma_k\)</span>. This is due
+to the fact that we are only guaranteed that <span class="math notranslate nohighlight">\(F(\mathbf{x}_{k+1}) \leq
+F(\mathbf{x}_k)\)</span> for sufficiently small <span class="math notranslate nohighlight">\(\gamma_k\)</span>. The problem is to
+determine an optimal learning rate. If the learning rate is chosen too
+small the method will take a long time to converge and if it is too
+large we can experience erratic behavior.</p>
+<p>Many of these shortcomings can be alleviated by introducing
+randomness. One such method is that of Stochastic Gradient Descent
+(SGD), see below.</p>
+</section>
+<section id="convex-functions">
+<h2>Convex functions<a class="headerlink" href="#convex-functions" title="Permalink to this heading">#</a></h2>
+<p>Ideally we want our cost/loss function to be convex(concave).</p>
+<p>First we give the definition of a convex set: A set <span class="math notranslate nohighlight">\(C\)</span> in
+<span class="math notranslate nohighlight">\(\mathbb{R}^n\)</span> is said to be convex if, for all <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> in <span class="math notranslate nohighlight">\(C\)</span> and
+all <span class="math notranslate nohighlight">\(t \in (0,1)\)</span> , the point <span class="math notranslate nohighlight">\((1 − t)x + ty\)</span> also belongs to
+C. Geometrically this means that every point on the line segment
+connecting <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> is in <span class="math notranslate nohighlight">\(C\)</span> as discussed below.</p>
+<p>The convex subsets of <span class="math notranslate nohighlight">\(\mathbb{R}\)</span> are the intervals of
+<span class="math notranslate nohighlight">\(\mathbb{R}\)</span>. Examples of convex sets of <span class="math notranslate nohighlight">\(\mathbb{R}^2\)</span> are the
+regular polygons (triangles, rectangles, pentagons, etc…).</p>
+</section>
+<section id="convex-function">
+<h2>Convex function<a class="headerlink" href="#convex-function" title="Permalink to this heading">#</a></h2>
+<p><strong>Convex function</strong>: Let <span class="math notranslate nohighlight">\(X \subset \mathbb{R}^n\)</span> be a convex set. Assume that the function <span class="math notranslate nohighlight">\(f: X \rightarrow \mathbb{R}\)</span> is continuous, then <span class="math notranslate nohighlight">\(f\)</span> is said to be convex if $<span class="math notranslate nohighlight">\(f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) \)</span><span class="math notranslate nohighlight">\( for all \)</span>x_1, x_2 \in X<span class="math notranslate nohighlight">\( and for all \)</span>t \in [0,1]<span class="math notranslate nohighlight">\(. If \)</span>\leq<span class="math notranslate nohighlight">\( is replaced with a strict inequaltiy in the definition, we demand \)</span>x_1 \neq x_2<span class="math notranslate nohighlight">\( and \)</span>t\in(0,1)<span class="math notranslate nohighlight">\( then \)</span>f<span class="math notranslate nohighlight">\( is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting \)</span>f(x_1)<span class="math notranslate nohighlight">\( and \)</span>f(x_2)<span class="math notranslate nohighlight">\(, the value of the function on the interval \)</span>[x_1,x_2]$ is always below the line as illustrated below.</p>
+</section>
+<section id="conditions-on-convex-functions">
+<h2>Conditions on convex functions<a class="headerlink" href="#conditions-on-convex-functions" title="Permalink to this heading">#</a></h2>
+<p>In the following we state first and second-order conditions which
+ensures convexity of a function <span class="math notranslate nohighlight">\(f\)</span>. We write <span class="math notranslate nohighlight">\(D_f\)</span> to denote the
+domain of <span class="math notranslate nohighlight">\(f\)</span>, i.e the subset of <span class="math notranslate nohighlight">\(R^n\)</span> where <span class="math notranslate nohighlight">\(f\)</span> is defined. For more
+details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](<a class="reference external" href="http://stanford.edu/boyd/cvxbook/">http://stanford.edu/boyd/cvxbook/</a>, 2004).</p>
+<p><strong>First order condition.</strong></p>
+<p>Suppose <span class="math notranslate nohighlight">\(f\)</span> is differentiable (i.e <span class="math notranslate nohighlight">\(\nabla f(x)\)</span> is well defined for
+all <span class="math notranslate nohighlight">\(x\)</span> in the domain of <span class="math notranslate nohighlight">\(f\)</span>). Then <span class="math notranslate nohighlight">\(f\)</span> is convex if and only if <span class="math notranslate nohighlight">\(D_f\)</span>
+is a convex set and $<span class="math notranslate nohighlight">\(f(y) \geq f(x) + \nabla f(x)^T (y-x) \)</span><span class="math notranslate nohighlight">\( holds
+for all \)</span>x,y \in D_f<span class="math notranslate nohighlight">\(. This condition means that for a convex function
+the first order Taylor expansion (right hand side above) at any point
+a global under estimator of the function. To convince yourself you can
+make a drawing of \)</span>f(x) = x^2+1<span class="math notranslate nohighlight">\( and draw the tangent line to \)</span>f(x)$ and
+note that it is always below the graph.</p>
+<p><strong>Second order condition.</strong></p>
+<p>Assume that <span class="math notranslate nohighlight">\(f\)</span> is twice
+differentiable, i.e the Hessian matrix exists at each point in
+<span class="math notranslate nohighlight">\(D_f\)</span>. Then <span class="math notranslate nohighlight">\(f\)</span> is convex if and only if <span class="math notranslate nohighlight">\(D_f\)</span> is a convex set and its
+Hessian is positive semi-definite for all <span class="math notranslate nohighlight">\(x\in D_f\)</span>. For a
+single-variable function this reduces to <span class="math notranslate nohighlight">\(f''(x) \geq 0\)</span>. Geometrically this means that <span class="math notranslate nohighlight">\(f\)</span> has nonnegative curvature
+everywhere.</p>
+<p>This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition.</p>
+</section>
+<section id="more-on-convex-functions">
+<h2>More on convex functions<a class="headerlink" href="#more-on-convex-functions" title="Permalink to this heading">#</a></h2>
+<p>The next result is of great importance to us and the reason why we are
+going on about convex functions. In machine learning we frequently
+have to minimize a loss/cost function in order to find the best
+parameters for the model we are considering.</p>
+<p>Ideally we want the
+global minimum (for high-dimensional models it is hard to know
+if we have local or global minimum). However, if the cost/loss function
+is convex the following result provides invaluable information:</p>
+<p><strong>Any minimum is global for convex functions.</strong></p>
+<p>Consider the problem of finding <span class="math notranslate nohighlight">\(x \in \mathbb{R}^n\)</span> such that <span class="math notranslate nohighlight">\(f(x)\)</span>
+is minimal, where <span class="math notranslate nohighlight">\(f\)</span> is convex and differentiable. Then, any point
+<span class="math notranslate nohighlight">\(x^*\)</span> that satisfies <span class="math notranslate nohighlight">\(\nabla f(x^*) = 0\)</span> is a global minimum.</p>
+<p>This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.</p>
+</section>
+<section id="some-simple-problems">
+<h2>Some simple problems<a class="headerlink" href="#some-simple-problems" title="Permalink to this heading">#</a></h2>
+<ol class="arabic simple">
+<li><p>Show that <span class="math notranslate nohighlight">\(f(x)=x^2\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span> using the definition of convexity. Hint: If you re-write the definition, <span class="math notranslate nohighlight">\(f\)</span> is convex if the following holds for all <span class="math notranslate nohighlight">\(x,y \in D_f\)</span> and any <span class="math notranslate nohighlight">\(\lambda \in [0,1]\)</span> <span class="math notranslate nohighlight">\(\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0\)</span>.</p></li>
+<li><p>Using the second order condition show that the following functions are convex on the specified domain.</p></li>
+</ol>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(f(x) = e^x\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>.</p></li>
+<li><p><span class="math notranslate nohighlight">\(g(x) = -\ln(x)\)</span> is convex for <span class="math notranslate nohighlight">\(x \in (0,\infty)\)</span>.</p></li>
+</ul>
+<ol class="arabic simple" start="3">
+<li><p>Let <span class="math notranslate nohighlight">\(f(x) = x^2\)</span> and <span class="math notranslate nohighlight">\(g(x) = e^x\)</span>. Show that <span class="math notranslate nohighlight">\(f(g(x))\)</span> and <span class="math notranslate nohighlight">\(g(f(x))\)</span> is convex for <span class="math notranslate nohighlight">\(x \in \mathbb{R}\)</span>. Also show that if <span class="math notranslate nohighlight">\(f(x)\)</span> is any convex function than <span class="math notranslate nohighlight">\(h(x) = e^{f(x)}\)</span> is convex.</p></li>
+<li><p>A norm is any function that satisfy the following properties</p></li>
+</ol>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(f(\alpha x) = |\alpha| f(x)\)</span> for all <span class="math notranslate nohighlight">\(\alpha \in \mathbb{R}\)</span>.</p></li>
+<li><p><span class="math notranslate nohighlight">\(f(x+y) \leq f(x) + f(y)\)</span></p></li>
+<li><p><span class="math notranslate nohighlight">\(f(x) \leq 0\)</span> for all <span class="math notranslate nohighlight">\(x \in \mathbb{R}^n\)</span> with equality if and only if <span class="math notranslate nohighlight">\(x = 0\)</span></p></li>
+</ul>
+<p>Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).</p>
+</section>
+<section id="standard-steepest-descent">
+<h2>Standard steepest descent<a class="headerlink" href="#standard-steepest-descent" title="Permalink to this heading">#</a></h2>
+<p>Before we proceed, we would like to discuss the approach called the
+<strong>standard Steepest descent</strong> (different from the above steepest descent discussion), which again leads to us having to be able
+to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).</p>
+<p><a class="reference external" href="https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf">The success of the CG method</a>
+for finding solutions of non-linear problems is based on the theory
+of conjugate gradients for linear systems of equations. It belongs to
+the class of iterative methods for solving problems from linear
+algebra of the type</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}.
+\]</div>
+<p>In the iterative process we end up with a problem like</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{r}= \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x},
+\]</div>
+<p>where <span class="math notranslate nohighlight">\(\boldsymbol{r}\)</span> is the so-called residual or error in the iterative process.</p>
+<p>When we have found the exact solution, <span class="math notranslate nohighlight">\(\boldsymbol{r}=0\)</span>.</p>
+</section>
+<section id="gradient-method">
+<h2>Gradient method<a class="headerlink" href="#gradient-method" title="Permalink to this heading">#</a></h2>
+<p>The residual is zero when we reach the minimum of the quadratic equation</p>
+<div class="math notranslate nohighlight">
+\[
+P(\boldsymbol{x})=\frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T\boldsymbol{b},
+\]</div>
+<p>with the constraint that the matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> is positive definite and
+symmetric.  This defines also the Hessian and we want it to be  positive definite.</p>
+</section>
+<section id="steepest-descent-method">
+<h2>Steepest descent  method<a class="headerlink" href="#steepest-descent-method" title="Permalink to this heading">#</a></h2>
+<p>We denote the initial guess for <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> as <span class="math notranslate nohighlight">\(\boldsymbol{x}_0\)</span>.
+We can assume without loss of generality that</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}_0=0,
+\]</div>
+<p>or consider the system</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
+\]</div>
+<p>instead.</p>
+</section>
+<section id="id1">
+<h2>Steepest descent  method<a class="headerlink" href="#id1" title="Permalink to this heading">#</a></h2>
+<p>One can show that the solution <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> is also the unique minimizer of the quadratic form</p>
+<div class="math notranslate nohighlight">
+\[
+f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
+\]</div>
+<p>This suggests taking the first basis vector <span class="math notranslate nohighlight">\(\boldsymbol{r}_1\)</span> (see below for definition)
+to be the gradient of <span class="math notranslate nohighlight">\(f\)</span> at <span class="math notranslate nohighlight">\(\boldsymbol{x}=\boldsymbol{x}_0\)</span>,
+which equals</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
+\]</div>
+<p>and
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_0=0\)</span> it is equal <span class="math notranslate nohighlight">\(-\boldsymbol{b}\)</span>.</p>
+</section>
+<section id="final-expressions">
+<h2>Final expressions<a class="headerlink" href="#final-expressions" title="Permalink to this heading">#</a></h2>
+<p>We can compute the residual iteratively as</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
+\]</div>
+<p>which equals</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{r}_k),
+\]</div>
+<p>or</p>
+<div class="math notranslate nohighlight">
+\[
+(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{r}_k,
+\]</div>
+<p>which gives</p>
+<div class="math notranslate nohighlight">
+\[
+\alpha_k = \frac{\boldsymbol{r}_k^T\boldsymbol{r}_k}{\boldsymbol{r}_k^T\boldsymbol{A}\boldsymbol{r}_k}
+\]</div>
+<p>leading to the iterative scheme</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}_{k+1}=\boldsymbol{x}_k+\alpha_k\boldsymbol{r}_{k},
+\]</div>
+</section>
+<section id="steepest-descent-example">
+<h2>Steepest descent example<a class="headerlink" href="#steepest-descent-example" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">numpy.linalg</span> <span class="k">as</span> <span class="nn">la</span>
+
+<span class="kn">import</span> <span class="nn">scipy.optimize</span> <span class="k">as</span> <span class="nn">sopt</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">pt</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">axes3d</span>
+
+<span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="mf">3.0</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span>
+
+<span class="k">def</span> <span class="nf">df</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">6</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]])</span>
+
+<span class="n">fig</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s2">&quot;3d&quot;</span><span class="p">)</span>
+
+<span class="n">xmesh</span><span class="p">,</span> <span class="n">ymesh</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="mi">50</span><span class="n">j</span><span class="p">,</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="mi">50</span><span class="n">j</span><span class="p">]</span>
+<span class="n">fmesh</span> <span class="o">=</span> <span class="n">f</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">xmesh</span><span class="p">,</span> <span class="n">ymesh</span><span class="p">]))</span>
+<span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">xmesh</span><span class="p">,</span> <span class="n">ymesh</span><span class="p">,</span> <span class="n">fmesh</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+<div class="cell_output docutils container">
+<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
+<span class="ne">ModuleNotFoundError</span><span class="g g-Whitespace">                       </span>Traceback (most recent call last)
+<span class="n">Cell</span> <span class="n">In</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">line</span> <span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">get_ipython</span><span class="p">()</span><span class="o">.</span><span class="n">run_line_magic</span><span class="p">(</span><span class="s1">&#39;matplotlib&#39;</span><span class="p">,</span> <span class="s1">&#39;inline&#39;</span><span class="p">)</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="kn">import</span> <span class="nn">numpy.linalg</span> <span class="k">as</span> <span class="nn">la</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432,</span> in <span class="ni">InteractiveShell.run_line_magic</span><span class="nt">(self, magic_name, line, _stack_depth)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2430</span>     <span class="n">kwargs</span><span class="p">[</span><span class="s1">&#39;local_ns&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">get_local_scope</span><span class="p">(</span><span class="n">stack_depth</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2431</span> <span class="k">with</span> <span class="bp">self</span><span class="o">.</span><span class="n">builtin_trap</span><span class="p">:</span>
+<span class="ne">-&gt; </span><span class="mi">2432</span>     <span class="n">result</span> <span class="o">=</span> <span class="n">fn</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+<span class="g g-Whitespace">   </span><span class="mi">2434</span> <span class="c1"># The code below prevents the output from being displayed</span>
+<span class="g g-Whitespace">   </span><span class="mi">2435</span> <span class="c1"># when using magics with decorator @output_can_be_silenced</span>
+<span class="g g-Whitespace">   </span><span class="mi">2436</span> <span class="c1"># when the last Python token in the expression is a &#39;;&#39;.</span>
+<span class="g g-Whitespace">   </span><span class="mi">2437</span> <span class="k">if</span> <span class="nb">getattr</span><span class="p">(</span><span class="n">fn</span><span class="p">,</span> <span class="n">magic</span><span class="o">.</span><span class="n">MAGIC_OUTPUT_CAN_BE_SILENCED</span><span class="p">,</span> <span class="kc">False</span><span class="p">):</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99,</span> in <span class="ni">PylabMagics.matplotlib</span><span class="nt">(self, line)</span>
+<span class="g g-Whitespace">     </span><span class="mi">97</span>     <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Available matplotlib backends: </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">backends_list</span><span class="p">)</span>
+<span class="g g-Whitespace">     </span><span class="mi">98</span> <span class="k">else</span><span class="p">:</span>
+<span class="ne">---&gt; </span><span class="mi">99</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shell</span><span class="o">.</span><span class="n">enable_matplotlib</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="o">.</span><span class="n">lower</span><span class="p">()</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="k">else</span> <span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">)</span>
+<span class="g g-Whitespace">    </span><span class="mi">100</span>     <span class="bp">self</span><span class="o">.</span><span class="n">_show_matplotlib_backend</span><span class="p">(</span><span class="n">args</span><span class="o">.</span><span class="n">gui</span><span class="p">,</span> <span class="n">backend</span><span class="p">)</span>
+
+<span class="nn">File ~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606,</span> in <span class="ni">InteractiveShell.enable_matplotlib</span><span class="nt">(self, gui)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3585</span> <span class="k">def</span> <span class="nf">enable_matplotlib</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">gui</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="g g-Whitespace">   </span><span class="mi">3586</span><span class="w">     </span><span class="sd">&quot;&quot;&quot;Enable interactive matplotlib and inline figure support.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3587</span><span class="sd"> </span>
+<span class="g g-Whitespace">   </span><span class="mi">3588</span><span class="sd">     This takes the following steps:</span>
+<span class="sd">   (...)</span>
+<span class="g g-Whitespace">   </span><span class="mi">3604</span><span class="sd">         display figures inline.</span>
+<span class="g g-Whitespace">   </span><span class="mi">3605</span><span class="sd">     &quot;&quot;&quot;</span>
+<span class="ne">-&gt; </span><span class="mi">3606</span>     <span class="kn">from</span> <span class="nn">matplotlib_inline.backend_inline</span> <span class="kn">import</span> <span class="n">configure_inline_support</span>
+<span class="g g-Whitespace">   </span><span class="mi">3608</span>     <span class="kn">from</span> <span class="nn">IPython.core</span> <span class="kn">import</span> <span class="n">pylabtools</span> <span class="k">as</span> <span class="n">pt</span>
+<span class="g g-Whitespace">   </span><span class="mi">3609</span>     <span class="n">gui</span><span class="p">,</span> <span class="n">backend</span> <span class="o">=</span> <span class="n">pt</span><span class="o">.</span><span class="n">find_gui_and_backend</span><span class="p">(</span><span class="n">gui</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">pylab_gui_select</span><span class="p">)</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="fm">__init__</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">1</span>
+<span class="ne">----&gt; </span><span class="mi">1</span> <span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">backend_inline</span><span class="p">,</span> <span class="n">config</span>  <span class="c1"># noqa</span>
+<span class="g g-Whitespace">      </span><span class="mi">2</span> <span class="n">__version__</span> <span class="o">=</span> <span class="s2">&quot;0.1.6&quot;</span>  <span class="c1"># noqa</span>
+
+<span class="n">File</span> <span class="o">~/</span><span class="n">miniforge3</span><span class="o">/</span><span class="n">lib</span><span class="o">/</span><span class="n">python3</span><span class="mf">.9</span><span class="o">/</span><span class="n">site</span><span class="o">-</span><span class="n">packages</span><span class="o">/</span><span class="n">matplotlib_inline</span><span class="o">/</span><span class="n">backend_inline</span><span class="o">.</span><span class="n">py</span><span class="p">:</span><span class="mi">6</span>
+<span class="g g-Whitespace">      </span><span class="mi">1</span><span class="w"> </span><span class="sd">&quot;&quot;&quot;A matplotlib backend for publishing figures via display_data&quot;&quot;&quot;</span>
+<span class="g g-Whitespace">      </span><span class="mi">3</span> <span class="c1"># Copyright (c) IPython Development Team.</span>
+<span class="g g-Whitespace">      </span><span class="mi">4</span> <span class="c1"># Distributed under the terms of the BSD 3-Clause License.</span>
+<span class="ne">----&gt; </span><span class="mi">6</span> <span class="kn">import</span> <span class="nn">matplotlib</span>
+<span class="g g-Whitespace">      </span><span class="mi">7</span> <span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">colors</span>
+<span class="g g-Whitespace">      </span><span class="mi">8</span> <span class="kn">from</span> <span class="nn">matplotlib.backends</span> <span class="kn">import</span> <span class="n">backend_agg</span>
+
+<span class="ne">ModuleNotFoundError</span>: No module named &#39;matplotlib&#39;
+</pre></div>
+</div>
+</div>
+</div>
+<p>And then as countor plot</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
+<span class="n">pt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xmesh</span><span class="p">,</span> <span class="n">ymesh</span><span class="p">,</span> <span class="n">fmesh</span><span class="p">)</span>
+<span class="n">guesses</span> <span class="o">=</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mf">2.</span><span class="o">/</span><span class="mi">5</span><span class="p">])]</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Find guesses</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="n">guesses</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">s</span> <span class="o">=</span> <span class="o">-</span><span class="n">df</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Run it!</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">f1d</span><span class="p">(</span><span class="n">alpha</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">f</span><span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="n">alpha</span><span class="o">*</span><span class="n">s</span><span class="p">)</span>
+
+<span class="n">alpha_opt</span> <span class="o">=</span> <span class="n">sopt</span><span class="o">.</span><span class="n">golden</span><span class="p">(</span><span class="n">f1d</span><span class="p">)</span>
+<span class="n">next_guess</span> <span class="o">=</span> <span class="n">x</span> <span class="o">+</span> <span class="n">alpha_opt</span> <span class="o">*</span> <span class="n">s</span>
+<span class="n">guesses</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">next_guess</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">next_guess</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>What happened?</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">pt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">&quot;equal&quot;</span><span class="p">)</span>
+<span class="n">pt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xmesh</span><span class="p">,</span> <span class="n">ymesh</span><span class="p">,</span> <span class="n">fmesh</span><span class="p">,</span> <span class="mi">50</span><span class="p">)</span>
+<span class="n">it_array</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">guesses</span><span class="p">)</span>
+<span class="n">pt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">it_array</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">it_array</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s2">&quot;x-&quot;</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Note that we did only one iteration here. We can easily add more using our previous guesses.</p>
+</section>
+<section id="conjugate-gradient-method">
+<h2>Conjugate gradient method<a class="headerlink" href="#conjugate-gradient-method" title="Permalink to this heading">#</a></h2>
+<p>In the CG method we define so-called conjugate directions and two vectors
+<span class="math notranslate nohighlight">\(\boldsymbol{s}\)</span> and <span class="math notranslate nohighlight">\(\boldsymbol{t}\)</span>
+are said to be
+conjugate if</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{s}^T\boldsymbol{A}\boldsymbol{t}= 0.
+\]</div>
+<p>The philosophy of the CG method is to perform searches in various conjugate directions
+of our vectors <span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> obeying the above criterion, namely</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}_i^T\boldsymbol{A}\boldsymbol{x}_j= 0.
+\]</div>
+<p>Two vectors are conjugate if they are orthogonal with respect to
+this inner product. Being conjugate is a symmetric relation: if <span class="math notranslate nohighlight">\(\boldsymbol{s}\)</span> is conjugate to <span class="math notranslate nohighlight">\(\boldsymbol{t}\)</span>, then <span class="math notranslate nohighlight">\(\boldsymbol{t}\)</span> is conjugate to <span class="math notranslate nohighlight">\(\boldsymbol{s}\)</span>.</p>
+</section>
+<section id="id2">
+<h2>Conjugate gradient method<a class="headerlink" href="#id2" title="Permalink to this heading">#</a></h2>
+<p>An example is given by the eigenvectors of the matrix</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{v}_i^T\boldsymbol{A}\boldsymbol{v}_j= \lambda\boldsymbol{v}_i^T\boldsymbol{v}_j,
+\]</div>
+<p>which is zero unless <span class="math notranslate nohighlight">\(i=j\)</span>.</p>
+</section>
+<section id="id3">
+<h2>Conjugate gradient method<a class="headerlink" href="#id3" title="Permalink to this heading">#</a></h2>
+<p>Assume now that we have a symmetric positive-definite matrix <span class="math notranslate nohighlight">\(\boldsymbol{A}\)</span> of size
+<span class="math notranslate nohighlight">\(n\times n\)</span>. At each iteration <span class="math notranslate nohighlight">\(i+1\)</span> we obtain the conjugate direction of a vector</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}_{i+1}=\boldsymbol{x}_{i}+\alpha_i\boldsymbol{p}_{i}.
+\]</div>
+<p>We assume that <span class="math notranslate nohighlight">\(\boldsymbol{p}_{i}\)</span> is a sequence of <span class="math notranslate nohighlight">\(n\)</span> mutually conjugate directions.
+Then the <span class="math notranslate nohighlight">\(\boldsymbol{p}_{i}\)</span>  form a basis of <span class="math notranslate nohighlight">\(R^n\)</span> and we can expand the solution
+<span class="math notranslate nohighlight">\(  \boldsymbol{A}\boldsymbol{x} = \boldsymbol{b}\)</span> in this basis, namely</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}  = \sum^{n}_{i=1} \alpha_i \boldsymbol{p}_i.
+\]</div>
+</section>
+<section id="id4">
+<h2>Conjugate gradient method<a class="headerlink" href="#id4" title="Permalink to this heading">#</a></h2>
+<p>The coefficients are given by</p>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{A}\mathbf{x} = \sum^{n}_{i=1} \alpha_i \mathbf{A} \mathbf{p}_i = \mathbf{b}.
+\]</div>
+<p>Multiplying with <span class="math notranslate nohighlight">\(\boldsymbol{p}_k^T\)</span>  from the left gives</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{x} = \sum^{n}_{i=1} \alpha_i\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{p}_i= \boldsymbol{p}_k^T \boldsymbol{b},
+\]</div>
+<p>and we can define the coefficients <span class="math notranslate nohighlight">\(\alpha_k\)</span> as</p>
+<div class="math notranslate nohighlight">
+\[
+\alpha_k = \frac{\boldsymbol{p}_k^T \boldsymbol{b}}{\boldsymbol{p}_k^T \boldsymbol{A} \boldsymbol{p}_k}
+\]</div>
+</section>
+<section id="conjugate-gradient-method-and-iterations">
+<h2>Conjugate gradient method and iterations<a class="headerlink" href="#conjugate-gradient-method-and-iterations" title="Permalink to this heading">#</a></h2>
+<p>If we choose the conjugate vectors <span class="math notranslate nohighlight">\(\boldsymbol{p}_k\)</span> carefully,
+then we may not need all of them to obtain a good approximation to the solution
+<span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span>.
+We want to regard the conjugate gradient method as an iterative method.
+This will us to solve systems where <span class="math notranslate nohighlight">\(n\)</span> is so large that the direct
+method would take too much time.</p>
+<p>We denote the initial guess for <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> as <span class="math notranslate nohighlight">\(\boldsymbol{x}_0\)</span>.
+We can assume without loss of generality that</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{x}_0=0,
+\]</div>
+<p>or consider the system</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{A}\boldsymbol{z} = \boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_0,
+\]</div>
+<p>instead.</p>
+</section>
+<section id="id5">
+<h2>Conjugate gradient method<a class="headerlink" href="#id5" title="Permalink to this heading">#</a></h2>
+<p>One can show that the solution <span class="math notranslate nohighlight">\(\boldsymbol{x}\)</span> is also the unique minimizer of the quadratic form</p>
+<div class="math notranslate nohighlight">
+\[
+f(\boldsymbol{x}) = \frac{1}{2}\boldsymbol{x}^T\boldsymbol{A}\boldsymbol{x} - \boldsymbol{x}^T \boldsymbol{x} , \quad \boldsymbol{x}\in\mathbf{R}^n.
+\]</div>
+<p>This suggests taking the first basis vector <span class="math notranslate nohighlight">\(\boldsymbol{p}_1\)</span>
+to be the gradient of <span class="math notranslate nohighlight">\(f\)</span> at <span class="math notranslate nohighlight">\(\boldsymbol{x}=\boldsymbol{x}_0\)</span>,
+which equals</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{A}\boldsymbol{x}_0-\boldsymbol{b},
+\]</div>
+<p>and
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_0=0\)</span> it is equal <span class="math notranslate nohighlight">\(-\boldsymbol{b}\)</span>.
+The other vectors in the basis will be conjugate to the gradient,
+hence the name conjugate gradient method.</p>
+</section>
+<section id="id6">
+<h2>Conjugate gradient method<a class="headerlink" href="#id6" title="Permalink to this heading">#</a></h2>
+<p>Let  <span class="math notranslate nohighlight">\(\boldsymbol{r}_k\)</span> be the residual at the <span class="math notranslate nohighlight">\(k\)</span>-th step:</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{r}_k=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k.
+\]</div>
+<p>Note that <span class="math notranslate nohighlight">\(\boldsymbol{r}_k\)</span> is the negative gradient of <span class="math notranslate nohighlight">\(f\)</span> at
+<span class="math notranslate nohighlight">\(\boldsymbol{x}=\boldsymbol{x}_k\)</span>,
+so the gradient descent method would be to move in the direction <span class="math notranslate nohighlight">\(\boldsymbol{r}_k\)</span>.
+Here, we insist that the directions <span class="math notranslate nohighlight">\(\boldsymbol{p}_k\)</span> are conjugate to each other,
+so we take the direction closest to the gradient <span class="math notranslate nohighlight">\(\boldsymbol{r}_k\)</span><br />
+under the conjugacy constraint.
+This gives the following expression</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{p}_{k+1}=\boldsymbol{r}_k-\frac{\boldsymbol{p}_k^T \boldsymbol{A}\boldsymbol{r}_k}{\boldsymbol{p}_k^T\boldsymbol{A}\boldsymbol{p}_k} \boldsymbol{p}_k.
+\]</div>
+</section>
+<section id="id7">
+<h2>Conjugate gradient method<a class="headerlink" href="#id7" title="Permalink to this heading">#</a></h2>
+<p>We can also  compute the residual iteratively as</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{r}_{k+1}=\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_{k+1},
+\]</div>
+<p>which equals</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{b}-\boldsymbol{A}(\boldsymbol{x}_k+\alpha_k\boldsymbol{p}_k),
+\]</div>
+<p>or</p>
+<div class="math notranslate nohighlight">
+\[
+(\boldsymbol{b}-\boldsymbol{A}\boldsymbol{x}_k)-\alpha_k\boldsymbol{A}\boldsymbol{p}_k,
+\]</div>
+<p>which gives</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{r}_{k+1}=\boldsymbol{r}_k-\boldsymbol{A}\boldsymbol{p}_{k},
+\]</div>
+</section>
+<section id="revisiting-our-first-homework">
+<h2>Revisiting our first homework<a class="headerlink" href="#revisiting-our-first-homework" title="Permalink to this heading">#</a></h2>
+<p>We will use linear regression as a case study for the gradient descent
+methods. Linear regression is a great test case for the gradient
+descent methods discussed in the lectures since it has several
+desirable properties such as:</p>
+<ol class="arabic simple">
+<li><p>An analytical solution (recall homework set 1).</p></li>
+<li><p>The gradient can be computed analytically.</p></li>
+<li><p>The cost function is convex which guarantees that gradient descent converges for small enough learning rates</p></li>
+</ol>
+<p>We revisit an example similar to what we had in the first homework set. We had a function  of the type</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>with <span class="math notranslate nohighlight">\(x_i \in [0,1] \)</span> is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution <span class="math notranslate nohighlight">\(\cal {N}(0,1)\)</span>.
+The linear regression model is given by</p>
+<div class="math notranslate nohighlight">
+\[
+h_\beta(x) = \boldsymbol{y} = \beta_0 + \beta_1 x,
+\]</div>
+<p>such that</p>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{y}_i = \beta_0 + \beta_1 x_i.
+\]</div>
+</section>
+<section id="gradient-descent-example">
+<h2>Gradient descent example<a class="headerlink" href="#gradient-descent-example" title="Permalink to this heading">#</a></h2>
+<p>Let <span class="math notranslate nohighlight">\(\mathbf{y} = (y_1,\cdots,y_n)^T\)</span>, <span class="math notranslate nohighlight">\(\mathbf{\boldsymbol{y}} = (\boldsymbol{y}_1,\cdots,\boldsymbol{y}_n)^T\)</span> and <span class="math notranslate nohighlight">\(\beta = (\beta_0, \beta_1)^T\)</span></p>
+<p>It is convenient to write <span class="math notranslate nohighlight">\(\mathbf{\boldsymbol{y}} = X\beta\)</span> where <span class="math notranslate nohighlight">\(X \in \mathbb{R}^{100 \times 2} \)</span> is the design matrix given by (we keep the intercept here)</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+X \equiv \begin{bmatrix}
+1 &amp; x_1  \\
+\vdots &amp; \vdots  \\
+1 &amp; x_{100} &amp;  \\
+\end{bmatrix}.
+\end{split}\]</div>
+<p>The cost/loss/risk function is given by (</p>
+<div class="math notranslate nohighlight">
+\[
+C(\beta) = \frac{1}{n}||X\beta-\mathbf{y}||_{2}^{2} = \frac{1}{n}\sum_{i=1}^{100}\left[ (\beta_0 + \beta_1 x_i)^2 - 2 y_i (\beta_0 + \beta_1 x_i) + y_i^2\right]
+\]</div>
+<p>and we want to find <span class="math notranslate nohighlight">\(\beta\)</span> such that <span class="math notranslate nohighlight">\(C(\beta)\)</span> is minimized.</p>
+</section>
+<section id="the-derivative-of-the-cost-loss-function">
+<h2>The derivative of the cost/loss function<a class="headerlink" href="#the-derivative-of-the-cost-loss-function" title="Permalink to this heading">#</a></h2>
+<p>Computing <span class="math notranslate nohighlight">\(\partial C(\beta) / \partial \beta_0\)</span> and <span class="math notranslate nohighlight">\(\partial C(\beta) / \partial \beta_1\)</span> we can show  that the gradient can be written as</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\nabla_{\beta} C(\beta) = \frac{2}{n}\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} = \frac{2}{n}X^T(X\beta - \mathbf{y}),
+\end{split}\]</div>
+<p>where <span class="math notranslate nohighlight">\(X\)</span> is the design matrix defined above.</p>
+</section>
+<section id="the-hessian-matrix">
+<h2>The Hessian matrix<a class="headerlink" href="#the-hessian-matrix" title="Permalink to this heading">#</a></h2>
+<p>The Hessian matrix of <span class="math notranslate nohighlight">\(C(\beta)\)</span> is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\boldsymbol{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &amp;  \\
+\end{bmatrix} = \frac{2}{n}X^T X.
+\end{split}\]</div>
+<p>This result implies that <span class="math notranslate nohighlight">\(C(\beta)\)</span> is a convex function since the matrix <span class="math notranslate nohighlight">\(X^T X\)</span> always is positive semi-definite.</p>
+</section>
+<section id="simple-program">
+<h2>Simple program<a class="headerlink" href="#simple-program" title="Permalink to this heading">#</a></h2>
+<p>We can now write a program that minimizes <span class="math notranslate nohighlight">\(C(\beta)\)</span> using the gradient descent method with a constant learning rate <span class="math notranslate nohighlight">\(\gamma\)</span> according to</p>
+<div class="math notranslate nohighlight">
+\[
+\beta_{k+1} = \beta_k - \gamma \nabla_\beta C(\beta_k), \ k=0,1,\cdots
+\]</div>
+<p>We can use the expression we computed for the gradient and let use a
+<span class="math notranslate nohighlight">\(\beta_0\)</span> be chosen randomly and let <span class="math notranslate nohighlight">\(\gamma = 0.001\)</span>. Stop iterating
+when <span class="math notranslate nohighlight">\(||\nabla_\beta C(\beta_k) || \leq \epsilon = 10^{-8}\)</span>. <strong>Note that the code below does not include the latter stop criterion</strong>.</p>
+<p>And finally we can compare our solution for <span class="math notranslate nohighlight">\(\beta\)</span> with the analytic result given by
+<span class="math notranslate nohighlight">\(\beta= (X^TX)^{-1} X^T \mathbf{y}\)</span>.</p>
+</section>
+<section id="id8">
+<h2>Gradient Descent Example<a class="headerlink" href="#id8" title="Permalink to this heading">#</a></h2>
+<p>Here our simple example</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Importing various packages</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>
+<span class="kn">from</span> <span class="nn">matplotlib.ticker</span> <span class="kn">import</span> <span class="n">LinearLocator</span><span class="p">,</span> <span class="n">FormatStrFormatter</span>
+<span class="kn">import</span> <span class="nn">sys</span>
+
+<span class="c1"># the number of datapoints</span>
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="c1"># Get the eigenvalues</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">beta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">beta_linreg</span><span class="p">)</span>
+<span class="n">beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">1000</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradient</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span> <span class="o">@</span> <span class="n">beta</span><span class="o">-</span><span class="n">y</span><span class="p">)</span>
+    <span class="n">beta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradient</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+<span class="n">xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">],[</span><span class="mi">2</span><span class="p">]])</span>
+<span class="n">xbnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">xnew</span><span class="p">]</span>
+<span class="n">ypredict</span> <span class="o">=</span> <span class="n">xbnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+<span class="n">ypredict2</span> <span class="o">=</span> <span class="n">xbnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">beta_linreg</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict2</span><span class="p">,</span> <span class="s2">&quot;b-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">,</span><span class="s1">&#39;ro&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$x$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$y$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Gradient descent example&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="and-a-corresponding-example-using-scikit-learn">
+<h2>And a corresponding example using <strong>scikit-learn</strong><a class="headerlink" href="#and-a-corresponding-example-using-scikit-learn" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Importing various packages</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">SGDRegressor</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">beta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">beta_linreg</span><span class="p">)</span>
+<span class="n">sgdreg</span> <span class="o">=</span> <span class="n">SGDRegressor</span><span class="p">(</span><span class="n">max_iter</span> <span class="o">=</span> <span class="mi">50</span><span class="p">,</span> <span class="n">penalty</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">eta0</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
+<span class="n">sgdreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">sgdreg</span><span class="o">.</span><span class="n">intercept_</span><span class="p">,</span> <span class="n">sgdreg</span><span class="o">.</span><span class="n">coef_</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="gradient-descent-and-ridge">
+<h2>Gradient descent and Ridge<a class="headerlink" href="#gradient-descent-and-ridge" title="Permalink to this heading">#</a></h2>
+<p>We have also discussed Ridge regression where the loss function contains a regularized term given by the <span class="math notranslate nohighlight">\(L_2\)</span> norm of <span class="math notranslate nohighlight">\(\beta\)</span>,</p>
+<div class="math notranslate nohighlight">
+\[
+C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta||^2, \ \lambda \geq 0.
+\]</div>
+<p>In order to minimize <span class="math notranslate nohighlight">\(C_{\text{ridge}}(\beta)\)</span> using GD we adjust the gradient as follows</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\nabla_\beta C_{\text{ridge}}(\beta)  = \frac{2}{n}\begin{bmatrix} \sum_{i=1}^{100} \left(\beta_0+\beta_1x_i-y_i\right) \\
+\sum_{i=1}^{100}\left( x_i (\beta_0+\beta_1x_i)-y_ix_i\right) \\
+\end{bmatrix} + 2\lambda\begin{bmatrix} \beta_0 \\ \beta_1\end{bmatrix} = 2 (\frac{1}{n}X^T(X\beta - \mathbf{y})+\lambda \beta).
+\end{split}\]</div>
+<p>We can easily extend our program to minimize <span class="math notranslate nohighlight">\(C_{\text{ridge}}(\beta)\)</span> using gradient descent and compare with the analytical solution given by</p>
+<div class="math notranslate nohighlight">
+\[
+\beta_{\text{ridge}} = \left(X^T X + n\lambda I_{2 \times 2} \right)^{-1} X^T \mathbf{y}.
+\]</div>
+</section>
+<section id="the-hessian-matrix-for-ridge-regression">
+<h2>The Hessian matrix for Ridge Regression<a class="headerlink" href="#the-hessian-matrix-for-ridge-regression" title="Permalink to this heading">#</a></h2>
+<p>The Hessian matrix of Ridge Regression for our simple example  is given by</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}
+\boldsymbol{H} \equiv \begin{bmatrix}
+\frac{\partial^2 C(\beta)}{\partial \beta_0^2} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1}  \\
+\frac{\partial^2 C(\beta)}{\partial \beta_0 \partial \beta_1} &amp; \frac{\partial^2 C(\beta)}{\partial \beta_1^2} &amp;  \\
+\end{bmatrix} = \frac{2}{n}X^T X+2\lambda\boldsymbol{I}.
+\end{split}\]</div>
+<p>This implies that the Hessian matrix  is positive definite, hence the stationary point is a
+minimum.
+Note that the Ridge cost function is convex being  a sum of two convex
+functions. Therefore, the stationary point is a global
+minimum of this function.</p>
+</section>
+<section id="program-example-for-gradient-descent-with-ridge-regression">
+<h2>Program example for gradient descent with Ridge Regression<a class="headerlink" href="#program-example-for-gradient-descent-with-ridge-regression" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>
+<span class="kn">from</span> <span class="nn">matplotlib.ticker</span> <span class="kn">import</span> <span class="n">LinearLocator</span><span class="p">,</span> <span class="n">FormatStrFormatter</span>
+<span class="kn">import</span> <span class="nn">sys</span>
+
+<span class="c1"># the number of datapoints</span>
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+
+<span class="c1">#Ridge parameter lambda</span>
+<span class="n">lmbda</span>  <span class="o">=</span> <span class="mf">0.001</span>
+<span class="n">Id</span> <span class="o">=</span> <span class="n">n</span><span class="o">*</span><span class="n">lmbda</span><span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">XT_X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">lmbda</span><span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">XT_X</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<span class="c1"># Get the eigenvalues</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+
+<span class="n">beta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">XT_X</span><span class="o">+</span><span class="n">Id</span><span class="p">)</span> <span class="o">@</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">beta_linreg</span><span class="p">)</span>
+<span class="c1"># Start plain gradient descent</span>
+<span class="n">beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">100</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="o">*</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span> <span class="o">@</span> <span class="p">(</span><span class="n">beta</span><span class="p">)</span><span class="o">-</span><span class="n">y</span><span class="p">)</span><span class="o">+</span><span class="mi">2</span><span class="o">*</span><span class="n">lmbda</span><span class="o">*</span><span class="n">beta</span>
+    <span class="n">beta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+<span class="n">ypredict</span> <span class="o">=</span> <span class="n">X</span> <span class="o">@</span> <span class="n">beta</span>
+<span class="n">ypredict2</span> <span class="o">=</span> <span class="n">X</span> <span class="o">@</span> <span class="n">beta_linreg</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">ypredict</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">ypredict2</span><span class="p">,</span> <span class="s2">&quot;b-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">,</span><span class="s1">&#39;ro&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$x$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$y$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Gradient descent example for Ridge&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="using-gradient-descent-methods-limitations">
+<h2>Using gradient descent methods, limitations<a class="headerlink" href="#using-gradient-descent-methods-limitations" title="Permalink to this heading">#</a></h2>
+<ul class="simple">
+<li><p><strong>Gradient descent (GD) finds local minima of our function</strong>. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.</p></li>
+<li><p><strong>GD is sensitive to initial conditions</strong>. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.</p></li>
+<li><p><strong>Gradients are computationally expensive to calculate for large datasets</strong>. In many cases in statistics and ML, the cost/loss/risk function is a sum of terms, with one term for each data point. For example, in linear regression, <span class="math notranslate nohighlight">\(E \propto \sum_{i=1}^n (y_i - \mathbf{w}^T\cdot\mathbf{x}_i)^2\)</span>; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over <em>all</em> <span class="math notranslate nohighlight">\(n\)</span> data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called “mini batches”. This has the added benefit of introducing stochasticity into our algorithm.</p></li>
+<li><p><strong>GD is very sensitive to choices of learning rates</strong>. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would <em>adaptively</em> choose the learning rates to match the landscape.</p></li>
+<li><p><strong>GD treats all directions in parameter space uniformly.</strong> Another major drawback of GD is that unlike Newton’s method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive.</p></li>
+<li><p>GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.</p></li>
+</ul>
+</section>
+<section id="improving-gradient-descent-with-momentum">
+<h2>Improving gradient descent with momentum<a class="headerlink" href="#improving-gradient-descent-with-momentum" title="Permalink to this heading">#</a></h2>
+<p>We discuss here some simple examples where we introduce what is called ‘memory’about previous steps, or what is normally called momentum gradient descent. The mathematics is explained below in connection with Stochastic gradient descent.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">asarray</span>
+<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">arange</span>
+<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <span class="n">rand</span>
+<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <span class="n">seed</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span>
+ 
+<span class="c1"># objective function</span>
+<span class="k">def</span> <span class="nf">objective</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+	<span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mf">2.0</span>
+ 
+<span class="c1"># derivative of objective function</span>
+<span class="k">def</span> <span class="nf">derivative</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+	<span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="mf">2.0</span>
+ 
+<span class="c1"># gradient descent algorithm</span>
+<span class="k">def</span> <span class="nf">gradient_descent</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">derivative</span><span class="p">,</span> <span class="n">bounds</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">step_size</span><span class="p">):</span>
+	<span class="c1"># track all solutions</span>
+	<span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(),</span> <span class="nb">list</span><span class="p">()</span>
+	<span class="c1"># generate an initial point</span>
+	<span class="n">solution</span> <span class="o">=</span> <span class="n">bounds</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">rand</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bounds</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="n">bounds</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">bounds</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
+	<span class="c1"># run the gradient descent</span>
+	<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_iter</span><span class="p">):</span>
+		<span class="c1"># calculate gradient</span>
+		<span class="n">gradient</span> <span class="o">=</span> <span class="n">derivative</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="c1"># take a step</span>
+		<span class="n">solution</span> <span class="o">=</span> <span class="n">solution</span> <span class="o">-</span> <span class="n">step_size</span> <span class="o">*</span> <span class="n">gradient</span>
+		<span class="c1"># evaluate candidate point</span>
+		<span class="n">solution_eval</span> <span class="o">=</span> <span class="n">objective</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="c1"># store solution</span>
+		<span class="n">solutions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="n">scores</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">solution_eval</span><span class="p">)</span>
+		<span class="c1"># report progress</span>
+		<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&gt;</span><span class="si">%d</span><span class="s1"> f(</span><span class="si">%s</span><span class="s1">) = </span><span class="si">%.5f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">solution</span><span class="p">,</span> <span class="n">solution_eval</span><span class="p">))</span>
+	<span class="k">return</span> <span class="p">[</span><span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span><span class="p">]</span>
+ 
+<span class="c1"># seed the pseudo random number generator</span>
+<span class="n">seed</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<span class="c1"># define range for input</span>
+<span class="n">bounds</span> <span class="o">=</span> <span class="n">asarray</span><span class="p">([[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
+<span class="c1"># define the total iterations</span>
+<span class="n">n_iter</span> <span class="o">=</span> <span class="mi">30</span>
+<span class="c1"># define the step size</span>
+<span class="n">step_size</span> <span class="o">=</span> <span class="mf">0.1</span>
+<span class="c1"># perform the gradient descent search</span>
+<span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span> <span class="o">=</span> <span class="n">gradient_descent</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">derivative</span><span class="p">,</span> <span class="n">bounds</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">step_size</span><span class="p">)</span>
+<span class="c1"># sample input range uniformly at 0.1 increments</span>
+<span class="n">inputs</span> <span class="o">=</span> <span class="n">arange</span><span class="p">(</span><span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
+<span class="c1"># compute targets</span>
+<span class="n">results</span> <span class="o">=</span> <span class="n">objective</span><span class="p">(</span><span class="n">inputs</span><span class="p">)</span>
+<span class="c1"># create a line plot of input vs result</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">results</span><span class="p">)</span>
+<span class="c1"># plot the solutions found</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span><span class="p">,</span> <span class="s1">&#39;.-&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;red&#39;</span><span class="p">)</span>
+<span class="c1"># show the plot</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="same-code-but-now-with-momentum-gradient-descent">
+<h2>Same code but now with momentum gradient descent<a class="headerlink" href="#same-code-but-now-with-momentum-gradient-descent" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">asarray</span>
+<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">arange</span>
+<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <span class="n">rand</span>
+<span class="kn">from</span> <span class="nn">numpy.random</span> <span class="kn">import</span> <span class="n">seed</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span>
+ 
+<span class="c1"># objective function</span>
+<span class="k">def</span> <span class="nf">objective</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+	<span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mf">2.0</span>
+ 
+<span class="c1"># derivative of objective function</span>
+<span class="k">def</span> <span class="nf">derivative</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+	<span class="k">return</span> <span class="n">x</span> <span class="o">*</span> <span class="mf">2.0</span>
+ 
+<span class="c1"># gradient descent algorithm</span>
+<span class="k">def</span> <span class="nf">gradient_descent</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">derivative</span><span class="p">,</span> <span class="n">bounds</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">step_size</span><span class="p">,</span> <span class="n">momentum</span><span class="p">):</span>
+	<span class="c1"># track all solutions</span>
+	<span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(),</span> <span class="nb">list</span><span class="p">()</span>
+	<span class="c1"># generate an initial point</span>
+	<span class="n">solution</span> <span class="o">=</span> <span class="n">bounds</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">rand</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">bounds</span><span class="p">))</span> <span class="o">*</span> <span class="p">(</span><span class="n">bounds</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">bounds</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])</span>
+	<span class="c1"># keep track of the change</span>
+	<span class="n">change</span> <span class="o">=</span> <span class="mf">0.0</span>
+	<span class="c1"># run the gradient descent</span>
+	<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_iter</span><span class="p">):</span>
+		<span class="c1"># calculate gradient</span>
+		<span class="n">gradient</span> <span class="o">=</span> <span class="n">derivative</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="c1"># calculate update</span>
+		<span class="n">new_change</span> <span class="o">=</span> <span class="n">step_size</span> <span class="o">*</span> <span class="n">gradient</span> <span class="o">+</span> <span class="n">momentum</span> <span class="o">*</span> <span class="n">change</span>
+		<span class="c1"># take a step</span>
+		<span class="n">solution</span> <span class="o">=</span> <span class="n">solution</span> <span class="o">-</span> <span class="n">new_change</span>
+		<span class="c1"># save the change</span>
+		<span class="n">change</span> <span class="o">=</span> <span class="n">new_change</span>
+		<span class="c1"># evaluate candidate point</span>
+		<span class="n">solution_eval</span> <span class="o">=</span> <span class="n">objective</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="c1"># store solution</span>
+		<span class="n">solutions</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">solution</span><span class="p">)</span>
+		<span class="n">scores</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">solution_eval</span><span class="p">)</span>
+		<span class="c1"># report progress</span>
+		<span class="nb">print</span><span class="p">(</span><span class="s1">&#39;&gt;</span><span class="si">%d</span><span class="s1"> f(</span><span class="si">%s</span><span class="s1">) = </span><span class="si">%.5f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">solution</span><span class="p">,</span> <span class="n">solution_eval</span><span class="p">))</span>
+	<span class="k">return</span> <span class="p">[</span><span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span><span class="p">]</span>
+ 
+<span class="c1"># seed the pseudo random number generator</span>
+<span class="n">seed</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<span class="c1"># define range for input</span>
+<span class="n">bounds</span> <span class="o">=</span> <span class="n">asarray</span><span class="p">([[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
+<span class="c1"># define the total iterations</span>
+<span class="n">n_iter</span> <span class="o">=</span> <span class="mi">30</span>
+<span class="c1"># define the step size</span>
+<span class="n">step_size</span> <span class="o">=</span> <span class="mf">0.1</span>
+<span class="c1"># define momentum</span>
+<span class="n">momentum</span> <span class="o">=</span> <span class="mf">0.3</span>
+<span class="c1"># perform the gradient descent search with momentum</span>
+<span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span> <span class="o">=</span> <span class="n">gradient_descent</span><span class="p">(</span><span class="n">objective</span><span class="p">,</span> <span class="n">derivative</span><span class="p">,</span> <span class="n">bounds</span><span class="p">,</span> <span class="n">n_iter</span><span class="p">,</span> <span class="n">step_size</span><span class="p">,</span> <span class="n">momentum</span><span class="p">)</span>
+<span class="c1"># sample input range uniformly at 0.1 increments</span>
+<span class="n">inputs</span> <span class="o">=</span> <span class="n">arange</span><span class="p">(</span><span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
+<span class="c1"># compute targets</span>
+<span class="n">results</span> <span class="o">=</span> <span class="n">objective</span><span class="p">(</span><span class="n">inputs</span><span class="p">)</span>
+<span class="c1"># create a line plot of input vs result</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">results</span><span class="p">)</span>
+<span class="c1"># plot the solutions found</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">solutions</span><span class="p">,</span> <span class="n">scores</span><span class="p">,</span> <span class="s1">&#39;.-&#39;</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;red&#39;</span><span class="p">)</span>
+<span class="c1"># show the plot</span>
+<span class="n">pyplot</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="overview-video-on-stochastic-gradient-descent">
+<h2>Overview video on Stochastic Gradient Descent<a class="headerlink" href="#overview-video-on-stochastic-gradient-descent" title="Permalink to this heading">#</a></h2>
+<p><a class="reference external" href="https://www.youtube.com/watch?v=vMh0zPT0tLI&amp;ab_channel=StatQuestwithJoshStarmer">What is Stochastic Gradient Descent</a></p>
+</section>
+<section id="batches-and-mini-batches">
+<h2>Batches and mini-batches<a class="headerlink" href="#batches-and-mini-batches" title="Permalink to this heading">#</a></h2>
+<p>In gradient descent we compute the cost function and its gradient for all data points we have.</p>
+<p>In large-scale applications such as the <a class="reference external" href="https://www.image-net.org/challenges/LSVRC/">ILSVRC challenge</a>, the
+training data can have on order of millions of examples. Hence, it
+seems wasteful to compute the full cost function over the entire
+training set in order to perform only a single parameter update. A
+very common approach to addressing this challenge is to compute the
+gradient over batches of the training data. For example, a typical batch could contain some thousand  examples from
+an  entire training set of several millions. This batch is then used to
+perform a parameter update.</p>
+</section>
+<section id="stochastic-gradient-descent-sgd">
+<h2>Stochastic Gradient Descent (SGD)<a class="headerlink" href="#stochastic-gradient-descent-sgd" title="Permalink to this heading">#</a></h2>
+<p>In stochastic gradient descent, the extreme case is the case where we
+have only one batch, that is we include the whole data set.</p>
+<p>This process is called Stochastic Gradient
+Descent (SGD) (or also sometimes on-line gradient descent). This is
+relatively less common to see because in practice due to vectorized
+code optimizations it can be computationally much more efficient to
+evaluate the gradient for 100 examples, than the gradient for one
+example 100 times. Even though SGD technically refers to using a
+single example at a time to evaluate the gradient, you will hear
+people use the term SGD even when referring to mini-batch gradient
+descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD
+for “Batch gradient descent” are rare to see), where it is usually
+assumed that mini-batches are used. The size of the mini-batch is a
+hyperparameter but it is not very common to cross-validate or bootstrap it. It is
+usually based on memory constraints (if any), or set to some value,
+e.g. 32, 64 or 128. We use powers of 2 in practice because many
+vectorized operation implementations work faster when their inputs are
+sized in powers of 2.</p>
+<p>In our notes with  SGD we mean stochastic gradient descent with mini-batches.</p>
+</section>
+<section id="stochastic-gradient-descent">
+<h2>Stochastic Gradient Descent<a class="headerlink" href="#stochastic-gradient-descent" title="Permalink to this heading">#</a></h2>
+<p>Stochastic gradient descent (SGD) and variants thereof address some of
+the shortcomings of the Gradient descent method discussed above.</p>
+<p>The underlying idea of SGD comes from the observation that the cost
+function, which we want to minimize, can almost always be written as a
+sum over <span class="math notranslate nohighlight">\(n\)</span> data points <span class="math notranslate nohighlight">\(\{\mathbf{x}_i\}_{i=1}^n\)</span>,</p>
+<div class="math notranslate nohighlight">
+\[
+C(\mathbf{\beta}) = \sum_{i=1}^n c_i(\mathbf{x}_i,
+\mathbf{\beta}).
+\]</div>
+</section>
+<section id="computation-of-gradients">
+<h2>Computation of gradients<a class="headerlink" href="#computation-of-gradients" title="Permalink to this heading">#</a></h2>
+<p>This in turn means that the gradient can be
+computed as a sum over <span class="math notranslate nohighlight">\(i\)</span>-gradients</p>
+<div class="math notranslate nohighlight">
+\[
+\nabla_\beta C(\mathbf{\beta}) = \sum_i^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}).
+\]</div>
+<p>Stochasticity/randomness is introduced by only taking the
+gradient on a subset of the data called minibatches.  If there are <span class="math notranslate nohighlight">\(n\)</span>
+data points and the size of each minibatch is <span class="math notranslate nohighlight">\(M\)</span>, there will be <span class="math notranslate nohighlight">\(n/M\)</span>
+minibatches. We denote these minibatches by <span class="math notranslate nohighlight">\(B_k\)</span> where
+<span class="math notranslate nohighlight">\(k=1,\cdots,n/M\)</span>.</p>
+</section>
+<section id="sgd-example">
+<h2>SGD example<a class="headerlink" href="#sgd-example" title="Permalink to this heading">#</a></h2>
+<p>As an example, suppose we have <span class="math notranslate nohighlight">\(10\)</span> data points <span class="math notranslate nohighlight">\((\mathbf{x}_1,\cdots, \mathbf{x}_{10})\)</span>
+and we choose to have <span class="math notranslate nohighlight">\(M=5\)</span> minibathces,
+then each minibatch contains two data points. In particular we have
+<span class="math notranslate nohighlight">\(B_1 = (\mathbf{x}_1,\mathbf{x}_2), \cdots, B_5 =
+(\mathbf{x}_9,\mathbf{x}_{10})\)</span>. Note that if you choose <span class="math notranslate nohighlight">\(M=1\)</span> you
+have only a single batch with all data points and on the other extreme,
+you may choose <span class="math notranslate nohighlight">\(M=n\)</span> resulting in a minibatch for each datapoint, i.e
+<span class="math notranslate nohighlight">\(B_k = \mathbf{x}_k\)</span>.</p>
+<p>The idea is now to approximate the gradient by replacing the sum over
+all data points with a sum over the data points in one the minibatches
+picked at random in each gradient descent step</p>
+<div class="math notranslate nohighlight">
+\[
+\nabla_{\beta}
+C(\mathbf{\beta}) = \sum_{i=1}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta}) \rightarrow \sum_{i \in B_k}^n \nabla_\beta
+c_i(\mathbf{x}_i, \mathbf{\beta}).
+\]</div>
+</section>
+<section id="the-gradient-step">
+<h2>The gradient step<a class="headerlink" href="#the-gradient-step" title="Permalink to this heading">#</a></h2>
+<p>Thus a gradient descent step now looks like</p>
+<div class="math notranslate nohighlight">
+\[
+\beta_{j+1} = \beta_j - \gamma_j \sum_{i \in B_k}^n \nabla_\beta c_i(\mathbf{x}_i,
+\mathbf{\beta})
+\]</div>
+<p>where <span class="math notranslate nohighlight">\(k\)</span> is picked at random with equal
+probability from <span class="math notranslate nohighlight">\([1,n/M]\)</span>. An iteration over the number of
+minibathces (n/M) is commonly referred to as an epoch. Thus it is
+typical to choose a number of epochs and for each epoch iterate over
+the number of minibatches, as exemplified in the code below.</p>
+</section>
+<section id="simple-example-code">
+<h2>Simple example code<a class="headerlink" href="#simple-example-code" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> 
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1">#100 datapoints </span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">10</span> <span class="c1">#number of epochs</span>
+
+<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n_epochs</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="c1">#Pick the k-th minibatch at random</span>
+        <span class="c1">#Compute the gradient using the data in minibatch Bk</span>
+        <span class="c1">#Compute new suggestion for </span>
+        <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Taking the gradient only on a subset of the data has two important
+benefits. First, it introduces randomness which decreases the chance
+that our opmization scheme gets stuck in a local minima. Second, if
+the size of the minibatches are small relative to the number of
+datapoints (<span class="math notranslate nohighlight">\(M &lt;  n\)</span>), the computation of the gradient is much
+cheaper since we sum over the datapoints in the <span class="math notranslate nohighlight">\(k-th\)</span> minibatch and not
+all <span class="math notranslate nohighlight">\(n\)</span> datapoints.</p>
+</section>
+<section id="when-do-we-stop">
+<h2>When do we stop?<a class="headerlink" href="#when-do-we-stop" title="Permalink to this heading">#</a></h2>
+<p>A natural question is when do we stop the search for a new minimum?
+One possibility is to compute the full gradient after a given number
+of epochs and check if the norm of the gradient is smaller than some
+threshold and stop if true. However, the condition that the gradient
+is zero is valid also for local minima, so this would only tell us
+that we are close to a local/global minimum. However, we could also
+evaluate the cost function at this point, store the result and
+continue the search. If the test kicks in at a later stage we can
+compare the values of the cost function and keep the <span class="math notranslate nohighlight">\(\beta\)</span> that
+gave the lowest value.</p>
+</section>
+<section id="slightly-different-approach">
+<h2>Slightly different approach<a class="headerlink" href="#slightly-different-approach" title="Permalink to this heading">#</a></h2>
+<p>Another approach is to let the step length <span class="math notranslate nohighlight">\(\gamma_j\)</span> depend on the
+number of epochs in such a way that it becomes very small after a
+reasonable time such that we do not move at all. Such approaches are
+also called scaling. There are many such ways to <a class="reference external" href="https://towardsdatascience.com/gradient-descent-the-learning-rate-and-the-importance-of-feature-scaling-6c0b416596e1">scale the learning
+rate</a>
+and <a class="reference external" href="https://www.jmlr.org/papers/volume23/20-1258/20-1258.pdf">discussions here</a>. See
+also
+<a class="reference external" href="https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1">https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1</a>
+for a discussion of different scaling functions for the learning rate.</p>
+</section>
+<section id="time-decay-rate">
+<h2>Time decay rate<a class="headerlink" href="#time-decay-rate" title="Permalink to this heading">#</a></h2>
+<p>As an example, let <span class="math notranslate nohighlight">\(e = 0,1,2,3,\cdots\)</span> denote the current epoch and let <span class="math notranslate nohighlight">\(t_0, t_1 &gt; 0\)</span> be two fixed numbers. Furthermore, let <span class="math notranslate nohighlight">\(t = e \cdot m + i\)</span> where <span class="math notranslate nohighlight">\(m\)</span> is the number of minibatches and <span class="math notranslate nohighlight">\(i=0,\cdots,m-1\)</span>. Then the function $<span class="math notranslate nohighlight">\(\gamma_j(t; t_0, t_1) = \frac{t_0}{t+t_1} \)</span><span class="math notranslate nohighlight">\( goes to zero as the number of epochs gets large. I.e. we start with a step length \)</span>\gamma_j (0; t_0, t_1) = t_0/t_1<span class="math notranslate nohighlight">\( which decays in *time* \)</span>t$.</p>
+<p>In this way we can fix the number of epochs, compute <span class="math notranslate nohighlight">\(\beta\)</span> and
+evaluate the cost function at the end. Repeating the computation will
+give a different result since the scheme is random by design. Then we
+pick the final <span class="math notranslate nohighlight">\(\beta\)</span> that gives the lowest value of the cost
+function.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> 
+
+<span class="k">def</span> <span class="nf">step_length</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">t0</span><span class="p">,</span><span class="n">t1</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">t0</span><span class="o">/</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">t1</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1">#100 datapoints </span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">500</span> <span class="c1">#number of epochs</span>
+<span class="n">t0</span> <span class="o">=</span> <span class="mf">1.0</span>
+<span class="n">t1</span> <span class="o">=</span> <span class="mi">10</span>
+
+<span class="n">gamma_j</span> <span class="o">=</span> <span class="n">t0</span><span class="o">/</span><span class="n">t1</span>
+<span class="n">j</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="n">n_epochs</span><span class="o">+</span><span class="mi">1</span><span class="p">):</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">k</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="c1">#Pick the k-th minibatch at random</span>
+        <span class="c1">#Compute the gradient using the data in minibatch Bk</span>
+        <span class="c1">#Compute new suggestion for beta</span>
+        <span class="n">t</span> <span class="o">=</span> <span class="n">epoch</span><span class="o">*</span><span class="n">m</span><span class="o">+</span><span class="n">i</span>
+        <span class="n">gamma_j</span> <span class="o">=</span> <span class="n">step_length</span><span class="p">(</span><span class="n">t</span><span class="p">,</span><span class="n">t0</span><span class="p">,</span><span class="n">t1</span><span class="p">)</span>
+        <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;gamma_j after </span><span class="si">%d</span><span class="s2"> epochs: </span><span class="si">%g</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="p">(</span><span class="n">n_epochs</span><span class="p">,</span><span class="n">gamma_j</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="code-with-a-number-of-minibatches-which-varies">
+<h2>Code with a Number of Minibatches which varies<a class="headerlink" href="#code-with-a-number-of-minibatches-which-varies" title="Permalink to this heading">#</a></h2>
+<p>In the code here we vary the number of mini-batches.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Importing various packages</span>
+<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">1000</span>
+
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="o">*</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="p">((</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">-</span><span class="n">y</span><span class="p">)</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+<span class="n">xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">],[</span><span class="mi">2</span><span class="p">]])</span>
+<span class="n">Xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">xnew</span><span class="p">]</span>
+<span class="n">ypredict</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+<span class="n">ypredict2</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="n">t0</span><span class="p">,</span> <span class="n">t1</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">50</span>
+
+<span class="k">def</span> <span class="nf">learning_schedule</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">t0</span><span class="o">/</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">t1</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+<span class="c1"># Can you figure out a better way of setting up the contributions to each batch?</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span> <span class="n">xi</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="p">((</span><span class="n">xi</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">-</span><span class="n">yi</span><span class="p">)</span>
+        <span class="n">eta</span> <span class="o">=</span> <span class="n">learning_schedule</span><span class="p">(</span><span class="n">epoch</span><span class="o">*</span><span class="n">m</span><span class="o">+</span><span class="n">i</span><span class="p">)</span>
+        <span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own sdg&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict2</span><span class="p">,</span> <span class="s2">&quot;b-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">,</span><span class="s1">&#39;ro&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$x$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$y$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Random numbers &#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="replace-or-not">
+<h2>Replace or not<a class="headerlink" href="#replace-or-not" title="Permalink to this heading">#</a></h2>
+<p>In the above code, we have use replacement in setting up the
+mini-batches. The discussion
+<a class="reference external" href="https://sebastianraschka.com/faq/docs/sgd-methods.html">here</a> may be
+useful.</p>
+</section>
+<section id="momentum-based-gd">
+<h2>Momentum based GD<a class="headerlink" href="#momentum-based-gd" title="Permalink to this heading">#</a></h2>
+<p>The stochastic gradient descent (SGD) is almost always used with a
+<em>momentum</em> or inertia term that serves as a memory of the direction we
+are moving in parameter space.  This is typically implemented as
+follows</p>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{v}_{t}=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t) \nonumber
+\]</div>
+<!-- Equation labels as ordinary links -->
+<div id="_auto1"></div>
+<div class="math notranslate nohighlight">
+\[
+\begin{equation} 
+\boldsymbol{\theta}_{t+1}= \boldsymbol{\theta}_t -\mathbf{v}_{t},
+\label{_auto1} \tag{2}
+\end{equation}
+\]</div>
+<p>where we have introduced a momentum parameter <span class="math notranslate nohighlight">\(\gamma\)</span>, with
+<span class="math notranslate nohighlight">\(0\le\gamma\le 1\)</span>, and for brevity we dropped the explicit notation to
+indicate the gradient is to be taken over a different mini-batch at
+each step. We call this algorithm gradient descent with momentum
+(GDM). From these equations, it is clear that <span class="math notranslate nohighlight">\(\mathbf{v}_t\)</span> is a
+running average of recently encountered gradients and
+<span class="math notranslate nohighlight">\((1-\gamma)^{-1}\)</span> sets the characteristic time scale for the memory
+used in the averaging procedure. Consistent with this, when
+<span class="math notranslate nohighlight">\(\gamma=0\)</span>, this just reduces down to ordinary SGD as discussed
+earlier. An equivalent way of writing the updates is</p>
+<div class="math notranslate nohighlight">
+\[
+\Delta \boldsymbol{\theta}_{t+1} = \gamma \Delta \boldsymbol{\theta}_t -\ \eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t),
+\]</div>
+<p>where we have defined <span class="math notranslate nohighlight">\(\Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1}\)</span>.</p>
+</section>
+<section id="more-on-momentum-based-approaches">
+<h2>More on momentum based approaches<a class="headerlink" href="#more-on-momentum-based-approaches" title="Permalink to this heading">#</a></h2>
+<p>Let us try to get more intuition from these equations. It is helpful
+to consider a simple physical analogy with a particle of mass <span class="math notranslate nohighlight">\(m\)</span>
+moving in a viscous medium with drag coefficient <span class="math notranslate nohighlight">\(\mu\)</span> and potential
+<span class="math notranslate nohighlight">\(E(\mathbf{w})\)</span>. If we denote the particle’s position by <span class="math notranslate nohighlight">\(\mathbf{w}\)</span>,
+then its motion is described by</p>
+<div class="math notranslate nohighlight">
+\[
+m {d^2 \mathbf{w} \over dt^2} + \mu {d \mathbf{w} \over dt }= -\nabla_w E(\mathbf{w}).
+\]</div>
+<p>We can discretize this equation in the usual way to get</p>
+<div class="math notranslate nohighlight">
+\[
+m { \mathbf{w}_{t+\Delta t}-2 \mathbf{w}_{t} +\mathbf{w}_{t-\Delta t} \over (\Delta t)^2}+\mu {\mathbf{w}_{t+\Delta t}- \mathbf{w}_{t} \over \Delta t} = -\nabla_w E(\mathbf{w}).
+\]</div>
+<p>Rearranging this equation, we can rewrite this as</p>
+<div class="math notranslate nohighlight">
+\[
+\Delta \mathbf{w}_{t +\Delta t}= - { (\Delta t)^2 \over m +\mu \Delta t} \nabla_w E(\mathbf{w})+ {m \over m +\mu \Delta t} \Delta \mathbf{w}_t.
+\]</div>
+</section>
+<section id="momentum-parameter">
+<h2>Momentum parameter<a class="headerlink" href="#momentum-parameter" title="Permalink to this heading">#</a></h2>
+<p>Notice that this equation is identical to previous one if we identify
+the position of the particle, <span class="math notranslate nohighlight">\(\mathbf{w}\)</span>, with the parameters
+<span class="math notranslate nohighlight">\(\boldsymbol{\theta}\)</span>. This allows us to identify the momentum
+parameter and learning rate with the mass of the particle and the
+viscous drag as:</p>
+<div class="math notranslate nohighlight">
+\[
+\gamma= {m \over m +\mu \Delta t }, \qquad \eta = {(\Delta t)^2 \over m +\mu \Delta t}.
+\]</div>
+<p>Thus, as the name suggests, the momentum parameter is proportional to
+the mass of the particle and effectively provides inertia.
+Furthermore, in the large viscosity/small learning rate limit, our
+memory time scales as <span class="math notranslate nohighlight">\((1-\gamma)^{-1} \approx m/(\mu \Delta t)\)</span>.</p>
+<p>Why is momentum useful? SGD momentum helps the gradient descent
+algorithm gain speed in directions with persistent but small gradients
+even in the presence of stochasticity, while suppressing oscillations
+in high-curvature directions. This becomes especially important in
+situations where the landscape is shallow and flat in some directions
+and narrow and steep in others. It has been argued that first-order
+methods (with appropriate initial conditions) can perform comparable
+to more expensive second order methods, especially in the context of
+complex deep learning models.</p>
+<p>These beneficial properties of momentum can sometimes become even more
+pronounced by using a slight modification of the classical momentum
+algorithm called Nesterov Accelerated Gradient (NAG).</p>
+<p>In the NAG algorithm, rather than calculating the gradient at the
+current parameters, <span class="math notranslate nohighlight">\(\nabla_\theta E(\boldsymbol{\theta}_t)\)</span>, one
+calculates the gradient at the expected value of the parameters given
+our current momentum, <span class="math notranslate nohighlight">\(\nabla_\theta E(\boldsymbol{\theta}_t +\gamma
+\mathbf{v}_{t-1})\)</span>. This yields the NAG update rule</p>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{v}_{t}=\gamma \mathbf{v}_{t-1}+\eta_{t}\nabla_\theta E(\boldsymbol{\theta}_t +\gamma \mathbf{v}_{t-1}) \nonumber
+\]</div>
+<!-- Equation labels as ordinary links -->
+<div id="_auto2"></div>
+<div class="math notranslate nohighlight">
+\[
+\begin{equation} 
+\boldsymbol{\theta}_{t+1}= \boldsymbol{\theta}_t -\mathbf{v}_{t}.
+\label{_auto2} \tag{3}
+\end{equation}
+\]</div>
+<p>One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of <span class="math notranslate nohighlight">\(\gamma\)</span>.</p>
+</section>
+<section id="second-moment-of-the-gradient">
+<h2>Second moment of the gradient<a class="headerlink" href="#second-moment-of-the-gradient" title="Permalink to this heading">#</a></h2>
+<p>In stochastic gradient descent, with and without momentum, we still
+have to specify a schedule for tuning the learning rates <span class="math notranslate nohighlight">\(\eta_t\)</span>
+as a function of time.  As discussed in the context of Newton’s
+method, this presents a number of dilemmas. The learning rate is
+limited by the steepest direction which can change depending on the
+current position in the landscape. To circumvent this problem, ideally
+our algorithm would keep track of curvature and take large steps in
+shallow, flat directions and small steps in steep, narrow directions.
+Second-order methods accomplish this by calculating or approximating
+the Hessian and normalizing the learning rate by the
+curvature. However, this is very computationally expensive for
+extremely large models. Ideally, we would like to be able to
+adaptively change the step size to match the landscape without paying
+the steep computational price of calculating or approximating
+Hessians.</p>
+<p>Recently, a number of methods have been introduced that accomplish
+this by tracking not only the gradient, but also the second moment of
+the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and
+<a class="reference external" href="https://arxiv.org/abs/1412.6980">ADAM</a>.</p>
+</section>
+<section id="rms-prop">
+<h2>RMS prop<a class="headerlink" href="#rms-prop" title="Permalink to this heading">#</a></h2>
+<p>In RMS prop, in addition to keeping a running average of the first
+moment of the gradient, we also keep track of the second moment
+denoted by <span class="math notranslate nohighlight">\(\mathbf{s}_t=\mathbb{E}[\mathbf{g}_t^2]\)</span>. The update rule
+for RMS prop is given by</p>
+<!-- Equation labels as ordinary links -->
+<div id="_auto3"></div>
+<div class="math notranslate nohighlight">
+\[
+\begin{equation}
+\mathbf{g}_t = \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto3} \tag{4}
+\end{equation}
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{s}_t =\beta \mathbf{s}_{t-1} +(1-\beta)\mathbf{g}_t^2 \nonumber
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\theta}_{t+1}=\boldsymbol{\theta}_t - \eta_t { \mathbf{g}_t \over \sqrt{\mathbf{s}_t +\epsilon}}, \nonumber
+\]</div>
+<p>where <span class="math notranslate nohighlight">\(\beta\)</span> controls the averaging time of the second moment and is
+typically taken to be about <span class="math notranslate nohighlight">\(\beta=0.9\)</span>, <span class="math notranslate nohighlight">\(\eta_t\)</span> is a learning rate
+typically chosen to be <span class="math notranslate nohighlight">\(10^{-3}\)</span>, and <span class="math notranslate nohighlight">\(\epsilon\sim 10^{-8} \)</span> is a
+small regularization constant to prevent divergences. Multiplication
+and division by vectors is understood as an element-wise operation. It
+is clear from this formula that the learning rate is reduced in
+directions where the norm of the gradient is consistently large. This
+greatly speeds up the convergence by allowing us to use a larger
+learning rate for flat directions.</p>
+</section>
+<section id="adam-optimizer">
+<h2><a class="reference external" href="https://arxiv.org/abs/1412.6980">ADAM optimizer</a><a class="headerlink" href="#adam-optimizer" title="Permalink to this heading">#</a></h2>
+<p>A related algorithm is the ADAM optimizer. In
+<a class="reference external" href="https://arxiv.org/abs/1412.6980">ADAM</a>, we keep a running average of
+both the first and second moment of the gradient and use this
+information to adaptively change the learning rate for different
+parameters.  The method isefficient when working with large
+problems involving lots data and/or parameters.  It is a combination of the
+gradient descent with momentum algorithm and the RMSprop algorithm
+discussed above.</p>
+<p>In addition to keeping a running average of the first and
+second moments of the gradient
+(i.e. <span class="math notranslate nohighlight">\(\mathbf{m}_t=\mathbb{E}[\mathbf{g}_t]\)</span> and
+<span class="math notranslate nohighlight">\(\mathbf{s}_t=\mathbb{E}[\mathbf{g}^2_t]\)</span>, respectively), ADAM
+performs an additional bias correction to account for the fact that we
+are estimating the first two moments of the gradient using a running
+average (denoted by the hats in the update rule below). The update
+rule for ADAM is given by (where multiplication and division are once
+again understood to be element-wise operations below)</p>
+<!-- Equation labels as ordinary links -->
+<div id="_auto4"></div>
+<div class="math notranslate nohighlight">
+\[
+\begin{equation}
+\mathbf{g}_t = \nabla_\theta E(\boldsymbol{\theta}) 
+\label{_auto4} \tag{5}
+\end{equation}
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{m}_t = \beta_1 \mathbf{m}_{t-1} + (1-\beta_1) \mathbf{g}_t \nonumber
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\mathbf{s}_t =\beta_2 \mathbf{s}_{t-1} +(1-\beta_2)\mathbf{g}_t^2 \nonumber
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\mathbf{m}}_t={\mathbf{m}_t \over 1-\beta_1^t} \nonumber
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\mathbf{s}}_t ={\mathbf{s}_t \over1-\beta_2^t} \nonumber
+\]</div>
+<div class="math notranslate nohighlight">
+\[
+\boldsymbol{\theta}_{t+1}=\boldsymbol{\theta}_t - \eta_t { \boldsymbol{\mathbf{m}}_t \over \sqrt{\boldsymbol{\mathbf{s}}_t} +\epsilon}, \nonumber
+\]</div>
+<!-- Equation labels as ordinary links -->
+<div id="_auto5"></div>
+<div class="math notranslate nohighlight">
+\[
+\begin{equation} 
+\label{_auto5} \tag{6}
+\end{equation}
+\]</div>
+<p>where <span class="math notranslate nohighlight">\(\beta_1\)</span> and <span class="math notranslate nohighlight">\(\beta_2\)</span> set the memory lifetime of the first and
+second moment and are typically taken to be <span class="math notranslate nohighlight">\(0.9\)</span> and <span class="math notranslate nohighlight">\(0.99\)</span>
+respectively, and <span class="math notranslate nohighlight">\(\eta\)</span> and <span class="math notranslate nohighlight">\(\epsilon\)</span> are identical to RMSprop.</p>
+<p>Like in RMSprop, the effective step size of a parameter depends on the
+magnitude of its gradient squared.  To understand this better, let us
+rewrite this expression in terms of the variance
+<span class="math notranslate nohighlight">\(\boldsymbol{\sigma}_t^2 = \boldsymbol{\mathbf{s}}_t -
+(\boldsymbol{\mathbf{m}}_t)^2\)</span>. Consider a single parameter <span class="math notranslate nohighlight">\(\theta_t\)</span>. The
+update rule for this parameter is given by</p>
+<div class="math notranslate nohighlight">
+\[
+\Delta \theta_{t+1}= -\eta_t { \boldsymbol{m}_t \over \sqrt{\sigma_t^2 +  m_t^2 }+\epsilon}.
+\]</div>
+</section>
+<section id="algorithms-and-codes-for-adagrad-rmsprop-and-adam">
+<h2>Algorithms and codes for Adagrad, RMSprop and Adam<a class="headerlink" href="#algorithms-and-codes-for-adagrad-rmsprop-and-adam" title="Permalink to this heading">#</a></h2>
+<p>The algorithms we have implemented are well described in the text by <a class="reference external" href="https://www.deeplearningbook.org/contents/optimization.html">Goodfellow, Bengio and Courville, chapter 8</a>.</p>
+<p>The codes which implement these algorithms are discussed after our presentation of automatic differentiation.</p>
+</section>
+<section id="practical-tips">
+<h2>Practical tips<a class="headerlink" href="#practical-tips" title="Permalink to this heading">#</a></h2>
+<ul class="simple">
+<li><p><strong>Randomize the data when making mini-batches</strong>. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.</p></li>
+<li><p><strong>Transform your inputs</strong>. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.</p></li>
+<li><p><strong>Monitor the out-of-sample performance.</strong> Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This <em>early stopping</em> significantly improves performance in many settings.</p></li>
+<li><p><strong>Adaptive optimization methods don’t always have good generalization.</strong> Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.</p></li>
+</ul>
+<p>Geron’s text, see chapter 11, has several interesting discussions.</p>
+</section>
+<section id="automatic-differentiation">
+<h2>Automatic differentiation<a class="headerlink" href="#automatic-differentiation" title="Permalink to this heading">#</a></h2>
+<p><a class="reference external" href="https://en.wikipedia.org/wiki/Automatic_differentiation">Automatic differentiation (AD)</a>,
+also called algorithmic
+differentiation or computational differentiation,is a set of
+techniques to numerically evaluate the derivative of a function
+specified by a computer program. AD exploits the fact that every
+computer program, no matter how complicated, executes a sequence of
+elementary arithmetic operations (addition, subtraction,
+multiplication, division, etc.) and elementary functions (exp, log,
+sin, cos, etc.). By applying the chain rule repeatedly to these
+operations, derivatives of arbitrary order can be computed
+automatically, accurately to working precision, and using at most a
+small constant factor more arithmetic operations than the original
+program.</p>
+<p>Automatic differentiation is neither:</p>
+<ul class="simple">
+<li><p>Symbolic differentiation, nor</p></li>
+<li><p>Numerical differentiation (the method of finite differences).</p></li>
+</ul>
+<p>Symbolic differentiation can lead to inefficient code and faces the
+difficulty of converting a computer program into a single expression,
+while numerical differentiation can introduce round-off errors in the
+discretization process and cancellation</p>
+<p>Python has tools for so-called <strong>automatic differentiation</strong>.
+Consider the following example</p>
+<div class="math notranslate nohighlight">
+\[
+f(x) = \sin\left(2\pi x + x^2\right)
+\]</div>
+<p>which has the following derivative</p>
+<div class="math notranslate nohighlight">
+\[
+f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
+\]</div>
+<p>Using <strong>autograd</strong> we have</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+
+<span class="c1"># To do elementwise differentiation:</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">elementwise_grad</span> <span class="k">as</span> <span class="n">egrad</span> 
+
+<span class="c1"># To plot:</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span> 
+
+
+<span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="k">def</span> <span class="nf">f_grad_analytic</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">*</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
+
+<span class="c1"># Do the comparison:</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1000</span><span class="p">)</span>
+
+<span class="n">f_grad</span> <span class="o">=</span> <span class="n">egrad</span><span class="p">(</span><span class="n">f</span><span class="p">)</span>
+
+<span class="n">computed</span> <span class="o">=</span> <span class="n">f_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+<span class="n">analytic</span> <span class="o">=</span> <span class="n">f_grad_analytic</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s1">&#39;Derivative computed from Autograd compared with the analytical derivative&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">computed</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;autograd&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">analytic</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">&#39;analytic&#39;</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">&#39;x&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">&#39;y&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The max absolute difference is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">computed</span> <span class="o">-</span> <span class="n">analytic</span><span class="p">))))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="using-autograd">
+<h2>Using autograd<a class="headerlink" href="#using-autograd" title="Permalink to this heading">#</a></h2>
+<p>Here we
+experiment with what kind of functions Autograd is capable
+of finding the gradient of. The following Python functions are just
+meant to illustrate what Autograd can do, but please feel free to
+experiment with other, possibly more complicated, functions as well.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">f1</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="mi">1</span>
+
+<span class="n">f1_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f1</span><span class="p">)</span>
+
+<span class="c1"># Remember to send in float as argument to the computed gradient from Autograd!</span>
+<span class="n">a</span> <span class="o">=</span> <span class="mf">1.0</span>
+
+<span class="c1"># See the evaluated gradient at a using autograd:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The gradient of f1 evaluated at a = </span><span class="si">%g</span><span class="s2"> using autograd is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">f1_grad</span><span class="p">(</span><span class="n">a</span><span class="p">)))</span>
+
+<span class="c1"># Compare with the analytical derivative, that is f1&#39;(x) = 3*x**2 </span>
+<span class="n">grad_analytical</span> <span class="o">=</span> <span class="mi">3</span><span class="o">*</span><span class="n">a</span><span class="o">**</span><span class="mi">2</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The gradient of f1 evaluated at a = </span><span class="si">%g</span><span class="s2"> by finding the analytic expression is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">grad_analytical</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="autograd-with-more-complicated-functions">
+<h2>Autograd with more complicated functions<a class="headerlink" href="#autograd-with-more-complicated-functions" title="Permalink to this heading">#</a></h2>
+<p>To differentiate with respect to two (or more) arguments of a Python
+function, Autograd need to know at which variable the function if
+being differentiated with respect to.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f2</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">):</span>
+    <span class="k">return</span> <span class="mi">3</span><span class="o">*</span><span class="n">x1</span><span class="o">**</span><span class="mi">3</span> <span class="o">+</span> <span class="n">x2</span><span class="o">*</span><span class="p">(</span><span class="n">x1</span> <span class="o">-</span> <span class="mi">5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+
+<span class="c1"># By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1</span>
+<span class="n">f2_grad_x1</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f2</span><span class="p">,</span><span class="mi">0</span><span class="p">)</span>
+
+<span class="c1"># ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad</span>
+<span class="n">f2_grad_x2</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">x1</span> <span class="o">=</span> <span class="mf">1.0</span>
+<span class="n">x2</span> <span class="o">=</span> <span class="mf">3.0</span> 
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Evaluating at x1 = </span><span class="si">%g</span><span class="s2">, x2 = </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;-&quot;</span><span class="o">*</span><span class="mi">30</span><span class="p">)</span>
+
+<span class="c1"># Compare with the analytical derivatives:</span>
+
+<span class="c1"># Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:</span>
+<span class="n">f2_grad_x1_analytical</span> <span class="o">=</span> <span class="mi">9</span><span class="o">*</span><span class="n">x1</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">x2</span>
+
+<span class="c1"># Derivative of f2 w.r.t x2 is: x1 - 5:</span>
+<span class="n">f2_grad_x2_analytical</span> <span class="o">=</span> <span class="n">x1</span> <span class="o">-</span> <span class="mi">5</span>
+
+<span class="c1"># See the evaluated derivations:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The derivative of f2 w.r.t x1: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span> <span class="n">f2_grad_x1</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">)</span> <span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical derivative of f2 w.r.t x1: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span> <span class="n">f2_grad_x1</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">)</span> <span class="p">))</span>
+
+<span class="nb">print</span><span class="p">()</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The derivative of f2 w.r.t x2: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span> <span class="n">f2_grad_x2</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">)</span> <span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical derivative of f2 w.r.t x2: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span> <span class="n">f2_grad_x2</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">)</span> <span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable.</p>
+</section>
+<section id="more-complicated-functions-using-the-elements-of-their-arguments-directly">
+<h2>More complicated functions using the elements of their arguments directly<a class="headerlink" href="#more-complicated-functions-using-the-elements-of-their-arguments-directly" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f3</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="c1"># Assumes x is an array of length 5 or higher</span>
+    <span class="k">return</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">5</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mi">7</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="mi">11</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span><span class="o">**</span><span class="mi">2</span>
+
+<span class="n">f3_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f3</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="c1"># Print the computed gradient:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed gradient of f3 is: &quot;</span><span class="p">,</span> <span class="n">f3_grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+
+<span class="c1"># The analytical gradient is: (2, 3, 5, 7, 22*x[4])</span>
+<span class="n">f3_grad_analytical</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">22</span><span class="o">*</span><span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">]])</span>
+
+<span class="c1"># Print the analytical gradient:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical gradient of f3 is: &quot;</span><span class="p">,</span> <span class="n">f3_grad_analytical</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Note that in this case, when sending an array as input argument, the
+output from Autograd is another array. This is the true gradient of
+the function, as opposed to the function in the previous example. By
+using arrays to represent the variables, the output from Autograd
+might be easier to work with, as the output is closer to what one
+could expect form a gradient-evaluting function.</p>
+</section>
+<section id="functions-using-mathematical-functions-from-numpy">
+<h2>Functions using mathematical functions from Numpy<a class="headerlink" href="#functions-using-mathematical-functions-from-numpy" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f4</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span><span class="o">+</span><span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span><span class="p">)</span>
+
+<span class="n">f4_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f4</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="mf">2.7</span>
+
+<span class="c1"># Print the computed derivative:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed derivative of f4 at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f4_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
+
+<span class="c1"># The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi</span>
+<span class="n">f4_grad_analytical</span> <span class="o">=</span> <span class="n">x</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span>
+
+<span class="c1"># Print the analytical gradient:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical gradient of f4 at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f4_grad_analytical</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="more-autograd">
+<h2>More autograd<a class="headerlink" href="#more-autograd" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f5</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">if</span> <span class="n">x</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">return</span> <span class="o">-</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span>
+
+<span class="n">f5_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f5</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="mf">2.7</span>
+
+<span class="c1"># Print the computed derivative:</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed derivative of f5 at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f5_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="and-with-loops">
+<h2>And  with loops<a class="headerlink" href="#and-with-loops" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f6_for</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="n">val</span> <span class="o">=</span> <span class="mi">0</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
+        <span class="n">val</span> <span class="o">=</span> <span class="n">val</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="n">i</span>
+    <span class="k">return</span> <span class="n">val</span>
+
+<span class="k">def</span> <span class="nf">f6_while</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="n">val</span> <span class="o">=</span> <span class="mi">0</span>
+    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
+    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">10</span><span class="p">:</span>
+        <span class="n">val</span> <span class="o">=</span> <span class="n">val</span> <span class="o">+</span> <span class="n">x</span><span class="o">**</span><span class="n">i</span>
+        <span class="n">i</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
+    <span class="k">return</span> <span class="n">val</span>
+
+<span class="n">f6_for_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f6_for</span><span class="p">)</span>
+<span class="n">f6_while_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f6_while</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="mf">0.5</span>
+
+<span class="c1"># Print the computed derivaties of f6_for and f6_while</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed derivative of f6_for at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f6_for_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed derivative of f6_while at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f6_while_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
+</pre></div>
+</div>
+</div>
+</div>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="c1"># Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9</span>
+<span class="c1"># The analytical derivative is: sum(i*x**(i-1)) </span>
+<span class="n">f6_grad_analytical</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
+    <span class="n">f6_grad_analytical</span> <span class="o">+=</span> <span class="n">i</span><span class="o">*</span><span class="n">x</span><span class="o">**</span><span class="p">(</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical derivative of f6 at x = </span><span class="si">%g</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">f6_grad_analytical</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="using-recursion">
+<h2>Using recursion<a class="headerlink" href="#using-recursion" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">f7</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="c1"># Assume that n is an integer</span>
+    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+        <span class="k">return</span> <span class="mi">1</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">return</span> <span class="n">n</span><span class="o">*</span><span class="n">f7</span><span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">f7_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f7</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mf">2.0</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The computed derivative of f7 at n = </span><span class="si">%d</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">f7_grad</span><span class="p">(</span><span class="n">n</span><span class="p">)))</span>
+
+<span class="c1"># The function f7 is an implementation of the factorial of n.</span>
+<span class="c1"># By using the product rule, one can find that the derivative is:</span>
+
+<span class="n">f7_grad_analytical</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+    <span class="n">tmp</span> <span class="o">=</span> <span class="mi">1</span>
+    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+        <span class="k">if</span> <span class="n">k</span> <span class="o">!=</span> <span class="n">i</span><span class="p">:</span>
+            <span class="n">tmp</span> <span class="o">*=</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">)</span>
+    <span class="n">f7_grad_analytical</span> <span class="o">+=</span> <span class="n">tmp</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The analytical derivative of f7 at n = </span><span class="si">%d</span><span class="s2"> is: </span><span class="si">%g</span><span class="s2">&quot;</span><span class="o">%</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="n">f7_grad_analytical</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.</p>
+</section>
+<section id="unsupported-functions">
+<h2>Unsupported functions<a class="headerlink" href="#unsupported-functions" title="Permalink to this heading">#</a></h2>
+<p>Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.</p>
+<p>Assigning a value to the variable being differentiated with respect to</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f8</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="c1"># Assume x is an array</span>
+    <span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">3</span>
+    <span class="k">return</span> <span class="n">x</span><span class="o">*</span><span class="mi">2</span>
+
+<span class="n">f8_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f8</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="mf">8.4</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The derivative of f8 is:&quot;</span><span class="p">,</span><span class="n">f8_grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Here, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.</p>
+</section>
+<section id="the-syntax-a-dot-b-when-finding-the-dot-product">
+<h2>The syntax a.dot(b) when finding the dot product<a class="headerlink" href="#the-syntax-a-dot-b-when-finding-the-dot-product" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f9</span><span class="p">(</span><span class="n">a</span><span class="p">):</span> <span class="c1"># Assume a is an array with 2 elements</span>
+    <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">])</span>
+    <span class="k">return</span> <span class="n">a</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+
+<span class="n">f9_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f9</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">])</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The derivative of f9 is:&quot;</span><span class="p">,</span><span class="n">f9_grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Here we are told that the ‘dot’ function does not belong to Autograd’s
+version of a Numpy array.  To overcome this, an alternative syntax
+which also computed the dot product can be used:</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+<span class="k">def</span> <span class="nf">f9_alternative</span><span class="p">(</span><span class="n">x</span><span class="p">):</span> <span class="c1"># Assume a is an array with 2 elements</span>
+    <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">])</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">b</span><span class="p">)</span> <span class="c1"># The same as x_1*b_1 + x_2*b_2</span>
+
+<span class="n">f9_alternative_grad</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">f9_alternative</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">3.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">])</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;The gradient of f9 is:&quot;</span><span class="p">,</span><span class="n">f9_alternative_grad</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
+
+<span class="c1"># The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively</span>
+<span class="c1"># w.r.t x is (b_1, b_2).</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="recommended-to-avoid">
+<h2>Recommended to avoid<a class="headerlink" href="#recommended-to-avoid" title="Permalink to this heading">#</a></h2>
+<p>The documentation recommends to avoid inplace operations such as</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">+=</span> <span class="n">b</span>
+<span class="n">a</span> <span class="o">-=</span> <span class="n">b</span>
+<span class="n">a</span><span class="o">*=</span> <span class="n">b</span>
+<span class="n">a</span> <span class="o">/=</span><span class="n">b</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="using-autograd-with-ols">
+<h2>Using Autograd with OLS<a class="headerlink" href="#using-autograd-with-ols" title="Permalink to this heading">#</a></h2>
+<p>We conclude the part on optmization by showing how we can make codes
+for linear regression and logistic regression using <strong>autograd</strong>. The
+first example shows results with ordinary leats squares.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients for OLS</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">beta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">beta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">1000</span>
+<span class="c1"># define the gradient</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="n">training_gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+<span class="n">xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">],[</span><span class="mi">2</span><span class="p">]])</span>
+<span class="n">Xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">xnew</span><span class="p">]</span>
+<span class="n">ypredict</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+<span class="n">ypredict2</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict2</span><span class="p">,</span> <span class="s2">&quot;b-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">,</span><span class="s1">&#39;ro&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$x$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$y$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Random numbers &#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="id9">
+<h2>Same code but now with momentum gradient descent<a class="headerlink" href="#id9" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients for OLS</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">beta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">beta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="c1">#+np.random.randn(n,1)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">30</span>
+
+<span class="c1"># define the gradient</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="n">training_gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+    <span class="nb">print</span><span class="p">(</span><span class="nb">iter</span><span class="p">,</span><span class="n">gradients</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">gradients</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+<span class="c1"># Now improve with momentum gradient descent</span>
+<span class="n">change</span> <span class="o">=</span> <span class="mf">0.0</span>
+<span class="n">delta_momentum</span> <span class="o">=</span> <span class="mf">0.3</span>
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="c1"># calculate gradient</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="n">training_gradient</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+    <span class="c1"># calculate update</span>
+    <span class="n">new_change</span> <span class="o">=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span><span class="o">+</span><span class="n">delta_momentum</span><span class="o">*</span><span class="n">change</span>
+    <span class="c1"># take a step</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">new_change</span>
+    <span class="c1"># save the change</span>
+    <span class="n">change</span> <span class="o">=</span> <span class="n">new_change</span>
+    <span class="nb">print</span><span class="p">(</span><span class="nb">iter</span><span class="p">,</span><span class="n">gradients</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">gradients</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd wth momentum&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="but-noen-of-these-can-compete-with-newton-s-method">
+<h2>But noen of these can compete with Newton’s method<a class="headerlink" href="#but-noen-of-these-can-compete-with-newton-s-method" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Newton&#39;s method</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">beta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">beta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">beta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">beta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="c1"># Note that here the Hessian does not depend on the parameters beta</span>
+<span class="n">invH</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">beta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">5</span>
+
+<span class="c1"># define the gradient</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="n">training_gradient</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+    <span class="n">beta</span> <span class="o">-=</span> <span class="n">invH</span> <span class="o">@</span> <span class="n">gradients</span>
+    <span class="nb">print</span><span class="p">(</span><span class="nb">iter</span><span class="p">,</span><span class="n">gradients</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="n">gradients</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;beta from own Newton code&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="including-stochastic-gradient-descent-with-autograd">
+<h2>Including Stochastic Gradient Descent with Autograd<a class="headerlink" href="#including-stochastic-gradient-descent-with-autograd" title="Permalink to this heading">#</a></h2>
+<p>In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using <strong>autograd</strong>.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using SGD</span>
+<span class="c1"># OLS example</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="c1"># Note change from previous example</span>
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">theta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">1000</span>
+
+<span class="c1"># Note that we request the derivative wrt third argument (theta, 2 here)</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+<span class="n">xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">],[</span><span class="mi">2</span><span class="p">]])</span>
+<span class="n">Xnew</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">xnew</span><span class="p">]</span>
+<span class="n">ypredict</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+<span class="n">ypredict2</span> <span class="o">=</span> <span class="n">Xnew</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict</span><span class="p">,</span> <span class="s2">&quot;r-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xnew</span><span class="p">,</span> <span class="n">ypredict2</span><span class="p">,</span> <span class="s2">&quot;b-&quot;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="p">,</span><span class="s1">&#39;ro&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mf">2.0</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$x$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;$y$&#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;Random numbers &#39;</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="n">t0</span><span class="p">,</span> <span class="n">t1</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">50</span>
+<span class="k">def</span> <span class="nf">learning_schedule</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">t0</span><span class="o">/</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">t1</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+<span class="c1"># Can you figure out a better way of setting up the contributions to each batch?</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">yi</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+        <span class="n">eta</span> <span class="o">=</span> <span class="n">learning_schedule</span><span class="p">(</span><span class="n">epoch</span><span class="o">*</span><span class="n">m</span><span class="o">+</span><span class="n">i</span><span class="p">)</span>
+        <span class="n">theta</span> <span class="o">=</span> <span class="n">theta</span> <span class="o">-</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own sdg&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="id10">
+<h2>Same code but now with momentum gradient descent<a class="headerlink" href="#id10" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using SGD</span>
+<span class="c1"># OLS example</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="c1"># Note change from previous example</span>
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">theta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">x</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mi">4</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+<span class="c1"># Hessian matrix</span>
+<span class="n">H</span> <span class="o">=</span> <span class="p">(</span><span class="mf">2.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span> <span class="n">XT_X</span>
+<span class="n">EigValues</span><span class="p">,</span> <span class="n">EigVectors</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">H</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;Eigenvalues of Hessian Matrix:</span><span class="si">{</span><span class="n">EigValues</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">1.0</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">EigValues</span><span class="p">)</span>
+<span class="n">Niterations</span> <span class="o">=</span> <span class="mi">100</span>
+
+<span class="c1"># Note that we request the derivative wrt third argument (theta, 2 here)</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="nb">iter</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">Niterations</span><span class="p">):</span>
+    <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">n</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">X</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+    <span class="n">theta</span> <span class="o">-=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own gd&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+
+
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="n">t0</span><span class="p">,</span> <span class="n">t1</span> <span class="o">=</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">50</span>
+<span class="k">def</span> <span class="nf">learning_schedule</span><span class="p">(</span><span class="n">t</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">t0</span><span class="o">/</span><span class="p">(</span><span class="n">t</span><span class="o">+</span><span class="n">t1</span><span class="p">)</span>
+
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="n">change</span> <span class="o">=</span> <span class="mf">0.0</span>
+<span class="n">delta_momentum</span> <span class="o">=</span> <span class="mf">0.3</span>
+
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">yi</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+        <span class="n">eta</span> <span class="o">=</span> <span class="n">learning_schedule</span><span class="p">(</span><span class="n">epoch</span><span class="o">*</span><span class="n">m</span><span class="o">+</span><span class="n">i</span><span class="p">)</span>
+        <span class="c1"># calculate update</span>
+        <span class="n">new_change</span> <span class="o">=</span> <span class="n">eta</span><span class="o">*</span><span class="n">gradients</span><span class="o">+</span><span class="n">delta_momentum</span><span class="o">*</span><span class="n">change</span>
+        <span class="c1"># take a step</span>
+        <span class="n">theta</span> <span class="o">-=</span> <span class="n">new_change</span>
+        <span class="c1"># save the change</span>
+        <span class="n">change</span> <span class="o">=</span> <span class="n">new_change</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own sdg with momentum&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="similar-second-order-function-now-problem-but-now-with-adagrad">
+<h2>Similar (second order function now) problem but now with AdaGrad<a class="headerlink" href="#similar-second-order-function-now-problem-but-now-with-adagrad" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent</span>
+<span class="c1"># OLS example</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="c1"># Note change from previous example</span>
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">theta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">1000</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span><span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+
+<span class="c1"># Note that we request the derivative wrt third argument (theta, 2 here)</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+<span class="c1"># Define parameters for Stochastic Gradient Descent</span>
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="c1"># Guess for unknown parameters theta</span>
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="c1"># Value for learning rate</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">0.01</span>
+<span class="c1"># Including AdaGrad parameter to avoid possible division by zero</span>
+<span class="n">delta</span>  <span class="o">=</span> <span class="mf">1e-8</span>
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+    <span class="n">Giter</span> <span class="o">=</span> <span class="mf">0.0</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">yi</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+        <span class="n">Giter</span> <span class="o">+=</span> <span class="n">gradients</span><span class="o">*</span><span class="n">gradients</span>
+        <span class="n">update</span> <span class="o">=</span> <span class="n">gradients</span><span class="o">*</span><span class="n">eta</span><span class="o">/</span><span class="p">(</span><span class="n">delta</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Giter</span><span class="p">))</span>
+        <span class="n">theta</span> <span class="o">-=</span> <span class="n">update</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own AdaGrad&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+<p>Running this code we note an almost perfect agreement with the results from matrix inversion.</p>
+</section>
+<section id="rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent">
+<h2>RMSprop for adaptive learning rate with Stochastic Gradient Descent<a class="headerlink" href="#rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent</span>
+<span class="c1"># OLS example</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="c1"># Note change from previous example</span>
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">theta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">1000</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span><span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="c1"># +np.random.randn(n,1)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+
+<span class="c1"># Note that we request the derivative wrt third argument (theta, 2 here)</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+<span class="c1"># Define parameters for Stochastic Gradient Descent</span>
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="c1"># Guess for unknown parameters theta</span>
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="c1"># Value for learning rate</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">0.01</span>
+<span class="c1"># Value for parameter rho</span>
+<span class="n">rho</span> <span class="o">=</span> <span class="mf">0.99</span>
+<span class="c1"># Including AdaGrad parameter to avoid possible division by zero</span>
+<span class="n">delta</span>  <span class="o">=</span> <span class="mf">1e-8</span>
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+    <span class="n">Giter</span> <span class="o">=</span> <span class="mf">0.0</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">yi</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+	<span class="c1"># Accumulated gradient</span>
+	<span class="c1"># Scaling with rho the new and the previous results</span>
+        <span class="n">Giter</span> <span class="o">=</span> <span class="p">(</span><span class="n">rho</span><span class="o">*</span><span class="n">Giter</span><span class="o">+</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">rho</span><span class="p">)</span><span class="o">*</span><span class="n">gradients</span><span class="o">*</span><span class="n">gradients</span><span class="p">)</span>
+	<span class="c1"># Taking the diagonal only and inverting</span>
+        <span class="n">update</span> <span class="o">=</span> <span class="n">gradients</span><span class="o">*</span><span class="n">eta</span><span class="o">/</span><span class="p">(</span><span class="n">delta</span><span class="o">+</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">Giter</span><span class="p">))</span>
+	<span class="c1"># Hadamard product</span>
+        <span class="n">theta</span> <span class="o">-=</span> <span class="n">update</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own RMSprop&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="and-finally-adam">
+<h2>And finally <a class="reference external" href="https://arxiv.org/pdf/1412.6980.pdf">ADAM</a><a class="headerlink" href="#and-finally-adam" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent</span>
+<span class="c1"># OLS example</span>
+<span class="kn">from</span> <span class="nn">random</span> <span class="kn">import</span> <span class="n">random</span><span class="p">,</span> <span class="n">seed</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="c1"># Note change from previous example</span>
+<span class="k">def</span> <span class="nf">CostOLS</span><span class="p">(</span><span class="n">y</span><span class="p">,</span><span class="n">X</span><span class="p">,</span><span class="n">theta</span><span class="p">):</span>
+    <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y</span><span class="o">-</span><span class="n">X</span> <span class="o">@</span> <span class="n">theta</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+
+<span class="n">n</span> <span class="o">=</span> <span class="mi">1000</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">y</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">+</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span><span class="mi">4</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="c1"># +np.random.randn(n,1)</span>
+
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">n</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="p">]</span>
+<span class="n">XT_X</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span>
+<span class="n">theta_linreg</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">XT_X</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Own inversion&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta_linreg</span><span class="p">)</span>
+
+
+<span class="c1"># Note that we request the derivative wrt third argument (theta, 2 here)</span>
+<span class="n">training_gradient</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">CostOLS</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+<span class="c1"># Define parameters for Stochastic Gradient Descent</span>
+<span class="n">n_epochs</span> <span class="o">=</span> <span class="mi">50</span>
+<span class="n">M</span> <span class="o">=</span> <span class="mi">5</span>   <span class="c1">#size of each minibatch</span>
+<span class="n">m</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">n</span><span class="o">/</span><span class="n">M</span><span class="p">)</span> <span class="c1">#number of minibatches</span>
+<span class="c1"># Guess for unknown parameters theta</span>
+<span class="n">theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+
+<span class="c1"># Value for learning rate</span>
+<span class="n">eta</span> <span class="o">=</span> <span class="mf">0.01</span>
+<span class="c1"># Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980</span>
+<span class="n">beta1</span> <span class="o">=</span> <span class="mf">0.9</span>
+<span class="n">beta2</span> <span class="o">=</span> <span class="mf">0.999</span>
+<span class="c1"># Including AdaGrad parameter to avoid possible division by zero</span>
+<span class="n">delta</span>  <span class="o">=</span> <span class="mf">1e-7</span>
+<span class="nb">iter</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_epochs</span><span class="p">):</span>
+    <span class="n">first_moment</span> <span class="o">=</span> <span class="mf">0.0</span>
+    <span class="n">second_moment</span> <span class="o">=</span> <span class="mf">0.0</span>
+    <span class="nb">iter</span> <span class="o">+=</span> <span class="mi">1</span>
+    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+        <span class="n">random_index</span> <span class="o">=</span> <span class="n">M</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="n">m</span><span class="p">)</span>
+        <span class="n">xi</span> <span class="o">=</span> <span class="n">X</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">yi</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">random_index</span><span class="p">:</span><span class="n">random_index</span><span class="o">+</span><span class="n">M</span><span class="p">]</span>
+        <span class="n">gradients</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span><span class="o">/</span><span class="n">M</span><span class="p">)</span><span class="o">*</span><span class="n">training_gradient</span><span class="p">(</span><span class="n">yi</span><span class="p">,</span> <span class="n">xi</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+        <span class="c1"># Computing moments first</span>
+        <span class="n">first_moment</span> <span class="o">=</span> <span class="n">beta1</span><span class="o">*</span><span class="n">first_moment</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">beta1</span><span class="p">)</span><span class="o">*</span><span class="n">gradients</span>
+        <span class="n">second_moment</span> <span class="o">=</span> <span class="n">beta2</span><span class="o">*</span><span class="n">second_moment</span><span class="o">+</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">beta2</span><span class="p">)</span><span class="o">*</span><span class="n">gradients</span><span class="o">*</span><span class="n">gradients</span>
+        <span class="n">first_term</span> <span class="o">=</span> <span class="n">first_moment</span><span class="o">/</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="n">beta1</span><span class="o">**</span><span class="nb">iter</span><span class="p">)</span>
+        <span class="n">second_term</span> <span class="o">=</span> <span class="n">second_moment</span><span class="o">/</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="n">beta2</span><span class="o">**</span><span class="nb">iter</span><span class="p">)</span>
+	<span class="c1"># Scaling with rho the new and the previous results</span>
+        <span class="n">update</span> <span class="o">=</span> <span class="n">eta</span><span class="o">*</span><span class="n">first_term</span><span class="o">/</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">second_term</span><span class="p">)</span><span class="o">+</span><span class="n">delta</span><span class="p">)</span>
+        <span class="n">theta</span> <span class="o">-=</span> <span class="n">update</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;theta from own ADAM&quot;</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="and-logistic-regression">
+<h2>And Logistic Regression<a class="headerlink" href="#and-logistic-regression" title="Permalink to this heading">#</a></h2>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">grad</span>
+
+<span class="k">def</span> <span class="nf">sigmoid</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+    <span class="k">return</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">tanh</span><span class="p">(</span><span class="n">x</span> <span class="o">/</span> <span class="mf">2.</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+
+<span class="k">def</span> <span class="nf">logistic_predictions</span><span class="p">(</span><span class="n">weights</span><span class="p">,</span> <span class="n">inputs</span><span class="p">):</span>
+    <span class="c1"># Outputs probability of a label being true according to logistic model.</span>
+    <span class="k">return</span> <span class="n">sigmoid</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">weights</span><span class="p">))</span>
+
+<span class="k">def</span> <span class="nf">training_loss</span><span class="p">(</span><span class="n">weights</span><span class="p">):</span>
+    <span class="c1"># Training loss is the negative log-likelihood of the training labels.</span>
+    <span class="n">preds</span> <span class="o">=</span> <span class="n">logistic_predictions</span><span class="p">(</span><span class="n">weights</span><span class="p">,</span> <span class="n">inputs</span><span class="p">)</span>
+    <span class="n">label_probabilities</span> <span class="o">=</span> <span class="n">preds</span> <span class="o">*</span> <span class="n">targets</span> <span class="o">+</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">preds</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">targets</span><span class="p">)</span>
+    <span class="k">return</span> <span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">label_probabilities</span><span class="p">))</span>
+
+<span class="c1"># Build a toy dataset.</span>
+<span class="n">inputs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.52</span><span class="p">,</span> <span class="mf">1.12</span><span class="p">,</span>  <span class="mf">0.77</span><span class="p">],</span>
+                   <span class="p">[</span><span class="mf">0.88</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.08</span><span class="p">,</span> <span class="mf">0.15</span><span class="p">],</span>
+                   <span class="p">[</span><span class="mf">0.52</span><span class="p">,</span> <span class="mf">0.06</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.30</span><span class="p">],</span>
+                   <span class="p">[</span><span class="mf">0.74</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.49</span><span class="p">,</span> <span class="mf">1.39</span><span class="p">]])</span>
+<span class="n">targets</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="kc">True</span><span class="p">,</span> <span class="kc">True</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="kc">True</span><span class="p">])</span>
+
+<span class="c1"># Define a function that returns gradients of training loss using Autograd.</span>
+<span class="n">training_gradient_fun</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">training_loss</span><span class="p">)</span>
+
+<span class="c1"># Optimize weights using gradient descent.</span>
+<span class="n">weights</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Initial loss:&quot;</span><span class="p">,</span> <span class="n">training_loss</span><span class="p">(</span><span class="n">weights</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
+    <span class="n">weights</span> <span class="o">-=</span> <span class="n">training_gradient_fun</span><span class="p">(</span><span class="n">weights</span><span class="p">)</span> <span class="o">*</span> <span class="mf">0.01</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Trained loss:&quot;</span><span class="p">,</span> <span class="n">training_loss</span><span class="p">(</span><span class="n">weights</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+<section id="introducing-jax">
+<h2>Introducing <a class="reference external" href="https://jax.readthedocs.io/en/latest/">JAX</a><a class="headerlink" href="#introducing-jax" title="Permalink to this heading">#</a></h2>
+<p>Presently, instead of using <strong>autograd</strong>, we recommend using <a class="reference external" href="https://jax.readthedocs.io/en/latest/">JAX</a></p>
+<p><strong>JAX</strong> is Autograd and <a class="reference external" href="https://www.tensorflow.org/xla">XLA (Accelerated Linear Algebra))</a>,
+brought together for high-performance numerical computing and machine learning research.
+It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.</p>
+<p>Here’s a simple example on how you can use <strong>JAX</strong> to compute the derivate of the logistic function.</p>
+<div class="cell docutils container">
+<div class="cell_input docutils container">
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">jax.numpy</span> <span class="k">as</span> <span class="nn">jnp</span>
+<span class="kn">from</span> <span class="nn">jax</span> <span class="kn">import</span> <span class="n">grad</span><span class="p">,</span> <span class="n">jit</span><span class="p">,</span> <span class="n">vmap</span>
+
+<span class="k">def</span> <span class="nf">sum_logistic</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+  <span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">+</span> <span class="n">jnp</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">x</span><span class="p">)))</span>
+
+<span class="n">x_small</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">3.</span><span class="p">)</span>
+<span class="n">derivative_fn</span> <span class="o">=</span> <span class="n">grad</span><span class="p">(</span><span class="n">sum_logistic</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">derivative_fn</span><span class="p">(</span><span class="n">x_small</span><span class="p">))</span>
+</pre></div>
+</div>
+</div>
+</div>
+</section>
+</section>
+
+    <script type="text/x-thebe-config">
+    {
+        requestKernel: true,
+        binderOptions: {
+            repo: "binder-examples/jupyter-stacks-datascience",
+            ref: "master",
+        },
+        codeMirrorConfig: {
+            theme: "abcdef",
+            mode: "python"
+        },
+        kernelOptions: {
+            name: "python3",
+            path: "./."
+        },
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+    <i class="fa-solid fa-list"></i> Contents
+  </div>
+  <nav class="bd-toc-nav page-toc">
+    <ul class="visible nav section-nav flex-column">
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#plan-for-week-39">Plan for week 39</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#optimization-the-central-part-of-any-machine-learning-algortithm">Optimization, the central part of any Machine Learning algortithm</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-logistic-regression-case">Revisiting our Logistic Regression case</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations-to-solve">The equations to solve</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#solving-using-newton-raphson-s-method">Solving using Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#brief-reminder-on-newton-raphson-s-method">Brief reminder on Newton-Raphson’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-equations">The equations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-geometric-interpretation">Simple geometric interpretation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#extending-to-more-than-one-variable">Extending to more than one variable</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent">Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-steepest-descent">More on Steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-ideal">The ideal</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-sensitiveness-of-the-gradient-descent">The sensitiveness of the gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-functions">Convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#convex-function">Convex function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conditions-on-convex-functions">Conditions on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-convex-functions">More on convex functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#some-simple-problems">Some simple problems</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#standard-steepest-descent">Standard steepest descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-method">Gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent-method">Steepest descent  method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id1">Steepest descent  method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#final-expressions">Final expressions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#steepest-descent-example">Steepest descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id2">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id3">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id4">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#conjugate-gradient-method-and-iterations">Conjugate gradient method and iterations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id5">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id6">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id7">Conjugate gradient method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#revisiting-our-first-homework">Revisiting our first homework</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-example">Gradient descent example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-derivative-of-the-cost-loss-function">The derivative of the cost/loss function</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix">The Hessian matrix</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-program">Simple program</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id8">Gradient Descent Example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-a-corresponding-example-using-scikit-learn">And a corresponding example using <strong>scikit-learn</strong></a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#gradient-descent-and-ridge">Gradient descent and Ridge</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-hessian-matrix-for-ridge-regression">The Hessian matrix for Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#program-example-for-gradient-descent-with-ridge-regression">Program example for gradient descent with Ridge Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-gradient-descent-methods-limitations">Using gradient descent methods, limitations</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#improving-gradient-descent-with-momentum">Improving gradient descent with momentum</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#same-code-but-now-with-momentum-gradient-descent">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#overview-video-on-stochastic-gradient-descent">Overview video on Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#batches-and-mini-batches">Batches and mini-batches</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent-sgd">Stochastic Gradient Descent (SGD)</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#stochastic-gradient-descent">Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#computation-of-gradients">Computation of gradients</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#sgd-example">SGD example</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-gradient-step">The gradient step</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#simple-example-code">Simple example code</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#when-do-we-stop">When do we stop?</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#slightly-different-approach">Slightly different approach</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#time-decay-rate">Time decay rate</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#code-with-a-number-of-minibatches-which-varies">Code with a Number of Minibatches which varies</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#replace-or-not">Replace or not</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-based-gd">Momentum based GD</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-on-momentum-based-approaches">More on momentum based approaches</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#momentum-parameter">Momentum parameter</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#second-moment-of-the-gradient">Second moment of the gradient</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rms-prop">RMS prop</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#adam-optimizer">ADAM optimizer</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#algorithms-and-codes-for-adagrad-rmsprop-and-adam">Algorithms and codes for Adagrad, RMSprop and Adam</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#practical-tips">Practical tips</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#automatic-differentiation">Automatic differentiation</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd">Using autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#autograd-with-more-complicated-functions">Autograd with more complicated functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-complicated-functions-using-the-elements-of-their-arguments-directly">More complicated functions using the elements of their arguments directly</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#functions-using-mathematical-functions-from-numpy">Functions using mathematical functions from Numpy</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#more-autograd">More autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-with-loops">And  with loops</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-recursion">Using recursion</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#unsupported-functions">Unsupported functions</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-syntax-a-dot-b-when-finding-the-dot-product">The syntax a.dot(b) when finding the dot product</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#recommended-to-avoid">Recommended to avoid</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#using-autograd-with-ols">Using Autograd with OLS</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id9">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#but-noen-of-these-can-compete-with-newton-s-method">But noen of these can compete with Newton’s method</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#including-stochastic-gradient-descent-with-autograd">Including Stochastic Gradient Descent with Autograd</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#id10">Same code but now with momentum gradient descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#similar-second-order-function-now-problem-but-now-with-adagrad">Similar (second order function now) problem but now with AdaGrad</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent">RMSprop for adaptive learning rate with Stochastic Gradient Descent</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-finally-adam">And finally ADAM</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#and-logistic-regression">And Logistic Regression</a></li>
+<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introducing-jax">Introducing JAX</a></li>
+</ul>
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diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
index f470b9c6d..e339ffdc5 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter1.ipynb
@@ -342,18 +342,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter1_9_0.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Importing various packages\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -512,22 +514,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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499StW7cm1w4AAFo+y88RkiRH7ejO/8cYU6dNkpxOp6ZMmaKFCxeqZ8+ePi9/7ty5qqysdE+lpaVNrhkAALR8lg6oGB8fr4iIiDq9P0ePHq3TSyRJp06d0q5du1RcXKx7771XknTmzBkZYxQZGaktW7Zo1KhRdR4XHR2t6Ojo0KwEAABosSztEYqKilJ6eroKCws92gsLC5WZmVln/tjYWH344Yfau3eve8rNzVWvXr20d+9eDR06NFylAwCAVsDyW2zMnDlTU6dOVUZGhoYNG6aVK1eqpKREubm5klyHtcrKyrRmzRq1adNG/fv393j8BRdcoJiYmDrtAAAAjbE8COXk5Oj48eNatGiRysvL1b9/fxUUFCglJUWSVF5e3uiYQgAAAIGwfBwhKzCOEAAALU+rG0cIAADASgQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgWwQhAABgW5FWF2CpoiKpqkpKSpKysqSICKsrAgAAYWTvIHTttf/6PjlZWrpUmjjRunoAAEBYcWisVlmZNGmStHmz1ZUAAIAwIQjVMsb1NS9PcjotLQUAAIQHQehsxkilpa5zhwAAQKtHEPKmvNzqCgAAQBgQhLxJSrK6AgAAEAb2vmrsXA6H6+qxrCyrKwEAAGFAj1Ath8P1dckSxhMCAMAmCEK1kpOljRsZRwgAABux96GxV15hZGkAAGzM3kEoK0uKjbW6CgAAYBEOjQEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANsiCAEAANtqFkFo+fLlSktLU0xMjNLT01VUVFTvvDt27NAVV1yhzp07q127durdu7f+8Ic/hLFaAADQWkRaXcD69euVl5en5cuX64orrtDjjz+usWPHat++ferevXud+Tt06KB7771Xl156qTp06KAdO3borrvuUocOHfSzn/3MgjUAAAAtlcMYY6wsYOjQoRo8eLBWrFjhbuvTp48mTJig/Px8n5YxceJEdejQQc8884xP81dVVSkuLk6VlZWKjY0NqG4AABBeodh/W3porKamRrt371Z2drZHe3Z2tnbu3OnTMoqLi7Vz504NHz683nmqq6tVVVXlMQEAAFgahCoqKuR0OpWYmOjRnpiYqCNHjjT42OTkZEVHRysjI0P33HOP7rzzznrnzc/PV1xcnHvq1q1bUOoHAAAtW7M4WdrhcHj8bIyp03auoqIi7dq1S4899piWLFmidevW1Tvv3LlzVVlZ6Z5KS0uDUjcAAGjZLD1ZOj4+XhEREXV6f44ePVqnl+hcaWlpkqQf/vCH+vLLL7VgwQLddNNNXueNjo5WdHR0cIoGAACthqU9QlFRUUpPT1dhYaFHe2FhoTIzM31ejjFG1dXVwS4PAAC0cpZfPj9z5kxNnTpVGRkZGjZsmFauXKmSkhLl5uZKch3WKisr05o1ayRJy5YtU/fu3dW7d29JrnGFHn74Yf385z+3bB0AAEDLZHkQysnJ0fHjx7Vo0SKVl5erf//+KigoUEpKiiSpvLxcJSUl7vnPnDmjuXPn6uDBg4qMjNTFF1+s3/zmN7rrrrusWgUAANBCWT6OkBUYRwgAgJan1Y0jBAAAYCWCEAAAsC2CEAAAsC2CEAAAsC2CEAAAsC2CEAAAsC2CEAAAsC2CEAAAsC2CEAAAsK0mBaF3331Xa9eulSSdOHFChw8fDkpRAAAA4RDwvcYWLFigPXv26OOPP9aUKVP03XffafLkydqxY0cw6wMAAAiZgHuEXnzxRb300kvq0KGDJKlr1646depU0AoDAAAItYCDUHR0tCTJ4XBIkk6ePOn+HgAAoCUIOAjdfffdysnJUUVFhRYvXqysrCzNmjUrmLUBAACElMMYYwJ98P79+/X666/LGKNRo0apX79+wawtZKqqqhQXF6fKykrFxsZaXQ4AAPBBKPbfAZ8sXVBQoOzsbPXp0ycohQAAAIRbwIfGNm7cqF69emnatGkqKCjQ6dOng1kXAABAyAUchJ5++ml98sknmjx5sjZt2qTevXvr9ttvD2ZtAAAAIRXwoTFJioyMVGZmpo4dO6YvvvhC27dvD1JZAAAAoRdwj9Dq1as1btw4DRkyRB9++KEWLlyogwcPBrM2AACAkAq4R2j//v1auHChMjIyglkPAABA2DTp8vmWisvnAQBoeZrF5fNTp07VM888o8suu8xjJGljjBwOh957772gFAYAABBqfgehhx56SJJ0ww036Oabb3a3G2Pcd6IHAABoCQI+NDZ48GDt2bPHo23AgAH64IMPglJYKHFoDACAlqdZHBp74okntHLlSn3yyScaMmSIu/3UqVMaNGhQUIoCAAAIB797hCorK/XVV1/p/vvv169//Wt3e8eOHdWpU6egFxgK9AgBANDyhGL/3eSrxr788ktVV1e7f+7evXuTiwo1ghAAAC1PKPbfAQ+o+OKLL6pPnz66+OKLNWbMGKWlpWn8+PFBKQoAACAcAg5CDzzwgN59911dcskl2r9/v9555x0NHDgwiKUBAACEVsBBKDo62t0tVVNToyFDhrSIK8YAAABqBXyLjaSkJJ08eVLXXXedrrnmGnXu3FkJCQnBrA0AACCkgnKLje3bt6uqqkpjxoxRdHR0MOoKKU6WBgCg5WkW4wh5M2LEiGAsBgAAIKz8DkLn3mPsXNxrDAAAtBR+B6GNGzeGog4AAICw8/uqsZSUFPd05MgRvf3220pJSVFsbKwiIiJCUSMAAEBIBHyO0IIFC7Rnzx59/PHHmjJlir799ltNnjxZO3bsCGZ9AAAAIdOkkaVfeukldejQQZLUtWtXVVVVBa0wAACAUGvSgIqS3CdOnzx5Um3aBLw4AACAsAs4udx9993KyclRRUWFFi9erKysLM2aNSuYtQEAAIRUwAMqfv/99/rHP/6h119/XcYYjRo1Sv369Qt2fSHBgIoAALQ8zWZAxTNnzuiyyy7T3r171adPn6AUAgAAEG4BHRpr06aNhgwZoo8++ijY9QAAAIRNwJfPv/feexo0aJB69uyp9u3byxgjh8PByNIAAKDFCDgIvfTSS8GsAwAAIOx8DkKjR4/WL37xC40dO1aSa4RpSXI6nYwoDQAAWiSfzxHatWuXUlNTJUkHDx50tz/11FOaOnVq0AsDAAAINZ+DUE1NjTp27ChJGjBggD777DNJUmZmpl5//fXQVAcAABBCPh8au+SSS/Tuu++qY8eO+uabb3Ty5ElJUseOHXXixIlQ1QcAABAyPvcITZ8+XXfeeaeGDx+uAQMGaOXKlZKkoqIiJSYmhqxAAACAUPG5Ryg3N1cJCQn69NNP9e///u+aPHmyLrroIpWXl+vee+8NZY0AAAAhEfAtNk6fPq0XXnhBNTU1mjx5cou6coxbbAAA0PI0m1tsSFJkZKR+8pOfBKUIAAAAKwR893kAAICWjiAEAABsiyAEAABsiyAEAABsiyAEAABsiyAEAABsiyAEAABsiyAEAABsiyAEAABsq1kEoeXLlystLU0xMTFKT09XUVFRvfNu3rxZV199tRISEhQbG6thw4bptddeC2O1AACgtbA8CK1fv155eXmaN2+eiouLlZWVpbFjx6qkpMTr/G+99ZauvvpqFRQUaPfu3Ro5cqSuu+46FRcXh7lyAADQ0gV809VgGTp0qAYPHqwVK1a42/r06aMJEyYoPz/fp2X069dPOTk5euCBB3yan5uuAgDQ8oRi/21pj1BNTY12796t7Oxsj/bs7Gzt3LnTp2WcOXNGp06dUqdOneqdp7q6WlVVVR4TAACApUGooqJCTqdTiYmJHu2JiYk6cuSIT8t45JFH9M033+jGG2+sd578/HzFxcW5p27dujWpbgAA0DpYfo6QJDkcDo+fjTF12rxZt26dFixYoPXr1+uCCy6od765c+eqsrLSPZWWlja5ZgAA0PJFWvnk8fHxioiIqNP7c/To0Tq9ROdav369fvrTn2rDhg0aPXp0g/NGR0crOjq6yfUCAIDWxdIeoaioKKWnp6uwsNCjvbCwUJmZmfU+bt26dZo2bZrWrl2rcePGhbpMAADQSlnaIyRJM2fO1NSpU5WRkaFhw4Zp5cqVKikpUW5uriTXYa2ysjKtWbNGkisE3XrrrVq6dKkuv/xyd29Su3btFBcXZ9l6AACAlsfyIJSTk6Pjx49r0aJFKi8vV//+/VVQUKCUlBRJUnl5uceYQo8//rhOnz6te+65R/fcc4+7/bbbbtPq1avDXT4AAGjBLB9HyAqMIwQAQMvT6sYRAgAAsBJBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2BZBCAAA2Fak1QVYqqhIqqqSkpKkrCwpIsLqigAAQBjZOwhde+2/vk9OlpYulSZOtK4eAAAQVhwaq1VWJk2aJG3ebHUlAAAgTAhCtYxxfc3Lk5xOS0sBAADhQRA6mzFSaanr3CEAANDqEYS8KS+3ugIAABAGBCFvkpKsrgAAAISBva8aO5fD4bp6LCvL6koAAEAY0CNUy+FwfV2yhPGEAACwCYJQreRkaeNGxhECAMBG7H1o7JVXGFkaAAAbs3cQysqSYmOtrgIAAFiEQ2MAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2CEIAAMC2mkUQWr58udLS0hQTE6P09HQVFRXVO295ebmmTJmiXr16qU2bNsrLywtfoQAAoFWxPAitX79eeXl5mjdvnoqLi5WVlaWxY8eqpKTE6/zV1dVKSEjQvHnzNGDAgDBXCwAAWhOHMcZYWcDQoUM1ePBgrVixwt3Wp08fTZgwQfn5+Q0+dsSIERo4cKCWLFni13NWVVUpLi5OlZWViuXu8wAAtAih2H9b2iNUU1Oj3bt3Kzs726M9OztbO3fuDNrzVFdXq6qqymMCAACwNAhVVFTI6XQqMTHRoz0xMVFHjhwJ2vPk5+crLi7OPXXr1i1oywYAAC2X5ecISZLD4fD42RhTp60p5s6dq8rKSvdUWloatGUDAICWK9LKJ4+Pj1dERESd3p+jR4/W6SVqiujoaEVHRwdteQAAoHWwtEcoKipK6enpKiws9GgvLCxUZmamRVUBAAC7sLRHSJJmzpypqVOnKiMjQ8OGDdPKlStVUlKi3NxcSa7DWmVlZVqzZo37MXv37pUkff311zp27Jj27t2rqKgo9e3b14pVAAAALZTlQSgnJ0fHjx/XokWLVF5erv79+6ugoEApKSmSXAMonjum0KBBg9zf7969W2vXrlVKSooOHToUztIBAEALZ/k4QlZgHCEAAFqeVjeOEAAAgJUIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYIQgAAwLYirS6gRXI6paIiqbxcSkqSsrKkiAirqwIAAH4iCPlr82Zpxgzp8OF/tSUnS0uXShMnWlcXAADwG4fG/LF5szRpkmcIkqSyMlf75s3W1AUAAAJCEPKV0+nqCTKm7u9q2/LyXPMBAIAWgSDkq6Kiuj1BZzNGKi11zQcAAFoEgpCvysuDOx8AALAcQchXSUnBnQ8AAFiOIOSrrCzX1WEOh/ffOxxSt26u+QAAQItAEPJF7bhBkyZ5P1m6NhwtWcJ4QgAAtCCMI9QYb+MGRUR4Xh2WnOwKQYwjBABAi0IQakjtuEHn9gKdOeP6mpcnjR/PyNIAALRQHBqrT2PjBjkc0qZNhCAAAFowglB9GDcIAIBWjyBUH8YNAgCg1eMcofqEa9wg7mQPAIBl6BGqTzjGDdq8WUpNlUaOlKZMcX1NTeXmrQAAhAlBqD4REdLSpa7vzw1DwRg3iDvZAwBgOYJQQyZOlDZulLp29WxPTna1BzpuEHeyBwCgWeAcocZMnOgaKyiY5/H4c0XaiBGBPw8AAGgQQcgXERHBDSRckQYAQLPAoTErcCd7AACaBYKQFbiTPQAAzQJByAqhviINAAD4hCBklWBckeZ0Stu3S+vWub5ylRkAAH7hZGkrNeWKtM2bXZfgn331WXKyq6cp0Mv6AQCwGYcx3gazad2qqqoUFxenyspKxcbGWl2O/2oHYzx309UeVmvKGEcAADRTodh/c2ispWEwRgAAgoZDY8EQjBun+roMBmMEACBoCEJNtXGjNH26dOzYv9r8PVfHn/N9GIwRAICg4dBYU8yeLf3kJ54hSHIFGl9vnOrvzVcZjBEAgKDhZOlAT7basEG68caG5+nWTTp4sP7DZE6nlJpa/6Euh8PVM3T2MmofU1bm/Twhb49proJxSBEAYBucLN1cOJ2uw2GNqT1Xpz7+nO9TKxSDMQY6HlFTxjHavNkV6EaOlKZMcX1NTfWtFw3hwThVAGyAc4QCUVQkVVT4Nm9D5+oEer7PxInSrFnS73/vuXNq00aaObPxc5PO7on59FNp5UpXD1MtX85xaso4RvVd/l97OJDL/+sXrl40xqkCYBfGhiorK40kU1lZGdgC1q41xrUbb3zatq3+5WzbFtgyNm0yxuHwPq/D4fp9fTZtMiY5ueHnczgaXk59z9/Y44wx5vTpxp8/Odk1XyidPu16XdeudX0N9fMFg7dtl5zc8Osd6PMEun0BIISavP/2gnOEAjnGuH2761BOYxISXP+5N3aOkD/n+wRyXlGt+npi/FlOU55f8v21mz9fWrCg8fkCEarejoZ6a5rakxOuQTSbun2b+tycM2ZfbH/4ICQDIgctUrUgTU6UvvRqSMZs2ND4smr/+z73P/D6/vsOtBfJ15obW06gz1/Ln960X/7Sp83hl1D1djTUW9PUnpzGtp3D4fr91q1N7+Fq6vYNVLh6uwLREnsPW5pwbn+2Z4sWih4hglCgGjo85e9O3NuHQLdu3j8EfA0Sa9d6Ps7XHVxjywn0+QOto7Ew6c+Hmi+BIiHBmGef9e8DsqFw1dBz+Rq8Atl2Z+9E/HmNmrp9A9GcD8U154DWWoRz+7M9WzyCUJAE7YX09keVkGDMn//s/7J83VkF+h+7Pz0xDS2nqT0G/vZMJSTU/1r48qF29uv6hz8EHibqE2hPW+0Hfbdunuvn7X0QyLar3Yn88pf+ffD7un23bm34dfGVL+H03Nco1Gq3QV5ew6+t3XeewehZ8Xf7+/qc3uZrroHbl3WiF8uNIBQkAb2Q9b0RA32DNuVxyckNnyztbccRSK+Ct+X48/z1reOmTU0LY7XLaOxDzZcTw30JEw19QAba0+Zt/eoLdgsXNv05fF2vxrZv7dS1a3B2HFYdiquPr+8ZKwJaMPnbk+otVJz7OnXq5Hqv+vOa+LP9fe3N8TZf167GdO4cnO0ZzODy5z8bEx/vWUt8vDHz5//rsRs2BK8Xqyn7na1bjbn/fte0dasx1dWeyzr35xD9bRCEgsTvFzLY3alNXZ6/5xUZ4/sO7uzpF78I/PkbW0d/du61h6rO/oNr7L/Izp39W9eGpoQE13N6E2hP29nT2rWNH2qNjQ3Oupy7Xt4OAzZWi7f3mr8fsLXz33uv769RqPmy3udO3gJaKP7Db2z+2t8/+6yr57Ohw7v+fP54m7ehQFH7e18/y3z9+8nL8603x99/srxtz4Zea19eO19f35kzm1arL71YZ6/LwoWB7Xc2bfK+zdu0afjnxoJxQ69zA79rtUFo2bJlJjU11URHR5vBgwebt956q8H5t2/fbgYPHmyio6NNWlqaWbFihV/P59cLGezu1GAtz5/zihp77oamhi6hr+/5GztnZuFC1we1rzv3hISGfw7HFB/v/bUIRo/Q1q1N67kKxnT2B2J9H3zetme3bq7/av35gA2kpy7UPUKBHuJ89tnG1y3QHaWv8zf0enp77ob+NseOdQWp6urAPi/OXl4wz39r6G++9n1YXe3b+7ahKS+v4YsefOmFbug1qz3n8brrgvN327mzf6cONFR7fcsIRo2+9NrVvs7eesm6dnXtN9auNZWvvGJaXRB6/vnnTdu2bc0TTzxh9u3bZ2bMmGE6dOhgPv/8c6/zf/bZZ6Z9+/ZmxowZZt++feaJJ54wbdu2NRs3bvT5OX0OQsE+fyEUy/O3K3LTJldS9/VN3FA93p6/KefMNPfJ2wdGID1t527vrVubx7rVnlMUjJ60+j5gA9m5RkQEdt6dPwINtAkJnoEk0B2lv6+XP9urdrn+/G22aWPMD37QtPeAL59lGzb49hr78nwPPxy6vw2p8UNrycmuHXZj7+WMjODWt3Bh3dfVn7+z+vY7p083PVie+x5s7D3tw7IqJdPqgtCQIUNMbm6uR1vv3r3NnDlzvM4/e/Zs07t3b4+2u+66y1x++eU+P6fPQSjY5y80l/Mh/N3x+lNPMHpImutU3wdGQ4cK6/sjP3vH58/htbOvbKvtSQrWIUCHw/VBHarXq6knlofyZNZnnw28LofD+3kc586XnOz/icGNvV6+bi+rAndDnx2+vh+uuca355owoWnv1WC+98M5depU97BSMIZKCfa5ibW9dk38RzkUQcjSe43V1NRo9+7dys7O9mjPzs7Wzp07vT7mnXfeqTP/mDFjtGvXLn3//ffBLTDQW2CEa75AjRjhGhTPV/7UE2jtbc55KyYkBLacUDLG+/3jJk50DWjYtatne3KytGmTa/L2u9pBEJOS/Kvh2DHX8q66qvH7zvnDmODeT+zc16uxe+s1Ji8vdPc7O3YssMcZ4/o6fXrj9w08fNi/ewv68nr5+nqUlroGMw23hj4PfH0/7Njh23P94Ae+zedNsN/74XTihOdnUqB/Z2dvK6fzX58twVJaKi1f3rTPgBCx9F5jFRUVcjqdSkxM9GhPTEzUkSNHvD7myJEjXuc/ffq0KioqlORlp1JdXa3q6mr3z5WVlZJcI1Q2yNdRK2NjpcaWFYrlNUV+vjR1avDrCXSkzzNnXDUlJEgXXih98YX0s58FtixJOv986auvAn98Qw4ckAYP9mwbPVr6f/9P2rlTOnLEtQ6Zmf8aGbe+31VVSQMGSF26uNbZ3xpGj5bWrJH+8z89H9+li/TjH0uPPtr09W2q2loPHAh8GbUh4dVXXSMOB1uHDoE/tjacBkswXi9vzvoMDJuGPjt8XT9fPns6d3b9U/Hss77Xdrbx46WXXgrssc3B2Z9Jgb5vzt5WRUWugBVs+/c3eRG17wZT+09IMAStbykAZWVlRpLZuXOnR/vixYtNr169vD6mR48e5sEHH/Ro27Fjh5FkysvLvT5m/vz5Rv/XncbExMTExMTUsqcDBw4EJ4gYYyztEYqPj1dERESd3p+jR4/W6fWpdeGFF3qdPzIyUp07d/b6mLlz52rmzJnun0+ePKmUlBSVlJQoLi6uiWuBpqiqqlK3bt1UWloavPvGICBsi+aDbdG8sD2aj8rKSnXv3l2dOnUK2jItDUJRUVFKT09XYWGhbrjhBnd7YWGhxo8f7/Uxw4YN01/+8hePti1btigjI0Nt27b1+pjo6GhFR0fXaY+Li+NN3UzExsayLZoJtkXzwbZoXtgezUebc88rbcqygrakAM2cOVNPPvmknn76ae3fv1/33XefSkpKlJubK8nVm3Prrbe658/NzdXnn3+umTNnav/+/Xr66af11FNPadasWVatAgAAaKEs7RGSpJycHB0/flyLFi1SeXm5+vfvr4KCAqWkpEiSysvLVVJS4p4/LS1NBQUFuu+++7Rs2TJ16dJFjz76qH784x9btQoAAKCFsjwISdL06dM1ffp0r79bvXp1nbbhw4drz549AT9fdHS05s+f7/VwGcKLbdF8sC2aD7ZF88L2aD5CsS0cxgTzGjQAAICWw/JzhAAAAKxCEAIAALZFEAIAALZFEAIAALbVaoPQ8uXLlZaWppiYGKWnp6vo3BtlnuPNN99Uenq6YmJidNFFF+mxxx4LU6Wtnz/bYvPmzbr66quVkJCg2NhYDRs2TK+99loYq23d/P27qPX2228rMjJSAwcODG2BNuLvtqiurta8efOUkpKi6OhoXXzxxXr66afDVG3r5u+2eO655zRgwAC1b99eSUlJuv3223X8+PEwVdt6vfXWW7ruuuvUpUsXORwOvfjii40+Jij77qDdrKMZef75503btm3NE088Yfbt22dmzJhhOnToYD7//HOv83/22Wemffv2ZsaMGWbfvn3miSeeMG3btjUbN24Mc+Wtj7/bYsaMGea3v/2tee+998zf//53M3fuXNO2bVuzZ8+eMFfe+vi7LWqdPHnSXHTRRSY7O9sMGDAgPMW2coFsi+uvv94MHTrUFBYWmoMHD5p3333XvP3222GsunXyd1sUFRWZNm3amKVLl5rPPvvMFBUVmX79+pkJEyaEufLWp6CgwMybN89s2rTJSDIvvPBCg/MHa9/dKoPQkCFDTG5urkdb7969zZw5c7zOP3v2bNO7d2+PtrvuustcfvnlIavRLvzdFt707dvXLFy4MNil2U6g2yInJ8fcf//9Zv78+QShIPF3W/zv//6viYuLM8ePHw9Hebbi77b43e9+Zy666CKPtkcffdQkJyeHrEY78iUIBWvf3eoOjdXU1Gj37t3Kzs72aM/OztbOnTu9Puadd96pM/+YMWO0a9cuff/99yGrtbULZFuc68yZMzp16lRQb7BnR4Fui1WrVunAgQOaP39+qEu0jUC2xcsvv6yMjAw99NBD6tq1q3r27KlZs2bpu+++C0fJrVYg2yIzM1OHDx9WQUGBjDH68ssvtXHjRo0bNy4cJeMswdp3N4uRpYOpoqJCTqezzt3rExMT69y1vtaRI0e8zn/69GlVVFQoKSkpZPW2ZoFsi3M98sgj+uabb3TjjTeGokTbCGRbfPrpp5ozZ46KiooUGdnqPiosE8i2+Oyzz7Rjxw7FxMTohRdeUEVFhaZPn64TJ05wnlATBLItMjMz9dxzzyknJ0f//Oc/dfr0aV1//fX64x//GI6ScZZg7btbXY9QLYfD4fGzMaZOW2Pze2uH//zdFrXWrVunBQsWaP369brgggtCVZ6t+LotnE6npkyZooULF6pnz57hKs9W/Pm7OHPmjBwOh5577jkNGTJE11xzjX7/+99r9erV9AoFgT/bYt++ffqP//gPPfDAA9q9e7deffVVHTx40H2jcIRXMPbdre7fvPj4eEVERNRJ80ePHq2THGtdeOGFXuePjIxU586dQ1ZraxfItqi1fv16/fSnP9WGDRs0evToUJZpC/5ui1OnTmnXrl0qLi7WvffeK8m1MzbGKDIyUlu2bNGoUaPCUntrE8jfRVJSkrp27aq4uDh3W58+fWSM0eHDh9WjR4+Q1txaBbIt8vPzdcUVV+iXv/ylJOnSSy9Vhw4dlJWVpcWLF3MEIYyCte9udT1CUVFRSk9PV2FhoUd7YWGhMjMzvT5m2LBhdebfsmWLMjIy1LZt25DV2toFsi0kV0/QtGnTtHbtWo67B4m/2yI2NlYffvih9u7d655yc3PVq1cv7d27V0OHDg1X6a1OIH8XV1xxhb744gt9/fXX7ra///3vatOmjZKTk0Nab2sWyLb49ttv1aaN564zIiJC0r96IxAeQdt3+3VqdQtReznkU089Zfbt22fy8vJMhw4dzKFDh4wxxsyZM8dMnTrVPX/tJXj33Xef2bdvn3nqqae4fD5I/N0Wa9euNZGRkWbZsmWmvLzcPZ08edKqVWg1/N0W5+KqseDxd1ucOnXKJCcnm0mTJpmPPvrIvPnmm6ZHjx7mzjvvtGoVWg1/t8WqVatMZGSkWb58uTlw4IDZsWOHycjIMEOGDLFqFVqNU6dOmeLiYlNcXGwkmd///vemuLjYPZRBqPbdrTIIGWPMsmXLTEpKiomKijKDBw82b775pvt3t912mxk+fLjH/Nu3bzeDBg0yUVFRJjU11axYsSLMFbde/myL4cOHG0l1pttuuy38hbdC/v5dnI0gFFz+bov9+/eb0aNHm3bt2pnk5GQzc+ZM8+2334a56tbJ323x6KOPmr59+5p27dqZpKQkc/PNN5vDhw+HuerWZ9u2bQ1+/odq3+0whr48AABgT63uHCEAAABfEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAtHjr1q1TTEyMysrK3G133nmnLr30UlVWVlpYGYDmjnuNAWjxjDEaOHCgsrKy9Kc//UkLFy7Uk08+qb/97W/q2rWr1eUBaMYirS4AAJrK4XDo17/+tSZNmqQuXbpo6dKlKioqIgQBaBQ9QgBajcGDB+ujjz7Sli1bNHz4cKvLAdACcI4QgFbhtdde08cffyyn06nExESrywHQQtAjBKDF27Nnj0aMGKFly5bp+eefV/v27bVhwwarywLQAnCOEIAW7dChQxo3bpzmzJmjqVOnqm/fvrrsssu0e/dupaenW10egGaOHiEALdaJEyd0xRVX6Morr9Tjjz/ubh8/fryqq6v16quvWlgdgJaAIAQAAGyLk6UBAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBtEYQAAIBt/X/nLuOuGeokhgAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter1_17_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -577,36 +564,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The intercept alpha: \n",
-      " [1.89563529]\n",
-      "Coefficient beta : \n",
-      " [[5.26512016]]\n",
-      "Mean squared error: 0.27\n",
-      "Variance score: 0.87\n",
-      "Mean squared log error: 0.01\n",
-      "Mean absolute error: 0.41\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter1_19_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np \n",
     "import matplotlib.pyplot as plt \n",
@@ -819,29 +777,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter1_33_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.0049999999999999845\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1188,18 +1124,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'                                                                                                                         \\nThis is taken from the data file of the mass 2016 evaluation.                                                               \\nAll files are 3436 lines long with 124 character per line.                                                                  \\n       Headers are 39 lines long.                                                                                           \\n   col 1     :  Fortran character control: 1 = page feed  0 = line feed                                                     \\n   format    :  a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5                     \\n   These formats are reflected in the pandas widths variable below, see the statement                                       \\n   widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),                                                            \\n   Pandas has also a variable header, with length 39 in this case.                                                          \\n'"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"                                                                                                                         \n",
     "This is taken from the data file of the mass 2016 evaluation.                                                               \n",
@@ -1234,21 +1159,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "Length of colspecs must match length of names",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [8]\u001b[0m, in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Read the experimental data with Pandas\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m Masses \u001b[38;5;241m=\u001b[39m \u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mread_fwf\u001b[49m\u001b[43m(\u001b[49m\u001b[43minfile\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43musecols\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m6\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[43m              \u001b[49m\u001b[43mnames\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mN\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mZ\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mA\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mElement\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mEbinding\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      4\u001b[0m \u001b[43m              \u001b[49m\u001b[43mwidths\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m13\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m9\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m9\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m12\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      5\u001b[0m \u001b[43m              \u001b[49m\u001b[43mheader\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m39\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      6\u001b[0m \u001b[43m              \u001b[49m\u001b[43mindex_col\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;66;03m# Extrapolated values are indicated by '#' in place of the decimal place, so\u001b[39;00m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m# the Ebinding column won't be numeric. Coerce to float and drop these entries.\u001b[39;00m\n\u001b[1;32m     10\u001b[0m Masses[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEbinding\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mto_numeric(Masses[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEbinding\u001b[39m\u001b[38;5;124m'\u001b[39m], errors\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcoerce\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/util/_decorators.py:311\u001b[0m, in \u001b[0;36mdeprecate_nonkeyword_arguments.<locals>.decorate.<locals>.wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    305\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(args) \u001b[38;5;241m>\u001b[39m num_allow_args:\n\u001b[1;32m    306\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\n\u001b[1;32m    307\u001b[0m         msg\u001b[38;5;241m.\u001b[39mformat(arguments\u001b[38;5;241m=\u001b[39marguments),\n\u001b[1;32m    308\u001b[0m         \u001b[38;5;167;01mFutureWarning\u001b[39;00m,\n\u001b[1;32m    309\u001b[0m         stacklevel\u001b[38;5;241m=\u001b[39mstacklevel,\n\u001b[1;32m    310\u001b[0m     )\n\u001b[0;32m--> 311\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/io/parsers/readers.py:871\u001b[0m, in \u001b[0;36mread_fwf\u001b[0;34m(filepath_or_buffer, colspecs, widths, infer_nrows, **kwds)\u001b[0m\n\u001b[1;32m    869\u001b[0m                     len_index \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(index_col)\n\u001b[1;32m    870\u001b[0m         \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(names) \u001b[38;5;241m+\u001b[39m len_index \u001b[38;5;241m!=\u001b[39m \u001b[38;5;28mlen\u001b[39m(colspecs):\n\u001b[0;32m--> 871\u001b[0m             \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mLength of colspecs must match length of names\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    873\u001b[0m kwds[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcolspecs\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m colspecs\n\u001b[1;32m    874\u001b[0m kwds[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124minfer_nrows\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m infer_nrows\n",
-      "\u001b[0;31mValueError\u001b[0m: Length of colspecs must match length of names"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Read the experimental data with Pandas\n",
     "Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11),\n",
@@ -5129,7 +5040,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
index 3d8c9ceb8..32c9f88d0 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb
@@ -537,27 +537,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "inputs = (n_inputs, pixel_width, pixel_height) = (1797, 8, 8)\n",
-      "labels = (n_inputs) = (1797,)\n",
-      "X = (n_inputs, n_features) = (1797, 64)\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# import necessary packages\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1200x1200 with 5 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_39_1.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -635,16 +628,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Number of training images: 1437\n",
-      "Number of test images: 360\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.model_selection import train_test_split\n",
     "\n",
@@ -858,24 +842,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "probabilities = (n_inputs, n_categories) = (1437, 10)\n",
-      "probability that image 0 is in category 0,1,2,...,9 = \n",
-      "[5.41511965e-04 2.17174962e-03 8.84355903e-03 1.44970586e-03\n",
-      " 1.10378326e-04 5.08318298e-09 2.03256632e-04 1.92507116e-03\n",
-      " 9.84443254e-01 3.11507992e-04]\n",
-      "probabilities sum up to: 1.0\n",
-      "\n",
-      "predictions = (n_inputs) = (1437,)\n",
-      "prediction for image 0: 8\n",
-      "correct label for image 0: 6\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# setup the feed-forward pass, subscript h = hidden layer\n",
     "\n",
@@ -1065,30 +1032,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Old accuracy on training data: 0.1440501043841336\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "New accuracy on training data: 0.09951287404314545\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# to categorical turns our integer vector into a onehot representation\n",
     "from sklearn.metrics import accuracy_score\n",
@@ -1321,15 +1265,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Accuracy score on test set:  0.9444444444444444\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "epochs = 100\n",
     "batch_size = 100\n",
@@ -1370,718 +1306,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.11666666666666667\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.20833333333333334\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.12222222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.14722222222222223\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.17777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.16111111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.20277777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.5305555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.5944444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.5888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.6111111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.5222222222222223\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.5555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.8055555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.85\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.85\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.875\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.8666666666666667\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.8638888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.9555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.925\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9472222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.9277777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.9472222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9305555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.9555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.7694444444444445\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.19166666666666668\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.08611111111111111\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.08611111111111111\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.09166666666666666\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n",
-      "  exp_term = np.exp(self.z_o)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n",
-      "  self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.07777777777777778\n",
-      "\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "eta_vals = np.logspace(-5, 1, 7)\n",
     "lmbd_vals = np.logspace(-5, 1, 7)\n",
@@ -2123,52 +1348,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7604/953065564.py:4: RuntimeWarning: overflow encountered in exp\n",
-      "  return 1/(1 + np.exp(-x))\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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Xq3K10jp9Kk0/zlujudOXFbh9QIC/ut93rbrc0kilo4vp2NFk/fbTJs2dvlzZ2dbc7dp2qqu7+rdVxaqllJaSqfWr9mjau0t06mSqEV/rqsIqWO5BAmKAui1q6qU5Q/Tn/FX6fOx81W9dW/1G3ymTn0lzJvxwwX2r1a+kMV8PVUBg3j+qrg901KCJ92nu2z9q/W9bVadZdT306t0KDjVr7luuJTdFQd2m1fTi9IH68/v1mjH+R9VrXl39RnSVn59Jc977+YL7VqtbXi9//rACAv3zvFeqXHG9tXCoDu5O1BtPfC5zcKD6De+qV2c9pkc7vy5LRpanvlKhU7dFDb00Z7BjDL8yX/Vb11K/F+6Uyc/PtTH81ZMFjOHrNOjt+zR34iLnMRwW5FtjuFl1vTjjUf357VrNeP071WtZU/1G3eYYw+/83wX3rRZbQS9/+Vi+Y7h46QhFlSmmKaO/1vY1e53eS05Kcet3KOyIsWfVbVpVL057UH/+sF4zxi9ynIeH3Sw/k0lz3r/wxaBqdcvr5U8fyhPfpMTTGnr7xDzb39Kvrdrf0kQ/z13h1u9Q2MU2qqSX3umtPxZv1ecf/Kp6jSur/+PXy89k0uxpf+a7zyPDblSXWxvry0/+0L9bD6lmTHn1feQ6lSlXXBNf/laS1K5zrJ4ff7d+nLdan33wq0qUDNN9j16vNz/ur8fvmaIsS7aRXxM+ggTEAH1G3a49m/dr/EOfSJLW/rJF/gH+umvozZr//uJ8f5ENCPTXbQ931n3P31HgL7p3Db1Zf3yzSp++NE+StOGPbapYM1q3P9zZp355u3fojdoTd0gThnwhSVr7+zYFBPqr5+OdNf+T3wqO7/3t1XdY1wLj2/fpm5WekqFne72vzJxtjh44oRenP6RaDStp66o9nvtShUyfkTlj+OGpkqS1S7fIP9Bfdz3pwhh+rlvBY/jJm/XH/PPGcI2yuv2hTr41hp/pqj1bD2rCE59Jktb+FqeAAD/1HHSD5n+0tOD4PnCd+o64TZYMS76fW6N+JUnS3z9uyDO752uIsWfd+2TOefjJLyVJa//Y7jgPP9ZJ8z/5XZbMAuLbv536PnNzvvHPsli1fX28U1uthpXU/pYm+vzNH7V19d48+xRl9z50nfbsOKLxL8yXJK35e5cCAvx11/1t9c3Mv2XJdE4UIiJD1LVHM0179xfNm/GXJGnDKkfMBg79n6ZPWqLTSWm6Z2AHrVz2rya9+t/FpAN7j+u9Lx9Wy/a1tfyXOIO+IXwJ94B4WKA5QA3a1tFf3611al/+7RqFRoSo/rW1892v+f8a6t6Rt2vOhB80ffTX+W7z/J1va9ror5zasizZCgzynbwy0Byghq1r6a+fNjq1L/9xg0LDg1W/RY1892t+fazuHXqT5k76WdNf+y7fba69qaEWz1mRm3xI0s5NB9Sn2Qs+lXzkjuHv1zm1O8Zw8IXH8IjbNOetHzX9xQLGcPeJmnbe+M7KsvreGL62lv76cb1T+/If1jvGcMua+e7XvHN93ftMV8199ydNH7sw322q16+oM6fSfPoXY4kYe1qg2V8NW9XUX/+3yan9v/Nw9Xz3a94xVvc+eaPmvrdE08d979KxHh/bQwd2HdWCqb9fabevKoGB/mrYrKqW/7rNqX3ZL1sVGhak+k2q5NknNDxIP85boxV/bHdqP7T/uCQpukIJmUwmrV+5Rz/NX+O0zcGcUtnyFaPc+TWKBKtMhfLnakMC4mHRVUvLHBSoQ7uOOrUf3uN4XaFmdL77/btur/o1GKY5E36Q9Zw6zXMd+DdBiQccJ4nwEmG68b726ty7jb7/5Fc3foPCLbpySQUGBejQnkSn9sP7jkmSKlQvne9+/27cr36tX9Kc937ON75lK0UpvFiojh48qcfG9tTczeP07a639NKnD6l0+RLu/yKF2H9j+IhT++GcmFeoUTbf/f5dt1f9Gg7PGcO2fLfJO4bbqXOva/X9J7+58RsUbtFVSikwKFCHdp83hvfmjOEaZfLd79/1+9Sv2fOa887/FXiOqFG/klJOp+n56Q9p3s63NX/PRI2c8oBKlIl075co5IixZ0VXLpVzHj7m1H443vGL7gXPw9eO0Zz3lxR4jjjXdbdfozqNq+ijlxbI5mNroUZXLCGzOUCH4p3voTuccz9SxSol8+xz9PApvT/uRx08b58218cqKytbh+JPyG636+O3F+uf33c4bdP2+rqSpH3n/e4CuIvXLzNmZ2fr559/1po1a3T48GFZLBaFhIQoOjpazZo1U5cuXRQQ4PVuXrbw4qGSpLQz6U7taWcyJEmhEcH57nci4ZTLx4htWVNvL3lOkuOXPl+6gTcsMkTSf/E8Ky0lU5IUGl5AfI+cvuDnFisZLkkaMOo27dgQrzce/1zFSoXr/pG36o2vBunRLq8rMz3/koyiJrzY2TF8XozPjuGcP4PzXfIY/vlZSY5f+r6d4kNjuFjOGE45fwyfPUcUEN+LjGFJql6vokqVK67/m7lcC6b8qsq1o9Vn+C16c+FTeqLza8pM840xTIw9K/c8nCe+FzkPH714fM/V/aGO2rp6jzav2HUZvby6hef8rpCWmunUnpYzvkLDglz6nLad6qpT14ZaOGulUs47p59VvnKUHnzyf9oZd1ir//K9WMMYXv3Nfv/+/Ro4cKCOHj2q2NhYlSlTRsWKFVNmZqa2bdumb775Ru+9956mTp2q8uXLe7Orl81kckyL2e35X62xu+EqzpH44xp20+sqWb6E+j7bTe/98aIGXzdGp3xg9RU/v5xpxwLCaCsg7hcTmHPD9KnjZzR24LTcP7+Efcc18bundP2dzfTTl39f1mdfbUx+Bo3hm19XyXI5Y/j30Rrc8RXfGMOms2M4/zjabBe/MlyQt5+coayMLO3eclCStHXlLsVvP6y3fhimzj1b6cfP879xtaghxp7133m4gPhe5nn4XLHNqqlmg0p6+YGpV/xZV6OL/S7hSozbdo7ViFe7a/PaeE2flP/CAJWqldK4D+9TVpZVrwybW+DxfJnNfvWVOxVGXk1AXn75ZVWsWFHz5s1TREREnveTk5M1dOhQjRkzRh999JEXenjlUk+nScp7he3szEdqcnqefS7VySOndPLIKUnSjjW7NW3967qxX/uLrk5UFKTkxO/8maTQcMfVoLTk/K/wXMzZK3mrf4tzOgFvX7dPZ06lqUa9ipf1uVeji4/htCs+htMYXrtH09aN870xHH7+GM654nmZY1hSnlWZJClu9R6lnE5TtXoVLvtzrzbE2LMKju+VnYfP1fbmRjpzKlWrf/PNG6JTz844nzfTERpqlvTfbFNB7uzTWg8++T9tWrNPLw2draysvCWFjZpV1Qtv9VJ6aqZGPvq5jh4+5Z7OA/nw6j0ga9eu1fDhw/NNPiQpMjJSw4YN0+rVqw3umfsc3psoa7ZV5as71xiXr+6om9+//fBlfW5IeLA63tVK5c773IS9x5RyKk2lK/jGjWMJ8cdlzbaqXNVSTu3lqzpqjvfvPJLfbq59rtWmQHPeHD0g0N/pxvSiruAx7Hh9RWO454XGsG/ca5Ow75hjDFc7L77VcsbwvwmX9blhkSH6X+/Wqlw7731mAYEBSvah9f2JsWcVeB6u4nh9uefhc7XoVE//LN7i0r0iRdHhg0mO83Al53s9yldy/Fsff959kOd6bMTNevjpG7X8lzi9MGimMvIpH+54YwO9OrmvTiQma2j/aXnuGwHczasJSGRkpBITC/5LI0mHDx9WcHD+9aNXg6zMbG3+61+1ua2pU3vb25vpTFKqdqy9vNWUbFabhr4/QD2H3OTUXvuaaoqMCteeLQcuu89Xk6zMbG1euVttbmrk1N62a2OdOZWmHRviC9jzwjLSLNq6yvG55yYhjdvUVkhYkLau2n1F/b6aZGVma/Pf/6rNrdc4tbe9vZnOnErVjrWXtxSmYwzfn88Yrup7Y3jFLrXp2tipve0tTRxjeP2+y/rc7KxsPf56b/UcdINTe+ubGik41KxNf/97mT2++hBjz8o9D9+Yz3n4dJp2bNh/RZ8fXixUFaqV1tY1vrP64PmyLNnavC5ebTrVdWpv17meziSna8eWQ/nud/+gzrq9V0t9M/NvvTby63xnPpq3raVhr9yhuI0HNPT+aTqeWPRLX6+Et1e7KiqrYHm1BKtHjx4aNWqUBg8erJYtW6pcuXIym82yWCw6evSoVq1apQkTJqhHjx7e7OYVmz3+e4377hk99/ljWjxzmWJb1lSPITdq+uivZcnIUmhEsCrHlFfCnmM6feKMS5+ZmW7RV+8s0j3Db9WZk6la//tWVagZrT6jbtfuTfv188yCn4xa1Mx5d7Fem/O4nv3ofv08d4XqNq2m7o9cr+mvfeeIb3iwKteOVsK+4zp90vUHg3067nu9+fVgjZnxsL6Z8quKl4rQgGdv0/Z1+7Ti580e/EaFz+zx32vct8/ouc8f1eIvljvG8OAbNf3Fef+N4TrllbD3csdwitb/HqcKNcuqz8izY3i5h79V4TFn4k967evBevaTB/Xz7H9Ut3l1dX+8i6a/svC/MVynnBL2HdPpE66N4cz0LM374Gfd83RXnTp2Rmt/26qqsRXU55lbtHLJZm34c/vFP6QIIcaeNee9JXpt1qN69sP++nnuStVtWlXdH+6o6eO+lyUzS6HhQapcK1oJ8cd1+hJnhqrFlJMk7d/p2ysyzZr6p17/6D499+ZdWvztOsU2qqwe/a7VtHd/kSUzW6FhQapcvbQSDp7U6aQ0Va8drbv6t9GOrYf0589bFdPAuXR4/55jysqyaujo25SWZtGcqX+qcjXnFcuOH00mIYFHeDUBGTRokPz8/PTGG28oLS1vHXlYWJjuvfdeDRkyxAu9c5+Nf27T2D4fqO+z3TR61iCdOJykqc9/pfnvL5Yk1WxURW8uGqm3HpmqJbP+cvlzvxz3rZKOntYtD16vbo910ZmkVP25YLU+f2W+sjJ958mlG//eqVcfmq4+T9+k0VMH6viRU5o29lvN/9ixlGuNBhX15teD9dbQmfrl61Uuf+72dfs04q731G/ELXru4weUmW7RP4s3a+orC31uCciNf27X2L6T1XfU7Ro96wmdSDilqS987TyGfxyhtx6ddmlj+PXvlJR4Wrc8cL26PXrOGB67wLfG8PIdenXAx+oz/BaN/uxhHT9yWtNenq/5Hy2VJNVoWElvLnhKbw3+XL9cwtOfZ47/UUnHzqhr//a6dUAHnUlK1aIZyzRzfNG/t+Z8xNizNv69U68+/Kn6PHWTRn/ygI4fPaVpr36n+Z/8LsmxXPGbXz2ht56apV/muX4elhxPm5eklNNXfr/Z1Wzj6r165Zm56vtIR734dm+dSEzW1HeW6JsvHAui1Iwpp/FT79eE0Qu05PsNatuprvz8/FSnXgW9O2Ngns8b9uCnMvmZVLK0Y8nocR/1y7PNFx/9pplTfvfo94JvMtkLwRIHWVlZ2rZtm44ePar09HQFBwcrOjpaMTExMpvNbjvOjZH3u+2zkJcpMv97eeA+9jOuz+Dg0pmCXVvKEijUghjHnmQrWczbXSjyFq9/2dtdKNDq/VW93YV8Na+8z9tduCSF4gEbgYGBatiwobe7AQAAAMDDeBI6AAAAAMMUihkQAAAAoLDjQYTuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAuuxof+FUbMgAAAAAAwDAkIAAAAAMNQggUAAAC4wGrn2r07EEUAAAAAhiEBAQAAAGAYSrAAAAAAF9i4du8WRBEAAACAYUhAAAAAABiGEiwAAADABTyI0D2YAQEAAABgGBIQAAAAAIahBAsAAABwAQ8idA+iCAAAAPgom82mSZMmqV27dmrUqJEGDBig+Pj4Arc/cOCAHnnkEbVo0UJt2rTR2LFjlZ6efknHJAEBAAAAfNTkyZM1Z84cjR07VnPnzpXJZNLAgQNlsVjybHvmzBn17t1bp0+f1tSpU/XRRx9py5Ytevzxxy/pmCQgAAAAgAtsMhXKn8tlsVg0ffp0DRo0SB06dFBMTIwmTpyoo0ePasmSJXm2X7BggVJSUvTBBx+oYcOGatCggSZOnKi///5ba9ascfm4JCAAAACAD9q+fbtSU1PVqlWr3LbIyEjFxsZq9erVebbfu3evqlevrqioqNy2cuXKqUSJElq1apXLx+UmdAAAAOAq1qlTpwu+v3Tp0nzbjxw5IsmRRJyrTJkySkhIyLN96dKldezYMVmtVvn7+0uSUlJSdPr0aZ04ccLl/jIDAgAAALjAKr9C+XO5zt48bjabndqDgoKUmZmZZ/uuXbvq9OnTeu2115Samqrk5GS9+OKLMplM+d4zUhBmQAAAAICrWEEzHBcTHBwsyXEvyNn/l6TMzEyFhITk2b5KlSp67733NHr0aH355ZcKDg5W3759Vb9+fYWHh7t8XBIQAAAAwAedLb1KTExU5cqVc9sTExMVExOT7z4dOnTQH3/8oWPHjikiIkLBwcG69tprdeedd7p8XEqwAAAAABdY7X6F8udyxcTEKDw8XCtXrsxtS05OVlxcnJo1a5Zn+7Vr16pPnz6yWCwqXbq0goODtWrVKiUlJenaa691+bjMgAAAAAA+yGw2q0+fPpowYYKioqJUoUIFjR8/XtHR0erSpYusVqtOnjyZO9NRo0YN7dy5U6+99poeeOABHThwQMOHD1evXr1UqVIll49LAgIAAAD4qMGDBys7O1vPP/+8MjIy1Lx5c02bNk1ms1kHDx5Up06dNG7cON15550qXry4Pv74Y40bN0633nqrSpQooV69eunRRx+9pGOa7Ha73UPfp9C5MfJ+b3ehSDNFRni7C0We/UyKt7tQpJmCg7zdBeDKBTGOPclWspi3u1DkLV7/sre7UKBv9zT2dhfydXv1Dd7uwiXhHhAAAAAAhiEBAQAAAGAY7gEBAAAAXGC1m7zdhSKBGRAAAAAAhiEBAQAAAGAYSrAAAAAAF1i5du8WRBEAAACAYUhAAAAAABiGBAQAAACAYbgHBAAAAHCBzc61e3cgigAAAAAMQwICAAAAwDCUYAEAAAAuYBle9yCKAAAAAAxDAgIAAADAMJRgAQAAAC6w2k3e7kKRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAtsXLt3C59KQLa/H+PtLhRp5jCLt7tQ5FlSKni7C0VaVOkz3u5CkZeZ5VP/7HhF6qkQb3ehSHu4+R/e7gJw1SONAwAAAGAYLkUBAAAALrDauXbvDkQRAAAAgGFIQAAAAAAYhhIsAAAAwAU28SBCd2AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFrILlHkQRAAAAgGFIQAAAAAAYhhIsAAAAwAVWrt27BVEEAAAAYBgSEAAAAACGoQQLAAAAcIHNzoMI3YEZEAAAAACGIQEBAAAAYBhKsAAAAAAXsAqWexBFAAAAAIYhAQEAAABgGEqwAAAAABfY7Fy7dweiCAAAAMAwJCAAAAAADEMJFgAAAOACq3gQoTswAwIAAADAMCQgAAAAAAxDCRYAAADgAlbBcg+iCAAAAMAwJCAAAAAADEMJFgAAAOACVsFyD2ZAAAAAABiGBAQAAACAYSjBAgAAAFzAKljuQRQBAAAAGIYEBAAAAIBhKMECAAAAXGClBMstiCIAAAAAw5CAAAAAADAMJVgAAACAC2w8iNAtmAEBAAAAYBgSEAAAAACGoQQLAAAAcAGrYLkHUQQAAABgGBIQAAAAAIahBAsAAABwgc3OKljuwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAusXLt3CxIQg3QoX01PN26nWsVL6URGmmb9u0GTt6y44D4dK1TXkEZtFFO8tJIyM/R/+3fozfV/Kj07K8+24YFm/d+tA/TOxuWat3uLp75GodWubA09We861YworZOZqZqzd52m7PjrgvtcF11TT9Rtr9rFyuhUZroWH96mt7f8pnTrf/H9q+tQlQ4Oz7PvtT+8reOZqW7/HoVZh/LV9HSTc8bwDhfHcONzxnD8RcbwbQP0zgbfHMPXlqqlx+p0VrXw0jplSdO8/av06e4/L7hP29K19VCt61UzoqxOW9K09MhWvf/vEmWcM4ZvrdBEfau3VaXQKB3PTNGPh9Zr6q7flW23eforFTpty9TUoLrXq0Z4aSVZUjV33xpN3bn8gvu0L1tLj9W5TrUiy+iUJV1LDsfp3W1LlW7NUvmQ4lryvycL3HfB/vV6fv23bv4WhRfnCM87uC5N62ed1KkDFgUX81edGyLV4M7iMpnyvy/BZrVry8JT2rn0jNJPZiuiXKAadi+ham3z/rt21qrpxxX3/Wn1X1DDU18DIAExwjWlK+iTjt31w75temvDMjUrU1HPNGkvk8mkDzb/k+8+nSrW0MfX3an5e7bqjXV/qFaxUhrWpL2igkM1ZNn3TtsWMwdr6vXdVTG8mBFfp9BpElVRH157t346sFXvbP1dTUtW0tB6HWWSSR/tyP+Xi47lamly67u0MH6TJmz5VTUjS+mpetcryhymp1cvkCSVDApT6eBwvbbxZ60/edBp/1OWdI9/r8LkmtIV9Mn1OWN4/TI1K1tRz1zjwhjumDOG1/6hWsUZwwVpWLySJja7Vz8nbNHkHb+ocVQVPV67s/xk0rTdf+S7T/sydfRW03v146ENem/Hz6oeXlqP1+6iEkFhem7D15Kk3lVba1hsVy1J2KJ3tv+fSgSG6eHa16tmRLSeWTfLyK/odY1LVNL7LXvrp0Nb9N62X3VNVGUNqdtJfiaTPv53Wb77XFe2tia17KXvDmzUxLhfVCOitIbU7aSooDANX/uNjmWeUe8/p+bZr3e15rqpQn3Nj1/v6a9VaHCO8LzE7Rn6dVyCqrYJV5N7opS4LV3rvjwpu01q1LNEvvtsmHNSm+efUqO7SqhMTLDi/0nVH28dlclPqnpt3iTkyNZ0bfvxtKe/CkACYoQnG7VRXNJRPfXXj5KkPw7vVaCfnx6t31JT41Yr05qdZ5/RzTvpp/3/atjfiyRJ/xzZL3+TSf3rNlWwf4AycvbpUqmmXmzeWWGBZuO+UCHzRGx7bT91RMPWOK40Lju6WwF+/nqozrX6dOcKZdryxve5hv/T4kPbNWqt4x+5Fcf2yc/kp/tqNM+Nb2zxaEnSz4e363Cab5+Qc8fw8nPGsMlPjza4wBhukTOG/3JhDLforLAA3x3DD9e6XjuSj+iFjfMkSX8f36kAk5/612ivmXv/yncMP123q5Ye2aqXNs2XJK0+sUd+Jj/1qtJawX6Bstiy9VDNjvrn2C6NWD8nd7+45EP6pv0QtSxVQyuP7zbmCxYCj8V00PbTRzRqneMCw/LEXQrw89ODtdrq813/5BvjEQ1u1JLD23JnMVYe3ys/k0n3Vm+pYP9AZViztCnJ+eJEveLldVOF+nonbqnWndzv+S9WSHCO8LwNc08qqmqQ2j9ZVpJU8ZpQ2azS5vlJqndbMQUE5S0N2rn0jKq1C1fju6MkSeUbherE3kxt/+l0ngQkK8Omv95LVEgJf6WdsHr+C12lWAXLPShk8zCzn79alq2kxfv/dWpfFL9D4YFBalGmYp596kWVUZWIEvp8+1qn9k+3r1WHBR/nnpQjA4P0UYc7tPLoft33y1ee+xKFWKCfv1qWqqKfD213al98KE7hgUFqVqpynn3qFotW5fAozdy1yql9xq5V6rz4g9z41i1WVqct6T6ffJj9/NUyupIWxxcwhsteYAxvO28Mb1urDvPPG8PX3aGVR3x7DDeNqqZfj8Q5tf9yZKvCAoLUJKpqnn3qRJZTpbAozd3nXN4ye98/uv2Pt5Vhy1JUULiKmUP1Z6Lz3429KceUlJmqdqXruP27FFaBfv5qXrKqfknY5tT+8+E4hQUEqWnJKnn2iSkWrcphUfpyz0qn9pl7VuqmXyY5lbmd64WGXbXnzDHN2J3/Vf+iiHOE51mz7DqyJV2VW4U5tVdtHabsDLuObsvIdz9bll3mEOdf9YIj/JV5Jm8J5prPTiikRIBqXR/pvo4DBWAGxMMqRRRXkH+A9iQnObXvO+N4XS0ySssS9jm9F1vCcXUjw5qtadd3V5voKsq0WrVg71aNW/ObMm2OKxPp1ix1+W6a9iSfVMUw3zxhVA4rIbN/gPalnHRqj0/JiW9ElP5K3OP0Xt3i/8V3yrV3q3WZasq0Zuu7/Zv1xuZfZMmJb93i0UrOytD7rXqqdZmq8jP56feEnXpt0886lpFiwLcrHFwaw4f3Ob0XG3XeGC6XM4b35DOGv/XtMVwxJEpm/wDtTz3u1H4g9YQkqUpYSa04vsvpvTqR5SRJGbYsvdusj5qXrCGLLVuLDm3QO9sXy2LLVkpWhrJsVpUPKe60b0RAsCICg1UhNP+SjaKoUujZ88QJp/b9qY7zRtXwkvr7mPNsUEwxxwxopi1bH7S8R61KO84TPxzcpAlbl8iSz4xJ1woN1KBEBfVf/plssnvo2xQ+nCM878yRLNmypWLlA53aI8o5XicfzlKFxnn3i72tuDbPT1LF5mEqExOsA6tTdWh9mpr2iXLa7vCGNO3+/Yxufaui9izznX/f4D0kIB5WLDBIkpSSlenUnpplkeS4qe58UcEhkqQp192h7/bGaerW1WpYKlpDG7VVqeBQPfHnd5KkLJtNe5JP5tnfl0ScjW/2efHNeR0eEJRnn6igUEnSB6176vsDWzV95wo1KFFeg2M7qGRQmJ5c5ShpqVu8rMqGROqrvev12c4VqhFZSoNjr9PM9vep29JPnG5WL8qKmS9jDAfljOGOd+i7PXGaGrdaDUtGa2hjxvD5IgKDJeUdw2lWR3zDAoLz7FPC7BjDb11zr/7v8EZ9secv1SteQQ/X6qQoc7hGbpirDFuWliRs1t1VWmlPSqJ+PRKnqKBwDYu9Wdl2m0L8faecpaAYp2afjXE+5wmz40rzuy3u1qKDm/X57r9Vv3gFPR5znaKCwvTMmnl59ulf81qtO7Ffq0/sc/M3KNw4R3ieJdUxYxEY6jybEZgzu5GVlv+iEnW7FtPRben65ZWE3LZanSJU/47/LkBYUq3664Njatw7SsUq+M554XLZKB5yCxIQDzu7MoW9gIth9nyukgX6+UuSFu//V6+vc9yA+s/R/fIzmTTimuv09oblnJBz+OXGN/8A2/JpPxvfJYd3aMKWpZKklcfi5SeTnmnQSe/G/aG9KSc0cs13yrRate30EUnSmhMHtDP5mOZcd7+6VWmo2XvW5vnsosiki4zh/GLsn88YPpIzhpsyhs/13+o1ro/hAJPj1P3b0ThN2vGzJGnNyb0yyU+DY/6nD3cuVXzqcb265TtZbFa90KCbXmx4p9KzLfp8zzIF+5uVnpPg+IKLnScudB5emrBdb8f9IkladXyf/EwmDY3trPe3/+Y0o9IkqpJii5fTEytnu7v7hR7nCM/LjWFBtx/k027Nsuun5w4pPcmq1o+UUrEKZh3dlqFN85IUEOynlg+WkiStmn5CoSX9Ve9W373B39fZbDa9//77+vrrr5WcnKymTZvqxRdfVJUqectTJenYsWMaN26c/vrLsdpoq1atNGrUKEVHR7t8TNI4D0u2OK4IRZx3BejsTeNnLJl59jl71ejXg84lAX8c2itJio0q4/Z+Xq3Oxjc80PkK5tkrmmey84lvzlXP3xJ2OrUvO+qI99kSrQ0nD+UmH2etO3FQyZYMxRQr64beXx2Sc65qRpgLGMNZjOErcSbLUbt9/lX40JwZipTsvLXdaVZHzJcl7nBq//uYowa/TqTjH4F0q0VjNi9Qu5/Hqsefk9Rp6Th9vOs3lQsprtNZvrOSW3JOjPOeJ86O4bwxPjuL+scR5/salh91lMPFRDr/Q/u/8rE6bUnXsqPO5xVfwDnC88xhjoTt/JmOrHRbzvt5f52L/ydFSfssaj+0jOrcUEzR9UPUqGcJNetXUtt+PK2k+EwdWJ2qvctTdO1jZWS3O5btVc4hbFa77DbfKSX0ZZMnT9acOXM0duxYzZ07VyaTSQMHDpTFkv+FqqFDhyohIUGffvqpPv30Ux05ckSPPfbYJR3T6zMgffv2LXD96vPNmDHDw71xv/1nkpRts6lKpHO9ddUIx+udp0/k2WdvTt2sOecK0VkBfo4TTEZ23tpjX7U/9aSybTZVDneuZ60S7ojvruRjefaJz7lfpMD4WrMVERik/5WP0YaTh7T7jHNtfqCfv5Iy09z2HQq7/ck5YziigDF8Kp8xnFMLbvYrOMZwOJh2Utk2qyqFlnRqrxTmeL0nJTHPPvtz7g/JG1/H67PxbVemjpKz0rUxaX/u55Qwh6lscKS2nz7s3i9SiB1IdYzhymHO54mzr3efucB5ooAxfP6qWR3K1tbShO0++XwVzhGeFxEdIJOfdCbBufT37OviFfOWTqUcc8SwTIxzGWd0PcfrUweydHBdmqwWu74dciDP/jN67FGNjhFqN5hk8FzWIrYKlsVi0fTp0zVs2DB16NBBkjRx4kS1a9dOS5YsUdeuXZ22T05O1urVq/Xhhx8qNjZWkvTQQw/pscceU1JSkkqUcO3+Qq/PgLRu3VqrV6/WiRMnVKFChQv+XI0ybVatOnpAN1au7dR+c5U6Op2ZoQ3HE/Lss+roAaVmWXRbtVin9s6VainLZtW6Y4c82uericVm1erj8fpf+Rin9hsqOK5GbjqZ95es1cfilZpt0S0V6zu1X1+ujrJsVq0/cVBZNqteanKzHq7TxmmbzuXrKCQgUKuOx7v/yxRSHhnDiYzhsyy2bK0/Ga/ro8+LVXQ9JWela+upg3n2WXdyn9KyM3VD+YZO7R3KxCjLZtWmU47lX3tUbq6hMTc6bXNv1WtltdvzzJ4UZRZbttaeiFfncnWd2s/OWmxOyjse156IV1q2RTdXbODU3jHacZ7YcPK/X9iKBYaoSnhJrfehZXfPxTnC8wLMfiobG6z4FalOJW37/kmVOcxPpWrlvY+pWAXHDernr5CVuD1nRrBMgBr3KqFbxldw+qndJUKSdMv4Cmrcy3cWq/BV27dvV2pqqlq1apXbFhkZqdjYWK1evTrP9kFBQQoNDdXChQuVkpKilJQUffvtt6pataqKFXO9jM/rMyCPPfaYQkNDNWnSJE2ZMkUVK+Zdru9q997mv/Vll176oP3t+nrXZl1TpoIeqtdSr6/7XZnWbIUHmlWrWCnFn0nSycx0pWVn6e0Ny/VC8+t1OjND/7f/XzUtXUGP1GupT7et1clM3ymdcMWH25frs3Z99G7L7vpm3wY1KVlJD9ZurfFblirTlq2wALNqRpbW/pQkJVnSlGbN0qS43zWq4f+UnJWunw9tV5OSlTSwzrWasWuVkiyO2Y1P/v1bT9Rtr+OZKVp2ZLfqFCurQbHt9VvCv/o7ca+Xv7Wx3tv0t778Xy990CFnDJeuoIfqt9Tra10Yw5YM/V/8v2papoIeqc8Yzs/U3b/rwxb99UaTXvr24Fo1Kl5Z91Vvq0nbf84Zw0GqHl5aB9JO6pQlTelWiz7cuVRP171ZZ7LS9euRODUsUVn9a7TT7H3/6FTOGJ69b4Umt+ivZ+rerD8St6t5yeoaULODpu/+Q4fSky7Sq6Jlyr9/auq19+ntZj01f/96NYmqpPtrttHbcUtyY1wjorQOpJ7MOU9Y9P723zS8/g1KzkrXksPb1CSqkh6o1VYz96zMPU9IUq1IxxXi/GZSfAXnCM9r1LOEFr+UoN/HH1WtThFK3JGpLQtPqVnfKAUE+cmSZtOpAxZFRgcquJi/KjUPU6naQVo28WjuDebH/nXcA1KpeahK13bMhESUcV5Z68Aax9guVTPvAhgoeo4ccZSalytXzqm9TJkySkjIe/EgKChIr776qsaMGaNmzZrJZDKpdOnSmjlzpvz8XJ/XMNkLuivPYA8++KCKFy+uCRMmeOwYVWe84bHPvpgbKtXSk43bqnpklI6mpWjGjnWaGufILFuVraQ5N9yjZ/76UfN2b8ndp2eNBnowtrmqRpZQYlqKZu/cqA+3rMj3VtWKYZFa3v3RPJ9hJHOY925q7VK+jgbFdlD18JI6mnFGX+5eo+k7Hc9IaFGqimZ2uE8j1nyrBfGbcve5s0ojDajVSlXDo3Q044y+2rteH+/4Kze+Jkn3VG+m3tWbqnJ4CZ3KTNf3B7ZoUtwf+T60zAiWFO+tUHJD5Vp6slFbVS+WM4a3nzeGb7xHzyw/bwzXPG8M/3uRMdzj0TyfYaSo0me8clxJ6li2rh6p1UlVwkopMTNZX8Wv1My9jhv8mkZV0yetHtCLG7/R94f+e7r2bRWvUZ9qbVQ5tKSOZZ7R/AOr9dnuZU43Vd9QrqEerNlB5UNL6Ej6KX0Vv0pz41fkOb5RMrO8d92rU7kYPV6no6rlnCdm712lz3Oe19G8ZFV91ra/nlu3UAsPbMjdp1vlxupf41pVCYtSYsYZfR2/VtN2/uUc4/L19Hbznrpl6fvam3L8/MMaLvVUiFeO6wvnCEl6uPkfXjt2/IoUbZiTpNOHLAotGaCYm4qp/u3FJUkJW9K1+IXDajOodO6zPCxpNq378oTi/0lVZopNEWUDVOO6CNW7rbj8A/MvJVo/56Q2zk1S/wU1jPpaeYyKXeS1Y1/MkPW9vd2FfG15Jm+57rmWLl2ab/u3336r4cOHa9u2bU4JxPDhw5WYmKjPPvvMaXu73a533nlH//77rx588EFZrVZNnDhRKSkpmj17tsLDw+WKQpOAHD16VHFxcerYsaPHjuHNBMQXeDMB8RXeTEB8gTcTEF/hzQTEV3grAfEV3kxAfAUJyKW73ARk8eLFGjx4sDZu3Kjg4P9mvYYMGSKLxaIPP/zQafsffvhBL7/8sn777bfcZOP06dPq2LGjhgwZon79+rnU30LzL0HZsmVVtqzvrCwEAAAAuENBCcbFnC29SkxMVOXKlXPbExMTFRMTk2f7tWvXqlq1ak4zHcWKFVO1atW0b98+l4/r9ZvQAQAAgKuBze5XKH8uV0xMjMLDw7Vy5crctuTkZMXFxalZs2Z5ti9Xrpzi4+OVmfnf8trp6ek6ePBggc8NyQ8JCAAAAOCDzGaz+vTpowkTJmjp0qXavn27hg4dqujoaHXp0kVWq1XHjh1TRoZj9bRu3bpJkp588klt3749d3uz2aw777zT5eOSgAAAAAA+avDgwerRo4eef/559e7dW/7+/po2bZrMZrMSEhLUtm1bLVrkuC+nTJkymjVrlux2u/r166f7779fgYGBmj17tiIjI10+ZqG5BwQAAAAozKwqWg8ilCR/f38NGzZMw4YNy/NexYoVtWOH83OjatSooY8++uiKjskMCAAAAADDkIAAAAAAMAwlWAAAAIALbPaiV4LlDcyAAAAAADAMCQgAAAAAw1CCBQAAALjgSh76h/8QRQAAAACGIQEBAAAAYBhKsAAAAAAX2Irggwi9gRkQAAAAAIYhAQEAAABgGEqwAAAAABdYeRChWzADAgAAAMAwJCAAAAAADEMJFgAAAOACHkToHkQRAAAAgGFIQAAAAAAYhhIsAAAAwAU2VsFyC2ZAAAAAABiGBAQAAACAYSjBAgAAAFxgEyVY7sAMCAAAAADDkIAAAAAAMAwlWAAAAIALWAXLPZgBAQAAAGAYEhAAAAAAhqEECwAAAHCBzc61e3cgigAAAAAMQwICAAAAwDCUYAEAAAAuYBUs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFNlGC5Q7MgAAAAAAwDAkIAAAAAMNQggUAAAC4gFWw3IMZEAAAAACGIQEBAAAAYBhKsAAAAAAXUILlHsyAAAAAADAMCQgAAAAAw1CCBQAAALiAEiz3YAYEAAAAgGFIQAAAAAAYxqdKsJZ1esfbXSjSrHZv9wC4Mlliat3T/MWJwtPK+Qd7uwtF2kFrpre7AC+iBMs9mAEBAAAAYBgSEAAAAACG8akSLAAAAOBy2SjVdQtmQAAAAAAYhgQEAAAAgGEowQIAAABcwCpY7sEMCAAAAADDkIAAAAAAMAwlWAAAAIALKMFyD2ZAAAAAABiGBAQAAACAYSjBAgAAAFxACZZ7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4AJKsNyDGRAAAAAAhiEBAQAAAGAYSrAAAAAAF9gpwXILZkAAAAAAGIYEBAAAAIBhKMECAAAAXGATJVjuwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAt4EKF7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4AIeROgezIAAAAAAMAwJCAAAAADDUIIFAAAAuKAoroJls9n0/vvv6+uvv1ZycrKaNm2qF198UVWqVMmz7Xvvvaf3338/38+58847NW7cOJeOyQwIAAAA4KMmT56sOXPmaOzYsZo7d65MJpMGDhwoi8WSZ9sBAwZo+fLlTj9PPvmkgoOD1a9fP5ePSQICAAAA+CCLxaLp06dr0KBB6tChg2JiYjRx4kQdPXpUS5YsybN9WFiYSpcunfuTnp6uKVOmaOTIkYqJiXH5uCQgAAAAgAvsdlOh/Llc27dvV2pqqlq1apXbFhkZqdjYWK1evfqi+7/++uuqVauW7r777ks6LveAAAAAAD7oyJEjkqRy5co5tZcpU0YJCQkX3Hfz5s1aunSpPv/8c/n5XdqcBgkIAAAAcBXr1KnTBd9funRpvu3p6emSJLPZ7NQeFBSk06dPX/AzP/vsMzVq1Mhp9sRVJCAAAACAC4raKljBwcGSHPeCnP1/ScrMzFRISEiB+6WlpWnJkiV68cUXL+u4JCAAAADAVaygGY6LOVt6lZiYqMqVK+e2JyYmXvCm8mXLlslms6lLly6XdVxuQgcAAAB8UExMjMLDw7Vy5crctuTkZMXFxalZs2YF7rd27VrVq1dPkZGRl3VcZkAAAAAAF9jt3u6Be5nNZvXp00cTJkxQVFSUKlSooPHjxys6OlpdunSR1WrVyZMnFRER4VSitX37dtWuXfuyj8sMCAAAAOCjBg8erB49euj5559X79695e/vr2nTpslsNishIUFt27bVokWLnPY5fvy4ihcvftnHNNntRS2XK9iBQ+UuvhEum9VnRhKKqiwVrZsLCyN/caLwtHL+wRffCJftoDXT210o8mpVPOztLhSo+U/PersL+Vp902ve7sIloQQLAAAAcIGNC1VuQQkWAAAAAMOQgAAAAAAwDCVYAAAAgAvsRexBhN7CDAgAAAAAw5CAAAAAADAMJVgGWbXKX59ND1Z8vJ+KFbPrltss6t3bIlMBM3kWizTj8yAt/SVQp0+bVKmyTXfdlalOnbOdttu/30+fTAnSxo0B8g+wq2EDqx5+NEPly/vWUperV/nr80+DtT8nvl1vtejui8R35gxHfJNz4tujZ6auPy++vXqEKykpb54+++sziooixu6I8f79fpr2cZA2bQyQv79dDRpa9dAjGSrnY2N47Sp/ffFpkA7E+ymymF033ZqlnheIb5ZF+nKGWb/nxLdiZZvu6GlRx/Pi26dHmE7lM4a/+DpFJXxsDK9Z5a8Z54zhm2+16K6LjOEvZwTp13Ni3D2fMXxPAeeJL33sPPHXSpM+mOavPfEmlSgu9bjNqgH32C4Y348+89ePS/x06rRUtbJd991tU9cuNqftfl1m0idf+GvffpNKRUld/2fVA/faFBjo+e9U2HCe8D4bJVhuQQJigK1b/DX6+VBdd12W+g/I0JbNAfp0WpDsNunePpZ893n1lRCtWBGgnndZ1OSabO3a6a+Jb4fo9OlM3dndsU9ioklDBoeqUkWbnn0uXZmZ0qfTgzRyeJg+mZaioCAjv6X3bN3qr5deCFWH67LU7/4Mbd0SoM+mB8lml+65N//4jhsbopUrAtTjLosaN8nW7l3+eneiI7535MQ36aRJSUl+evjRDNWNtTrtHxnpWydkT8U4MdGkpwaHqmIlm0Y8my6LRfp8epBGjQjTlKm+M4a3bfXTKy+EqN112ep7f6bitvjri+lm2e3S3QXE942xwVq9IkB33GVR4yZW7d7lpw8mBiv5dKZu754lyTGGTyX56cFHMxRz3hiO8LExHLfVXy+/EKr212Xpvpwx/HnOGO5dQIxfHxuiVSsC1P2cMfzexBAln85Ut/POEw/lE2NfOk9s2GLSkOcCdENHmx5/wKr1m/30/lR/2WzSwL62fPcZMSZAy/4x6b67bWpxjU3bd5k09i1/nTot3dvDsc8/a0x6erTjcwc/ZNWuPSa994m/kk6ZNOpJa76fW1RxnkBRQgJigBkzglSjhk0jn82QJLVoYZXVKs2ZHaQePS15fsnaudNPf/0VqAEPZOT+cte0qVXBIXZ9MiVY/7vBovBw6fPPghQaIr05IU3BOc+dii5n0+jnQ/XvDn81aOgbJ+cvZwSpeg2bho9yxLd5C6uys6WvZgepe4+88d21009//xWo/gMycn/xuKapVcHBdk39OFhdcuK7a5fjalCbdlkqW9a3T8KeivEXnwcpNFR6ffw5Yzjaphdf8K0xPGtGkKrVsOnpnPg2zYnvvNlmdcsnvrt3+mnFX4G6b0Cm7sqJb+OmVgUHS59+HKRON2QpPFzakzOGr22XrTKMYVWvYdOwnBg3y4nx17ODdGcBY/ifvwLVb0CGeuXEuEnOGJ72cbA654zh3bkx9u3zxJTP/VWnpl2vPuf4O9umpVXZVunTWf7qe5dNwefFd/tOk35b7qcnHszWg30cyUarZnaFBEvvfOSvW2+wKTJC+vYnP0WXkV59zip/f6l1M7tOJpk0c56fnnnCqkAf+i2G8wSKEu4B8TCLRdq00V9t22U5tbdrn6X0dJM2b/LPs8/+/Y4/llatnadIGzW0KiPDpA3rA2S3S8uXBeqmmy25v7hJUp06Ns39OsVnfnG7WHy3bHY9vg0aOeK7cYPjX7Q9u/0VHm736V8qJM/F2G6X/loWqBtuch7DtevYNPsr3xnDWRZp80Z/XdvOOVZt2mcrPd2krfnE90BOfFucF9/6OfHddM4YDgu3+/wvFWfHcJvzxnDbC4zhszFuyXnioiwWac0Gkzq1c57p6NzBprR0k9Ztyluysife0dbhWue4NW1kV3qGSWs2ON7PyjIpJMQu/3P+iIoXsysry6S0NDd/kUKM80ThYbcXzp+rDQmIhyUk+Ckry6SKFZ1PzBUqOF4fPJj3j6B4McdIOnrE+b3Dhx2vjxzx05EjJqWmmlS2rF2T3g3WHd3CddMNEXr+2RAdPeo79YlHcuJb4bz4lr9AfIsVEN+Es/FNcPx39y5/hUfYNebFEN1xW4Ru7xqh114J0YkTvhNfyXMxPnp2DEfb9f67werRLVy33Bih0c+FKNHHxnD2BeJ76ILxdY7TkcOO10cTHP/ds8tP4RF2vfpisO66LVw9uobrjVeCddIHx/Dlxzj/MXz0vPPEKy+GqPttEbqja4TGvRLiUzE+mOBIFKpUcv4tqHIFx+v9B/LGokRxx3uHj5z3WYcd/z2UM4Z73WHV/oMmfTbHT8lnpE1bTfpynr/atrKpWKSbv0ghxnkCRY3XE5C9e/fqvffe09ixY/XHH3/keT8lJUWjRo3yQs/cIzXF8Rc4NMz5xBwa6vhvWlrev+ANG1lVrpxNH7wfrHXr/JWaKm3e5K+pnwTJz8+ujAzp9CnHflM/CdLx4yY991y6nn4mQ7t3++uZp8KUnu7Z71VYpJyNb2gB8U0tOL6TPwjW+nPiO+2c+ErS7t1+On7MpNp1rBozNk0PP5qhTRv9NWxoqDJ8JL6S52J86rRjv2k5Y3jU8+ka+rRjDA9/OsxnYpyS4vjv+fENyYlvej7xrd/IquhyNn38QbA2rPNXWqq0ZZO/Ps2Nr2Ofvbv9dOKYSbXq2DR6bLoefDRTmzf6a6SPjeHUyxjDDXJi/NE5Y3jLJn9NP+88seec88TLY9M08NEMbd7or+E+FOMzOfENC3VuDw1x/Dcln5mKZo3sqljerjcmBWjlWpNSUqV1m0x6d0qA/PzsSs+Jb7PGdvXvZdM7HwWo/a1m3fd4oKJK2DXu+ey8H1qEcZ5AUePV6sm1a9fqgQceUNmyZWW32/Xll1+qc+fOeuutt2Q2myVJGRkZWrhwocaNG+fNrl42W865oqAVKvJrDwyUXn8zVRPeDNHwZ8IkSSVL2vT4Exka+0qIgoOlrGzHjsVL2PXSy+ny85Mkq8pXsGnwE2Fa+kugbrk1K++HFzH2i8TXL58UOzBQevWNVL09PkQjhzniG1XSpscez9BrY0Nyy4GeHpYhs9mumrUcV5gaNLSqSlWbnhoSpiVLAnXrbUU/vpLnYpyd5fjAEiXsGn3eGH5ykGMMd/WJMZwT2ILOEQXEd8wbaXp3fLCeH+b4DSSqpE0PPZ6pN8cGKzjY8Yc2ZFiGzGapRs4Yrt/QqspVbRo+JFS/LgnUzT4yhs+ehwuK8YXG8MTxIXr2nDH8yOMZev2c88RTwzIUeM55on7OeeKZIWH6ZUmgbvGBGNtyLsoXeI4o4N+5yW9m6aU3A/Tw047lrEqXtGv4oGyNGBOgkJz4jn3bX9/+5KeBfa1qcY1Nh46Y9NGn/np8eICmvJ2du11Rx3mi8OBBhO7h1QTkrbfeUo8ePfT8889Lkn766Sc999xzeuSRRzRlyhQFFoE19sJzZj7Ov8J2tnY1LCz/wr0KFeya+G6akpJMSk52lHAlJppks5kUEWHPvQrSokW20z+esbFWhYfbtWuXv6Sif9IIC8+Jb1r+8T1/5umsChXseuudNJ3KiW+FijYdOye+khRbL+89CPXqWxUWZtee3b4RX8lzMQ7JGcPNmjuP4bo5Y3i3j8S4oPimX+QcUb6CXW+8k65TSSadSTapfD5juG69vKsPxeaOYa9PgBsm/DLHcPkKdo2/yHmi7gXOE3t9ZAxHhDv+m3reTEdaztXz8PD896tcUZo+KVsnk6RTyVLlCtLRY5LNZlJkhOP/5//gpwfudaysJUnNZVf9Onb1GBCobxf5qded+a+wVdRwnkBR49WRtWPHDvXp0yf39U033aRPPvlE69ev1/Dhw73YM/cpX8EmPz+7Dh1yDvXZ11Wq5v2Ln5kp/bIkUAkJJpUoYVeVKjb5+0s7/3XcZFarllXlyzs+Nyuff9uys6WgoKvwjqTLcDYOh8+L79nXVarkH9+lSwJ1JMGk4iXsqnxefGvWsiolRVr8U6Di9zl/rt3uiO/Z2lpf4KkYX3QMm30jxuVy4pBwyPkXi7PxrVRAfH9bEpAb30o58d2VE98atWxKSZF+/ilA+xnD58Q4/zFcuYAY/3qF54lIH4lxpfJ2+fvZtf+8MXz2dfUqeeOQkSn9+LOfDiVIUSWk6lWkgAApbodjn7q17TqSaJLdblLjBs5/PjWr21U80q7d+3znSjTnCRQ1Xk1AwsPDlZSU5NTWtGlTjR8/XosXL75qy67OZTZLDRtatXx5gNMqBcv+DFR4uF0xMXmvngUESO9NCtaPP5hz26xWaeECsypUsKpqNZtCQqT6DaxavixQlnOW/163zl8ZGSY1aOAbKwiZzY7SqL+W5R/fOgXE94P3grXoR+f4frvQrPI58Q0IkN57N1hz55id9v3nrwBlZprUsJHv1B97KsZnx/Bfy53H8PqcMVzfR1bBMpsdJQ9/Lwt0iu9ffwYoLNyu2gXE96P3gvV/P/43S2y1Sj8sDFS5CjZVyRnDH74brK/PG8MrcsZwg0a+EV+p4DG8/CJjePJ7wfrpvDH8Xc4YPhvjD/KJsa+dJ4KCpGsa2fXrn35O8f3lDz9FhNtVv27eX2IDA6Rx7/rrm+//W73JapXmLPBXpQp21axmV6UKjsRm3SbnX1X27ZdOJZtUvpzv/HLMeaLwsNtNhfLnauPVEqwOHTpozJgxeumllxQbG5tbctW5c2c9++yzGjt2rBISErzZRbe4t0+mhg8L1Ssvh+jGm7K0dau/vppr1oMDMxUUJKWmSvHx/ipf3qbixR3LDd52u0XzvzGrVCmbKlex6dsFZm3Z4q8xY9Nzy1UefDBTTz8VqudGharnXRYlJZn0ySdBiqmbrdbX+sY/fJJ0T59MjRwWqlfHhOiGG7MUF+eveV+Z9cA58d0f769y58T3ltssWjjfrJKlbKpc2abvFpq1dYu/XnrFEd/gYKnn3RbNmhmkEiXsatY8W3v3+OuLGUFq0TJL1zT1rZOyJ2IsSfc/kKnhT4fqhWdD1aOnYwxPyxnD5y/hW5Td3cei54eF6PUxwepyY5a2xflr/ldm9c+Jb1qqtD/eT+XK21UsJ74332bRd/PNKlnKrkqVbfphYaDitvjrhXPGcPe7LZqTM4avaZ6tfXv8NGtGkJq3zFZjHxvDvfpk6tlhoXptTIj+lxPjb74ya4CLY7hSZZu+X2hW3BZ/vXhOjHvcbdHsmUEqXsKups2ztW+Pv2bmnCea+FCMB/a16uGnAzTspQB1u9mqjVv89PkcPw152KrgICklVdqzz6SKFeyKKi75+0t3dbNp1jw/lSllV7Uqds1Z4K8Nm02a+KqjLDOquOOBhDPmOE4YrZvZdPiISVM+91e5snZ1v8U3yq/O4jyBosRkt3tv9eDTp09r6NCh+ueffzRlyhS1b9/e6f1Zs2bptddek9Vq1bZt2674eAcOlbviz7hcy5cF6PPPg3TwgJ9KlrLr9tst6nmX47Lvhg2OlauGDU/XDTc66lGys6UZnwdpyZJAnUk2qUZNq/r2zVSz5s4ng61b/DV9epC2b/NXUJBdbdpm6+FHMgqsufUkqxcvRv21PEBffBakgwcd8b31Not65MR34wbHqkpPD0vX/86J78wZQfrlnPje2zdTTZv9F1+bTfrhu0D98L1ZCYf9FBlpV8frs9S3f6bPPKH7XJ6IseR4yvpn04K0Y7tjDF/bJlsDvTSGswq6w9MAfy8P0KzPzLnx7XqbRXfe5Yjlpg3+evbpUD05LF2db3QkZtnZ0uwZZv2aE9/qNa3q1deia84bw4u+C9Si7wN15LCfIiLt6nB9tu714hj2l/dOFH8tD9DMnDFcqpRdt9xmUfecMbxpg79GPB2mp4alq8s5Y/jLGUFaek6M78nnPPHjd4H6Mec8EZFznujjxRiX8/fOndm/LjPpw0/9te+ASWVKSXd3s+q+ux1Jwur1Jg0cGqiXR2Tr9pscbVnZ0pTP/PXDz346nSzVqWnXQ/2surb5f2PEbpe+nOened/569ARqVSU1Lq5TU88aFVUcW98S+mgNdM7B5bvnCdqVTzsnQO7oMF3L3q7C/nafNvL3u7CJfFqAnLW/v37VaJECUVEROR5b+/evfr555/18MMPX/FxvJmA+AJvJiCAO3gzAfEV3kxAfIW3EhBf4c0ExFcU5gSk3rcvebsL+dp6+0ve7sIl8WoJ1lmVK1cu8L1q1aq5JfkAAAAA4H2srwYAAADAMIViBgQAAAAo7Lx/40LRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgAuuxof+FUbMgAAAAAAwDAkIAAAAAMNQggUAAAC4gBIs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAFPIfQPZgBAQAAAGAYEhAAAAAAhqEECwAAAHABq2C5BzMgAAAAAAxDAgIAAADAMJRgAQAAAK5gGSy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAWsguUezIAAAAAAMAwJCAAAAADDUIIFAAAAuMDOKlhuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAtYBcs9mAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC3gQoXswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAX2HkQoVswAwIAAADAMCQgAAAAAAxDCRYAAADgClbBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcwCpY7sEMCAAAAADDkIAAAAAAMAwlWAAAAIArWAXLLZgBAQAAAGAYn5oBqeAf4e0uAADgUWOO1/V2F4q0Ffc08HYXirz/2+TtHsDTfCoBAQAAAC4fq2C5AyVYAAAAAAxDAgIAAADAMJRgAQAAAK5gFSy3YAYEAAAAgGFIQAAAAAAfZbPZNGnSJLVr106NGjXSgAEDFB8fX+D2WVlZeuutt9SuXTs1btxYffr00bZt2y7pmCQgAAAAgCvshfTnCkyePFlz5szR2LFjNXfuXJlMJg0cOFAWiyXf7V966SXNmzdPr7zyir755hsVL15cAwcO1JkzZ1w+JgkIAAAA4IMsFoumT5+uQYMGqUOHDoqJidHEiRN19OhRLVmyJM/2Bw4c0Lx58zRu3Dhdd911qlGjhl577TWZzWZt2bLF5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fn2X758uWKjIxU+/btnbb/9ddf1bp1a5ePyypYAAAAgCvshfNBhJ06dbrg+0uXLs23/ciRI5KkcuXKObWXKVNGCQkJebbft2+fKlWqpJ9//lkff/yxjh49qtjYWI0cOVI1atRwub/MgAAAAAA+KD09XZJkNpud2oOCgpSZmZln+5SUFO3fv1+TJ0/WU089pQ8//FABAQG65557dOLECZePywwIAAAAcBUraIbjYoKDgyU57gU5+/+SlJmZqZCQkDzbBwYG6syZM5o4cWLujMfEiRPVoUMHLViwQA8++KBLx2UGBAAAAHCB3V44fy7X2dKrxMREp/bExERFR0fn2T46OloBAQFO5VbBwcGqVKmSDh486PJxSUAAAAAAHxQTE6Pw8HCtXLkyty05OVlxcXFq1qxZnu2bNWum7Oxsbd68ObctIyNDBw4cUJUqVVw+LiVYAAAAgA8ym83q06ePJkyYoKioKFWoUEHjx49XdHS0unTpIqvVqpMnTyoiIkLBwcFq1qyZrr32Wo0YMUJjxoxR8eLFNWnSJPn7++v22293+bjMgAAAAACu8PYDBz3wIMLBgwerR48eev7559W7d2/5+/tr2rRpMpvNSkhIUNu2bbVo0aLc7d977z21aNFCTzzxhHr06KGUlBTNmDFDUVFRLh/TZLdfSeXY1cV2pLa3uwAAgEeNOV7X210o0lbc08DbXSjy/m/TWG93oUBVpr3p7S7kK/6B4d7uwiVhBgQAAACAYbgHBAAAAHBFIX0Q4dWGGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5h8Zukmz2IGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAK7gQYRuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgCtYBcstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAKyjBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcYTd5uwdFAjMgAAAAAAxDAgIAAADAMJRgAQAAAC4wsQqWWzADAgAAAMAwJCAAAAAADEMJFgAAAOAKSrDcghkQAAAAAIYhASnEEhKlFl2lVeu93ZOiixh7FvH1PGLsecTYNYfXp2jx8H36qvcOffvwLm2df0J2e8GXi21Wu+Lmn9D3j+/WV/fs0E9P71X8X8l5tjvwT7IWj9inr/v8q28f2qUV7x1W+qlsT36VQqtpm1qaNPtRLVw5Wp//3zO6+4H2F9w+IMBfdz/QXp98O0QLV47W1O+G6J6HOyogwD/f7UPDgvT5T0+ry21NPNF9IBclWIXUoSPSwGHSmRSTmO/zDGLsWcTX84ix5xFj1xzbnqZlrx9U5Wsj1aB3KR3flq5Ns45JNrvq9SiV7z5b5h5X3IITqtezlErXCdGBFWf099uHZfKTKreOlCTt/ztZf711WDX/V1wNe5dWxqlsbZ57XL++uF83jq8qf7PvXEet26iSXpp0r/78vy36/P1fVL9JFfUb1FkmP5PmfPJHvvs8POJmdbmtiWZN+V3/bj2omnXLq8+j16tsueKa+NICp23DI0P08qQ+KluhhBFfBz6OBKSQsdmkhf8nvfmht3tSdBFjzyK+nkeMPY8YX5otX51Q8arBaj2kvCSpfJNwxwzHgpOqc2uUAoLyJgp7fj2tKm0j1eAuR4IS3ShMSXsztPOnU7kJyJavT6j8NWFq/nB07n6RFc36eUS8Dq1Nyd3OF/R55Hrt2X5E45+bJ0la+9dO+Qf46a4B7TV/xl+yZDrPCoVHhqhrz+aa/s7PmvfZcknShpV7JEkPPnWjpr+7WKeT0iRJra6L0aMjb1FIqNnAbwRfdkmXDo4dO6aXXnpJDzzwgEaMGKHPPvtMa9asUXp6uqf653N27JZenih1u0F64zlv96ZoIsaeRXw9jxh7HjF2nTXLpsStaarUMsKpvVLrCGVn2HRsW/6/I1izbAoMdf41JCjSX5lnrJIku82u6EahqtGluNM2EeUcvySnHMly0zco/AID/dWgeTX9tTTOqX35kq0KDQtS/Wuq5tknLCJYP369Wit+3+7UfnDfcUlSdMWo3O1emHiPNq3Zq+ce+cwj/QfOd0kzIM8++6yWL1+uWrVq6eDBg/r+++9lt9vl5+en6tWrq379+mrQoIEaNGigmJgYBQYGeqrfRVa5stLiL6XoMtQbewox9izi63nE2POIsetSjmbJlm1XRHnnq+cR0Y7XZw5bVK5xWJ79Ym6NUtyCkyrfLFyl64To0JoUJaxPVaN7S0uSTH4mXdO/bJ79Dq48I0kqVjnI3V+l0IquGCWzOUCH4o87tR/ef0KSVKFKSa37Z5fTe0cPJemDV7/P81ltOtdTVla2DuUkIpnpWXr4jkk6uO+4ypYv7pkvUITwIEL3uKQEZP369Ro2bJgGDBggSUpLS9PWrVu1efNmbd68WatXr9aCBY6aQrPZrE2bNl30MzMzM7Vz507VrFlTwcHB2rZtm2bOnKmjR4+qVq1a6tevn6Kjoy/6OUVF8UhJvjOj7BXE2LOIr+cRY88jxq7LSrVJkgJDnGczAnJeZ6Vb892v9s0llLgtXX+MPZjbVv36YqrbrWSBxzpz2KL1M46pRPUglW+SN6kpqsIjgiVJaSmZTu1paRZJUmh4sEuf06ZzrDrd0kgLv/xHKWcyJEnZ2dbcWRHAKJeUgAQFBSk2Njb3dWhoqJo3b67mzZvntp06dUqbNm3Sli1bLvp5u3fvVv/+/XXs2DGVL19eY8eO1WOPPaaKFSuqRo0a+uWXXzR//nzNmjVLNWrUuJSuAgAAA+SudGXK/32TKe8b1iybfnl+v9JPZav5w2UVWSFIx7alaes3JxQQ7KemD+Sd+Th9MFO/vXxA/oEmtX2mgkx+BRywCDr7Xe0FLIRgt138snzbLvU0fFxPbV6zT5++87Nb+wdcqku6B6Rz586Ki4u74DbFixdX+/bt9dhjj13089588001adJECxcuVNOmTfXoo4/q1ltv1ffff693331XP/30k9q0aaNx48ZdSjcBAIBBzKGOJV2z0m1O7dk5r8+/z0OSDqw4o1Pxmbp2SHnV/F8JlakXqno9SqnxfWX076IknYrPcNr+6OZULXk2XiY/6fqXKim8rG/dLJ2aM1sRGuZcdhaac9N4akpGnn3OdWffazXqzbu1dX28Xhw0U1lZ+c9KwQV2U+H8ucpcUgLSvXt3/fTTT9q1a9fFN3bBqlWr9OSTTyomJkYjRoxQZmamevfunXu1JCAgQI888ojWrl3rluMBAAD3Co8OlMlPSkmwOLWfOeJ4XaxS3ns1Uo85VmwqFRPi1F6mXqgk6fTB/z5r37LT+n3sAYVGBajLa1UUWcF37v046/CBk7JmW1W+snN52tnX+3cnFrjvoyO76qFhN2v5kq0a/dgMZaRbCtwWMMolJSB33XWXtmzZop49e2rUqFFatGiR4uPjL/vgwcHByshwZO2lSpXSXXfdpaAg5xNLcnKyIiIi8tsdAAB4mb/ZT6VjQ3Vg5RmnBw8e+OeMAsP8FFUz7/0JkRUcV+7PXyHr+HbHsrDhZRyL2Bxem6IVkxJUqk6IOr9aRaElfXNxmyxLtjavi1ebTrFO7W271NOZ5HTt2HIw3/3uH9xFt9/TWvNn/KVxw+cy84FC45LuARk7dqy2bdumrVu36qefftKCBQtkMpkUFham2NhY1a9fX8OHD3f589q2batXXnlFY8eOVY0aNTRmzJjc9+x2u1atWqWXX35ZnTt3vpRuAgAAA9XrUVK/vXxAf711WNWvL6bjO9K17duTatyntAKC/JSVZtXpgxaFlw1UcLEAVWgWrpK1gvXPu4fV4O5Siqxg1omdGdr6zfGc90Jktdi06sMjCgjxU2z3Uko+5HzlPrRkgE8lJLM//l3jPu6v5yb00uKFaxXbqLJ69G+r6e/8LEtmtkLDglS5RmklHDip00lpql4nWj0HtNO/Ww7qz583K6ZhRafP27/7mNJSMws4GgrEKlhucUkJSI8ePXL/32azaffu3dq6dau2bNmiuLg4zZkz55ISkFGjRumRRx7R5MmT9dZbbzm9t2jRIj399NNq166dnnrqqUvpJgAAMFB0gzC1HVZBm+cc17I3DikkKkCN7yuturc5SoRO7snQry8eUMvHo1X9+uLy8zep4+hK2jjrmLbOO6HMFKvCywaqXvdSqnOr4/kUx3akKz3JUar1+5gDeY5Z/66SanB3aeO+pJdtXLVHY5+arb6PddLod+7VicRkTX17sebP+EuSVLNueb05/QG99fw3WvLderXpVE9+fn6qXb+i3pn5SJ7PGz5gmjat2Wv01wAkSSb7ufOlV8hut+e72sXFnDp1SsWLF3dqO3nypBITExUTE+Om3km2I7Xd9lkAABRGY47X9XYXirQV9zTwdheKvP/bNNbbXShQ9Xfe9nYX8rXnyavrYv0lzYBczOUkH5LyJB+SFBUVpaioqCvsEQAAAOAmlGC5xSXdhA4AAAAAV4IEBAAAAIBh3FqCBQAAABRVJkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAABXUILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAU8iNA9mAEBAAAAYBgSEAAAAACGoQQLAAAAcIXd5O0eFAnMgAAAAAAwDAkIAAAAAMNQggUAAAC4glWw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAX8CBC92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAC5gFSz3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFMyAAAACAj7LZbJo0aZLatWunRo0aacCAAYqPjy9w+wULFqhOnTp5fi60z/mYAQEAAAB81OTJkzVnzhyNGzdOZcuW1fjx4zVw4ED98MMPMpvNebbfsWOHWrRoobffftupPSoqyuVjMgMCAAAAuMJeSH8uk8Vi0fTp0zVo0CB16NBBMTExmjhxoo4ePaolS5bku8+///6rmJgYlS5d2unH39/f5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fnu8+OHTtUs2bNKzouJVgAAADAVaxTp04XfH/p0qX5th85ckSSVK5cOaf2MmXKKCEhIc/2J0+e1PHjx7V69Wp98cUXOnXqlBo1aqRnnnlG1apVc7m/zIAAAAAALjDZC+fP5UpPT5ekPPd6BAUFKTMzM8/2//77ryTJ399fb7zxhiZOnKi0tDTdc889On78uMvHZQYEAAAAuIoVNMNxMcHBwZIc94Kc/X9JyszMVEhISJ7tW7VqpVWrVqlYsWK5bR988IE6duyo+fPn66GHHnLpuMyAAAAAAD7obOlVYmKiU3tiYqKio6Pz3efc5EOSQkNDVbFiRR09etTl45KAAAAAAD4oJiZG4eHhWrlyZW5bcnKy4uLi1KxZszzbz5o1Sy1btlRGRkZuW0pKivbt23dJN6aTgAAAAAA+yGw2q0+fPpowYYKWLl2q7du3a+jQoYqOjlaXLl1ktVp17Nix3ISjY8eOstvtGj58uHbu3KnNmzdr0KBBioqK0h133OHycUlAAAAAAB81ePBg9ejRQ88//7x69+4tf39/TZs2TWazWQkJCWrbtq0WLVokyVGy9fnnnys1NVW9e/dW//79FRERoRkzZjjdQ3IxJrvdfgX3zl9dbEdqe7sLAAB41Jjjdb3dhSJtxT0NvN2FIu//No31dhcKVGfMRG93IV87Rg/1dhcuCTMgAAAAAAxDAgIAAADAMDwHBAAAAHDBlTz0D/9hBgQAAACAYUhAAAAAABiGEiwAAADAFZRguYVPJSA3lG/k7S4AKMxMTAp7nN3m7R4UfYxjz7Lv8HYPgKseZykAAAAAhvGpGRAAAADgslGC5RbMgAAAAAAwDAkIAAAAAMNQggUAAAC4gAcRugczIAAAAAAMQwICAAAAwDCUYAEAAACuoATLLZgBAQAAAGAYEhAAAAAAhqEECwAAAHABq2C5BzMgAAAAAAxDAgIAAADAMJRgAQAAAK6gBMstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAUlWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC3gQoXswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAABXUILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiABxG6BzMgAAAAAAxDAgIAAADAMJRgAQAAAK6gBMstmAEBAAAAYBgSEAAAAACGoQQLAAAAcAGrYLkHMyAAAAAADEMCAgAAAMAwlGABAAAArqAEyy2YAQEAAABgGBIQAAAAAIYhAQEAAABgGO4BAQAAAFzBPSBuwQwIAAAAAMOQgAAAAAAwDCVYAAAAgAtM3u5AEcEMCAAAAADDkIAAAAAAMAwJiJc0u6GxPlj1ur5PmamZeyer18huLu9b65rq+ilztspWKe25DhYBxNiziK/nNbuhkT5Y+Zq+PzNDM/e8r14jurm8b61rqumnjC+J8UUwjj2LMex5jGGD2Qvpz1WGBMQLYlvX1phvR2j/tkN6ufsE/TLzT90/trfuefbOi+5bvWEVjf1hlAICuX3nQoixZxFfz4ttXVtjFg7X/u2H9HKPt/TLzGW6f+zdumfUHRfdt3rDKhr7/UhifBGMY89iDHseYxhXK0adF/Qd3VO7N+zTG/3ekyStWbxBAYH+untEN817+wdZMix59gkIDFC3QTeq35hesqTnfR/OiLFnEV/P6zu6R06MP5AkrVm8MSfGt2vexB9kycjKs09AoL+6PXGT+o25ixi7gHHsWYxhz2MM42rFDIjBAs0BanhdPS1fsNKp/c95KxQaEaIG7WLy3a/FzU3UZ3RPzX5tvqaOnGlEV69axNiziK/nBZoD1LBDrJYvWOXU/uc3K3NiXDff/Rwx7q7Zry3Q1FGzjOjqVYtx7FmMYc9jDHuHyV44f642JCAGK1e9rMxBgTr072Gn9sO7jkiSKtYun+9+O1bvVt9qj2vWa/NlzbZ5vJ9XM2LsWcTX83JjvDPBqT03xrXK5bvfjtW71bf6E5o1boGs2VaP9/Nqxjj2LMaw5zGGcTUrtAnIrbfeqoSEhItveJUJKx4mSUpNTndqTzvjeB0aGZLvficOn9SZpBTPdq6IIMaeRXw9L6x4qKTLiXGSziSlerZzRQTj2LMYw57HGMbVzKv3gCxcuLDA9+Lj4/XTTz8pKipKktStWzdjOuVhfn45j7Cx5z9fZrNdhfNohQwx9izi63l+fjnXhoixxzCOPYsx7HmMYS8hrG7h1QTk5ZdfVkZGhiTJns9foDfffFOSZDKZikwCknLKcWUnNDLUqT00wnGlIvV0muF9KmqIsWcRX8/7L8bOVzBzY5xMjK8U49izGMOexxjG1cyrCcj8+fP1zDPPKCIiQm+88YbKli2b+16TJk303XffqVKlSl7sofsd3n1U1myryteMdmo/+3p/3EFvdKtIIcaeRXw9LzfGNYixpzCOPYsx7HmMYVzNvHoPSLVq1TR37lw1bNhQt99+uxYtWuTN7hgiKzNLm/7cprZ3tHRqb9+jlc4kpWj7ql1e6lnRQYw9i/h63n8xbuHU3r57S2LsJoxjz2IMex5j2Eu8/cBBHkToHgEBAXrqqaf03nvvacKECXr66ad15swZb3fLo2a9+o1iWtbUC3OfUvMbG6vfmLvV85nbNHvcAlkyLAqNCFHdlrVUrFSkt7t61SLGnkV8PW/Wa/NzYjzUEeOX71LPZ27V7HELZcnIOifGEd7u6lWLcexZjGHPYwzjauX1BOSs5s2b596UfssttygrK+8DioqKDb9t0Zgeb6linfJ6acFwdbqnnT4Z/oW+nvCdJKnmNdU06Z/X1LLrNV7u6dWLGHsW8fW8Db9t1Zieb6ti7XJ6af4z6nRPW30y/Et9/db3knJi/PdYYnwFGMeexRj2PMYwrlYme353f3vZwoULNX/+fE2YMEFlypRx2+d28evpts8CUASZCs01maLLznMHPI5x7FmMYY9bYvva210oUONBE73dhXxteG+ot7twSbx6E3pBunXrVmRWvQIAAADwHy6TAAAAADBMoZwBAQAAAAqdQnfjwtWJGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5gowXILZkAAAAAAH2Wz2TRp0iS1a9dOjRo10oABAxQfH+/Svt9//73q1KmjgwcPXtIxSUAAAAAAHzV58mTNmTNHY8eO1dy5c2UymTRw4EBZLJYL7nfo0CG9/PLLl3VMEhAAAADAFfZC+nOZLBaLpk+frkGDBqlDhw6KiYnRxIkTdfToUS1ZsqTA/Ww2m4YNG6Z69epd1nFJQAAAAAAftH37dqWmpqpVq1a5bZGRkYqNjdXq1asL3O+jjz5SVlaWHn744cs6LjehAwAAAD7oyJEjkqRy5co5tZcpU0YJCQn57rNp0yZNnz5d8+bN09GjRy/ruCQgAAAAgAsK6ypYnTp1uuD7S5cuzbc9PT1dkmQ2m53ag4KCdPr06Tzbp6Wl6ZlnntEzzzyjqlWrXnYCQgkWAAAA4IOCg4MlKc8N55mZmQoJCcmz/dixY1W1alX16tXrio7LDAgAAABwFStohuNizpZeJSYmqnLlyrntiYmJiomJybP9N998I7PZrCZNmkiSrFarJOmWW27RbbfdpjFjxrh0XBIQAAAAwBWFtATrcsXExCg8PFwrV67MTUCSk5MVFxenPn365Nn+559/dnq9ceNGDRs2TB9//LFq1Kjh8nFJQAAAAAAfZDab1adPH02YMEFRUVGqUKGCxo8fr+joaHXp0kVWq1UnT55URESEgoODVaVKFaf9z97EXr58eZUsWdLl43IPCAAAAOCjBg8erB49euj5559X79695e/vr2nTpslsNishIUFt27bVokWL3HpMk91uL2KTSQXr4tfT210AUJiZuCbjcXabt3tQ9DGOPYsx7HFLbF97uwsFuubhid7uQr7WTRnq7S5cEs5SAAAAAAxDAgIAAADAMNyEDgAAALigsD6I8GrDDAgAAAAAw5CAAAAAADAMJVgAAACAKyjBcgtmQAAAAAAYhgQEAAAAgGEowQIAAABcYPKd53d7FDMgAAAAAAxDAgIAAADAMJRgAQAAAK6gAsstmAEBAAAAYBgSEAAAAACGoQQLAAAAcIGJEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFMyAAAAAADEMCAgAAAMAwlGABAAAALmAVLPdgBgQAAACAYUhAAAAAABiGEiwAAADAFZRguQUzIAAAAAAMQwICAAAAwDCUYAEAAAAuYBUs92AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAzjWzMgJvItAPAqzsOeZ7d5uwdFG2MYuGK+lYAAAAAAl4lVsNyDNB4AAACAYUhAAAAAABiGEiwAAADAFXZqsNyBGRAAAAAAhiEBAQAAAGAYSrAAAAAAF7AKlnswAwIAAADAMCQgAAAAAAxDCRYAAADgCkqw3IIZEAAAAACGIQEBAAAAYBhKsAAAAAAXmGze7kHRwAwIAAAAAMOQgAAAAAAwDCVYAAAAgCtYBcstmAEBAAAAYBgSEAAAAACGoQQLAAAAcIGJEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBV2arDcgRkQAAAAAIYhAQEAAABgGEqwAAAAABewCpZ7MAMCAAAAwDAkIAAAAAAMQwkWAAAA4ApKsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAF7AKlnswAwIAAADAMCQgAAAAAAxDCRYAAADgCjs1WO7ADAgAAAAAw5CAAAAAADAMJVgAAACAC1gFyz2YAQEAAABgGBIQAAAAAIahBAsAAABwBSVYbsEMCAAAAADDkIAAAAAAMAwJCAAAAOACk71w/lwJm82mSZMmqV27dmrUqJEGDBig+Pj4ArffsmWL+vXrpyZNmqhVq1YaPXq0kpOTL+mYJCAAAACAj5o8ebLmzJmjsWPHau7cuTKZTBo4cKAsFkuebRMTE3X//fercuXKWrBggSZPnqx169ZpxIgRl3RMEhAAAADAB1ksFk2fPl2DBg1Shw4dFBMTo4kTJ+ro0aNasmRJnu0PHTqkdu3a6cUXX1TVqlV1zTXXqGfPnvrnn38u6bisggUAAAC4wla0lsHavn27UlNT1apVq9y2yMhIxcbGavXq1eratavT9k2aNFGTJk1yX+/atUsLFixQmzZtLum4JCAAAADAVaxTp04XfH/p0qX5th85ckSSVK5cOaf2MmXKKCEh4YKfecMNN2jfvn2qUKGCJk+efAm9pQTLa5rd0EgfrHxN35+ZoZl73levEd1c3rfWNdX0U8aXKlultOc6WAQQY88ivp5HjD2PGHtWsxsa64NVr+v7lJmauXeyeo3s5vK+ta6prp8yZxPfi2AM40qkp6dLksxms1N7UFCQMjMzL7jvhAkTNHPmTJUuXVr33XefUlNTXT4uMyBeENu6tsYsHK4/vvpbn46eq/ptYnT/2Lvl52fSrHELLrhv9YZVNPb7kQoI5I/uQoixZxFfzyPGnkeMPSu2dW2N+XaE/pj7tz59YY7qt43R/WN7y8/PT7Nem3/Bfas3rKKxP4wivhfBGPaCQlqBVdAMx8UEBwdLctwLcvb/JSkzM1MhISEX3LdBgwaSpPfee08dOnTQkiVL1K1bN5eOy6jzgr6je2j3hn16o98HkqQ1izcqINBfd4+4XfMm/iBLRlaefQIC/dXtiZvUb8xdsqTnXZUAzoixZxFfzyPGnkeMPavv6J458X1PkrRm8Yac+HbTvLd/kCUjb/wCAgPUbdCN6jemF/F1AWMYV+ps6VViYqIqV66c256YmKiYmJg82+/evVsHDx5Uhw4dctvKlCmjYsWK6ejRoy4flxIsgwWaA9SwQ6yWL1jl1P7nNysVGhGiBu3q5rtfi5ubqM/o7pr92gJNHTXLiK5etYixZxFfzyPGnkeMPSvQHKCG19XT8gUrndr/nLciJ755f7GRzsa3p2a/Nl9TR840oqtXLcYw3CEmJkbh4eFaufK/v6vJycmKi4tTs2bN8my/bNkyDRkyRCkpKblt+/fvV1JSkmrUqOHycUlADFauelmZgwJ1aKfzjT2HdzluAqpYq1x+u2nH6t3qW/0JzRq3QNZsq8f7eTUjxp5FfD2PGHseMfas3Pj+e9ipPTe+tcvnu9+O1bvVt9rjmvXafFmzbR7v59WMMewd3n7goLsfRGg2m9WnTx9NmDBBS5cu1fbt2zV06FBFR0erS5cuslqtOnbsmDIyMiRJt99+uyIiIjRs2DDt3LlTa9as0eDBg9WwYUN17NjR5eN6NQGZN29enoecrFixQg899JBuu+02Pf3009q1a5eXeucZYcVDJUmpyelO7WlnHK9DI/OvtztxOElnkly/uceXEWPPIr6eR4w9jxh7VljxMEmXE9+TOpOUku97cMYYhrsMHjxYPXr00PPPP6/evXvL399f06ZNk9lsVkJCgtq2batFixZJkkqUKKEZM2bIZrOpd+/eevzxxxUbG6tp06bJ39/f5WN69R6QF154QR07dlTJkiUlScuXL9fAgQPVpk0btW3bVlu2bFH37t316aef6pprrvFmV93Gzy8n57Pnn67aitj60t5AjD2L+HoeMfY8YuxZfn4mx/8QX49hDMNd/P39NWzYMA0bNizPexUrVtSOHTuc2qpVq6YpU6Zc0TG9moDYz/tLM3nyZN13330aNWpUbtu4ceM0YcIEzZpVNOoUU045rjqcf2UiNMLxOjU5zfA+FTXE2LOIr+cRY88jxp71X3xDndpz43ua+F4pxrCXFJDw4dIUqntA4uPjdfvttzu13X333YqLi/NSj9zv8O6jsmZbVb5GtFN7+ZqO1/vjDnqjW0UKMfYs4ut5xNjziLFn5ca3JvH1FMYwrmZeTUBMJpPT66pVqyotzTljT0pKUkREhJHd8qiszCxt+nOb2t7Rwqm9ffeWOpOUou2ritY9L95AjD2L+HoeMfY8YuxZ/8W3pVN7+x6tiK+bMIZxNfNqAmK329WpUyfdcccdeuaZZ2Q2mzV+/HhlZTnWrV63bp1efvllp7WGi4JZr81XTMuaemHuUDW/sbH6vXyXej5zq2aPWyhLRpZCI0JUt2UtFStVdBIvoxFjzyK+nkeMPY8Ye9asV7/Jie9TjviOuVs9n7lNs8ctkCXDck58I73d1asWY9h43l7tyt2rYHmLVxOQX3/9VRMnTtSNN94om82mY8eOaevWrbJaHcvCPfDAAwoNDdXTTz/tzW663YbftmpMz7dVsXY5vTT/GXW6p60+Gf6lvn7re0lSzWuqadLfY9Wya9G48d4biLFnEV/PI8aeR4w9a8NvWzSmx1uqWKe8XlowXJ3uaadPhn+hryd8Jyknvv+8RnyvAGMYVyuT/fw7wb0sKytLgYGBkqQdO3aodu3aeUq1LlcX/7vd8jkAABRadp6f4VGmQnX7bJG0xDrX210oUMcb3vB2F/L12+IR3u7CJfHqKlj5OZt8SFKdOnW82BMAAADgHIXqsv3VizQeAAAAgGFIQAAAAAAYptCVYAEAAACFkalw3Tp91WIGBAAAAIBhSEAAAAAAGIYSLAAAAMAVrHLtFsyAAAAAADAMCQgAAAAAw1CCBQAAALiAVbDcgxkQAAAAAIYhAQEAAABgGEqwAAAAAFdQgeUWzIAAAAAAMAwJCAAAAADDUIIFAAAAuIJVsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAF5iowHILZkAAAAAAGIYEBAAAAIBhKMECAAAAXMEqWG7BDAgAAAAAw5CAAAAAADAMJVgAAACAC0w2b/egaGAGBAAAAIBhSEAAAAAAGIYSLAAAAMAVrILlFsyAAAAAADAMCQgAAAAAw1CCBQAAALiCCiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwAUmVsFyC2ZAAAAAABiGBAQAAACAYSjBAgAAAFxBCZZbMAMCAAAAwDAkIAAAAAAMQwkWAAAA4AqbtztQNDADAgAAAMAwJCAAAAAADEMJFgAAAOACHkToHsyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAAAwBWUYLkFCQgAAEWJieIGAIUbZykAAAAAhmEGBAAAAHCFzdsdKBqYAQEAAABgGBIQAAAAAIahBAsAAABwgYlVsNyCGRAAAAAAhiEBAQAAAGAYSrAAAAAAV1CC5RbMgAAAAAAwDAkIAAAAAMNQggUAAAC4ghIst2AGBAAAAIBhSEAAAAAAGIYSLAAAAMAVlGC5BTMgAAAAAAxDAgIAAADAMJRgAQAAAK6websDRQMzIAAAAAAMQwICAAAA+CibzaZJkyapXbt2atSokQYMGKD4+PgCt9+5c6ceeughtWzZUq1bt9bgwYN1+PDhSzomCQgAAADgApPdXih/rsTkyZM1Z84cjR07VnPnzpXJZNLAgQNlsVjybJuUlKT7779fYWFhmjlzpj755BMlJSXpwQcfVGZmpsvHJAEBAAAAfJDFYtH06dM1aNAgdejQQTExMZo4caKOHj2qJUuW5Nn+l19+UXp6ul5//XXVqlVL9evX1/jx47V7926tW7fO5eOSgAAAAAA+aPv27UpNTVWrVq1y2yIjIxUbG6vVq1fn2b5169b64IMPFBQUlOe906dPu3xcVsECAAAAXFFIH0TYqVOnC76/dOnSfNuPHDkiSSpXrpxTe5kyZZSQkJBn+4oVK6pixYpObVOmTFFQUJCaN2/ucn+ZAQEAAAB8UHp6uiTJbDY7tQcFBbl0T8eMGTM0a9YsPfXUUypZsqTLx2UGBAAAALiKFTTDcTHBwcGSHPeCnP1/ScrMzFRISEiB+9ntdr377rv68MMP9fDDD6t///6XdFwSEAAAAMAVtsJZgnW5zpZeJSYmqnLlyrntiYmJiomJyXefrKwsjRo1Sj/88IOGDx+uBx544JKPSwkWAAAA4INiYmIUHh6ulStX5rYlJycrLi5OzZo1y3ef4cOH6//+7//01ltvXVbyITEDAgAAAPgks9msPn36aMKECYqKilKFChU0fvx4RUdHq0uXLrJarTp58qQiIiIUHBys+fPna9GiRRo+fLhatGihY8eO5X7W2W1cwQwIAAAA4Aq7vXD+XIHBgwerR48eev7559W7d2/5+/tr2rRpMpvNSkhIUNu2bbVo0SJJ0g8//CBJevPNN9W2bVunn7PbuMJktxfS9cQ8oIv/3d7uAgAAAC5giXWut7tQoJtqj/B2F/L1079veLsLl4QZEAAAAACG4R4QAAAAwBW+UzjkUcyAAAAAADAMCQgAAAAAw1CCBQAAALiCEiy3YAYEAAAAgGFIQAAAAAAYhhIsAAD+v717D6qy3vc4/sHL4qLg0Y6CaTqCF1yphINbK5WdDtPeXjo6u709mA0mool5OWaXbRqZpF1IC2+NHtTOmImXoqS0ocYp9ZRiJk0SWireUigqES+Ass4fHWkYabfS9Tw/1uP7NbNmWj94Wp/5DKN++f3WswDAGzUcwfIFdkAAAAAA2IYBBAAAAIBtOIIFAAAAeMNTYzqBI7ADAgAAAMA2DCAAAAAAbMMRLAAAAMAbfBChT7ADAgAAAMA2DCAAAAAAbMMRLAAAAMAbfBChT7ADYkjcvTFaunu+tpz7H609skT/+cQIr6/t0ruTtl56Q+EdW1sX0AHo2Fr0az06th4dW4t+rUfH8EcMIAa47+yqZ3Me1/GiU5p7/8v6cO0OPZQ+SqP/OfJ3r43s1VHpW55Uk6ZsXv0rdGwt+rUeHVuPjq1Fv9ajY/grfuoMePDp+3V4f7FeSFoqSdr7QYGaNG2sUU/8hzYtylXVpeprrmnStLFGPPJXJT37D1VdrLI7st+hY2vRr/Xo2Hp0bC36tR4dG8BdsHyCHRCbNXU1Ua94t3a+vafO+iebdyskNFg9B3Sv97o/DYnVmKf/pjfnv63//uc6O6L6LTq2Fv1aj46tR8fWol/r0TH8GQOIzdpGhssV2FSnvjldZ/27b89Iktp3aVvvdQfzD+vByEe0bsHbunL5iuU5/RkdW4t+rUfH1qNja9Gv9egY/sz4EayCggLt3r1bEyZMkCR99tlnWrNmjU6ePKkOHTpo3LhxiouLM5zSd5r9W4gk6Xz5xTrrF8798jwkLLje68q++8naYA5Cx9aiX+vRsfXo2Fr0az06NoQjWD5hdAdk27ZtSkxM1J49v2wfbt++XQ899JA8Ho/i4+NVXV2tpKQkbd++3WRMn2rU6P8r/40f4Bpu73bD6Nha9Gs9OrYeHVuLfq1Hx/BnRndAlixZokceeUSpqamSpOXLl+vhhx/WtGnTar9n+fLlyszM1D333GMqpk9V/Hxe0rW/mQgJ/eX5+fILtmdyGjq2Fv1aj46tR8fWol/r0TH8mdEdkOPHj2v48OG1z0+ePKl77723zvcMGzZMhw8ftjuaZb47XKIrl6/o1qiIOuu3dv7l+fHCkyZiOQodW4t+rUfH1qNja9Gv9ejYEI+nYT78jNEB5LbbbtPHH39c+7x79+4qKiqq8z1ffvmlwsPD7Y5mmerKan35ydfqP/JPddYH/q2vzv1UoaI93xpK5hx0bC36tR4dW4+OrUW/1qNj+DOjA0hKSooWLFigjIwMFRUVKTU1VUuXLlV2drb27dun1atXKy0tTQ888IDJmD63bv5biu7bWXOy/0t9/nKHkub+Q3+fOVxvLshR1aVqhYQGq3vfLmrx76Gmo/otOrYW/VqPjq1Hx9aiX+vRMfyV0QFkxIgRmj9/vrZu3aoRI0ZozJgxOnHihNLS0jR69GgtWbJEycnJGjt2rMmYPrd/+wE9+/eFat+1rZ55a6YGj+6vlY+/oY0vb5Ekde7dSZn/m66+Q3sbTuq/6Nha9Gs9OrYeHVuLfq1HxwbU1DTMh58J8HgaxsGxI0eOqLi4WBUVFWratKkiIiLkdrsVGBjos9dIaDzKZ/8vAAAA+F7elWzTEX7TX9tONh2hXltPLzUd4Q8x/jkgV0VGRioyMtJ0DAAAAAAWajADCAAAANCgNYyDQ37P6HtAAAAAANxcGEAAAAAA2IYjWAAAAIA3OILlE+yAAAAAALANAwgAAAAA23AECwAAAPBGDUewfIEdEAAAAAC2YQABAAAAYBuOYAEAAABe8HhqTEdwBHZAAAAAANiGAQQAAACAbTiCBQAAAHiDu2D5BDsgAAAAAGzDAAIAAADANhzBAgAAALzh4QiWL7ADAgAAAMA2DCAAAAAAbMMRLAAAAMAbNXwQoS+wAwIAAADANgwgAAAAAGzDESwAAADAG9wFyyfYAQEAAABgGwYQAAAAALbhCBYAAADgBQ93wfIJdkAAAAAA2IYBBAAAAIBtOIIFAAAAeIO7YPkEOyAAAAAAbMMAAgAAAMA2HMECAAAAvFHDESxfYAcEAAAAgG0YQAAAAADYhiNYAAAAgDc8fBChL7ADAgAAAMA2DCAAAAAAbMMRLAAAAMALHu6C5RPsgAAAAACwDQMIAAAAANtwBAsAAADwBnfB8gl2QAAAAADYhgEEAAAAgG0YQAAAAAAveGo8DfJxI2pqapSZmakBAwYoJiZG48aN07Fjx7y6Ljk5WYsXL/7Dr8kAAgAAANykli1bpvXr1ys9PV3Z2dkKCAhQSkqKqqqqfvOaS5cu6bHHHtPOnTuv6zUZQAAAAICbUFVVlVatWqUpU6YoPj5e0dHRWrRokUpKSpSXl1fvNfv27dPIkSNVUFCgsLCw63pdBhAAAADAG56ahvm4TkVFRTp//rz69etXuxYWFia32638/Px6r9mxY4cSEhKUk5Oj0NDQ63pdbsMLAAAA3ITOnDkjSWrbtm2d9TZt2uj06dP1XjNt2rQbfl0GEAAAAMCPDR48+F9+/aOPPqp3/eLFi5Ikl8tVZz0wMFBnz571Tbh63FQDSN6VbNMRAAAA4KfyajaajlCv3xtAfktQUJCkX94LcvW/JamyslLBwcE+yVafm2oAAQAAAJzmt3Y4fs/Vo1elpaXq0KFD7Xppaamio6N9kq0+vAkdAAAAuAlFR0erefPm2r17d+1aeXm5CgsLFRcXZ9nrsgMCAAAA3IRcLpfGjBmjjIwMtWrVSu3atdNLL72kiIgIJSQk6MqVK/rxxx8VGhpa54jWjWIHBAAAALhJTZ06Vffff79mz56txMRENW7cWFlZWXK5XDp9+rT69++v999/36evGeDxeG7s89sBAAAAwEvsgAAAAACwDQMIAAAAANswgAAAAACwDQMIAAAAANswgAAAAACwDQMIAAAAANswgAAAAACwDQMIAAAAANswgDQwNTU1yszM1IABAxQTE6Nx48bp2LFjpmM51rJly/Tggw+ajuEoP//8s55++mkNHDhQvXv3VmJiovbu3Ws6lqOUlZXpscceU79+/RQbG6sJEybo22+/NR3LkY4eParY2Fi99dZbpqM4yqlTp9StW7drHhs3bjQdzVFycnI0ZMgQ9ezZU0OHDtXWrVtNRwIkMYA0OMuWLdP69euVnp6u7OxsBQQEKCUlRVVVVaajOc6aNWuUmZlpOobjzJgxQwUFBVq4cKE2bdqk22+/XcnJyTp8+LDpaI4xadIknThxQitXrtSmTZsUFBSksWPH6uLFi6ajOUp1dbVmzpypCxcumI7iOAcPHlRgYKB27NihnTt31j6GDx9uOppjvPPOO5o1a5ZGjRql3NxcDRkyRDNmzNAXX3xhOhrAANKQVFVVadWqVZoyZYri4+MVHR2tRYsWqaSkRHl5eabjOUZJSYnGjx+vV199VZ06dTIdx1GOHTumXbt2KS0tTXFxcYqMjNRTTz2l8PBw5ebmmo7nCD/99JPat2+vefPmqWfPnoqKilJqaqq+//57ffPNN6bjOcrixYvVrFkz0zEc6dChQ+rUqZPatGmj1q1b1z6CgoJMR3MEj8ejV199VUlJSUpKSlLHjh01efJk3XXXXdqzZ4/peAADSENSVFSk8+fPq1+/frVrYWFhcrvdys/PN5jMWQ4cOKAWLVro3XffVUxMjOk4jtKyZUutWLFCPXr0qF0LCAiQx+PR2bNnDSZzjpYtW2rhwoXq0qWLJOmHH35QVlaWIiIi1LlzZ8PpnCM/P1/Z2dl64YUXTEdxpIMHD/LzaqEjR47o1KlT1+woZWVlaeLEiYZSAb9qYjoAfnXmzBlJUtu2beust2nTRqdPnzYRyZEGDRqkQYMGmY7hSGFhYYqPj6+ztnXrVh0/flz9+/c3lMq55syZow0bNsjlcmn58uUKCQkxHckRysvL9fjjj2v27NnX/HkM3zh06JBat26t0aNHq7i4WB07dlRqaqoGDBhgOpojFBcXS5IuXLig5ORkFRYWqn379po0aRJ//6FBYAekAbl6ftvlctVZDwwMVGVlpYlIwA35/PPPNWvWLA0ePJi/9CyQlJSkzZs367777tPkyZN14MAB05Ec4ZlnntEdd9zB+xEsUlVVpeLiYlVUVGj69OlasWKFevbsqZSUFH366aem4zlCRUWFJOmJJ57QsGHDtGrVKt19991KTU2lYzQI7IA0IFfPvlZVVdU5B1tZWang4GBTsYDr8uGHH2rmzJmKiYnRwoULTcdxpKtHWObNm6f9+/dr7dq1WrBggeFU/i0nJ0d79+7Vli1bTEdxLJfLpfz8fDVp0qT2F249evTQ4cOHlZWVpTvvvNNwQv/XtGlTSVJycrJGjhwpSerevbsKCwu1evVqOoZx7IA0IFe3+ktLS+usl5aWKiIiwkQk4LqsXbtWU6ZM0cCBA7Vy5UreWOpDZWVlys3N1ZUrV2rXGjVqpKioqGv+7MAft3nzZpWVlenPf/6zYmNjFRsbK0lKS0vT0KFDDadzjpCQkGt2+7t27aqSkhJDiZzl6r8ZunbtWme9c+fOOnnypIlIQB0MIA1IdHS0mjdvrt27d9eulZeXq7CwUHFxcQaTAd5bt26d5s2bpwceeECvvPLKNf/IwI0pLS3Vo48+WudONtXV1SosLFRUVJTBZM6QkZGh999/Xzk5ObUPSZo6dapWrFhhNpxDFBUVKTY29prPB/rqq694Y7qPuN1uNWvWTAUFBXXWDx06pA4dOhhKBfyKI1gNiMvl0pgxY5SRkaFWrVqpXbt2eumllxQREaGEhATT8YDfdfToUc2fP18JCQmaOHGiysrKar8WFBSk0NBQg+mcITo6Wv3799fcuXOVnp6usLAwvfbaayovL9fYsWNNx/N74eHh9a7fcsstateunc1pnKlr167q0qWL5s6dq7S0NLVs2VIbNmzQ/v37tWnTJtPxHCEoKEjjx4/X0qVLFR4erl69eum9997Trl27tGbNGtPxAAaQhmbq1Km6fPmyZs+erUuXLqlPnz7Kysrit8jwCx988IGqq6uVl5d3zWfXjBw5Us8//7yhZM4REBCgV155RS+//LKmT5+uc+fOKS4uTm+88YZuvfVW0/GA39WoUSO99tprysjI0PTp01VeXi63263Vq1erW7dupuM5RmpqqoKDg2s/TywqKkqLFy9W3759TUcDFODxeDymQwAAAAC4OfAeEAAAAAC2YQABAAAAYBsGEAAAAAC2YQABAAAAYBsGEAAAAAC2YQABAAAAYBsGEAAAAAC2YQABAAAAYBsGEADwM5WVlXK73YqNjdW8efNMxwEA4A9hAAEAPxMQEKDXX39dvXr10tq1a3X06FHTkQAA8BoDCAD4GZfLpT59+mj8+PGSpAMHDhhOBACA9xhAAMBPRUZGSpK+/vprw0kAAPAeAwgA+KmVK1dKkoqKigwnAQDAewwgAOCHdu7cqTfffFMtWrRQYWGh6TgAAHiNAQQA/Ex5eblmzZqlwYMHKzExUT/++KNKSkpMxwIAwCsMIADgZ+bOnavLly8rPT1dbrdbEsewAAD+gwEEAPzItm3blJubq+eee06tWrWqHUB4IzoAwF8wgACAn/j++++VlpamUaNG6Z577pEk3XbbbQoLC+N9IAAAv8EAAgB+Ys6cOWrRooWefPLJOuvdu3fnCBYAwG8wgACAH9i4caM++eQTvfjiiwoJCanzNbfbrePHj6uiosJQOgAAvBfg8Xg8pkMAAAAAuDmwAwIAAADANgwgAAAAAGzDAAIAAADANgwgAAAAAGzDAAIAAADANgwgAAAAAGzDAAIAAADANgwgAAAAAGzDAAIAAADANgwgAAAAAGzDAAIAAADANgwgAAAAAGzzf8yxZeYYKTFsAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# visual representation of grid search\n",
     "# uses seaborn heatmap, you can also do this with matplotlib imshow\n",
@@ -2235,584 +1415,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.18333333333333332\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.18611111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.13055555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.24444444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.23333333333333334\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.12777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1e-05\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.1527777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9111111111111111\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.8888888888888888\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.8305555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.8888888888888888\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.8805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.0001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.8944444444444445\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.975\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.9777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.9805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.9805555555555555\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.9777777777777777\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.001\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.9444444444444444\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/neural_network/_multilayer_perceptron.py:692: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (100) reached and the optimization hasn't converged yet.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9861111111111112\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.9888888888888889\n",
-      "\n",
-      "Learning rate  =  0.01\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.9722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.01\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.9527777777777777\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.9027777777777778\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.8583333333333333\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.9055555555555556\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.8805555555555555\n",
-      "\n",
-      "Learning rate  =  0.1\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.8722222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  0.1\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.8666666666666667\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.08611111111111111\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.17777777777777778\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.08333333333333333\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  1.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.08888888888888889\n",
-      "\n",
-      "Learning rate  =  1.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.09444444444444444\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  1e-05\n",
-      "Accuracy score on test set:  0.17222222222222222\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.0001\n",
-      "Accuracy score on test set:  0.11666666666666667\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.001\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.01\n",
-      "Accuracy score on test set:  0.1388888888888889\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  0.1\n",
-      "Accuracy score on test set:  0.11388888888888889\n",
-      "\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Learning rate  =  10.0\n",
-      "Lambda =  1.0\n",
-      "Accuracy score on test set:  0.10555555555555556\n",
-      "\n",
-      "Learning rate  =  10.0\n",
-      "Lambda =  10.0\n",
-      "Accuracy score on test set:  0.09444444444444444\n",
-      "\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.neural_network import MLPClassifier\n",
     "# store models for later use\n",
@@ -2850,36 +1453,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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AAMAyJCAAAAAALEMJFgAAAOAFp4xAN+GqwAgIAAAAAMuQgAAAAACwDCVYAAAAgBdcPIjQJxgBAQAAAGAZEhAAAAAAlqEEyyL1m1ZS30faqUyFIjpzKkHzpq/WtAm/Zbu+w2FX97ubqv1NdVSkeD4dPxKrJfM26psJvyktzZlp/fA8Ifro24c1+eOftXDun348kpypfotrdPcTnVWmUlGdORmveVNW6ptPfvZq20rVS2rMt4+qX4e3dPTQKUlS0ZIFNPGXodlu89OM1Rrz7Lc+afuVon6barr7mRtV5poonTkRp3lf/qZv3v/Jq20r1SqtMd8/rX5Nh+nowZPZrnf/8O669f62uj7qEV81+4rRsFEF3duvlcqWLawzpxP03dx1mvL1imzXdzhsuu3269Sxcy0VKRKp48fOavGiLZry9e9KSzv/qKzSZQrp/gfaqHadsnKmObVx4wF9PHaxoqNPW3BUOV/9ZpXV97EO6X1zvOZ984emjV+a7foOh13d+zZT+5vrqUixfDp+5IyWzNugbz5bmmXffDVr0KmO7n2lp8pUK6Uzx2L1/Sc/aeobsy+6TbveLdTz2VsVVaGYju4/rm9Hz9H88Us81ml6c0P1fqGHSlcpoZMxp7Vo8q+a+vpspaWmZazz3NePq03PZpn2/2qvMfpl2u8+Ob6cqH7Lqrr7yetVpnIxnTkZp3lfrdA3Hy32attKNUppzMxB6tfmtYzfunNKVSiqfkNvVK3rKiktzanNf+zRuFfnKOZA9v11bsUsWL5BAmKBa2uX1rB379TSBZs18cPFqlG3rPo+2k6GzdDUz7L+oXtgyPXqcFMdff3pr/pryyFVujZKfR5so2JR+TRm+ByPdSPyhmn4u3eqWIkCVhxOjnNt3bJ6+eN7tHTeBn055kdVb1BefQd3ks1maOpHSy66bfmqURo+7j45guwey08di9UTt32Qaf0bezdRyxtq66dvV/v0GHK6axuU18tfPKClc9fpyze/V/VGFdT32ZvcMX53wUW3LV+tpIZPejhTjC9Uo3Elde3X2oetvnJUq15Sr7x6m375eas+H/+ratQsrfv6t5ZhM/T15KxPph5+tIM6dqqpyZOWa8f2aFWuXEx339NCxYrl1ehR8yRJRYpE6r3379KBAyf12sg5Cg526L5+rfTm6J7qf+9nSklJy3LfucW1tcto2Pt9tPTHTZr4/kLVqFdWfQd2kGGzaeq4X7Lc5oFnuqhD17r6+tOf9dfmg6p0bQn1eaidikXl15iXZ1l7AAFUrck1GjHnGf067Xd9/uJU1WheVfeO7CWbzaavX5uZ5TYtezTWkImPatZ787Tmxz/V9JZGGjzuISUnpmjJ18skSfXa19LLM57Sr9N+1/ihX6l8zTK679Veyl8knz54bHzGvirWKadFk5Zq7tgfPT7j4M5o/x10gF1br5xeHneflv7wp758e76qNyyvvk9d7+6HP1x00W3LX1tCwyf0z7IfLhyVX29Pf0wH9xzVm49PVnBokPo+eb1e/fJBPdR5lFKSU/11SMjFSEAs0OeBNtqzI0ajXnB3ymt/3yW7w6bb722hmZN+V0qy50lARN4wdenRQBPeXajpE5dLkv78Y48kqf8TnTThvYU6cypBktS4dVU9NOQGhYUHW3hEOUvvx9prz7bDGv30NEnS2t/+cl8dvr+NZk5Ymim+kuQIsqvrXc101+MdlZKUuXNNTXFq+5/7PZZVrlFKLW+orYnv/Kgta//2y7HkVL2fvEF7thzU6McmSpLW/rxVDoddtz3aUTM/WZJlDB1BdnW9r7XueuZGpSSmXHT/IWHBGjymj07GnFGRkrkvkb67bwvt3nVEb7z2nSRp9R975LDb1OvOJpr+zR+ZEoXIyFDd1LWexn2yRN9MWyVJWr/ub0nSAw+107hPf9GZMwnqe29LJSSm6Oknv1Zy+r+DmJjTeuXV21SlSpQ2bTpg3UHmQH0eaqs922M06rnpkqS1y3fK7rDr9n4tNfPLZVn3zbc31IQxCzT9C/cJ85+r0vvmJ6/XhP8tyOibr3Z3vXSbdv/5t97s+74kac2CP+UIsuuOZ27R9He+V0pS5n/z97zSS79NX6mPB7v7kTU/bVBkgQjdPeyOjASk0z1tdHT/cb1x1/tyuVxat2ij8hfNp26Pd9FHT3whZ5pTIWHBKlk5SlPfmKVtq3Zad9AB1ntQR/dv3eCvJUlrl25398MPttXMz37NMlFwBNnVtW9z3TX4+iz7aUm66/FOSoxP1nN9PlZy+jpHDpzQy+P6qXKtUtqyeq//Dgq5FveA+FlQkF01G5TT8sXbPJYvW7RF4XlCVKNe2Uzb5IkI0Q/T12jlL9s9lh/cd0KSVLxkQfd6kaF68e2e2rh2r55/+Es/HUHOFhRsV63rKmr5T5s9li/7cZPCI0JUo2H5LLdr2Kqqej/WXtM+WqIJo+Z79VmPDLtFB3Yf1azPsy+duxoFBTtUq0llLZ/3p8fyZd+vV3hEqGpcVzHL7Rq2q67eT16vae/+qAmvzslynXMGvNxNJ4/GauG07EuOrlZBQXbVrlNGv/22w2P50l+3Kzw8RDVrlc60TZ48Ifpu7jr9/rvnydfB9PK2qBL5JUktWlbR/B82ZCQfkvTXjhjd0eP9XJ98BAXZVbNheS1fvMVj+bKfNqf3zeUybZMnMlQ/fLM6+765VEG/tTcnCQp2qFbr6lo2a5XH8qXTVyo8Mkw1W1TNtE2xskVUukqJTNv8NmOFSlYqrpKVo9z7DnEoKT5ZLtf5MsIzx2MVHBKk8MgwSVKFWmVlt9u0+8+/fXxkOZf7t66Slv+40WP5svkb3P1wo2x+61pfq94DO2nah4s04c3vs1ynaedaWvDNqozkQ5J2bjqoPo2Hk3xkwSkjR/650pCA+FnxUgUUHOzQoX3HPZYf3u8+UShZplCmbY4cPq0PX/s+40ftnGbtrlVqalrGvpITU/VAt/f19ouzFHs6d1x1u1Dx0oUUFOzQob8viG967EqWK5Lldn9tOqC+rV/X1I+WyOn897rt1jfVUZXaZfTxyLly5bI5+IqXLaSgkCAd2nPUY/nhv49JkkpWKJbldn/9uU99G72kqe8ukPMf9yRcqG7Lqmp3WyONeWJyroutJEVF5VdwsEMHL6i1PpReo12qdOaT2piYM3rvfwsybdOiRRWlpjp18MBJFS+eTxERoYqJOaOBgzpp1pzHNf+nIRr52m0qWjSv/w7oClG8VEF333xh33HgXN9RONM2Rw6d0oevztXBC7Zp1q6aR998tYuqUEzBIUE69Ndhj+WHd8VIkkpdUyLTNmWuLSlJOviXZ4nUoYxt3AnInA9/VMnKUbrtqa7Kky9c115XWd0GddGqH9bp7Kk4Se7yK0m68cGOmnZ4nOYlTdE7v45Q1UaVfHeQOUzx0oUUFOLQob3HPJYfTv8ulixfNMvt/tp4QH1bjNTUDxdl2Q8XK1VQEXnDdOTgST08opumrXtFc7a/qWGf9VOR9AsZgD8EvAQrLS1NP/30k9asWaPDhw8rJSVFYWFhKl68uBo0aKAOHTrI4Qh4My9bRPoVm4T4ZI/lCQnu4enwiFCv9tOsXTW161Jbs79eqbizSZKktDRnpiQlt8kT6Y5fQlySx/Jz8Q6PCMlyuxNHYi/pc7r3a6Uta/ZqU3opXG6SJ2+4JCnh7AUxjkuPcWTW3+ETMWf+dd/hkaF6/J3emvTWD5kSnNwiIr0PSEi4oI9IdL/OE571d/hCLVpWUfuONTVzxmrFxSWpZCl3KduAB9pox/bDGvnKHBUoEK5+A9ro7TG9NaDfZ0rKpiQjN4jImx73C/vm+PS+OY93cW/Wvrra3VRHs79aobjYpH/f4CqQJ38eSVJ8bKLH8oSz7tfhecMybRORvk3CBdskpvcr4en9zIZftuibUXN0/1t36f637pIk7Vy3R6/1fjdjm3MJSEhosF7tNUZ5C0Wq5zO3aNSSYRrY5Dnt3eRZPns1yJMe00v/rbt4P5yvUIQk6b5nbtSODfv15qBJylcoUvc+fYPe/PphPXT9aCX/SwktcDkCema/f/9+DRgwQEeOHFG1atVUtGhR5cuXT8nJydq2bZtmzJih999/X5999plKlMh8ReVKYNjcw2JmNhd2TS+u+DZvX01DXuuhTWv36fN3F/qyeVc8W3p8lU0YfXFFvVq9sqpUvaSGP/jFf97XlejfY5z96Ma/eWBEDx0/fFqzPr34ZAFXs3/rI1zZvfEPLVtV1dDnu2rjhv367FP37G9B6TebnjoVr5dfnJGx/0OHTumDsfeofYca+v679f/9AK5QhnEu7lnHN7vl/9S8Q3UNeeN2bVrztz4fc/HJGK4m5/uErGOUVb97/nvu+Z5xblfp/cigj+9Xp3vaaPLI6Vq/eJOiyhfV3cPu0Ovzn9eQ9sOVnJiiGWN+0NJvV2j9kvOlt+sXb9IXf72vO5/rrld7jfmvh5jj+Ou37lw/cfr4WY188IuM/z7Rfx/XmFmD1PaW+po/JfeVxl6My7zyyp1yooAmIMOHD1epUqU0ffp0RUZGZno/NjZWTzzxhEaMGKGPP/44AC387+LPXRG64GpaePpN4/FxF79i1q1PU/V7oqM2rvlbwx//WqmpuWuax39z7orjhVd/zsX7wqtFl6N551o6ezpBq3/d/u8rX4XizqR/hy8Y6TgX84TLvOrbqH0Ntbq5vgZ2fkuGzZAhI+NH1ma3yXSZXp0EXuni0r+j4RdMJBEe5o5vfFxypm3+qcdtjXT/g2214c/9evGFbzP6iHOjrKtX7fY4T9y29bDOnk1UxUpZl87lFvHnrrznueB7nSfY4/3sdLu7mfoN7qyNq/dq+MDJuapvjjsdL+n8qMU55+7RiD+TuSQ4Lr1M+MLRkdD0EcD4MwkqVKKgbujfTlNen6WJL7knFdn461btWL1b4za9o873tdWcD3/Uwb8O6+AF5V/xZxK0Zfl2Vaid+b7Kq0Fc+sjRhVUTGb91//J9zc65EZTVv2z36G+3/7lPZ88kqGK1K/PiL3K+gCYga9eu1bRp07JMPiQpb968evrpp9W7d2+LW+Y7hw+ckjPNqRJlPOu4z73ev+dYVptJkh565gbd3Kuxfl2wSaNfmJmrfuC8Fb3/hJxpTkWV9azXLlHWfW/N/l3/vaynUZtrtWLRlovex3A1i953zB3jC+6nKZH+ev9lTnvZ/Ma6CgkL1ie/vpDpvR8Ovq+F01bqnccnXda+rySHD5+S0+lSyQtm/zr3et9F7it4dGBH3dqtgX5eslVvvv6dRx9xbr9BQZm7eYfDnuun1jx84GTWfXPp9L7jIiWBDw29UTff2US//rhRo5+bnuv65sO7j7hjV6m4x/Jzr/dvPZhpm4M73AlDyUrFPW4eL5m+zb6tB1W0TGHZbDZtWe55sefvLQd05nisylZ3T8jQ+o6mij0Rp3WLPG/IDgkLVuzxs//t4HKo6H3pv3UX3JtUIv31/l1HLnO/x939REjW/URyLi7ThH8F9Cb0vHnz6ujRi58gHj58WKGh3t0nkROlpqRp07p9ata2msfy5u2r62xsonZsztxRS9K9j7XXzb0aa+ak3/X6M9/muh84b6WmpGnT6r1q1rGGx/LmnWvq7JkE7djw32qBI/KFqWS5wrlu2t1/Sk1O06aVu9Tshtoey5vfWFdnTydox/p9l7XfyaN/0MDOb3r8mT/ZPRXnwM5vavLoH/5z268EqSlObdywXy1aVvFY3rJVVZ09m6jt2w5nuV2/Aa11a7cGmv7NKo0cMTtTH5GUmKpNmw6oecsqGWUWklS3XjmFhQVr48bcPQtWakqaNq39W83aV/dY3rxjDXffvCmbvnlQR918ZxPN/HKZXn96Wq7sm1OTU7Vx6TY1v/U6j+UtezTW2VNx2v7HrkzbHN4do8O7Y9SiexOP5S26N9GBHYd1dP9xHd4VI2eaUzVbXOuxTqlrSihf4byK2es+yb7poU4aOHaAHP9IrguVKKjqzapqw6+es5pdLVJT0rTpjz1q1qmmx/Lm19d2/9b9eXm/dUkJKdqy2r3foODz/USdppUVlieEWbCyEOjZrq6WWbACOgLSo0cPDR06VAMHDtR1112nqKgoBQcHKyUlRUeOHNEff/yh0aNHq0ePHoFs5n82Zdyvev2Tvnp+1O1aMHu9qtUurR59m2nCuwuVkpym8DwhKlOhiKIPntSZUwmqUKW4bru3uf7ackhLf9qsqjVLeexv/55jmW6czM2mjl2s1yYO0HPv9dFP01fr2npl1b1/K00YNd8d34gQlalUTNH7T+jMyfhL2nf5Ku6ZWS736tLVYur/ftRr3zym5z7tp5+mrtC1DSqo+8PtNWHkHKUkpSo8IlRlrimu6H3HdeZEnFf7PHrwZKanojdq704kd/7HxPFKM3nSco16+069NOxW/Thvg6rVKKXbezbWuE+WKCUlTeHhwSpbrrAOHzqtM2cSVLFSUfXs1UTbtx/WL79s07UXlEns+/u4EhJSNP7TX/T2/3rrtTfu0LfTVqpAwTwacH9bbd16SCt+zz3PT8jOlE9/0evj7tXzb/fUglnrVK1OGfW4p7kmjFlwvm+uWFTRB06k981Ruu2+Fvpr80EtXbBZVS+YInn/7qO5pm/++tUZenPhi3px2mD9+PkSVWtaRbc91VWfPfuVUpJSFB4ZprLVSunw7iM6c9w96cdXI2fo6c8fUezJs1oxd42adG2g1nc01St3vCPJPd3uzHd/0G1PdZUkrV24UcXKFlGfl27TkX3HNG+c+4nfk1+Zrtd/fEEvz3hKcz78UZEFI3T3y7fp7Kk4fTt6bmACYoGpHyzUa5Mf1HMf3q2fvvlD19Yvp+73t9aEN39QSnJq+m9dcUXvP35Jv3Wfv/WD3pryiEZMGKAZ435R/sKRuu/ZG7V9/T6tXLT533cAXAbDDGCRtWma+vDDD/X5558rISFzzWiePHnUu3dvDRo0SDbbfx+s6Vznpf+8j8vVtM21uuuhNipZrrBOHI3Vd9P+0MxJ7icc12pQTm99dp/efmmmFs79U3c91Fa9H2id7b6G9J+gjWv+9lhWrER+TZw3OGMfgWDEB24GmKYdqqvPwI4qVaGIjh85o+8nr9DMCe6nzNdsVEFvffWg3n5mmhbNXJtp2/bd6uvJN+9Q39av62j61KfntLi+lp57r48GdBqlgxcpl7NM3KUlUL7U9Pra6vNUF5WqWFTHY87o+8+XauYn7hOCmk0q662Zj+vtQZO06JuVmbZtf3tjPfnuXerb8MVMScc/9X7yBvV5qouuj3rEb8dxMSlVSgbkcyWpWfNrdM+9LVWqdEEdP35Wc2ev1bff/CFJql2njN75Xx+99cZ3WvDjJt1zb0vd1bd5tvsa/PhkbUi/Ilqtekn1699aVa8toeTkVC1f9pc+/mjxv95b4i9BJwL3Hc5K07bVdNcj7c73zVNWauaX7gfA1mpQXm993l9vvzBdC+es112PtFPvB9tmu68h936mjWsCf8XYueUvSz6n2S2NdPew21WqSgmdOHRSc8f+qOnvuJ81UatVNb3983CNuvdD/TTxl4xtutzfXrc92VVFShdS9J6jmvrGLC2avNRjv7cOukE3PtBRxcsX1cnoU1q7cKM+f35KRiIjuZ+Y3ufFHqpQq6xcLpfWLNigcc9M1rED/p8K2VE287N5rNK0Y031eaKTSpUv6v6tm7RMMz/7VZJU87qKemvqI3r7qSlaNGN1pm3bd2+oJ0f3Ut/mr2T6rbu2Xjn1feoGValTRsmJKVqxcLM+e3Xuv94L5S/z974TkM/1xrr9ZQLdhCzVK3NlXbgLaAJyTmpqqrZt26YjR44oMTFRoaGhKl68uKpWrargYN894TuQCUhuEMgEJNcIYAKSGwQyAcktcloCcjWyKgHJrQKZgOQWOTkBWb2/XKCbkKWGZf4OdBMuSY54wEZQUJBq1aoV6GYAAAAA8DOehA4AAADAMjliBAQAAADI6XgQoW8wAgIAAADAMiQgAAAAACxDCRYAAADghSvxoX85ESMgAAAAACxDAgIAAADAMpRgAQAAAF5wmly79wWiCAAAAMAyJCAAAAAALEMJFgAAAOAFF9fufYIoAgAAALAMCQgAAAAAy1CCBQAAAHiBBxH6BiMgAAAAACxDAgIAAADAMpRgAQAAAF7gQYS+QRQBAAAAWIYEBAAAAIBlKMECAAAAvOBiFiyfYAQEAAAAgGVIQAAAAABYhhIsAAAAwAtOrt37BFEEAAAAYBkSEAAAAACWoQQLAAAA8AIPIvQNoggAAADAMiQgAAAAACxDCRYAAADgBRfX7n2CKAIAAACwDAkIAAAAAMtQggUAAAB4wWkagW7CVYEREAAAAACWIQEBAAAAYBkSEAAAAACW4R4QAAAAwAtOrt37BFEEAAAAYBkSEAAAAACWoQQLAAAA8ILL5Nq9LxBFAAAAAJYhAQEAAABgGUqwAAAAAC8wC5ZvEEUAAAAAliEBAQAAAGAZSrAAAAAALzhNI9BNuCowAgIAAADAMiQgAAAAACxDCRYAAADgBRfX7n0iVyUgQ2dPDXQTrmpJZq76OgVEkhkc6CZc1ZJcQYFuwlWvdNCJQDfhqnfWFRroJlzVnNoW6CYAVzzSOAAAAACW4ZI1AAAA4AWnybV7XyCKAAAAACxDAgIAAADAMpRgAQAAAF5wiQcR+gIjIAAAAAAsQwICAAAAwDKUYAEAAABeYBYs3yCKAAAAACxDAgIAAADAMpRgAQAAAF5wcu3eJ4giAAAAAMuQgAAAAACwDCVYAAAAgBdcJg8i9AVGQAAAAABYhgQEAAAAgGUowQIAAAC8wCxYvkEUAQAAAFiGBAQAAACAZSjBAgAAALzgMrl27wtEEQAAAIBlSEAAAAAAWIYSLAAAAMALTvEgQl9gBAQAAACAZUhAAAAAAFiGEiwAAADAC8yC5RtEEQAAAIBlSEAAAAAAWIYSLAAAAMALzILlG4yAAAAAALAMCQgAAAAAy1CCBQAAAHiBWbB8gygCAAAAsAwJCAAAAADLUIIFAAAAeMFJCZZPEEUAAAAAliEBAQAAAGAZSrAAAAAAL7h4EKFPMAICAAAAwDIkIAAAAAAsQwkWAAAA4AVmwfINoggAAADAMiQgAAAAACxDCRYAAADgBZfJLFi+wAgIAAAAAMuQgAAAAACwDCVYAAAAgBecXLv3CRIQi2xeLc2ZKB3eL0Xmk1p1kTrfIRnZlBKmpkjfTZZWLZbiYqXipaWOPaTr2ma9fmK8NOIh6aY+UtOO/juOK8nWNaZ+mOhSzH4pIp/U7AZDHe4wZGQT9NQUU/Mnm1qzxFR8rFS0tNS2u6GGbelsJGnHGqd+/DJVR/ebypPPUOMb7GpzuyPbeDqdppbOSNMfC5yKPWGqcElDbW53qE4rz25nzcI0/TojTScOm4osaKh+O7va9XLI7shddbY716Rp8aQkHTvgUnheQw1vCFaL24IvGt/lM1K0bmGqzp5wqVAJm1rcHqKaLYM81tu2IlW/TEnWiUMuRRQwVLute7+OoNwVX0natNrQzC9sOrzfUGQ+qXUXl7r0dF20H549yaYVi22Ki5WiSkudezjVpJ3psd6a3wzN+8am6AOGwsKlanVN3dbfqXwFLDioHI5+2P+2rXFp3kSXjuw3FZFPanqDTe3usGUb47QUUz9OdmntEldGjNt0t6s+MYaFSEAssHuL9OEwqUEr6ea+0q4t0uwvJJdL6nJn1tuMe13auMqddFStIx3YLU1+V4o7I7W71XPd+Fjpg2HSiSOGJDOLveU+e7aaGjfMpbotDXXpa2jPZlM/TDRlmlKnXll3yhPfcGnzKvePXZU6hg7uNjXtPVPxsS61viV3d8x/b3Xqi+Epqt3Srs5327V3i0sLJqbJdEntegVluc3CyWn6+Zs0tb/ToXLVbNq0zKmv30iVzWaoVgu7JGnZ7DTN/SRVNZvb1KVfkOJjTS2cnKbovS71fSnEykMMqP1b0/T1Kwmq0SJI7e4K1b6taVr8ZbJMl9SqZ9Zx+PmrZP32bYpa9wpRmWvt2vp7qr59M1E2m1S9ufu/ya71aZr6aqJqtHCow72hOvK3U4snJiv+jEs3PhRm5SEG3M4tht592a5GrUx1u8epvza7kxHTlG6605XlNh+/ZteGVYY69XCpWl1T+3cZmviuXWdjXep4q3ub1UsNjR3pUOsuTnXr61LsaWnWRLveGuLQsA/TFBRs4UHmMPTD/rd3q0vjhzlVp6WhG/ratXezqXkTXTJNqUMve5bbfPmGU1tWmWrT3abKdQwd2m3qm/ecios11eqWrLcBfI0ExALffSWVriD1G+J+XaOh5EyTfvxG6tBdCr7g/GL/LunP3w3dco+pG3q5l1WrJ4WESjM+k5p0kMIj3Mv//F2a+pGUnGjd8VwJfpzsUskK0t1D3D9Y1RoYcjpdWvSNqTbdTAWHeP74HdhlauPv0o33GOrY071NlXqGgkNdmjPeVKP2psIjct8V43MWfZWmEhUM9XzafTZVpYFdrjTp52/T1LKbQ0EhmWOz+qc01W1tV4fe7pPhynXtOrw7Sb9/n6ZaLexyOU0t/CpVlevadNfz5/8RlKpk09sPJuuvdU5dUy93/Bj+PCVZxSvY1P0pd1JQuYFDrjTpt+nJanprcJbxXb8wVbVaBanNne7YVazrUPRul1Z9n5KRgKxfmKJ8RQx1fypMNruhSnUdij9tasXsFF0/IDRXjTLNmWxTmYqm7n/GKUmq2dCU0ynNm2ZTp+6uTP3wvl3Sut9t6n6vUzf2cicb1euZCgmVvvnMpuYdXAqPkOZ+ZVetRi71HXQ+iSle2qlXHnPoz5WGGrbMvReF6If9b8Fkl0pWMNRniPt07toGktMpLf7GpVbdbJlifHCXqU2/m7rhHps69HT3r1XqScGh0nfjXWrU3qYwYnxRzILlG1xO8LPUFOmvjVLd5p7L67eQkhMN7dyceZvo/e6/azX2XH5NTSk5ydCODe7XCXHSR69IVWpJg17zfduvVKkppnZukmo38+wk6jQ3lJwo7c4i5kcOuE8SalznuU2lmoZSkqSdG/zW3BwvLcXU7o0u1WjmmQzUbG5XSqK0d3PWV4+dqVJIuOey8HyGEmLdsT57WkqMk6pd57nfYmVtypNX2vaH02fHkJOlpZr6e6NT1zbxHEmq3jxIKYnSvi1ZxyEtq/jmNZR49vwJrzNVCgo1ZLMbHus403LXRYvUFGnHRkP1m3kmAw1amEpKNPTXpswnFIf3u5fVbuz5/a5Sy6XkJEPb/jTkcknV67nU6gbPdYqXcn/O0ejce6JCP+x/aSmmdm0yVfOCGNdOj/GezZmT33Mxrn6d5+lfxZq29Bjn3oQZ1iIB8bPjMVJaqqFiJT2XFynh/vvIwczbROZz/33iiOfyo9Hn9ym5R06Gfyrd+7QUkdd3bb7SnYhxn3gVLenZKZ+L+bFDmTvYiHzudS+M+fHoc/vMvZ3yiRhTzjSpcEnP7qJQCXfMsoqnJLW41aG1i53ascappHhT65ak6a81LtVr5044wvJINrt08qjn9glnTSXGSSdzScxPRbuyjG/BKPfrE4eyTvCa3hKsP5ekaueaNCUlmNrwc6p2rU1T7bbnE5lGNwbr5GGXls1IVmKcqQPb07RyTooqN3AoPDL3nBwfO9cPl/L8ThUr4X4dcyhzLPKe64djPN87l1QcjzFks0k9H3CpXlPP/a5d5l6nVLnc8R3OCv2w/2UX48IX6Zsj0r/XJ494vnci2v06t/S7CDxKsPwsIc79d+gFVyrPvU5KyLzNNbWkwlGmpo51JxnlrpEO7pFmjpcMm6nkJPd6jiD3zenwlJhNzEMuEvNKNaVCUdKMj1wKDrGpzDXS4b3S3AkuGTYpJcm/bc7JkuLdP0jZxTM5IesfrGZdHdq7xaXxL6ZkLGvY0a7WPdwnyMGhhmq3tOv3uWkqXsZQ9aZ2xZ0xNffjVNkcUmouiXlienxDwj1PIoIzvq9Zx/e6rsHatyVNk14+/4Wu1yFIzbufryUqX8uuZt2D9dOEZP00IVmSFFXRptuG5K77PxLi3LENu4R+uEotU0WiTH011q7gUKfKX2PqwB5D335m9+iHLxRzSPpmnF1lK5mq2TD3nszRD/tfYty5vsNz+cViXLGmoUJR0qyPnAoOkcpcY+jQXlPfTXASYy+5rsJr9y6XSx988IG+/fZbxcbGqn79+nr55ZdVtmzZLNc/duyYXn/9dS1fvlyS1LhxYw0dOlTFixf3+jNJQPzMTP/9yW6WFSOL77EjSHr8VWniO9KYZ90b5itoqufD0qevue8FQfbOxVzZxTyL5Y4gQw+/atPX77j04VD3Fee8BaXuD9n0xesuBefimJtZX4DPkNV3OC3F1EdPJ+vsKVPdHgtSkVKG/t7i0pJpaQoOS9HND7rvJen2WJAcQdL0d1P17f9SFRQitb7NodRkKSiXxPxyvq9pqabGD4lX3ClTNz0aqsKlbNq/xaml3yQrOMzQDQ+4g/fdB0lavyhVrXoGq0Jth04dcennr5L15UsJuufVcAWH5o5RkH/th7PsE6QnX0vThLftGvWM+6cyf0FTdz7s1Eev2bPshw/vl0Y/65AjSHrkxTTZrr7zFK/RD/uf67K+14YeeNWhqe849dFQd3ln3oLSrQ/Z9eXrTmKcS40dO1ZTp07V66+/rmLFimnUqFEaMGCAvv/+ewUHZ55J44knnpDT6dTnn38uSRo+fLgefvhhzZw50+vPJAHxs/A87r8vvBJx7vWFV+TOKVpSevptKfZ0+lSEJaVTxyTTZShPZO69quaNsGxinpz+OjRP1tsVKWFo0Gi7zqbHvEhJ6fQx9wl4nkj/tTenC02/ITE5u3iGZ/6V27Tcqei9pga8FqzKdd0lVxVr2RUWYWj22FQ16uRSVHmbQsIM3fZEsLo+aOrUUVMFixkKDjW0+qckVayVO87ewvKci6/nv+uUjO9r5vhuXZ6mI3td6jsyXBXrurvx8jUdCo0w9MNHSarfKUhhEYbWLkhVi9uD1e4u91lFeUklK9v14SPxWr8wVdfdlDumaArP445tYrzn8ox+OJs+oVhJaeg7TsWecirurPv1yaPp/XBez/9e2/409MEIu0LDpKffTFORKF8fxZWFftj/zvUd2cU4u+91kRKGHhvt0NnTphJipcL/iHFuKs2EW0pKiiZMmKCnn35arVq1kiSNGTNGLVq00MKFC9WlSxeP9WNjY7V69Wp99NFHqlatmiTp/vvv18MPP6xTp06pQAHv5h8PeAJy1113ZTtX9YW+/PJLP7fG94qUkGw2U0cPey4/lv46KovRrZRkad0yqVJ1qXBxKW9+9/J9O91/l6nkt+ZeFQqXkGw26fhhU/+8/HYu5sXLZP6+pSSb2rDMVIXqhgoVNxSZ3718/073SUapSrm3Uy4U5a51Px7tknT+hvETh92xKZpFPE+l39dRrppnElGhpvv1kf3uBGTrKqfCI6Ry1e0qXta9n7jTps4cM1WyUu5IQApE2WSzSSejPYeazr0uUiZzHE4fdb9XpprnDfzlarhfH93vUr4ihkwz8zrFytkVntfQ0f254yZ/SSqa0Q97TlV+5LD7O1eibOaLOinJ7ud7VK5uqkiUlDf9N/Xvne5tylY6v82KJYbGj7areElp8GtpKljEf8dypaAf9j/PGJ937nWxbGK8cZmp8hfE+MBOd59CjP+d8yqbBWv79u2Kj49X48bnZz7KmzevqlWrptWrV2dKQEJCQhQeHq7Zs2erUaNGkqQ5c+aoXLlyypcvn9efG/Bf+CZNmmj16tU6ceKESpYsedE/V6KgYKlyTWn98n8MSUta+5sUHmGqfJXM2zgc0pQPpaXzzi9zOaUlc6SiJUyVKOf3Zl/RgoINVawpbVhuyvxH0P9cZiosQiqbTcynjzW1fN759V1OU0vnulSkhBRVzoKG51BBwYbK17Rp83KnRzw3LXMqLEIqUyVzN1K0lHvZhTNk/b3V/bpgcff7K+el6fvPUj3W+W12mgybdG2jgHdPlggKNlS2hl1bf0/ziO+WZakKzSOVuibzVMSF0+N74QxZ+7e5XxcoZlOhEu7E5sJ1jh90KiHWVP5iuSO+krsfvqamqbXLDY9+eM1vhsIjTFWokjkBcTikyR/a9cu883FyOaXFc2wqWsJUyXLuZRv+MPTZW3ZVqmbquf+RfJxDP+x/QcGGKtQ0tPGCGG9Ij3GZKplPlB0OacZYp1bMO983u5ymls11qXAJqXg5K1qOnCQmxj2zUVSU57Bt0aJFFR0dnWn9kJAQvfrqq/rjjz/UoEEDNWzYUH/++afGjRsn2yXUnQZ8BOThhx9WeHi43nvvPX3yyScqVapUoJvkc13ulMY8K33yqtSsk7Rnq/TTdKlbP/dN5onx7ql3i0RJkfndMwO1vlFaNFvKX0iKKiP9PNf9QMOHhylX1xV7q1Mvmz4c6tLnr7rUuJNNe7eaWjLdVNf7DAWHGEqMNxWzXyocJUXmd09T2vxGQ7/MNpW/sEvFShv67TuX9m6RBrxsk812dV3xuFTtejo07rkUTX4tRQ07OrRvm0u/zkjT9fe5nwGSFG/qyH5ThaIMReQ3VK2xTWWqGJoyKkUd+wSpSGlDB3a4tHhKmq69zpaRtDTv6tBnL6Ro7scpqtbYrl0bXPp5Wpra3O5Qoajc80Vv1TNEE59P0DevJ6puxyAd2ObU8pkp6nBviDu+CaaO7XeqYJRNefLZVPU6h0pVsWvG6ES16R2iwqVsOrjDqaXTklWlkfs9SWp8c7CWz3BPAlCxjkNnjrr085Rk5StiqEGn3FF+dc5Nd7o0+lm7xo60q0Unl3ZtNfTjtzbd1s+V0Q8f3m+oSJSpvPnd/XDbm1xaOMumAoWlEmVMLZ5j084thgYOd8pmc0/v+8U7doWGSzf1cil6v2c/UaCwmasTEvph/+vYy6aPhjo18VWnrkuP8c/TXbrxPvczQJLiTcXsN1U4vW92x9imX2e7lK+wVKy0oWXfubR3i6n7XrYT4ytYu3btLvr+4sWLs1yemOiek/3Cez1CQkJ05syZTOubpqkdO3aobt266t+/v5xOp8aMGaNHHnlEU6ZMUUREhFftNcx/ps0B1L9/f+XPn1+jR4/222f8+vc1ftv3v1m/XJo7yT3tbv5CUuub3E85l6QdG6S3hxi650lTTTu6l6WlSd9PllYskhLOSqUqSjf2lqrXz3r/x2Ok5/p67sNqSWbA81kPG5abmj/JpSOH3DFvcZOhtt3dJ7U7N5h6/xmXeg82dF1H9zJnmqn5k02tXmwq/qxUqoLUqbdN19bPOR1ykhm4k8bNy536aXKqjh00la+woSY32tWqu3tGq90bnfrkmRTdPjhIDTq4vwdJ8aZ+nJiqTcudSjwrFSxuqH57u1rc6pAj6HxM1/+SpiVT0nTyiKkCRQ016eJQs5sD811KcmX9VHcrbP09VT9/lazjB13KW8hQoxuD1aybe0arvRvT9PnQBN36eKjqdnB/B5ISTC2emKStv6cp8aypAsVtqt02SE1vDc6Ir2maWjEnRWvmp+pUjEuRBQ1VrOtQ+74hypMvMAle6aATAflcyT097uxJdsUclAoUktp2dalzD/eV4O0bDL35tEP9nkpT847un8W0NGnOJJt+X2RT/FmpTEVTXXu7VKOB+/2t642MG9SzcnMfp265+19mcfCDs66ccyfx1dgPOwNfPOJh43KXfpzk1NFDUr5CUvObbGrT3X0RYtcGlz58xqleg+1q9I8YL5js0urFLiWclUpWMNSxt01V6+ec47qhfBYPiskhBq3vFegmZGnzU0cv+n52CciCBQs0cOBAbdiwQaGh5/uOQYMGKSUlRR999JHH+t9//72GDx+un3/+OSPZOHPmjNq0aaNBgwapb9++XrU3xyQgR44c0datW9WmTRu/fUYgE5DcIKclIFejQCYguUEgE5DcIpAJSG6RkxKQq1FOS0CuRiQgl+7dulMua7uNGzfqtttu08KFC1WmTJmM5b169VLVqlX18ssve6w/fPhwbdmyRd98843H8u7du6tWrVqZ1s9OjvlXVKxYMb8mHwAAAADOq1q1qiIiIrRq1aqMZbGxsdq6dasaNGiQaf2oqCjt27dPycnJGcsSExN18ODBbJ8bkpUck4AAAAAAOZnLtOXIP5crODhYffr00ejRo7V48WJt375dTzzxhIoXL64OHTrI6XTq2LFjSkpyP6XylltukSQ9/vjj2r59e8b6wcHB6tatm9efSwICAAAA5FIDBw5Ujx499MILL6hXr16y2+0aP368goODFR0drebNm2vePPfUrEWLFtXXX38t0zTVt29f3XvvvQoKCtKUKVOUN29erz8zx9wDYgXuAfEv7gHxP+4B8S/uAfE/7gHxP+4B8S/uAfG/nHwPyGPrege6CVl6v95XgW7CJeGMEQAAAPCCUzlnRrYrGWk8AAAAAMuQgAAAAACwDCVYAAAAgBdcJiVYvsAICAAAAADLkIAAAAAAsAwlWAAAAIAX/stD/3AeUQQAAABgGRIQAAAAAJahBAsAAADwgosHEfoEIyAAAAAALEMCAgAAAMAylGABAAAAXnDyIEKfYAQEAAAAgGVIQAAAAABYhhIsAAAAwAs8iNA3iCIAAAAAy5CAAAAAALAMJVgAAACAF1zMguUTjIAAAAAAsAwJCAAAAADLUIIFAAAAeMElSrB8gREQAAAAAJYhAQEAAABgGUqwAAAAAC8wC5ZvMAICAAAAwDIkIAAAAAAsQwkWAAAA4AWXybV7XyCKAAAAACxDAgIAAADAMpRgAQAAAF5gFizfYAQEAAAAgGVIQAAAAABYhhIsAAAAwAsuUYLlC4yAAAAAALAMCQgAAAAAy1CCBQAAAHiBWbB8gxEQAAAAAJYhAQEAAABgGUqwAAAAAC9QguUbjIAAAAAAsAwJCAAAAADLUIIFAAAAeIESLN9gBAQAAACAZUhAAAAAAFgmV5VgNQt1BboJV7mUQDfgqmdTWqCbAPxHuepnJyBSzaRAN+GqdspFfHMzSrB8gxEQAAAAAJYhAQEAAABgGcbCAQAAAC+4RAmWLzACAgAAAMAyJCAAAAAALEMJFgAAAOAFZsHyDUZAAAAAAFiGBAQAAACAZSjBAgAAALxACZZvMAICAAAAwDIkIAAAAAAsQwkWAAAA4AVKsHyDERAAAAAAliEBAQAAAGAZSrAAAAAAL1CC5RuMgAAAAACwDAkIAAAAAMtQggUAAAB4waQEyycYAQEAAABgGRIQAAAAAJahBAsAAADwgkuUYPkCIyAAAAAALEMCAgAAAMAylGABAAAAXuBBhL7BCAgAAAAAy5CAAAAAALAMJVgAAACAF3gQoW8wAgIAAADAMiQgAAAAACxDCRYAAADgBWbB8g1GQAAAAABYhgQEAAAAgGUowQIAAAC8wCxYvsEICAAAAADLkIAAAAAAsAwlWAAAAIAXmAXLNxgBAQAAAGAZEhAAAAAAlqEECwAAAPCCaQa6BVcHRkAAAAAAWIYEBAAAAIBlKMECAAAAvOASs2D5AiMgAAAAACxDAgIAAADAMpRgAQAAAF4weRChTzACAgAAAMAyJCAAAAAALEMCkoNFH5Uad7Hpj/WBbsnVixj7V/RRqVEXEV8/Isb+R4y9s2yVoZ7329Wok0Od7nDos69sF31oW0qK9O6nNnW4zaGGHR26vb9DPyzMXN4yZ76hW+9xqEEHhzr3dOjDz21KTfPjgeRgq/6w6/4Hw9Xx+gjd3jOPJn8d/K8x/nRcsHrckUcdOkeo3/3hWrgoc/X9vv02DX0+TNffGKGbbonQ8y+G6vBhSo2y4jKNHPnnSsM9IDnU4Rjp/qdtOht35X2prhTE2L8OxUgDnlZ6fHl0rD8QY/8jxt75c7Ohgc/b1bmNqUf7ObV+k6H3P7PJ5ZLuv8uV5TZDRti1dIWhvne4dF09U9t2GRrxtl2nzrjUp4d7m8nTbXrrA7s6tHJp8EMunT4jjf3crp27Df1vpNPKQwy4zZtteu6FMLVpnaZ+9yVr0ya7PhsfLNMl3dUnJctthr8SqhUrHep5e4rq1XNq506b3n4nVGfOJKtH91RJ0tGjhh4dGK7SpVx68flEJScbGj8hRE8NCdfn4+MVEmLlUSK3IAHJYVwuac6PhkZ9xEmxvxBj/3K5pNk/Sm99FOiWXL2Isf8R40vz8USbqlYy9drz7qSg+XWm0pzShK9tuvt2l0IvOIndtlNassymx/o7NaCPO9lo3MBUWKg05mObunZyKU+4e79NGrj09vDzyUa1a9J06z1BWrHGpSYNck9S+MWXIapU0aUXnkuSJF3XyKk0p/TVlGDdfltKpkThr502LVsepP79knVXb3eC0qC+U6Fh0iefhKhTp1RFRkgTvghReJipd0YnKDTUvW1UlEvPvRCm7Tvsql0rdyV6sAYlWDnMjt3SiDGGbu5k6o3ns75qhP+GGPvXjt3S8DHSLZ2kN58PdGuuTsTY/4ix91JSpNV/GmrXwjMZ6NDKVEKioXUbM1/s2bPPvaxVU88+uEFtlxKTDK3+09CJU1LsWUOtmnrut2I5qUA+U7+uyD0XkVJSpD832NWyhWftWauWaUpMNLRxoz3TNvv2u0/xmjbx3KZOLacSkwytX++QaUq//ebQDTekZiQfklS1ikszv40n+ciCaebMP1caRkBymKhi0vyvXCpelHpjfyHG/hVVTFrwlYivHxFj/yPG3jsYLaWmGipb2vMsqExJ9+t9Bww1bej5XsH87r8Pxxi6psL59w6k33dwKNq9jcNu6nCM5+fFnnX/ORSdexKQw9E2paYaKl3KM2ErVdL9+sBBmxo29EwW8udzxzUmxlDFCv/YV3qMo2MMxcQYios3VLyYS2PeDdGSn4OUlCjVr+/UE4OSVKzYFXhmiytCwEdA9u7dq/fff18jR47Ur7/+mun9uLg4DR06NAAtC4z8ed0/ePAfYuxfxNf/iLH/EWPvnbuPLiLcc3l4mPvvuITM2zSobapUCVNvvGfXyrWG4uKltRsN/e8Tu2w2U4lJUlio1KmNqSmzbJo1z1DsWWnvfve9Iw6HlJjk5wPLQeLi3H+H5/FMCMLSYx6fkDkZq1PbqRJRLr33QajWrrMrPl7asNGuj8eFyGYzlZRk6PRp93afjAvR8eOGXno+UU8/laRdu216fHC4EhP9eljIxQKagKxdu1a33nqrvv/+ey1dulQPPvigHnvsMaWknL+ZKikpSbNnzw5cIwEAQLZc5y7KZzMgYctieVCQ9PFbaSpe1NT9TzrUtEuQhgy365H73Ffxw9LLgV4c7NSNHUwNG2VX85uCdMf9DtWubqp6VTNjndzg3MPvjEuM8ai3ElS0iEuDnwrXDTdFavgroep3r/scKzTUVGqae8MCBUy9MjxJDRs61bFDmoa/nKjD0TYtXBTkl+O5kpmmkSP/XGkCWoL19ttvq0ePHnrhhRckSfPnz9fzzz+vBx98UJ988omCgvjiAwCQk0VGuK/Kx18w0pGQfvU8IiLr7cqUkr54z6kTp5w6EyuVKSnFHJNcLkP5It37DA+Xhg9x6plHpcNHpBLF3SMrs+c7VCoq95QHRaSPfMTHe55oJqbHPE+erGNRqqSp999N1KlThs7EGipVyqVjRw25XIbyRpoKD3dvd12jNNn+cUm6ejWXIiJM7dwV8EIZXKUC+s3asWOH+vTpk/H6+uuv17hx47R+/XoNGTIkgC0DAADeKF1CsttM7T/keXJ87nXFsplPjpOSpe9/MnQwWipUQKpQVnI4pK073Ntce417m19/N7R+k6HwcKlSeXfyceKUFHP0/Dq5QYmSLtltpg5dEOODh9ynceXKZZ5QJTlZ+mmhQ9HRhgoUMFWurEsOu7TjL/cN69dUdqlECZdsNlOpqZmvoDvTxBS88JuAJiARERE6deqUx7L69etr1KhRWrBggV5//fUAtQwAAHgjJESqV9vU4qWGx2w8C381FBlhqsa1mROFIIf0+rt2zfju/GmI0ylNmWVTmZKmKpV3L/t2rk1vf+R5qjJ5uk12m9SqSe6ZxTAkWKpVy6mly4I8YvzrUociIkxdWzXzbFUOh/Tue6H67vvz1SROpzRzVpBKlnSpfHmXwsOkWjWdWvqbQ/+oftfadXYlJhmqVZNZsC4U6FKrq6UEK6AJSKtWrTRixAht2LBBqampGcvbt2+v5557ThMnTtSIESMC2EIAAPBv7r/LpU3bDD01zK7fVhn6YLxNX0y1qX8f9zNA4uKlDVsMnTztXt9ul26/xaWvZtg0ZaZNK9caevJlu/7cZGjIo86McqA7u7u0catNb75v06p17ocbjv/Krr53uFSqRMAONyDu7pOibdtsenl4qFausmv8hGBNnRasPncmKyREio+Xtmy1ZdxYbrdLN9+coukzgzVzVpDWrrPrpWGh2rzZrsceScqI8YD+yTpxwtAzQ8O0cpVd83906JVXQ1XtWqeaNc2lj5yH3wU0AXnyySdVoEAB9ezZUytWrPB4r0+fPnrppZe0ZMmSALUOAAB447p6pt4Z4dTfBww9/oJdPyyyafCDLt3b0z1Kse0vQ3c94tBv/3h2x8P3unTXbS59PtWmQc/bdeq09OGbTrVscv4Sf9OGpt54MU0r19r02FC7Fi216dmBTg26P/eMfpxTr55TI4Yl6cBBm154KUwLFwfpoQeS1aun+wLuXzvtevjRPFqx8vwzQe67J0W390jRlGnBev6FMJ05Y+jN1xPVpPH5kY0a1V3639sJcpnSS8PC9NHHIWraJE1vvZkge+bHiwA+YZhm4B9fsn//fhUoUECRkZGZ3tu7d69++uknPfDAA//5c9JiKv3nfQCBZAv8zNkAcrhUk6vW/nTKlYvm/w2Q4iUPB7oJ2ao+Z1igm5ClLTcPC3QTLkmOeBBhmTJlsn2vfPnyPkk+AAAAAAQel1MBAAAAWCZHjIAAAAAAOV3gb1y4OjACAgAAAMAyJCAAAAAALEMJFgAAAOCFK/GhfzkRIyAAAAAALEMCAgAAAMAylGABAAAAXqAEyzcYAQEAAABgGRIQAAAAAJahBAsAAADwAs8h9A1GQAAAAABYhgQEAAAAgGUowQIAAAC8wCxYvsEICAAAAADLkIAAAAAAsAwlWAAAAIA3mAbLJxgBAQAAAGAZEhAAAAAAlqEECwAAAPACs2D5BiMgAAAAACxDAgIAAADAMpRgAQAAAF4wmQXLJxgBAQAAAGAZEhAAAAAAlqEECwAAAPACs2D5BiMgAAAAACxDAgIAAADAMpRgAQAAAN6gBMsnGAEBAAAAYBkSEAAAAACWoQQLAAAA8AIPIvQNRkAAAAAAWIYEBAAAAIBlKMECAAAAvEEJlk8wAgIAAADAMiQgAAAAACxDCRYAAADgBZMHEfoEIyAAAAAALEMCAgAAAMAylGABAAAA3mAWLJ9gBAQAAACAZUhAAAAAAFiGEiwAAADAC8yC5RuMgAAAAACwDAkIAAAAAMtQggUAAAB4g1mwfIIREAAAAACWyVUjIDbyLQDAVc5u8FvnT6lcAgf+M3opAAAAwCtGDv1z+Vwul9577z21aNFCtWvX1n333ad9+/Zlu35qaqrefvtttWjRQnXq1FGfPn20bdu2S/pMEhAAAAAglxo7dqymTp2qkSNHatq0aTIMQwMGDFBKSkqW6w8bNkzTp0/XK6+8ohkzZih//vwaMGCAzp496/VnkoAAAAAAuVBKSoomTJigxx57TK1atVLVqlU1ZswYHTlyRAsXLsy0/oEDBzR9+nS9/vrrat26tSpWrKjXXntNwcHB2rx5s9efSwICAAAAeMPMoX8u0/bt2xUfH6/GjRtnLMubN6+qVaum1atXZ1p/2bJlyps3r1q2bOmx/pIlS9SkSROvP5cEBAAAAMiFYmJiJElRUVEey4sWLaro6OhM6//9998qXbq0fvrpJ3Xr1k3NmjXTgAEDtHv37kv63Fw1CxYAAABwtWnXrt1F31+8eHGWyxMTEyVJwcHBHstDQkJ05syZTOvHxcVp//79Gjt2rIYMGaK8efPqo48+0p133ql58+apUKFCXrWXERAAAADAG4EutfJxCVZoaKgkZbrhPDk5WWFhYZnWDwoK0tmzZzVmzBg1b95ctWrV0pgxYyRJs2bN8vpzGQEBAAAArmDZjXD8m3OlV0ePHlWZMmUylh89elRVq1bNtH7x4sXlcDhUsWLFjGWhoaEqXbq0Dh486PXnMgICAAAA5EJVq1ZVRESEVq1albEsNjZWW7duVYMGDTKt36BBA6WlpWnTpk0Zy5KSknTgwAGVLVvW689lBAQAAADwhvnfHvqX0wQHB6tPnz4aPXq0ChYsqJIlS2rUqFEqXry4OnToIKfTqZMnTyoyMlKhoaFq0KCBmjZtqmeeeUYjRoxQ/vz59d5778lut+vmm2/2+nMZAQEAAAByqYEDB6pHjx564YUX1KtXL9ntdo0fP17BwcGKjo5W8+bNNW/evIz133//fTVq1EiPPvqoevToobi4OH355ZcqWLCg159pmKb5H25dubK4Yq4JdBMAAPArl1yBbsJVLdoZH+gmXPVKl8w8/WtOUe7ztwLdhCz9fe+QQDfhklCCBQAAAHgh91y29y9KsAAAAABYhgQEAAAAgGUowQIAAAC8QQmWTzACAgAAAMAyJCAAAAAALEMJFgAAAOCNq+xBhIHCCAgAAAAAy5CAAAAAALAMJVgAAACAFwxmwfIJRkAAAAAAWIYEBAAAAIBlKMECAAAAvEEJlk8wAgIAAADAMiQgAAAAACxDCRYAAADgDR5E6BOMgAAAAACwDAkIAAAAAMtQggUAAAB4g1mwfIIREAAAAACWIQEBAAAAYBlKsAAAAABvUILlE4yAAAAAALAMCQgAAAAAy1CCBQAAAHiDEiyfYAQEAAAAgGVIQAAAAABYhhIsAAAAwBumEegWXBUYAQEAAABgGRIQAAAAAJahBAsAAADwgsEsWD7BCAgAAAAAy5CAAAAAALAMJVgAAACANyjB8glGQAAAAABYhgQkB4s+KjXqIv2xPtAtuXoRY/8ivv5HjP2PGHvnt1XS7ffbVL+jTe1vt2ncZEPmRa4Wp6RIYz411K6HTfU62NS9n03fL8z8jIVZ8w3dfI9NdTvY1PEOmz6YYCg1zY8HkoP98YddDz+YR12uj9SdPSP09dfB/xrjz8aFqNcdEbqhc6QeuD+PFi/KXPyyf79NLz4fpq43RurWWyL08othOnyY513AfyjByqEOxUgDnpbOxhlivM8/iLF/EV//I8b+R4y9s36z9OhzNl3fxtRj/Uyt22To3c8MuUzpgbuyjttTw236dYV0T09TjeuZ2rbT0LC3DZ06I93Vw73NpOmG3njfpo6tTD31oEunzhj68HNDf+029N6rLisPMeC2bLbrpRfC1bp1qu65L0mbNzn0+fgQmS6pd5+ULLd59ZUwrVzp0G23p6huvTTt2mnXmHfCdOZMsrp1d29z9KihQQPDVbqUS889n6jkZOnzCSF6dkgejRsfp5AQK48SuQUJSA7jckmzf5Te+ijQLbl6EWP/Ir7+R4z9jxhfmrFf2FS1kvTGC+7EocV1ptLSpM++MtT3dlOhF5zEbvtLWrzM0KD+Lt2fnqA0aWAqLFR6+xNDN3cylSdcGvuFoaYNTI0ZcS7ZMFWtiqmb+9r1+2qpaUMLDzLAvvwyRBUruvTsc0mSpEaNnHI6palTQtTjtpRMicLOnTYtXx6k+/ol6c7e7mSjfn2nQsNMjfskVB07pSgiQpr4RYjCw6S3RicoNNS9bfEol156IVx/7bCrZi2nlYeJXOKSSrCOHTumYcOGqV+/fnrmmWf0xRdfaM2aNUpMTPRX+3KdHbul4WOkWzpJbz4f6NZcnYixfxFf/yPG/keMvZeSIq3+U2rf0nOko2MrUwmJhtZuzLzN7n3u8p7WTT23aVjHVGKioT/WSydOSbFnjUzrVConFchn6tcVuadEKCVF2rjBruYtUj2Wt2iZqsREQ5s22jNts3+/+xSvcRPPerXatZxKSjL053qHTFNa9luQrr8hJSP5kKQqVVya9m0cyQf85pJGQJ577jktW7ZMlStX1sGDB/Xdd9/JNE3ZbDZVqFBBNWrUUM2aNVWzZk1VrVpVQUFB/mr3VSuqmLTgK6l4UeqN/YUY+xfx9T9i7H/E2HsHDkupqYbKlfYsiSpTyv333wcMNWvomUQUzO9+fShGuqbi+eX7D7v/PhhtqFkjUw67qUMxnp935qwUG+deJ7eUxUVH25SaaqhUKc8Ylyzpfn3woE0NGnomC/nzuWNzJMamChXOb3f4sDsxiYmxKSbGUHy8oWLFTL33bqh+/tmhpERD9eun6bFBSSpWLHfE91LwIELfuKQEZP369Xr66ad13333SZISEhK0ZcsWbdq0SZs2bdLq1as1a9YsSVJwcLA2bszisscFkpOTtXPnTlWqVEmhoaHatm2bJk+erCNHjqhy5crq27evihcvfhmHdmXKn1dS3kC34upGjP2L+PofMfY/Yuy9s3HuvyPCPZfnCXP/HR+feZsGdaTSJUy9/p5NYaEu1agq7dgljfnYJpvNVGKSFBYqdW5r6utZhiqVk9q1NHXylPT6+zY57FJikj+PKmeJj3OP9oTn8Tz7DU+PeUJC5tGgWrWdiopy6cMPQhUSmqgqVZzas9uuz8aFyGYzlZQknTnt3u6zcSGqUtWp559P1OnTNo3/LERPDc6jTz+LU1iYf48NudMlJSAhISGqVq1axuvw8HA1bNhQDRueL8I8ffq0Nm7cqM2bN//r/nbv3q177rlHx44dU4kSJTRy5Eg9/PDDKlWqlCpWrKhFixZp5syZ+vrrr1WxYsV/3R8AALCWK/2c2MimIsrIotg7OEj6ZJRLL75pU7/B7vKhIoVMDR3o0lPDbQpLLwd6abCp4CDppVGGXnzLprBQU/f1MpWUZGSskxv8a4yzWB4UJL3xVrxGvxWmIU/lkSQVKuTSI48maeQrYQoNlVLT3BvmL2Bq2PBE2WyS5FSJki4NfDSPFi8K0o03pWbeOfAfXVIC0r59e23dulWNGzfOdp38+fOrZcuWatmy5b/u76233lLdunX18MMPa/z48XrooYfUtWtXjRgxQoZhKC0tTUOGDNHrr7+uzz777FKaCgAALJA3wv133AUjHfHpt4dG5sl6u7KlpC/fd+nEKen0GffrmGOSy2UoX173GXeecOmVZ0w9+5ip6CNSieJSeJg0c56hRiVyTy1MRPrIR0K8Z6aRkOD+O0+erGNRsqSpMe8m6NQpQ7Gx7hKuo0cNuVyGIiNNhYe7t2vUKC09+XCrVs2piAhTu3bZJZGAeDBzz71H/nRJN6F3795d8+fP165du3zy4X/88Ycef/xxVa1aVc8884ySk5PVq1cvGempvMPh0IMPPqi1a9f65PMAAIBvlS4h2e2m9h/yPDHbf9D9d8VymU+Ok5Kl734ydDBaKlRAqlhOcjikLTvc71e7xr3NL79L6za5E5FK5d3Jx4lTUsxRqVplfx5VzlKipEs2m6lDhzxP2869Llsu85TEycnSooVBio42VKCAqbJlXbLbpZ1/uUecKld2qkQJ935Ts8gx0tKkkJDck+TBWpeUgNx+++3avHmzbrvtNg0dOlTz5s3Tvn37LvvDQ0NDlZTkLuIsXLiwbr/9doVcMI9cbGysIiMjL/szAACA/4SESPVrSYuWej548KdfDeWNMFXz2szbBDmkV9819O1355MWp1P6eqZNZUqaqlzeveybuTaNHut5qjLpW0N2m9Sqae45OQ4OlmrVcmrZModHjH9bGqSICFNVq2aercrhkN5/L1Q/fB+csczplGbPClbJkk6VK+9SWJhUo6ZTy34LUso/HiWybp1dSUmGatZkFiz4xyWVYI0cOVLbtm3Tli1bNH/+fM2aNUuGYShPnjyqVq2aatSooSFDhni9v+bNm+uVV17RyJEjVbFiRY0YMSLjPdM09ccff2j48OFq3779pTQTAABY6IG7Xeo/2KbBL9vU7QaX1m8x9PlUQ4MfcD8DJC5e2v23VLqkVDC/ZLdLPW82NWm6oaKFpYplTX0906b1m6X3X3VllAP17u7S/U/Z9fr7hto0M7VqnaFxX9nUv7dLpUsE8oit17tPsoY8Ha5Xhoep8/Wp2rLFrm+mBav/gGSFhLhv9t+3z64SJVzKn9+U3S51vTlFM2cEq3Bhl8qUdWnOrGBt3mzXiJGJGTHu3z9ZTw4O1/NDw3Xb7Sk6dcrQuHEhqnptmpo0zaWPnL+Y3JP3+tUlJSA9evTI+P8ul0u7d+/Wli1btHnzZm3dulVTp069pARk6NChevDBBzV27Fi9/fbbHu/NmzdPTz75pFq0aKHBgwdfSjMBAICFGteT/jfCpQ8/t+mxF2wqVlh66iFT99zhPlvb+pd07+N2jXzWpVuvdy975D5Thk2aMMXQmbOGqlaSPnrTpWb/eLhgs4bSWy+69MkkQ9O/M1SimPTcQJd6d899Z4F16zn18rBETZwYopdfClOhwqbufyBZt93uHrrYudOupwbn0dNDEtWps7umqu89yTIMadq0EJ2NNVSxklOvvZ7gMWVvtepOjX47QRMmhGj4sDCFhJhq1jxNDzyYJHvmx4sAPmGYpumzf8WmaWbcv3EpTp8+rfz583ssO3nypI4ePaqqVav6qHWSK+Yan+0LAICcyKXM9wPAd6KdWcwrDJ8qXTI60E3IVoX/vRPoJmRpz+NX1sX6SxoB+TeXk3xIypR8SFLBggVVsGDB/9giAAAAwEdy3+CbX1zSTegAAAAA8F+QgAAAAACwjE9LsAAAAICrlUEJlk8wAgIAAADAMiQgAAAAACxDCRYAAADgDUqwfIIREAAAAACWIQEBAAAAYBlKsAAAAABvUILlE4yAAAAAALAMCQgAAAAAy1CCBQAAAHiBBxH6BiMgAAAAACxDAgIAAADAMpRgAQAAAN4wjUC34KrACAgAAAAAy5CAAAAAALAMJVgAAACAN5gFyycYAQEAAABgGRIQAAAAAJahBAsAAADwAg8i9A1GQAAAAABYhgQEAAAAgGUowQIAAAC8QQmWTzACAgAAAMAyJCAAAAAALEMJFgAAAOAFZsHyDUZAAAAAAFiGBAQAAACAZSjBAgAAALxBCZZPMAICAAAAwDIkIAAAAAAsQwkWAAAA4A1KsHyCERAAAAAAliEBAQAAAGAZSrAAAAAAL/AgQt9gBAQAAACAZUhAAAAAAFiGBAQAAACAZUhAAAAAAFiGBAQAAACAZZgFCwAAAPAGs2D5BCMgAAAAACxDAgIAAADAMpRgAQAAAF7gQYS+wQgIAAAAAMuQgAAAAACwDCVYAAAAgDcowfKJXJWArExOC3QTrmoxafkC3YSrXh5bcqCbcFWLtCUFugnAf+Y0KW7wp03JVQPdhKvew4FuAPyOXgoAAACAZXLVCAgAAABw2SjB8glGQAAAAABYhgQEAAAAgGUowQIAAAC8wIMIfYMREAAAAACWIQEBAAAAYBlKsAAAAABvUILlE4yAAAAAALAMCQgAAAAAy1CCBQAAAHiBWbB8gxEQAAAAAJYhAQEAAABgGUqwAAAAAG9QguUTjIAAAAAAsAwJCAAAAADLUIIFAAAAeIMSLJ9gBAQAAACAZUhAAAAAAFiGEiwAAADACzyI0DcYAQEAAABgGRIQAAAAAJahBAsAAADwBiVYPsEICAAAAADLkIAAAAAAsAwlWAAAAIA3KMHyCUZAAAAAAFiGBAQAAACAZSjBAgAAALzAgwh9gxEQAAAAAJYhAQEAAABgGUqwAAAAAG9QguUTjIAAAAAAsAwJCAAAAADLUIIFAAAAeIFZsHyDERAAAAAAliEBAQAAAGAZSrAAAAAAb1CC5ROMgAAAAACwDAkIAAAAAMuQgAAAAACwDPeAAAAAAN7gHhCfYAQEAAAAgGVIQAAAAABYhhIsAAAAwAtGoBtwlWAEBAAAAIBlSEAAAAAAWIYSLItsWm1o5hc2Hd5vKDKf1LqLS116umRkM5aXmiLNnmTTisU2xcVKUaWlzj2catLOc/qFNb8ZmveNTdEHDIWFS9Xqmrqtv1P5ClhwUDnIjjVOLfwyVUcPuJQnr6HrbnCo1e0OGdkE2Ok09duMNK35KU2xJ0wVLmmo9W1BqtXK85/E2oVp+m1mqk4cNhVZ0FDddna17Rkku4NB2K1rTP0w0aWY/VJEPqnZDYY63GFkG/PUFFPzJ5tas8RUfKxUtLTUtruhhm25DiLRR1iBGPvX5tXSrIk2Raf3Ca27mLr+DvOi8Z072dDKxYbiYqXipaVOPUw1bpv1NEOJ8dKwh2zq2sdUs465cyqiv9cmacVXZ3Vyf5rC8tlUs3O4GvSIyLbfdTlNrZ0Vpy0LExR/0qX8Jexq2CNS17QI81hv3N0xSjjtyrR9/4nFlKeA3S/HcsXKnV89nyMBscDOLYbefdmuRq1MdbvHqb82u38ETVO66c7M/+Al6ePX7NqwylCnHi5Vq2tq/y5DE9+162ysSx1vdW+zeqmhsSMdat3FqW59XYo9Lc2aaNdbQxwa9mGagoItPMgA2rfVqUkjklWzhV0d7g7Rvi1O/fRlqkxTatMzKMttFk9O1S/fpqltryCVq2bT5uVOTXkzRYZdqtnc/c9i+exUff9pqmo0t+v6+xyKjzW16KtUxew1ddeLIVYeYo6zZ6upccNcqtvSUJe+hvZsNvXDRFOmKXXqlfUP4cQ3XNq8yp10VKlj6OBuU9PeMxUf61LrW3J3EkIf4X/E2L92bZHeH2ZTw1ambu1raucWQ7O+MORySTfemfUZ26ev27RxldSxh6lr65jav9vQpHcNxZ2R2t/quU1crPTBMJtOHDGUW88AD29L0XevntQ1zcPUpHekDm9L0e+Tz8o0pUa3R2a5zcopZ7Vmepwa3RGpEtcGa9fviZo/6pQMm1S5mTsJiT/lVMJpl1r0y6uoKp5f2NDI3N03w39IQCwwZ7JNZSqauv8ZpySpZkNTTqc0b5pNnbq7FHzBuey+XdK6323qfq9TN/Zy/8hVr2cqJFT65jObmndwKTxCmvuVXbUaudR30Pkfz+KlnXrlMYf+XGmoYcvc0Ukv/jpVURVsuuNpdyCrNLDL6ZR++TZVzW91KCgk8wnxmoVO1W5lV/ve7gSlUl27Du92aeX3aarZ3CGX09Tir1NVqa5NvZ87/x+oZGWb/vdgknauc6pyvdx7VejHyS6VrCDdPcT941StgSGn06VF35hq081U8AUxP7DL1MbfpRvvMdSxp3ubKvUMBYe6NGe8qUbtTYVH5N5RJfoI/yPG/vXdVzaVriD1H+I+3hoNTTnTpPnfGOrY3cwU3/27pPW/G7r1Hpe69HJvUy09vtM/M9S0g6nwCPe663+XpnxkU3KilUeU86yaelZFygep02D30Fq5+qFypUlrZsSp3s0RcmTxW7d1UYKqtAxT417uBKVMnRAd25OqjfPiMxKQY3tSJUmVmoQqb1FOC2ENUls/S02Rdmw0VL+Z549QgxamkhIN/bUpc4dxeL97We3GnlflqtRyKTnJ0LY/3VeVqtdzqdUNnusUL+X+nKPRueNkLi3V1J6NLlVv6pkM1GhuV0qitHdL1lc201JNhYZ7xig8r5QQ645f3GlTiXHStdd57rdYGZvy5JW2/+H04VFcWVJTTO3cJNVu5hm/Os0NJSdKuzdn3ubIgfSTkus8t6lU01BKkrRzg9+am+PRR/gfMfYvd3yles0941u/hankREM7s+gTojPi67nNNTVNJScZ2p7eJyTESWNfsalKLVNPvJZ1f54bpKWaOrQpWRWbhHosr9QsVKmJpg5tTc5yO2eqqeALfutC89qUGHs+lsf2piokj0Hy4SXDzJl/rjQkIH52LEZKSzVUrJTnt6NYCffrmEOZf6Dy5nP/fSLG871zP2bHYwzZbFLPB1yq19Rzv2uXudcpVe4K/DZehpPR7qtshUt6xqpwlPurffxQ1j9YLW4N0roladqxxqmkBFPrf07TzrUu1W3r7oBD8xiy2aVTRzzjmHjWnZhcuDw3OREjOVOlohfEvEgJ99/HDmWOTUQ+97onjnguPx59bp+5N570Ef5HjP0rI74lPY+3aHqfcORg5vhG5HOve/yCPuFYep9wPD3uwSHSK5+61O9pUxF5fdvuK0lsTJqcaVKBEp5JQv4o9+vTh7K+KFb35ght+zlRf69NUnKCS9t/SdC+dcm6tk14xjrH96YqJMKm7187qY96Rmvs7dGaP+qk4k/m3gtt8L8cm+7edNNN+vTTTxUVFRXopvwnCXHuTjQs3HN5aPrrpITM21SpZapIlKmvxtoVHOpU+WtMHdhj6NvP7DJsppKTsv6smEPSN+PsKlvJVM2GueOHLzHefZwXjmYEp8c3OYv4SlKTrg7t3eLUFy+dv2rUoKNdLXu4S7KCQw3VamnXiu/SVKysTdWb2BV3xtR3n6TI5pBSknJHfLOSGOf+O/SC73TIRb7TlWpKhaKkGR+5FBxiU5lrpMN7pbkTXDJsUko23+ncgD7C/4ixf53rE7KLb2KW8ZWKRJmaOtamkBCXyl0jHdgjTR9v84ivI8h9c3pul5z+Wxcc7nndODjM/d1OTsj6YlvtG/Po8JYUzRl+MmNZtfbhqt8tIuP1sT1pijvhVI2O4ap7cx6dPJCmlV+f1fTnjuvO/xVRUCjXquF7AU1AZs+ene17+/bt0/z581WwYEFJ0i233GJNo3zMTP/9yW4WkKyWO4KkJ19L04S37Rr1jPs/Uf6Cpu582KmPXrMrJDTzNof3S6OfdcgRJD3yYppsuaS/MM/1uZcQ37RUU588naS4U6ZueTRIRUrbtG+LSz9PS1VwaIpuetB9E94tjwbLEZSime+maMb/pKAQqWWPIKUmuROU3Orcd/pSYu4IMvTwqzZ9/Y5LHw51/0fLW1Dq/pBNX7zuUnAW3+ncgj7C/4ixf7n+Lb5ZxMERJD3+qktfvGPT28+6S13zFTTV62GXPnnNlmV8czMzI8hZv59VjNNSTU1/9rjiT7nU9uF8KlDKocNbU7T6mzgFhxlqNcA9zNdhUH7ZgwwVrei+AFeyeogKlXHo22dPaNuSRNW6IY8/DunKlTuuK/hdQBOQ4cOHKynJfZnDNDP/F33rrbckSYZhXLEJSHge93ElxnsuP3fFLSybf9fFSkpD33Eq9pRTcWfdr08elUyXoTx5PWO17U9DH4ywKzRMevrNNBW5sgeNLklYxLmrP54xSUmPb2gW8d28zKmYvab6vRqiSnXdP3wVatoVmkea+1GqGnZyqHh5m0LCDHV/PEQ3PmDq9FFTBYoZCg41tPanNBWMyr0JyLnv7IVXjZMvEnNJKlLC0KDRdp097Z6Gt0hJ6fQxdxKZJ+sJXHIF+gj/I8b+FZ4evwtHOjLie8HIyDnFSkrPvO2eOSwuNj2+x9LjG8lZ3j+FRLgzjJQLRjpSEt1xCgnPnIHs+j1Rx/9O060jCqlMHfcsAKVqhCgkj02/fHJG1TuEq3C5IEVVzTxVW4lqIQrOY+jY36m+PhRAUoDvAZk5c6aqVaum6667Tr/++qu2b9+e8ScsLEwLFy7U9u3btW3btkA28z8pWkKy2UwdPex5wnok/XWJspk72ZRk6fdFho5FS3kLSCXKSHa79PdO9zZlK53fZsUSQ28/Z1eBQtLz/0tTVC4bqi4Y5a7DPnHYM47Ho92ddNEymb/ip4+61y1bzfO98jXdycjR/e5tt61y6u8tToWEGSpW1qbgUENxp02dOW6qRMVccmkzC4VLSDabdPyCmB877P67eJnMyVlKsqnVi106EWMqMr+h4mUM2e2G9u90v1+qUu5N6Ogj/I8Y+1d28T2a3idkF98Viw0di5Hy5j8f333pfUKZSiQg/5SvuEOGTToT7XlfxunoNElSwTKZryefPepet8S1nglGyRru1ycPpCk5zqUtCxN0Yr9nomGaplypUlje3PtbB/8K6DerfPnymjZtmmrVqqWbb75Z8+bNC2Rz/CIo2D2rx9rlhv45yLPmN0PhEaYqVMncyToc0uQP7fpl3vn/PC6ntHiOTUVLmCpZzr1swx+GPnvLrkrVTD33vzQVLOLng8mBgoINlath0+bfnR6jaJuXORUaIZW+JvNXvEhp94/khTNk7dvq7qwLFHe/v2pequaN9+yUl89OlWGTrm2Ue6fgDQo2VLGmtGG56RHzP5eZCouQylbJvI3DIU0fa2r5vPPru5ymls51qUgJKaqcBQ3Poegj/I8Y+5c7vtK6C+K7Nj2+5bPpE77+0NDSeeeTFpdTWnJBfOHmCDZUsnqwdq1I9Oh3dy1PUkgeQ8UrZx7FKFDKnZRcOENW9LYUSVLeYnbZgqSfPz6tNTPiPNbZsypJaSmmStXI3c+8ypKZQ/9cYQJ+E7rD4dDgwYPVokULPfPMM1q8eLGGDRsW6Gb51E13ujT6WbvGjrSrRSeXdm019OO3Nt3Wzz33fGK8e8rHIlGm8uaXbHap7U0uLZxlU4HCUokyphbPsWnnFkMDhztls7mnPfziHbtCw6WberkypjQ8p0BhM9f8ELbtGaTxzyfr69dT1KCDQ/u2OfXbjDR1vjdIQSGGkhJMHd3vUsEomyLyGbr2OrtKV7Hpm1HJat8nSEVK2XRgh0s/T01Nf8+dXDS9OUifv5Cs7z5JUbXr7Nq9walfvklTq9scKhiVu68Kdepl04dDXfr8VZcad7Jp71ZTS6ab6nqfoeAQQ4nxpmL2S4WjpMj8hmx2Q81vNPTLbFP5C7tUrLSh375zae8WacDLNtlsuXcERKKPsAIx9q8ud7r0zrM2ffyqTc07ubR7q6EF0w1172f+I75S0SgpMr87vm1uNLVotqEChaSoMqaWzLVp1xbp0WGuXHP/zKVodHukZr50QvPePKXqHcIVvS1Fa2fFqXnfvHKEGEpOcOnk/jTli7IrPJ9dFRqFqvg1QVrwzmk17hWpAqUcivnLfQ9I+UYhKn6NO2mp3y1Cf0yLU3h+m8rWC9Xxv1O1aspZlWsQklG6BfiaYWZ180WAxMbGavjw4VqzZo1OnDih+fPnq3Rp341l/76vgs/2danWLjM0e5JdMQelAoWktl1d6tzDfQV++wZDbz7tUL+n0tS8o/s/R1qaNGeSTb8vsin+rFSmoqmuvV2q0cD9/tb1RsaNkVm5uY9Tt9xt7ZzpMWn5LP28f9rye5oWTU7VsYOm8hY21ORGh1p0c99Qt2ejU+OeTVaPJ4JVv4M7ZkkJpn6amKrNy51KPGuqYHFDdds51PxWhxxB508i/vwlTT9PTdWpI6byFzXUuItDTbtm/XR1K+SxZT3XeyBsWG5q/iSXjhyS8heSWtxkqG1391nDzg2m3n/Gpd6DDV3X0b3MmWZq/mRTqxebij8rlaogdept07X1c07yEWkL3HRcuaGPCLTcEmOnGZiz93XL3fE6ctDdJ7S5yVSnHu5Ybd8gjR5i171PutTsH/H9brKhFYsMxZ+VSleUburtUvX6We//eIz0bF/PfQTCpuTA1djtWpGolV+f1elDacpTyK7aN+RRvVvdM1od3JSsGc+fUIdB+VWtnfvGm+QEl1ZMOqtdKxKVdNalfMUdqtomTPVujpA9/bfOdJnaOD9Bm+bH63RMmsIibe6HF96ZN8uHG1rh4So/B+RzvVF74JhANyFLG957ItBNuCQ5KgE5Z/bs2Zo5c6ZGjx6tokWL+my/gUxAcoNAJiC5RU5KQK5GgUxAAF8JVAKSWwQyAcktcnICUuexnJmA/Pn+5ScgLpdLH3zwgb799lvFxsaqfv36evnll1W2bNl/3fa7777TU089pcWLF6tUqVJef2aO7KVuueUWffnllz5NPgAAAAB4Gjt2rKZOnaqRI0dq2rRpMgxDAwYMUEpKykW3O3TokIYPH35Zn5kjExAAAAAA/pWSkqIJEyboscceU6tWrVS1alWNGTNGR44c0cKFC7PdzuVy6emnn1b16tUv63NJQAAAAABvBHq2Kx/PgrV9+3bFx8ercePGGcvy5s2ratWqafXq1dlu9/HHHys1NVUPPPDAZX1uwGfBAgAAAHD52rVrd9H3Fy9enOXymJgYSVJUlOfTU4sWLaro6Ogst9m4caMmTJig6dOn68iRI5fRWkZAAAAAgFwpMTFRkhQc7PksmZCQECUnZ574JiEhQU899ZSeeuoplStX7rI/lxEQAAAAwAtGjps71i27EY5/ExoaKsl9L8i5/y9JycnJCgsLy7T+yJEjVa5cOfXs2fPyGpqOBAQAAADIhc6VXh09elRlypTJWH706FFVrVo10/ozZsxQcHCw6tatK0lyOp2SpBtvvFFdu3bViBEjvPpcEhAAAAAgF6pataoiIiK0atWqjAQkNjZWW7duVZ8+fTKt/9NPP3m83rBhg55++ml9+umnqlixotefSwICAAAAeCOHlmBdruDgYPXp00ejR49WwYIFVbJkSY0aNUrFixdXhw4d5HQ6dfLkSUVGRio0NDTTwwnP3cReokQJFSpUyOvP5SZ0AAAAIJcaOHCgevTooRdeeEG9evWS3W7X+PHjFRwcrOjoaDVv3lzz5s3z6WcapmleZblc9n7fVyHQTbiqxaTlC3QTrnp5bJlnpIDvRNqSAt0E4D9zmlxb9KdNyaUD3YSr3sNVfg50E7JV9+ExgW5CltaPfSLQTbgklGABAAAAXsips2BdabhMAgAAAMAyJCAAAAAALEMJFgAAAOANSrB8ghEQAAAAAJYhAQEAAABgGUqwAAAAAG9QguUTjIAAAAAAsAwJCAAAAADLUIIFAAAAeIEHEfoGIyAAAAAALEMCAgAAAMAylGABAAAA3qAEyycYAQEAAABgGRIQAAAAAJahBAsAAADwgmFSg+ULjIAAAAAAsAwJCAAAAADLUIIFAAAAeIMKLJ9gBAQAAACAZUhAAAAAAFiGEiwAAADACwYlWD7BCAgAAAAAy5CAAAAAALAMJVgAAACANyjB8glGQAAAAABYhgQEAAAAgGUowQIAAAC8wCxYvsEICAAAAADLkIAAAAAAsAwlWAAAAIA3KMHyCUZAAAAAAFiGBAQAAACAZSjBAgAAALzALFi+wQgIAAAAAMuQgAAAAACwDCVYAAAAgDcowfIJRkAAAAAAWCZXjYAMr9Ik0E0AkIPZoooFuglXPVf0kUA34epncG3Rn4ygXHXqFBAPxwa6BfA3/hUBAAAAXmAWLN/gMgkAAAAAy5CAAAAAALAMJVgAAACAN0xqsHyBERAAAAAAliEBAQAAAGAZSrAAAAAALzALlm8wAgIAAADAMiQgAAAAACxDCRYAAADgDUqwfIIREAAAAACWIQEBAAAAYBlKsAAAAAAvGK5At+DqwAgIAAAAAMuQgAAAAACwDCVYAAAAgDeYBcsnGAEBAAAAYBkSEAAAAACWoQQLAAAA8IJBCZZPMAICAAAAwDIkIAAAAAAsQwkWAAAA4A2TGixfYAQEAAAAgGVIQAAAAABYhhIsAAAAwAvMguUbjIAAAAAAsAwJCAAAAADLUIIFAAAAeIMSLJ9gBAQAAACAZUhAAAAAAFiGEiwAAADAC8yC5RuMgAAAAACwDAkIAAAAAMtQggUAAAB4w6QGyxcYAQEAAABgGRIQAAAAAJahBAsAAADwArNg+QYjIAAAAAAsQwICAAAAwDKUYAEAAADeoATLJxgBAQAAAGAZEhAAAAAAlqEECwAAAPACs2D5BiMgAAAAACxDAgIAAADAMpRgAQAAAN5wUYPlC4yAAAAAALAMCUiANOhQS+8vf0VzTk7Ql3+9qzue7ur1tpXqltMPZyeqWNnCfmzhlY8Y+xfx9a36Lavq3TlPaNbWN/TFshd0+0PtvN62Uo1S+u6vUSpaskDGsqIlC2j+3ney/fPEWz39cRhXHL7H/tWgQ029v2y45pz4TF/uGKM7nrrJ620r1S2nH2I/V7EyxPec+u1r6L1fXtLsmI81cfMo3TG4i9fbVqpTVt+fGKdiZQpleq9Z1/p69+cXNePgWE3a+rae/Kif8hfJ68umAx4owQqAao0ra9iMJ/Xr9JWaOOxbVW9WRfcMv002m6Epb8656LYVapbRK7OeliOI/3QXQ4z9i/j61rX1yunlcfdp6Q9/6su356t6w/Lq+9T1stkMTf1w0UW3LX9tCQ2f0F+OILvH8lPHYvXEre9mWv/Gu5upZZc6+umbVT49hisR32P/qta4soZNH+yO7/Dpqt60iu4Z3sMd37fmXnTbCjXL6JWZTxLff7i2USUNmzpIS2f+oYkjZ6pGk2vU96VuMmyGpo7+/qLblq9RWiO+fSLLeLa4pYGe//IR/TD+Z018ZaYKFM2ru567VW9+P0SPthym1OQ0fx3SlYkKLJ/gX3YA9H6+m/Zs2KdR930kSVqzcKMcDrtuf+omzXh3nlKSUjNt4wiy6+aHO+nul3soJTHF6iZfcYixfxFf3+o9qKP2bDus0YO/liStXbpdDoddtz3YVjM/+1UpyVnHs2vf5rpr8PVZxjs1xantf+7zWFa5Zim17FJHE0fP05Y1e/1zMFcQvsf+1fu5W7Rn4z6N6veJJGnNwk1yBNl1+1M3asZ78y8S3466+6XuxPcCfYberD2b9mvU/eMkSWsXbZbdYdftT9ygmR8syDaeXR9or7tfuDXL9yXpziFd9ceCDXr/iS8zlh34K0bv/fKSrutcR8vmrPHPASFXowTLYkHBDtVqea2WzVntsfy3WX8oPDJMNZpXzXK7hp3rqPfz3TT1zTka/8JUK5p6xSLG/kV8fSso2K5a11XS8h83eixfNn+DwiNCVaNR+Sy3a9j6WvUe2EnTPlykCW9e/OrnOY+80kMHdh/VrPG//ud2X+n4HvvX+fh6nrxmxLdZlSy3a9i5jno/d6umvjlX41+YZkVTrwhBwQ7VbF5Fy+eu9Vi+bM4adzybXpPldg071lLvZ2/W1NHfa8JL32Z63zAMrft5i+Z97tknHNwVI0mKKl/UR0cAeCIBsVjx8kUVHBKkQzujPZYf3u3+x16qUvEst/tr7R71rTJIU96cI2eay+/tvJIRY/8ivr5VvHQhBYU4dGjvMY/lh/8+Lkkqmc0JwF8bD6hvi5Ga+uEir+LZums9ValdRh8PnyUXs7jwPfaz8/GN8Vh+ePcRSVKpyheJb9UnNOWtucT3H4qXK+KO564jHssP73G/Lpnd93XdXvWt+bSmjv5ezjRnpvdN09S456dp5bz1Hsub3VRfkrRv20FfNP+qYpg588+VJqAlWNOnT1fXrl0VHBycsWzlypWaMGGCYmJiVLlyZT300EOqVKlSAFvpWxH5wyVJCWcTPZYnnE2SJIXnDctyuxOHT/m3YVcRYuxfxNe38qTHKyEuyWN5QnyyJCk8IiTL7U4cOXNJn9N9QGttWb1Hm1btvoxWXn34HvtXRnxjs4lvJPG9FP/6fY0MzXK7E9GnL/mzSlQspv4jb9fO9X9r9U+bLnl7wBsBHQF58cUXdfbs2YzXy5Yt07333iuXy6XmzZvr2LFj6t69u9atWxfAVvqWYXOH3MwmW+XK5H9HjP2L+PqWzWa4/48f41mtfjlVqlFK08f9/J/3dbXge+xfRvr32swmwK7sAo8sGcbF42n66Pta+poovfn9EKUmp2nk3R9m+3nAfxXQEZALv9hjx47V3XffraFDh2Yse/311zV69Gh9/fXXVjfPL+JPx0vKfPXn3NWLhDMJlrfpakOM/Yv4+lZc+hXi8AjPK5jhedwjH+eucP4Xza+vrbOnE7T6523/eV9XC77H/hV/2h2/C0eSzsc3MdM2yF58+vcxu+9rfOx/j2etFlX14uRHlRiXpKE3j9KRfcf/8z6vSiRlPpGj7gHZt2+fbr75Zo9ld9xxh7Zu3RqgFvne4T1H5UxzqkTFYh7LS1R012/u234oEM26qhBj/yK+vhW974ScaU5FlfN81kGJ9Nf7L6j5vhyN2lbTip82UVP/D3yP/Sv7+Lpf79tGfC/F4b3p8azgeU9YiQrueO7ffvg/7b/1bY316qwndSL6lAZ3eDXjJnTAXwKagJwbUjynXLlySkjwvOp06tQpRUZGWtksv0pNTtWmZdvV7OaGHstb3NpIZ0/Fa8dq6rP/K2LsX8TXt1JT0rTpjz1q1qmmx/Lm19fW2TMJ2vHn/v+0/4h84SpZvoi2rP37P+3nasP32L/c8d2hZjc38FieEd81xPdSpCanadPyv9Ssa32P5c1vbuCO59o9l73vhh1r6elP+mvbql0a3PE1Hec+HFggoAmIaZpq166dbr31Vj311FMKDg7WqFGjlJrqnqt63bp1Gj58uFq1ahXIZvrc12/MVtVGFfX8VwPVoGNt3f1yD/UY3EVT35qjlKRUhUeGqWqjSspX+OpJvKxGjP2L+PrW1A8WqkqdMnruw7vVoFVV3TW4s7rf31rTxi5WSnKqwiNCVLVOWeUrmOeS912+apQkaf9OrmheiO+xf339xhxVbVhRz3/1mBp0rKW7X+quHk/coKmj5qbHN1RVG1Ukvl6aMuo7VWlQQc9PfFgNOtTU3S/cqh6DOmva29+fj2fDCspXyPt4BoU49Pj79yjhbJKmjP5OZapEqWrDChl/Cpco4McjujIFerarq2UWrIAmIEuWLNGYMWPUuXNnuVwuHTt2TFu2bJHT6Z4qrl+/fgoP/397dx4WVfn/f/w1KIuIuJSKQpoKLrhi7mtmZpktflpNTXMtTDO3Sk3ii5lbKpp7mJkL5l6u2abpJ02t0MR9XxD8uCEugMLvDxR/E6CjDucww/NxXXNdcnPuM++5Z7yH97nf5xxP9evXz8ww7S7q12iFvR4uv/IlFLLwfT3xekN9+dF8LRq3UpLkH/SowjeEqs4zQSZH6rgY4+zF+NpX1O8H9Ok7X8uvbDENndZZzV54TBGffa/F09NOGi9X2U/jlr6n2s0C73nfhR72kiQlUHOfAZ/j7BW1PlphbSfIL8BHId/20ROvN9CXgyK1aNwqSZJ/jUcVvv4T1Xm6hrmBOoioDbs1rP0k+QX4aOi8Xmr2Sj19OeRbLZqwRpLkX720xv/0seq0rGbzPgPrBuihEoVVoHB+fbZ8gMb/9LHV4+mOTbLr5SCXs6TmsEscJCcny9XVVZK0d+9elS9fPkOp1v1q6dHOLvsB4JxcShS/+0Z4ICkxD35OC+7CkqNO73Q6FldTr9+TK6yJ/8rsELLUrOVIs0PI1C9rPzA7hHuS4/4X3Uo+JKlChczvlAoAAAAYLkcdtndcHCYBAAAAYBgSEAAAAACGyXElWAAAAEBOZMlZp047LFZAAAAAABiGBAQAAACAYSjBAgAAAGyRYnYAzoEVEAAAAACGIQEBAAAAYBhKsAAAAAAbcBUs+2AFBAAAAIBhSEAAAAAAGIYSLAAAAMAWVGDZBSsgAAAAAAxDAgIAAADAMJRgAQAAALbgKlh2wQoIAAAAAMOQgAAAAAAwDCVYAAAAgA0sVGDZBSsgAAAAAAxDAgIAAADAMJRgAQAAALbgKlh2wQoIAAAAAMOQgAAAAAAwDCVYAAAAgA0sKWZH4BxYAQEAAABgGBIQAAAAAIahBAsAAACwBVfBsgtWQAAAAAAYhgQEAAAAgGEowQIAAABsQQWWXbACAgAAAMAwJCAAAAAADEMJFgAAAGADC1fBsgtWQAAAAAAYhgQEAAAAgGEowQIAAABsQQmWXbACAgAAAMAwJCAAAAAADEMJFgAAAGCLFLMDcA6sgAAAAAAwDAkIAAAAAMNQggUAAADYgBsR2gcrIAAAAAAMQwICAAAAwDCUYAEAAAC2oATLLlgBAQAAAGAYEhAAAAAAhqEECwAAALAFJVh2kasSEJcypcwOwandOHDY7BCcniVPHrNDcG6Mb7ZzKehtdghOL+VivNkhOLXU5OtmhwA4PEqwAAAAABgmV62AAAAAAPctxewAnAMrIAAAAAAMQwICAAAAwDCUYAEAAAA2sHAVLLtgBQQAAACAYUhAAAAAABiGBAQAAACwRWpqznw8gJSUFE2YMEGNGzdW9erV1blzZx09ejTL7ffv36/u3burbt26ql+/vnr37q1Tp07d03OSgAAAAAC51OTJkxUZGalhw4ZpwYIFslgs6tatm5KSkjJse/78eb311lvKnz+/5syZoxkzZuj8+fPq2rWrEhMTbX5OEhAAAAAgF0pKStLMmTPVq1cvNW3aVBUrVtS4ceMUGxurdevWZdj+xx9/1NWrVzVixAgFBASoSpUqGj16tA4ePKg///zT5uclAQEAAABsYXaplZ1LsPbs2aPLly+rXr166W3e3t4KDAzU1q1bM2xfv359TZo0Se7u7hl+d/HiRZufl8vwAgAAAA6sefPmd/z9Tz/9lGn76dOnJUklSpSwai9WrJhiYmIybO/n5yc/Pz+rtmnTpsnd3V21a9e2OV5WQAAAAIBc6OrVq5IkNzc3q3Z3d3ebzumYPXu25s2bp759++qhhx6y+XlZAQEAAABskUNvRJjVCsfdeHh4SEo7F+TWvyUpMTFR+fLly7JfamqqwsPDNWXKFPXo0UOdOnW6p+dlBQQAAADIhW6VXsXFxVm1x8XFycfHJ9M+ycnJGjBggKZOnaqBAweqb9++9/y8JCAAAABALlSxYkV5eXlpy5Yt6W3x8fGKjo5WrVq1Mu0zcOBArVmzRp9//rm6dOlyX89LCRYAAABgixSzA7AvNzc3tW/fXmPGjFGRIkXk6+ur0aNHy8fHRy1atNCNGzd07tw5FShQQB4eHlqyZIlWrVqlgQMHqk6dOjpz5kz6vm5tYwtWQAAAAIBcqnfv3nr55Zc1ZMgQtW3bVnny5FFERITc3NwUExOjRo0aadWqVZKkFStWSJJGjRqlRo0aWT1ubWMLS2pqDj2bJhs8U+kjs0NwajcOHDY7BKdnyZPH7BCcmotfSbNDcH6XEsyOwOmlXIw3OwTnZuHYbXZbe/Ubs0PI0tOVB5sdQqbW7PrU7BDuCSVYAAAAgA0suee4fbYijQcAAABgGBIQAAAAAIahBAsAAACwBSVYdsEKCAAAAADDkIAAAAAAMAwlWAAAAIAtUijBsgdWQAAAAAAYhgQEAAAAgGEowQIAAABswVWw7IIVEAAAAACGIQEBAAAAYBhKsAAAAABbUIJlF6yAAAAAADAMCQgAAAAAw1CCBQAAANiCEiy7YAUEAAAAgGFIQAAAAAAYhhIsAAAAwBYplGDZAysgAAAAAAxDAgIAAADAMJRgAQAAALZITTE7AqfACggAAAAAw5CAAAAAADAMJVgAAACALbgRoV2wAgIAAADAMCQgAAAAAAxDCRYAAABgC25EaBesgBjksUblFb6wp5b+GapZPw3Uq92a2tzXP7Ckvt8xTMVKFsrwuydfrKkp372n5X//n75aN0Dt331SefI6/9ta66nq+mLzp/ru4tf65sBEvT7whbv2af5GI03/e7S+j5+tiH/G6unOzTJs0+LNppr+12ituDRbs/dNUIehLytP3jxZ7rP+c4/ph+RIVWsS+ECvxxHValFNEzeFafm5mZq9L1yvDXje5r7+QY9q5aWvVbz0w9kYoWN5rEkFhS/traU7P9Ws9YP06tsZP59Z8a/sq+93j1Ax38LpbcV8C2v1gdFZPt4f8Wp2vIwc7bFmgQpf+6GWHg7XrG3D9Grvljb39a9WSt+f+ELFHilyx+26/9/LWh075UFDdRrME9mvVouqmrgxVMvPfqnZe8fptf7P2dzXP+hRrYz/SsVLMcYwFisgBqhUo5RCJnXQhjU7NTt8nSo/Vlod+zwlFxeLIqf9ese+ZSr4KHRqJ+V1zfhH8AsdGujtQc/ptzU7FTF6tbwL51f7d59UmQo+Cus1J5tejfkC65dX6NIBWr/wd80a+q2qNKygTmGvyeJi0fwRyzLt0/iluhrwVbCWTVyjrWu/UYMXaqvvtB5Kupqkn+dvkiS92OsZBY/tqA2LNmvGh3Pl/XABvTn0ZZWtWkqhr4zNsM8CRbz03uRu2flSc6zAegH6ZHE/rV+0WV9/slCVG1ZQp9BX5OJi0fyRy+/Yt2zVUgpbOkB5XZl+bqkUVFohUztpw6oozR63VpUfe1Qd+z4tF4tFkVN+vmPfMhVLKPTLLhnmiPNn4vX+yxMzbN+6fQM1aVVdPyz8w66vIaerVKusQma/ow3Lt2v2iO9Uua6/On70fNo8PH7NHfuWCfRV6NzgTOfh/1+Vev56vqvtiaOzY57IfoH1AvTJor5pYxy6SJUbVFCn0JfTxnjUd3fsW7ZqKYUt6ccYwxR86gzQrmdzHdoTozEffCtJ2r5xn/LmzaNXuj2uJbM2KinxeoY+eV3z6Pl29dWhd4tMf+/iYlG74Ob6c9N+DX9/Xnr7gV0nNW3F+wpq4K+//nsg+16UidoPeUkHo45oVKdJkqRtP0Qpj2tevTbwBS0ev1JJ15Iz9OkU+pp+W7xFU/vPliRtX7dDBQp7qcPQV/Tz/E1ycbGo/ZCXtH3dDg1rOz693/4/D+nLHZ+rZvOq+vOnnVb77DWxi24k38i+F5qDtRv8Hx2KOqrRndOO9G5bt0N58+bRq/2f0+LwVZm+B3ld8+iF4JZ6M+RlJV1NMjrkHK1d7xY6tPuUxvSPlCRt37A3bY7o0UxLZm7Ieo54s6E69GmZ6XgnJ93Qnr+PWbUFVPFTk1bV9fXna7Rr+5FseS05Vbv+z+rQrhMa8+4sSdL2X6KVN6+LXunVUkum/pTlZ/b5Lo+rwwfPK+nanT+z7p5u6hv+ps6dvqCivndeJcktmCeyX7tBL+rQjqMa3WWaJGnbup3K65pHr/ZvrcUTVt9hjJ/Sm0NfYozvB1fBsgvnr9UxmatrHlWrU1ab1u2yat+49h955ndXlcfKZNqvdpMKatezuRZM+0UzP1+d4feFHvJSgUKe2vLLbqv2YwfjdPFcguo0rWi/F5GDuLrlVbWmgdq01Pro7W9LNsuzQD5VbVQpQ5/ipYvqkQoltWlZxj6+/j7yDSihQsULybuIlzav3G61zbHdJ3XhTLzqPlvTqr3pK/VV88mqmvHRXDu9Msfh6pZX1ZpU0sblW63af1v6hzwL5FOVRpl/9mo/XUPtBv9HkSOXK2JIpBGhOgRXtzyqVrecNv3wj1X7xjU75OnloSq1y2bar3bTimrXq4UWTP5JM0evsum5eoa20fGDcVr61YYHjtuRuLrlVbUGAdq08i+r9o0r/kob47r+mfar/WQVtev/rBaEr9bMYcvu+BzdQl7Subh4rYv83V5hOzTmiex3e4y3WbWnj3HDCpn2q/10DbUb1EaRI79TxJAFRoQKZEACks18HikiV7e8Onn0f1btp46l/ez7aOZ1l/t2nlDHJ0cpctqvunE9JcPvL1+6puvJN6xqviXJy9tDXt755ONXOEMfZ+BTtpjc3F11Yn+MVfupA7GSJN/yJTL0KVXRV5Iy9jmY1scvoIQuX7is68nXVbx0UattvArlV4HC+eXz6O32QsUK6t0Jb2lK3691LubCA78mR+NTJu09OJlhPE9Lkvz8fTLtt2/7IXWs8J7mj1ye6Wc6t/J55KG0OeLwGav2U0fPSpJ8y2Q1RxxXx6bDFTnlZ5vG8/HnaqhC9VKaOmy5UnLZSZQ+pR+Wq7urTh6Ms2o/dXPMfcsVy7Tfvr+OqGOtIYocv0Y3rme92hnUpKKav1pX496bnevGNivME9nv9hiftmq//d12hzGu+L7mj/qOMYZpTC/BioqK0pYtW9S9e3dJ0ubNmzVr1iydOHFCpUqVUufOnVWrVi2To7x/+b3zSZKuJFyzar9yOW3Z09PLPdN+Z+Pi77jfxGvJ2rB6h55vV1/HDsTqvz/uUsEiXnp70HO6fj1FHvnc7BB9zuNVKL8k6Ur8Vav2K5fSfvYskC9Dn/yFPDPtc/VWH+98SryapPULf9fzwS11NPqENi3bqkLFvPXO2I66nnxDHvk90vv1mdJNuzfv109zf8uVJ5973RrPS/9+D9I+457eGd8DSTp76nz2Buagbs8RiVbtVy6n/ezp5ZGhjySdjb3zHPFvL3Vtql3bDmvnlkP3EaVjy18wi3n45s+ZzRuSdPb0xbvu27OAh/qM66BvRn6vk4fi7rp9bsE8kf28svhuSx/jrD7XjPGDoQTLLkxdAVmzZo3atm2rP/5IK4355Zdf9NZbbyk1NVVNmzZVcnKyOnbsqF9++cXMMB+Ii8WS9o8sPq8PcrRsYugy/fz9X3ov7D9auCVEXyzupd1/H9O+f07ompPWdVpc0sYzq///qSkZj+a4ZNXn5ntzq0948Jf6ed5GvT+tu5acidDkPz7T7s37tW/bQV27nDaht+jQRFUaVdT44C/t8Gock8UlbdrI6j3gCPC9uT1HZD5u9hjPwJqPyr+ynxZ9uf6B9+WI7j7G938UuEfYK/pfzHktnXbniwXkNswT2e/292EWn2v+UEYOZuoKyBdffKF3331XwcHBkqQpU6bo7bff1nvvvZe+zZQpUzRhwgQ1a+aYVxZJuHWU/V8rHZ7501Yo/n1E7l5cu5Kk8UOWaOrwFSpWspBiT55X4tVkPfXSY9px/Nz9B52DXb5wRdLto8a33DrSc/lfR4IkKeFmn38fcct388jy5Ytpfa5dTtTY7tM0+f1ZKl66qGKPnNG1K4lq2elxxRyO00MlC+vtz9/U9IFzdCHuolzyuMglT9qXrEseF7m4WHLFl+rlC5clZTy65lkgbTyvXLxieEyO7PYcYb3S4Zk/bc64dTTzQTR6pqouXbiirb/uvvvGTighPosxvvnzlfj7G+M6Laqo6Yu11LvlCFlcLLLIkn7AwyWPi1JTUrP849DZMU9kv8tZfLfdHuOM34dATmFqAnLs2DE999zt61WfOHFCLVtaX5e9devWmjLFca+pHnPsnG5cv6ESpR6yai9585rbxw7e/5J9nccrKuHiVUX/dVTHDqTtp2CR/CrqU1AHok/df9A52KmDsbpx/YZKlitu1V7SP+3no9EnMvQ5sS9tLEqWK66Dfx+53efmPo7uTutTt1VNXbqQoOj/7kvfT6Gi3ir6yEM68Ndh1XyymgoU9lK/GW+r34y3rZ5j1A9DdPrIGb0Z0Ms+LzQHO3UoLvP3oFxavfHRPSfNCMthxRw9mzZHlP7XHHHz52M3z296EHWaVdLv6/7JtfXeMUfOpI1xGetzPUqWSTu369i+mMy63VWj1jXlns9N0zYMzfC7lacmaV3k7xr73uz72rejY57IflmP8a3vNsY4W+TSgwr2ZmoJ1iOPPKL162+XBFSqVEl79uyx2mbHjh0qXrz4v7s6jOSk69q57Ygatqhi1d6oZRVdunhVe3ccv+99t3qtrroObGXV9uKbDZVyI1V/OOmRzuTEZO38bbcatqlj1d74P/V06XyC9m7NeOnhUwdjdepgrBr/p16GPsf3nlLczQsCPNv9SXUf2d5qmza9WynlRoo2r/xTm1dsV896g6we4cEzJEnhwTM0tM0oe77UHCs5MVk7N+5RwxdqW7U3blNHl85f1t6tB02KzDElJ13Xzq2H1bBlVav2Rk9X06WLV7Q36lgWPW3jVTCffB8tql1/Hnmg/Tiy5MTr2rn5gBo+W8OqvVHrIF26cEV7/zpyX/udM2aFej/1mdVj9Te/SZJ6P/WZ5oxZ8YCROy7mieyXNsZ71fAF6/Nk08d4G2OMnMvUFZBu3bpp8ODBOn36tFq3bq3g4GB9+OGHSkxMVEBAgKKiojRp0iS9++67Zob5wCKn/qzhM7to0Lg39MOSbaoUVFovdW6smZ+vUVLidXnmd1cp/2KKOXZOF89ftnm/333zX30a0Vk9PmqtzT9Hq3q9cnq9RzMtmP6rTp9w3pPM5g1fqhFrB2vI/D5aO+tXBdYvr1f6tVbER/OUdC1ZngXyqVSgr2IOxuri/y5JkuYOX6IBEe/o0rlL+v377ar/3GN6/NX6Vvf8WP7FGn22epDe/vxNbf5+u2o0q6y2H76oyJHLdPpw2grTpXMJVrHku3ly+vG9MTryz/0nk45m3ohlGrHqIw2e21trv16vwPoBernvs4oYHHn7Pajkq5hDt98DZC1y0o8aPru7Bk1srx8WblWlmo/qpW5NNXPUqrQ5wstdpfyLK+bYWV08Z/scIUllKqRdGe7WKmluFTlutYYv7K1BM7rqh/m/q1LtsnqpZwvNDFuW9pn18lCpCiUUc+SMLp5NuPsOJcUdP6e4f5W71mmRduL6/gdMHJ0B80T2mzdiuUas+kCD5/ZKG+N6AXr5/VaKGLLg5hh73BzjOMYYOYqpKyAvvviihg8frtWrV+vFF19U+/btdfz4cYWEhOiNN97QF198oS5duqhTp05mhvnAorYc0qfvzZVfmYc19IsOata6hiJGr9bimWlHysoFltS4yGDVbpr5Nbuz8ud/92tEv0gFNfDXJ1M6qmGLKpoy7DvNGrc2O15GjvH3r7sU9uo4+VUooZDF/fRE24aa8cFcLRybdrTRP6iMJmwcpjqtbt+7Y93s9QoPnqGazavqk8X9VK1JoEZ2mqQNizanb7P9xx0a3n6Cajavqv9bPlCN2tTVpD5faSbXos8g6tdohb0eLr/yJRSy8H098XpDffnRfC0at1KS5B/0qMI3hKrOM0EmR+oYojYf1Kc9v5FfmWIaOrWTmj0fpIiRK7X45knj5Sr7atyiXqr9eMb73NxNoYe9JEkJubzmPmrjXn3aebr8/Itr6KweavZSHUWELtHiyeskSeWqPaJxqwaq9pNV7rIn2Ip5IvtFrY9WWNsJ8gvwUci3ffTE6w305aBILRqXdm8g/xqPKnz9J6rzdA1zA3UmKSk58+FgLKk55Ay5Q4cO6ciRI0pISJCrq6t8fHwUGBgod/fML1N7P56p9JHd9oWMbhw4bHYITs+SJ4/ZITg1F7+SZofg/C7ZtrqA+5dy8d4u0Yx7ZOEWatlt7dVvzA4hS8+U6Gl2CJlaHTPJ7BDuien3AbmlbNmyKls28zv+AgAAAHAOOSYBAQAAAHK0nFE45PBYRwQAAABgGBIQAAAAAIahBAsAAACwBSVYdsEKCAAAAADDkIAAAAAAMAwlWAAAAIAtUijBsgdWQAAAAAAYhgQEAAAAgGEowQIAAABskJqaYnYIToEVEAAAAACGIQEBAAAAYBhKsAAAAABbcBUsu2AFBAAAAIBhSEAAAAAAGIYSLAAAAMAWqZRg2QMrIAAAAAAMQwICAAAAwDCUYAEAAAC2SOFGhPbACggAAAAAw5CAAAAAADAMJVgAAACALbgKll2wAgIAAADAMCQgAAAAAAxDCRYAAABgg1SugmUXrIAAAAAAMAwJCAAAAADDUIIFAAAA2IKrYNkFKyAAAAAADEMCAgAAAMAwlGABAAAAtkihBMseWAEBAAAAYBgSEAAAAACGoQQLAAAAsEUqNyK0B1ZAAAAAABiGBAQAAACAYSjBAgAAAGyQylWw7IIVEAAAAACGIQEBAAAAYBhKsAAAAABbcBUsu2AFBAAAAIBhSEAAAAAAGIYSLAAAAMAGXAXLPlgBAQAAAGAYEhAAAAAAhqEECwAAALAFV8GyC1ZAAAAAABiGBAQAAACAYSypqamczg8AAADAEKyAAAAAADAMCQgAAAAAw5CAAAAAADAMCQgAAAAAw5CAAAAAADAMCQgAAAAAw5CAAAAAADAMCQgAAAAAw5CAAAAAADAMCQgAAAAAw5CAAAAAADAMCQgAAAAAw5CAAAAAADAMCUgOk5KSogkTJqhx48aqXr26OnfurKNHj5odltOaPHmyOnToYHYYTuXChQsaOnSomjRpopo1a6pt27batm2b2WE5lbNnz2rAgAGqV6+egoKC1L17dx04cMDssJzS4cOHFRQUpCVLlpgdilM5efKkKlSokOGxcOFCs0NzKsuWLVOrVq1UtWpVPfvss1q9erXZIQGSSEBynMmTJysyMlLDhg3TggULZLFY1K1bNyUlJZkdmtOZNWuWJkyYYHYYTqdv376KiorS2LFjtWjRIlWuXFldunTRwYMHzQ7Nabzzzjs6fvy4ZsyYoUWLFsnDw0OdOnXS1atXzQ7NqSQnJ6t///66cuWK2aE4nb1798rd3V2//fabNm7cmP547rnnzA7NaSxfvlyDBg3Sa6+9phUrVqhVq1bq27ev/vrrL7NDA0hAcpKkpCTNnDlTvXr1UtOmTVWxYkWNGzdOsbGxWrdundnhOY3Y2Fh17dpV4eHhKlOmjNnhOJWjR49q06ZNCgkJUa1atVS2bFkNHjxYxYsX14oVK8wOzymcP39efn5+CgsLU9WqVVWuXDkFBwfrzJkz2r9/v9nhOZWJEycqf/78ZofhlPbt26cyZcqoWLFiKlq0aPrDw8PD7NCcQmpqqsLDw9WxY0d17NhRpUuXVs+ePdWgQQP98ccfZocHkIDkJHv27NHly5dVr1699DZvb28FBgZq69atJkbmXHbt2qWCBQvqu+++U/Xq1c0Ox6kULlxY06dPV5UqVdLbLBaLUlNTdfHiRRMjcx6FCxfW2LFjFRAQIEn63//+p4iICPn4+Mjf39/k6JzH1q1btWDBAo0cOdLsUJzS3r17+bxmo0OHDunkyZMZVpQiIiLUo0cPk6ICbstrdgC47fTp05KkEiVKWLUXK1ZMMTExZoTklJ544gk98cQTZofhlLy9vdW0aVOrttWrV+vYsWNq1KiRSVE5r48//ljffvut3NzcNGXKFHl6epodklOIj4/XwIEDNWTIkAzzMexj3759Klq0qN544w0dOXJEpUuXVnBwsBo3bmx2aE7hyJEjkqQrV66oS5cuio6Olp+fn9555x2+/5AjsAKSg9yq33Zzc7Nqd3d3V2JiohkhAQ9k+/btGjRokJo3b86XXjbo2LGjFi9erOeff149e/bUrl27zA7JKXzyySeqUaMG5yNkk6SkJB05ckQJCQnq06ePpk+frqpVq6pbt276/fffzQ7PKSQkJEiSPvjgA7Vu3VozZ85Uw4YNFRwczBgjR2AFJAe5VfualJRkVQebmJiofPnymRUWcF9+/PFH9e/fX9WrV9fYsWPNDscp3SphCQsL099//605c+bos88+Mzkqx7Zs2TJt27ZN33//vdmhOC03Nzdt3bpVefPmTT/gVqVKFR08eFARERGqX7++yRE6PldXV0lSly5d1KZNG0lSpUqVFB0dra+++ooxhulYAclBbi31x8XFWbXHxcXJx8fHjJCA+zJnzhz16tVLTZo00YwZMzix1I7Onj2rFStW6MaNG+ltLi4uKleuXIa5A/du8eLFOnv2rB5//HEFBQUpKChIkhQSEqJnn33W5Oich6enZ4bV/vLlyys2NtakiJzLrb8Zypcvb9Xu7++vEydOmBESYIUEJAepWLGivLy8tGXLlvS2+Ph4RUdHq1atWiZGBthu3rx5CgsLU7t27TR+/PgMf2TgwcTFxalfv35WV7JJTk5WdHS0ypUrZ2JkzmHMmDFatWqVli1blv6QpN69e2v69OnmBuck9uzZo6CgoAz3B/rnn384Md1OAgMDlT9/fkVFRVm179u3T6VKlTIpKuA2SrByEDc3N7Vv315jxoxRkSJF5Ovrq9GjR8vHx0ctWrQwOzzgrg4fPqzhw4erRYsW6tGjh86ePZv+Ow8PDxUoUMDE6JxDxYoV1ahRI4WGhmrYsGHy9vbW1KlTFR8fr06dOpkdnsMrXrx4pu0PPfSQfH19DY7GOZUvX14BAQEKDQ1VSEiIChcurG+//VZ///23Fi1aZHZ4TsHDw0Ndu3bVpEmTVLx4cVWrVk0rV67Upk2bNGvWLLPDA0hAcprevXvr+vXrGjJkiK5du6batWsrIiKCo8hwCGvXrlVycrLWrVuX4d41bdq00YgRI0yKzHlYLBaNHz9en3/+ufr06aNLly6pVq1amjt3rkqWLGl2eMBdubi4aOrUqRozZoz69Omj+Ph4BQYG6quvvlKFChXMDs9pBAcHK1++fOn3EytXrpwmTpyounXrmh0aIEtqamqq2UEAAAAAyB04BwQAAACAYUhAAAAAABiGBAQAAACAYUhAAAAAABiGBAQAAACAYUhAAAAAABiGBAQAAACAYUhAAAAAABiGBAQAHExiYqICAwMVFBSksLAws8MBAOCekIAAgIOxWCz6+uuvVa1aNc2ZM0eHDx82OyQAAGxGAgIADsbNzU21a9dW165dJUm7du0yOSIAAGxHAgIADqps2bKSpN27d5scCQAAtiMBAQAHNWPGDEnSnj17TI4EAADbkYAAgAPauHGj5s+fr4IFCyo6OtrscAAAsBkJCAA4mPj4eA0aNEjNmzdX27Ztde7cOcXGxpodFgAANiEBAQAHExoaquvXr2vYsGEKDAyURBkWAMBxkIAAgANZs2aNVqxYoU8//VRFihRJT0A4ER0A4ChIQADAQZw5c0YhISF67bXX1KxZM0nSI488Im9vb84DAQA4DBIQAHAQH3/8sQoWLKgPP/zQqr1SpUqUYAEAHAYJCAA4gIULF2rDhg0aNWqUPD09rX4XGBioY8eOKSEhwaToAACwnSU1NTXV7CAAAAAA5A6sgAAAAAAwDAkIAAAAAMOQgAAAAAAwDAkIAAAAAMOQgAAAAAAwDAkIAAAAAMOQgAAAAAAwDAkIAAAAAMOQgAAAAAAwDAkIAAAAAMOQgAAAAAAwDAkIAAAAAMP8Pz17vUuskFxJAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# optional\n",
     "# visual representation of grid search\n",
@@ -2969,16 +1543,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (2259440937.py, line 1)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  Input \u001b[0;32mIn [12]\u001b[0;36m\u001b[0m\n\u001b[0;31m    conda create -n tf tensorflow\u001b[0m\n\u001b[0m          ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "conda create -n tf tensorflow\n",
     "conda activate tf"
@@ -3755,7 +2320,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
index 9115e9414..502da1094 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter11.ipynb
@@ -782,33 +782,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 367.01\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mautograd\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mautograd\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m grad, elementwise_grad\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.0666807\n",
-      "Max absolute difference: 0.0437499\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -982,44 +969,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 324.246\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.119936\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_52_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
@@ -1286,45 +1236,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 0.221805\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.000417932\n",
-      "The max absolute difference between the solutions is: 0.00424909\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
@@ -1609,61 +1521,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 0.221805\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.000417932\n",
-      "The max absolute difference between the solutions is: 0.00424909\n",
-      "Max absolute difference between Euler method and analytical: 0.011225\n",
-      "Max absolute difference between deep neural network and analytical: 0.00424909\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_66_3.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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bOXMmly9fJiwsjKFDhzJq1Khs+wk7g2G/1kNYkqu4uDgCAgKIjY0tVEvSJ6dZeXzqfWytsJdAKywfug13dy9XxxIREREpUVJSUjhx4gQ1atTAy0t/F7sedrudevXq8cgjj9zwVTdnuNa/0xvpBroCVsx4e5ipVH0Ugek2Lphhyaa3XB1JREREROSaoqOjee+994iMjOT+++93dZwCpQJWDPVvU4+aV0IAmH188TVXmhQRERERcbWKFSvy5ptv8sUXX1CmTBlXxylQWgWxGGpWpTSxDMfb9hpHTOls+nMO7ZsOd3UsEREREZEclaQLBroCVgwZhsGtrdvSJC4AgNl7vnBxIhERERERARWwYuuOsGAiLvXDZLez0RrH4dPrXB1JRERERKTEUwErpgJLeVK99i00S8hYdnPO5jddnEhERERERFTAirFBraqQdKkzAL8mnSbmygnXBhIRERERKeFUwIqxm+uU57SpF/WS7aQbBnPXv+zqSCIiIiIiJZoKWDHmZjZxV8uqlLrUDIAFF3aRlBrv2lAiIiIiIiWYClgxN7BlFTbG3UmwxUqcCRZvfM3VkURERESkiOncuTOjR492dYxiQQWsmKsR6EvT6pWpdrk6AF+f+g2rzeraUCIiIiIiJZQKWAlwd8sQdlwaSIDVxhnDyppd2hdMRERERMQVVMBKgD5NKpHsHkTj2DIAzNo/28WJRERERKSwSkxMZNiwYZQqVYpKlSoxZcqULMerV6/O66+/zgMPPICfnx9Vq1bliy/+/g/8J0+exDAMfvzxR7p06YKPjw9NmzZl06ZNzv4phZIKWAng4+FG36aVOXLxTtztdnbbEgk/9purY4mIiIiUGHa7nSRLkktedrv9hrI+/fTTrFmzhkWLFrF8+XLWrl3Ljh07soyZMmUKLVu2ZNeuXTz22GP85z//4eDBg1nGTJgwgXHjxhEeHk7dunUZPHgw6enp+f5nWdS5uTqAOMfdLavw3bZ69Iz3YKO/hTnb3qNZrVtdHUtERESkREhOT6bN3DYuOfeWIVvwcfe5rrEJCQnMmDGDOXPm0L17dwBmz55NSEhIlnG9e/fmscceA+DZZ5/l/fffZ+3atdSrVy9zzLhx4+jTpw8AkyZNomHDhhw9ejTLmJJIV8BKiOZVS1O7QikuX8z4f6RVKWeJuLDfxalEREREpDA5duwYaWlptGvXLvOzsmXLEhoammVckyZNMt8bhkFQUBDR0dG5jqlUqRJAtjElka6AlRCGYTCwZQivL+lI5+Ql7PA2+GbDK4y/Y56ro4mIiIgUe95u3mwZssVl575e13u7oru7e5Y/G4aBzWbLdYxhGADZxpREKmAlyJ1hIbz92yHMF1tCyHYWXdnDY0kXCfAp5+poIiIiIsWaYRjXfRugK9WuXRt3d3c2b95M1apVAbh8+TKHDx+mU6dOLk5XPOgWxBKkvJ8nXetVYEN8X+qkWUk2DBb+8YqrY4mIiIhIIVGqVClGjhzJ008/zapVq9i7dy8jRozAZFJtcBT9kyxhBrasQiqeVIutA8DcyDVY0tNcnEpERERECot33nmHm2++mdtvv51u3bpx00030aJFC1fHKjYM+42uSykAxMXFERAQQGxsLP7+/q6Oc93SrTbavbkaW3wUAXXeIMbNzKv17qdfm7GujiYiIiJSbKSkpHDixAlq1KiBl5eXq+OIA1zr3+mNdANdASth3Mwm+jcP4SJlaZ+SsRrN7EPzbnh/CBERERERuXEqYCXQ3S0z9nHYEnU73jYbR+wpbDq0yMWpRERERESKPxWwEqhW+VK0rFaGI+m16WHxA2D2ro9cnEpEREREpPhTASuhBraqAsDl2N6Y7HY2pl3gcNQOF6cSERERESneVMBKqD6NK+HjYebXi83pYjEDMGfT6y5OJSIiIiJSvKmAlVC+nm7c1qQSYFCVWwD4Ne4QMfFnXRtMREREpBjRQmfFh6P+XaqAlWCD/roNcfbpzjRLs5JuGMzVxswiIiIi+WY2Z9xhlJam/VaLi6SkJADc3d3zNY+bI8JI0dS8ahlqlvfleEwiXbzaEG7bzoJzf/BQWiI+Hr6ujiciIiJSZLm5ueHj40NMTAzu7u6YTLruUVTZ7XaSkpKIjo6mdOnSmeU6r1TASjDDMBjYsgpvLj3I77H9qeq1mdPubize9gFDOkxwdTwRERGRIsswDCpVqsSJEyc4deqUq+OIA5QuXZqgoKB8z2PYdWNqntzIbteFWXR8Cu3eWI3VZuflJtN5z3KMEDz4ZehWzKb8tXsRERGRks5ms+k2xGLA3d39mle+bqQb6ApYCVfBz4suoRVYeeA8iR4jCEh5njPmNNYc+I5uDe91dTwRERGRIs1kMuHl5eXqGFKI6GZUYWDLEABmHfRloFv5jPfhn7kykoiIiIhIsaQCJnSpV4HAUp5cSEijQaWRuNvt7E6/QnjEeldHExEREREpVlTABHezif7NgwH4LrIet1k9AJiz5W1XxhIRERERKXZUwASAu1tm7Am25vAF7qqV8ezXqoQTRFw54cpYIiIiIiLFigqYAFC7QilaVCuD1WZni603HdJs2AyDbzZqY2YREREREUdRAZNMVxfjmL/zPMOr9ABgUfQ2YlOuuDCViIiIiEjxoQImmfo0qYyPh5njFxLxqvYYoWnpJBuwcOu7ro4mIiIiIlIsqIBJplKebvRpXAmAuXuTGF62acb7E79isVpcGU1EREREpFhQAZMsBrbKWIzj1z1RdGwzgQrp6cSQzpI9X7k4mYiIiIhI0acCJlm0rFaGmoG+JKVZWR5VmiEelQGYvfcr7Ha7i9OJiIiIiBRtKmCShWEYmUvSz98ewYA2T+Nts3HEmsCmE8tdnE5EREREpGhTAZNs+jcPxmwy2HHqMjEBHehv8wJg9vb3XJxMRERERKRoUwGTbCr4e9G5bnkAFu48w72NH8Jkt7Mx+SyHY/a5OJ2IiIiISNGlAiY5uroYxw87IqnYbATdUm0AzNn8uitjiYiIiIgUaSpgkqOu9SoQWMqDCwmprD0ay/CatwPw68U/iUmMdnE6EREREZGiSQVMcuRuNnFnWDAAC7ZH0KTDM4SlWkg3YO6Wt1ycTkRERESkaFIBk1wN/Gs1xNUHo4m2+jA8sBUACyJWkmRJcmU0EREREZEiSQVMclWnoh9hVUtjtdlZtDOSzh1foKrFQhw2Fu+e7up4IiIiIiJFjgqYXNPVq2ALtkdgCqzLUK+qAHx94FusNqsro4mIiIiIFDkqYHJNtzWphLe7mWMxiew8fYV+7Z4jwGrljC2ZNUd/dnU8EREREZEiRQVMrsnPy53ejSsBsGBbBN41uzDQ7gvArJ0fuTKaiIiIiEiRowIm/2pgyxAAfvnzLIlpVoY0+w/udju7U2MIj9rm4nQiIiIiIkWHCpj8q9Y1ylK9nA+JaVaW7IkisOl93JZqB2COlqQXEREREbluKmDyrwzD4O5/LMaBmwfD6vQHYNWVQ0TERbgynoiIiIhIkaECJtelf/MQTAZsO3mZ4zEJ1G43hg4padgM+EZXwURERERErosKmFyXoAAvOodWAGDhjjPgXYbhFdsDsOjsOmJTY10ZT0RERESkSFABk+t2dTGOH3acId1qo+1NEwhNTSMZOwt3TnNxOhERERGRwk8FTK5b13oVKefrQXR8Kr8fjsEIrM1w31oAzD3yPRarxcUJRUREREQKNxUwuW4ebibuDAsG/lqMA7i1/XNUSE8nxp7GkoPzXRlPRERERKTQUwGTG3J1NcRVB6KJiU/FvXpHhuAPwOzdn2O3210ZT0RERESkUFMBkxsSGuRH0yqlSbfZWbwrEgyDAc0fx9tm44jlCpsifnd1RBERERGRQksFTG7YoH/sCWa32wlocg/9UzOOzd42xYXJREREREQKNxUwuWG3Na2El7uJI9EJ7Iq4AmZ37q03GJPdzsaEkxy+dMjVEUVERERECiUVMLlh/l7u9G5UCYCFfy3GEdLmcbolpwEwZ8vbLssmIiIiIlKYqYBJngxslXEb4v92R5GUlg7epRke3AWAX6O3EpMU48p4IiIiIiKFkgqY5EmbGmWpVs6HhNR0luw5B0CTm54jLCWVdGDejo9cG1BEREREpBBSAZM8MQyDu1uEAH/vCUbZGgz3CwVg/on/kWRJclU8EREREZFCSQVM8qx/ixBMBmw9cYkTFxIB6NzheapaLMTZ01m87xsXJxQRERERKVxUwCTPKgV4c3Pd8sDfi3GYq7ZlqFEGgK/3fYXVZnVZPhERERGRwkYFTPJl4F97gv2w8wzpVhsYBv1aPUmA1cqZ9ATWnFzm4oQiIiIiIoWHCpjkS7f6FSnr68H5uFTWH7kAgHfDAQxMy/g/rdk7proynoiIiIhIoaICJvni4WbijmbBAMzf9tdiHGY3hjQYhrvdTnjSWcKjw10XUERERESkEFEBk3wb2CpjNcSVB85zMSEVgMDWj3Bb0tWNmd9xWTYRERERkcJEBUzyrV6QP01DAki32Vm0KzLjQ68AhlXtCcCqS38SER/hwoQiIiIiIoWDCpg4xN1/LcaxYHsEdrsdgNodxtEhKQUb8M32D12YTkRERESkcFABE4fo27Qynm4mDp9PYPeZ2IwPy1RjeOlGACw6vZzY1FgXJhQRERERcT0VMHGIAG93ejeuBGRcBbuqbYfx1E1NIxkbC/fMdFU8EREREZFCQQVMHObulhmLcfwv/CzJaRkbMBtVWzPCnLFZ89wDc7FYLS7LJyIiIiLiaipg4jBta5SjSllv4lPTWbo3KvPzW1uPpkJ6OjG2FJYcXey6gCIiIiIiLubSArZu3Tr69u1L5cqVMQyDxYsXX3N8VFQUQ4YMITQ0FJPJxOjRo7ON6dy5M4ZhZHv16dMnc8zEiROzHQ8KCnLwryt5TCaDgS3+XozjKvcGdzAkzQ2A2bumZS7SISIiIiJS0ri0gCUmJtK0aVM+/vjj6xqfmppK+fLlmTBhAk2bNs1xzI8//khUVFTma+/evZjNZu6+++4s4xo2bJhl3J49e/L9ewT6twjBMGDz8UucupiY8aHZjQGNH8DbZuNI6gU2RW50bUgRERERERdxc+XJe/XqRa9eva57fPXq1Zk6dSoAM2fmvKBD2bJls/z5u+++w8fHJ1sBc3Nz01WvAlC5tDcd65Rn3eEYFm4/w7ieoQAEtBzJXbs/5dtSnsze/h7tQzq4OKmIiIiIiPMV+2fAZsyYwT333IOvr2+Wz48cOULlypWpUaMG99xzD8ePH7/mPKmpqcTFxWV5Sc4G/rUYx/c7zmC1/XW7oZc/91XvjcluZ2PsYQ5fPuzChCIiIiIirlGsC9jWrVvZu3cvDz74YJbP27Rpw5w5c1i2bBnTp0/n3LlztG/fnosXL+Y61xtvvEFAQEDmq0qVKgUdv8jq3qAipX3cOReXwvojMZmfh3QYS7ekZADmbJ/qqngiIiIiIi5TrAvYjBkzaNSoEa1bt87yea9evejfvz+NGzemW7du/PrrrwDMnj0717nGjx9PbGxs5isiIiLXsSWdp5uZO5oFA1kX46B0VYaXbQ7Ar2fXE5MUk9PXRURERESKrWJbwJKSkvjuu++yXf3Kia+vL40bN+bIkSO5jvH09MTf3z/LS3I3sGXGFcIV+89zKTEt8/MmNz1HWEoK6diZ9+d0V8UTEREREXGJYlvAFixYQGpqKvfdd9+/jk1NTeXAgQNUqlTJCclKhgaV/WkcHIDFamfxrsi/D4S0YLh7xj/n+Yd/IMmS5KKEIiIiIiLO59IClpCQQHh4OOHh4QCcOHGC8PBwTp8+DWTc9jds2LAs37k6PiEhgZiYGMLDw9m/f3+2uWfMmMEdd9xBuXLlsh0bN24cv//+OydOnGDLli0MGDCAuLg4hg8f7vgfWYJdXYxjwfaILHt/dW4zlqoWC3H2NBYfWuiqeCIiIiIiTufSArZ9+3bCwsIICwsDYOzYsYSFhfHSSy8BGRsvXy1jV10dv2PHDubOnUtYWBi9e/fOMubw4cNs2LCBkSNH5njeM2fOMHjwYEJDQ7nrrrvw8PBg8+bNVKtWrQB+Zcl1e9NgPNxMHDwXz57I2MzPzfX7MtTiDsDXf07HarO6KqKIiIiIiFMZ9n9empDrFhcXR0BAALGxsXoe7Bqe/G4XP4Wf5b62VXn1jsaZnydv/IjuBz8l1mzm/U5T6Fa9hwtTioiIiIjk3Y10g2L7DJgUDlcX4/gp/Cwplr+vdHm3GMHAJAsAs3d86JJsIiIiIiLOpgImBapdzXKElPEmPiWd3/ae+/uApx9Dat2Bu91OeMIpwqPDXZZRRERERMRZVMCkQJlMBne3yLgKlmVPMCCw/ZPclpCxCuIcXQUTERERkRJABUwKXP8WwRgGbDx2kdMX/7HsfEAIwyq0AWBV9DYi4rW5tYiIiIgUbypgUuBCyvhwU+1AAL7fkbVk1e7wNB2SkrEB34R/7oJ0IiIiIiLOowImTnF1MY7vd5zBavvHwpvBzRnumXFs0YlfiE2NzenrIiIiIiLFggqYOEX3BhUJ8HbnbGwKG45eyHKsbdux1E1NI9luZeH+b1yUUERERESk4KmAiVN4uZu5o1llIPtiHEa93oywegEwd//XWKwWp+cTEREREXEGFTBxmoGtMm41XLHvPJcT0/4+YDJza/P/UCE9nZj0RJYc/8VFCUVERERECpYKmDhNw8oBNKzsT5rVxuLwyCzH3MOGMiQpHYDZu6Zht9tzmkJEREREpEhTAROnuroYx/xtEVlLlocvA0Lvxttm40jyOTZFbXJRQhERERGRgqMCJk7Vr1llPNxMHDwXz76zcVmOBbR9nLv+2ph59o6PXBFPRERERKRAqYCJU5X28aBnwyAg4ypYFv6Vua9SR0x2Oxsv7eXw5cMuSCgiIiIiUnBUwMTpBrYMAeCn8EhSLNYsx0Laj6VbYsZVsDnhnzk9m4iIiIhIQVIBE6frUCuQ4NLexKWks2zfuawHKzdjuG8tAH49vZKYpBgXJBQRERERKRgqYOJ0JpPBgBYZV8H+/55gAE3ajSUsJYV07MzbN9vZ8URERERECowKmLjEgBYhGAb8cfQiEZeSsh6s05PhVl8A5h/8jiRLUg4ziIiIiIgUPSpg4hJVyvrQoVYgAN/vOJP1oMlE55aPUdViIc6WyuIji1yQUERERETE8VTAxGXu/msxju93nMFqy7rxsrnZvQxNylig4+s/v8Bqs2b7voiIiIhIUaMCJi7Ts2EQ/l5uRF5JZuOxC1kPevjSr/5gAqxWzqReYk3EGteEFBERERFxIBUwcRkvdzN3hAUDsGD7mWzHvdv8h4FXN2be9YlTs4mIiIiIFAQVMHGpgS2rALBs3zmuJKVlPehfiSHBXXG32wmPPUp4dLjzA4qIiIiIOJAKmLhUw8r+1K/kT1q6jZ/Cz2Y7Hth+NLclJALamFlEREREij4VMHEpwzAY1DL3PcGo1IRhfnUBWBX1BxHxOYwRERERESkiVMDE5fo1C8bDbGLf2Tj2RsZmO1673Vg6JCVjA77ZM9P5AUVEREREHEQFTFyujK8H3RtWBGBhTlfBandnuN0fgEVHFxObmr2kiYiIiIgUBSpgUigM+msxjsXhZ0mx/L89v0wm2rb6L3VT00i2p7Pw4HwXJBQRERERyT8VMCkUOtQOpHKAF7HJFpbvP5/tuNF0MCOSbQDM3TcLi9Xi7IgiIiIiIvmmAiaFgtlkMKBFxmIcOd6G6OHDrY3uo0J6OjGWeJacWOLkhCIiIiIi+acCJoXG3X/dhrjh6AXOXE7Kdty99aMMiU8GYHb4Z9jtdqfmExERERHJLxUwKTSqlPWhfa1y2O3w/Y4z2Qf4VWRAte5422wcSTzDpqhNzg8pIiIiIpIPKmBSqAz86yrYwu1nsNmyX+EKaPckd8VnbMw8Wxszi4iIiEgRowImhcqtjYLw83Ij8koym45fzD4gqBH3BTTAZLezMWYXhy8fdn5IEREREZE8UgGTQsXL3Uy/ZpUBWJDTYhxASPsxdEvMeEZszp8znJZNRERERCS/VMCk0Ll6G+LSveeITcphuflatzDcKAvAryd/IyYpxpnxRERERETyTAVMCp3GwQHUC/IjLd3Gz7sjsw8wmWjS5nHCUlJIx8a8A986P6SIiIiISB6ogEmhYxhG5lWwBdtzWA0RoMkghqdkvJ1/YC5JluzL1ouIiIiIFDYqYFIo3REWjLvZYE9kLPvPxmUf4O5N58bDqWqxEGdNZvHRxU7PKCIiIiJyo1TApFAq6+tBjwZBQO6LcZhbP8zQ+IwrX1//+SVWm9Vp+URERERE8kIFTAqtu1uGALA4PJLU9BzKVakK9KvRmwCrlTMpMayJWOPkhCIiIiIiN0YFTAqtjnXKUynAiytJFlbsP5/jGO/2TzIwPgGA2bs/d2Y8EREREZEbpgImhZbZZDCgRcZVsFwX46hQnyFlmuFutxN++SDh0eHOCygiIiIicoNUwKRQu1rA1h+J4eyV5BzHBLZ/ktsSEgGYs+dLp2UTEREREblRKmBSqFUr50vbmmWx2+H7HblcBavVlWHm8gCsOrOOiPicF+0QEREREXE1FTAp9Aa1ytgTbOGOCGw2e/YBhkHtNk/QISkZG3a+2TfHyQlFRERERK6PCpgUerc2rISfpxsRl5LZfOJizoMa383w1Iz/c1505AdiU2OdmFBERERE5PqogEmh5+1hpm+zygAs2JbL7YXuXrRt+gB1U9NItllYeGiBExOKiIiIiFwfFTApEga1zLgNcenec8QmW3IcY7R+kBHxGQt1zN03G4s153EiIiIiIq6iAiZFQpOQAEIr+pGabuN/u8/mPMg3kFtr306F9HRi0mJZcmKJc0OKiIiIiPwLFTApEgzD4O6WV/cEy32VQ/d2jzMkLh6A2X9Ox27PYdEOEREREREXUQGTIuPOsGDczQZ/nonlQFRczoMq1GNAYCu8bTaOxJ9iU9Qm54YUEREREbkGFTApMsqV8qRb/YoALNyey55gQED7UdwVn7Ex8+w/tTGziIiIiBQeKmBSpAz8azGORbvOkJpuzXlQzc7c5x6EyW5n4/ltHL582IkJRURERERypwImRcrNdcsT5O/F5SQLqw5E5zzIMAhp+wTdEpMAmLN3lvMCioiIiIhcgwqYFClmk0H/FsHAtRfjoPEAhqe5AfDriV+JSYpxRjwRERERkWtSAZMi5+4WGbchrjscQ1Rscs6D3Dxp0vwhwlJSSLfbmHdwrhMTioiIiIjkTAVMipzqgb60qVEWmx1+2JH7Yhy0fIDhCSkAzD8wlyRLkpMSioiIiIjkTAVMiqSri3Es2H4Gmy2Xvb58y9G5zl1UtViIS09i8dHFzgsoIiIiIpIDFTApkno1DqKUpxunLyWx5cSlXMeZ2/2XobEZGzN/vXcmVlsuKyeKiIiIiDiBCpgUST4ebvRtWhmAhddajKN8XfpVbEeA1cqZpPOsiVjjpIQiIiIiItmpgEmRNbBlCABL9kYRl2LJdZx3+ycYGJ8AwOw9M5ySTUREREQkJypgUmQ1q1KaOhVKkWKx8b/dZ3MfWONmhniE4G63E35xL+HR4U7LKCIiIiLyTypgUmQZhsGgVn8vxnGNgQS2e4LbEhIBbcwsIiIiIq6jAiZF2h1hwbiZDHZHXOHQufjcBzbqzzCLJwCrIlYTEX+N58ZERERERAqICpgUaYGlPLmlfgUAFlxrMQ43D2q3eJAOScnYsPPN/m+clFBERERE5G8qYFLkXb0NcdGuSNLSbbkPbPkAwxNSM8Ye/p7Y1FhnxBMRERERyaQCJkXezXXKU8HPk0uJaaw+eD73gT5laVtvAHVT00i2pbHw8ELnhRQRERERQQVMigE3s4n+LTKWpJ+/7drPdhnt/suIuDgA5u6bg8Wa+/L1IiIiIiKOpgImxcLAlhm3If5+OIZzsSm5Dwysza2VOlIhPZ2Y1MssObHESQlFRERERFTApJioEehL6+plsdnhh53XWJIecG//BEPiMlZMnL13Jna73RkRRURERERUwKT4uLtlxm2IC7dHXLtUVb+JAd7V8LbZOBJ7nE1Rm5yUUERERERKOhUwKTb6NKmEr4eZkxeT2HriUu4DDYOAdqO4Kz5jY+Zpuz7BZr/G6okiIiIiIg6iAibFho+HG32bVgZgwfZr34ZIwzsZYfXCx2Zj94U/+f7w905IKCIiIiIlnQqYFCt3/7UYx5I9UcSnXGOFQzcPglo+zKjLVwB4f8d7RCdFOyGhiIiIiJRkKmBSrDSvWppa5X1Jtlj55c+oaw9u/TD32P1pnJJKgiWRN7e+6ZyQIiIiIlJiqYBJsWIYBoNaZVwFW7D92nuC4VkKc89XefnCJdzsdlacWsHq06udkFJERERESioVMCl27gwLwWwy2HX6CkfOx197cMO7CA1uy/DYjM2ZX9vyGglpCU5IKSIiIiIlkQqYFDvl/TzpWq8CcB1XwQwDer/Do7EJhFgsRCdF89Guj5yQUkRERERKIhUwKZYG/bUYx487I7FY/2WJ+Qr18Wr9KC9euAzAvIPz2BOzp6AjioiIiEgJpAImxVLn0PKU9/PkYmIaqw9ex+qGnZ+jvVsAfeMTsWNn4qaJWGzXWEVRRERERCQPVMCkWHIzm7ireTAAC7b9y22IAF7+0P0Vxl26TGmrjcOXDzNn35wCTikiIiIiJY0KmBRbA/+6DXHNoWjOx6X8+xeaDKRsSBuevpRxK+Knuz8lIu46ypuIiIiIyHVSAZNiq1b5UrSsVgabPeNZsH/114IcfROTaZOcQqo1lcmbJ2O32ws+rIiIiIiUCCpgUqxdvQq2cHvE9RWpoMYYrR7ipQuX8LTD5qjN/HL8lwJOKSIiIiIlhQqYFGt9mlTCx8PM8QuJbD91+fq+1OV5qnqU5tHLVwB4e9vbXE65zu+KiIiIiFyDSwvYunXr6Nu3L5UrV8YwDBYvXnzN8VFRUQwZMoTQ0FBMJhOjR4/ONmbWrFkYhpHtlZKS9RmgadOmUaNGDby8vGjRogXr16934C+TwsLX043bmlQCrnMxDgDv0tB9EsNj46htSedK6hXe3f5uwYUUERERkRLDpQUsMTGRpk2b8vHHH1/X+NTUVMqXL8+ECRNo2rRpruP8/f2JiorK8vLy8so8Pn/+fEaPHs2ECRPYtWsXHTt2pFevXpw+fTrfv0kKn6u3If66J4qE1PTr+1LTIbgHt2RizAUM4OdjP7M5anPBhRQRERGREsGlBaxXr168+uqr3HXXXdc1vnr16kydOpVhw4YREBCQ6zjDMAgKCsry+qf33nuPkSNH8uCDD1K/fn0++OADqlSpwqeffpqv3yOFU4tqZahZ3pekNCu//nn2+r5kMkGfd2maauGe2HgAJm+aTEr6daymKCIiIiKSi2L5DFhCQgLVqlUjJCSE2267jV27dmUeS0tLY8eOHfTo0SPLd3r06MHGjRtznTM1NZW4uLgsLykaDMPIvAq2YPuZ6/9i5TBoeT+jLl+hgs0gIj6Cz//8vIBSioiIiEhJUOwKWL169Zg1axY///wz8+bNw8vLiw4dOnDkyBEALly4gNVqpWLFilm+V7FiRc6dO5frvG+88QYBAQGZrypVqhTo7xDHuqt5MGaTwY5TlzkaHX/9X+z6IqW8SjMhJhqAWXtncejSoQJKKSIiIiLFXbErYG3btuW+++6jadOmdOzYkQULFlC3bl0++uijLOMMw8jyZ7vdnu2zfxo/fjyxsbGZr4gIbdBblFTw86JLaAUAFt7IVTCfsnDLy3RNSqZbchrp9nQmb5qM1WYtoKQiIiIiUpwVuwL2/5lMJlq1apV5BSwwMBCz2Zztald0dHS2q2L/5Onpib+/f5aXFC0DW4YA8MPOSCxW2/V/sfkwqNSM52Ji8MXMnxf+ZP6h+QWUUkRERESKs2JfwOx2O+Hh4VSqlLEUuYeHBy1atGDFihVZxq1YsYL27du7IqI4SZd6FQgs5cmFhFTWHIy+/i+azNBnChWtVkZfiAHgw10fci4x91tWRURERERy4tIClpCQQHh4OOHh4QCcOHGC8PDwzOXgx48fz7Bhw7J85+r4hIQEYmJiCA8PZ//+/ZnHJ02axLJlyzh+/Djh4eGMHDmS8PBwHn300cwxY8eO5csvv2TmzJkcOHCAMWPGcPr06SxjpPhxN5vo3zwYuMHFOABCWkLYUAbGJ9DUaibRksgbW94ogJQiIiIiUpy5ufLk27dvp0uXLpl/Hjt2LADDhw9n1qxZREVFZdubKywsLPP9jh07mDt3LtWqVePkyZMAXLlyhYcffphz584REBBAWFgY69ato3Xr1pnfGzRoEBcvXmTy5MlERUXRqFEjlixZQrVq1Qrw10phcHfLED5fd5w1h6KJjk+hgp/Xv3/pqm4TMR34mZejzjAwJJjVEatZdWoVt1S7peACi4iIiEixYtjtdrurQxRFcXFxBAQEEBsbq+fBipi7pv3BztNXeK5XPR7tVOvGvrx1OiwZx4eBFZju50UF7wosvmMxfh5+BRNWRERERAq9G+kGxf4ZMJH/b1Crq3uCRXDD//2h5QMQ1JhHLkZTzeRNdHI0U3dOLYCUIiIiIlIcqYBJidOnSWW83c0cj0lk5+nLN/Zlkxl6v4unHV6KPAXAgkMLCI8Od3xQERERESl2VMCkxCnl6UafJhmrYs7flof93Kq2haaDaZ2SQj+rJ3bsTNo0CYvV4uCkIiIiIlLcqIBJiXT1NsRf/owiMTX9xifoNgk8/Rl35hhlzN4cvXKUWftmOTakiIiIiBQ7KmBSIrWsVoYagb4kpVn5dU/UjU/gVxE6j6e0zcYzFzNuY/xs92ecijvl4KQiIiIiUpyogEmJZBgGd7cMAWDG+hNYbXlYDLT1w1ChAX0uR9PevRxptjQmb5p84wt7iIiIiEiJoQImJda9rasR4O3OofPx/LDzBjdmBjC7Qe93MIAXju/By+TB1nNb+enYTw7PKiIiIiLFgwqYlFgBPu483qU2AO8tP0xymvXGJ6l+EzQaQJX0dB6zeADw7vZ3uZh80ZFRRURERKSYUAGTEm1Y+2qElPHmXFwKM/84kbdJerwKHqUYeno/9bwqEJsayzvb33FsUBEREREpFlTApETzdDPzdM9QAD5de4yLCak3Pol/Jej0DG7Ay5GnMRkmfj3+KxsjNzo2rIiIiIgUeSpgUuL1bVKZRsH+JKSm89Hqo3mbpM1/ILAujeKiGeJVFYDJmyeTnJ7swKQiIiIiUtSpgEmJZzIZPN+7PgDfbD7FiQuJNz6Jmwf0ehuAxw/+QZBXOSITIvl096eOjCoiIiIiRZwKmAjQvlYgXULLk26z886yg3mbpFYXaNAPX5uVCYkZS9HP2TeHg5fyOJ+IiIiIFDsqYCJ/ea5XfUwGLNlzjp2nL+dtkh6vgbsPnU+H06N0fax2KxM3TsRqy8MKiyIiIiJS7KiAifwlNMiPu1tUAeD1Xw/kbUPl0lWg41MAPHcsHD/3Uuy7uI95B+c5MqqIiIiIFFEqYCL/MKZ7XbzcTWw/dZnl+8/nbZL2T0DZWpSPO88Y75oAfLjrQ6ISohyYVERERESKIhUwkX8ICvDiwZsyStNbSw9isdpufBI3z8wFOfrv+Y2wMqEkpyfz2pbX8nZVTURERESKDRUwkf/nkU41KefrwfELiXy3LSJvk9TpBqF9MNnSeflSHG4mN34/8zsrTq1wbFgRERERKVJUwET+Hz8vd57sVgeAqSsPk5CanreJbn0d3LyodXILD1bsAMAbW98gLi3OUVFFREREpIhRARPJweDWVakR6MuFhDS+WHc8b5OUqQ43jQHgwT2rqO5XlQvJF/hgxwcOyykiIiIiRYsKmEgO3M0mnr01FIDp644THZeSt4k6PAmlq+EZf5aXPKoBsPDwQnae3+moqCIiIiJShKiAieSiZ8MgmlctTbLFyvsrD+dtEndv6PUWAK12LqB/lW4ATNo0iTRrmqOiioiIiEgRoQImkgvDMJjQpz4A87dFcOR8fN4mqnsr1OkBNgtjzhyjnFc5jsceZ+bemQ5MKyIiIiJFgQqYyDW0qFaWWxsGYbPDW78dzNskhgG3vglmDwKO/86zwRlXwb748wtOxJ5wYFoRERERKexUwET+xTO3hmI2Gaw8EM3m4xfzNkm5WhnPgwG3bvuOmyq1w2KzMGnTJGz2POw1JiIiIiJFkgqYyL+oWb4UQ1pXBeD1JQew2fK4mfJNYyGgCkZsBC9QDm83b3ac38Hio4sdF1ZERERECjUVMJHr8GS3Ovh6mPnzTCy/7onK2yQePtDzdQCCt3zJf+veA8C729/lQvIFR0UVERERkUJMBUzkOgSW8uTRTrUAeHvZQVLTrXmbqH5fqNkFrGnce2gT9cvWJz4tnre3vu3AtCIiIiJSWKmAiVynkR1rUMHPk4hLyXyz+XTeJjEM6P0OmNxxO7qcicHdMRkmlp5cyvoz6x0bWEREREQKHRUwkevk4+HG2O51Afho9RFiky15myiwDrT7LwAN1n3EfaEZtyK+uvlVkixJDskqIiIiIoWTCpjIDRjQIoS6FUtxJcnCtLVH8z7RzU+DX2W4cor/Jlqp7FuZs4lnmRY+zXFhRURERKTQUQETuQFuZhPP9aoHwFd/nCTySnLeJvIsBT1fBcBn40dMaPQQAF8f+Jr9F/c7JKuIiIiIFD4qYCI3qEtoBdrWLEtauo0pyw/lfaKGd0H1jpCews3hi+hVvRc2u42JGyeSbkt3XGARERERKTRUwERukGEYPN+7PgCLdkWy72xsXif6a0EONzj4C88EtsPPw48Dlw7w7YFvHZhYRERERAoLFTCRPGgSUprbm1bGboc3lx7M+0QV6kObRwEIXPUK48KeBOCT8E+ITIh0RFQRERERKURUwETy6OmeoXiYTaw/coF1h2PyPlGnZ6FURbh0jDujI2hZsSXJ6cm8uvlV7Ha74wKLiIiIiMupgInkUZWyPgxrVw2A15ccwGrLY1ny8ofurwBgrJ/CS40ewd3kzobIDSw7ucxRcUVERESkEFABE8mHx7vWxt/LjYPn4lm0Kx+3DDYZCFXbgSWJGhs/5aEmGasivrH1DWJT8/iMmYiIiIgUOipgIvlQ2seD/3apDcCU5YdIsVjzNtHVBTkME+xfzEifWtQMqMmllEu8v+N9ByYWEREREVdSARPJp+HtqxNc2puo2BRm/nEi7xMFNYZWGVe+PJZN4OXWzwPww5Ef2HZumyOiioiIiIiLqYCJ5JOXu5lxPesC8OmaY1xKTMv7ZF2eB59AuHCY5ie2cHfduwGYvGkyqdZUR8QVERERERdSARNxgH5Ng2lY2Z/41HQ+Wn0k7xN5l4bukzLe//4Wo+sMJtA7kJNxJ/lyz5cOySoiIiIirqMCJuIAJtPfmzN/s/kUpy4m5n2ypkMgpBWkJeD/+1uMbz0egC/3fMnxK8cdEVdEREREXEQFTMRBOtQOpFPd8lisdt5edijvE5lMGQtyYMCehXS3e9MppBPptnQmbZqEzW5zWGYRERERcS4VMBEHeq5XPQwDfv0zil2nL+d9osph0PJ+AIylzzCh1bN4u3mzM3onPxz5wUFpRURERMTZVMBEHKh+JX8GNA8B4I2lB7Hb87g5M0DXF8G7LETvp9L+XxgVNgqA97e/T0xSjCPiioiIiIiTqYCJONjYHnXxdDOx9cQlVh6IzvtEPmXhlpcy3q95ncEhXWlYriHxlnje3PqmY8KKiIiIiFOpgIk4WKUAb0beVAOAN5ceIN2aj2e2mg/LuB0xNQ7zqleY2H4iZsPM8lPLWRux1iF5RURERMR5VMBECsCjnWtR1teDYzGJLNh+Ju8TmczQ+92M97vnUi8hlmENhwHw2pbXSLIkOSCtiIiIiDiLCphIAfD3cmdU19oAvLfiMImp6XmfLKQlhA3NeL/kKf7T+GGCSwVzLvEcH+36yAFpRURERMRZVMBECsiQNtWoXs6HCwmpTF+fz/27uk0ErwA4twfv8Hm81Dbj2bC5B+ey98Le/IcVEREREadQARMpIB5uJp65tR4AX6w7TnR8St4n8w3MWBURYPUrtC9dlz41+2Cz25i4cSIWm8UBiUVERESkoKmAiRSgXo2CaFalNElpVj5YeSR/k7V8AIIaQ0osrJrE0y2fJsAzgEOXD/HN/m8cE1hERERECpQKmEgBMgyD53vXB2D+tgiORsfnfbJ/Lsix82vKXTzJuJbjAJgWPo2I+Ij8xhURERGRAqYCJlLAWtcoS/cGFbHa7Lz126H8TVa1LTQdDNhhyVP0q3EbrYNak2JN4dXNr+Zv42cRERERKXAqYCJO8Oyt9TCbDFbsP8/WE5fyN1m3SeDpD2d3YYR/w0vtXsLD5MHGsxv59cSvjgksIiIiIgVCBUzECWpXKMU9raoA8NqSA/m7UuVXETqPz3i/chLV3Px4tOmjALyz7R2upFzJZ1oRERERKSgqYCJO8mS3Ovh4mNkdcYUle87lb7LWD0OFBpB8CVa/yoiGI6hdujaXUi4xZccUxwQWEREREYdTARNxkgp+Xjxycy0A3l52kLR0W94nM7tB73cy3m+fifv5fbzc7mUMDBYfXcyWqC0OSCwiIiIijqYCJuJED3asQXk/T05dTOLbLafyN1n1m6DRADIW5BhHs8AmDAwdCMDkTZNJSc/HvmMiIiIiUiBUwEScyNfTjTHd6gLw4aojxKXkcwPlHq+CRyk4sw12z+PJ5k9SwbsCp+NP88WfXzggsYiIiIg4kgqYiJMNbBlC7QqluJxk4dO1x/I3mX8l6PRsxvsVL+FntfJ8m+cB+GrvVxy5nM/Nn0VERETEoVTARJzMzWziuVvrATBzwwnOXknO34RtHoXAupB0Ada8zi3VbqFrla6k29OZtGkSNns+njUTEREREYdSARNxgVvqV6B1jbKkptt4b8Xh/E3m5gG93s54v206nNvL+Dbj8XX3ZXfMbhYeWpj/wCIiIiLiECpgIi5gGAbP964PwA87z7D/bFz+JqzVBRr0A7sNlowjyKcio8JGAfDBzg84n3g+v5FFRERExAFUwERcpFmV0tzWpBJ2O7z528H8T9jzdXD3gdObYM9CBoUOoklgExIsCby59c38zy8iIiIi+aYCJuJCz/Ssh7vZYN3hGNYficnfZAEhcPO4jPfLX8CclshL7V7CzXBj5emVrDq9Kv+BRURERCRfVMBEXKhqOR+Gtq0OwBtLDmKz2fM3YbvHoWwtSDgPv79FaNlQRjQaAcDrW14nIS0hf/OLiIiISL6ogIm42BNda+Pn5cb+qDgWh0fmbzI3z78X5Nj8KUQf4JEmj1DFrwrRSdF8uOvD/AcWERERkTxTARNxsTK+HjzWuTYA7y47RIrFmr8J63SDereB3QpLnsbL7MlL7V4C4LuD3/FnzJ/5jSwiIiIieaQCJlII3N+hOpUDvDgbm8KsjSfzP2HP18HNC06uh30/0rZSW26vdTt27EzcNBGLzZL/c4iIiIjIDVMBEykEvNzNPNUjFIBP1hzlcmJa/iYsUw1uGpvxftkLkJrAuJbjKO1ZmiOXjzB73+x8JhYRERGRvFABEykk7ggLpn4lf+JT0vl4zdH8T9hhFJSuBvFnYd07lPEqwzOtngHgs92fcTrudP7PISIiIiI3RAVMpJAwmwye710PgDmbThJxKSl/E7p7Q6+3Mt5v+gQuHOG2mrfRtlJbUq2pTN48Gbs9n6suioiIiMgNUQETKUQ61ilPxzqBWKx23l52KP8ThvaCOj3BZoGlz2AAL7V9CU+zJ1uitvC/4//L/zlERERE5LqpgIkUMuN71ccw4H+7z7I74kr+J7z1DTB7wLHVcOB/VPGvwn+a/geAd7a9w+WUy/k/h4iIiIhcFxUwkUKmQWV/7goLAeD1JQfyf5tguVrQ4cmM98ueh7QkhjUcRt0ydbmSeoV3t7+bz8QiIiIicr1UwEQKoad61MXDzcSWE5dYfTA6/xPeNBYCqkBsBGx4D3eTOxPbTcTA4OdjP7Pp7Kb8n0NERERE/pUKmEghVLm0Nw90qAHAm0sPkm615W9CD5+MvcEA/pgKF4/RuHxjBtcbDMDkTZNJTk/O3zlERERE5F+pgIkUUv/pXIsyPu4ciU7g+x1n8j9h/b5QqytY0+C38QCMaj6Kij4VOZNwhs93f57/c4iIiIjINamAiRRSAd7uPNG1DgDvrThMUlp6/iY0DOj1Npjc4cgyOLQUX3dfJrSZAMCsfbM4dMkBKy+KiIiISK5UwEQKsfvaVqNqWR+i41P5cv2J/E8YWAfa/Tfj/dJnwZJCl6pd6F6tO1a7lUmbJmG1WfN/HhERERHJkQqYSCHm4Wbi6Z6hAHz++zFi4lPzP+nNT4NfZbhyKuN5MOC51s9Ryr0Uey7sYf6h+fk/h4iIiIjkSAVMpJC7rUklmoYEkJhmZeqqw/mf0LMU9Hw14/2G9+DySSr4VGBMizEATN05lXOJ5/J/HhERERHJxqUFbN26dfTt25fKlStjGAaLFy++5vioqCiGDBlCaGgoJpOJ0aNHZxszffp0OnbsSJkyZShTpgzdunVj69atWcZMnDgRwzCyvIKCghz4y0QcxzAMxveuD8C8rREci0nI/6QN74LqHSE9BZZlPAM2oO4AmpVvRlJ6Eq9teS3/+4+JiIiISDYuLWCJiYk0bdqUjz/++LrGp6amUr58eSZMmEDTpk1zHLN27VoGDx7MmjVr2LRpE1WrVqVHjx5ERkZmGdewYUOioqIyX3v27Mn37xEpKG1rlqNb/QpYbXbe/u1g/ic0DOj9Dpjc4OAvcGQlJsPEy+1exs3kxtqItaw6vSr/5xERERGRLFxawHr16sWrr77KXXfddV3jq1evztSpUxk2bBgBAQE5jvn222957LHHaNasGfXq1WP69OnYbDZWrcr6l0k3NzeCgoIyX+XLl8/37xEpSM/1qofJgGX7zrPt5KX8T1ihPrR5NOP90mcgPZXaZWrzQKMHAHh9y+vEp8Xn/zwiIiIikqnYPwOWlJSExWKhbNmyWT4/cuQIlStXpkaNGtxzzz0cP378mvOkpqYSFxeX5SXiTLUr+DGoVVUAXl9ywDG3CHZ6FkpVhEvHYFPGleiHmzxMNf9qxCTHMHXn1PyfQ0REREQyFfsC9txzzxEcHEy3bt0yP2vTpg1z5sxh2bJlTJ8+nXPnztG+fXsuXryY6zxvvPEGAQEBma8qVao4I75IFmO61cHHw8yu01f4ba8DFsrw8ofur2S8X/cuXInA0+zJy+1eBmD+ofmER4fn/zwiIiIiAhTzAvb2228zb948fvzxR7y8vDI/79WrF/3796dx48Z069aNX3/9FYDZs2fnOtf48eOJjY3NfEVERBR4fpH/r4K/Fw91rAnAW78dJC3dlv9JmwyEqu3BkgTLXwCgVVAr7qx9JwCTNk3CYrXk/zwiIiIiUnwL2Lvvvsvrr7/O8uXLadKkyTXH+vr60rhxY44cOZLrGE9PT/z9/bO8RFzhoZtrEljKk5MXk5i39XT+J7y6IIdhgv2L4dgaAJ5q+RRlvcpy9MpRvtr3Vf7PIyIiIiLFs4C98847vPLKK/z222+0bNnyX8enpqZy4MABKlWq5IR0IvlTytON0d3qADB11RHiUxxwdSqoEbR6KOP90mcgPY0AzwCebfUsAJ/v/pyTsSfzfx4RERGREs6lBSwhIYHw8HDCw8MBOHHiBOHh4Zw+nfFf9cePH8+wYcOyfOfq+ISEBGJiYggPD2f//v2Zx99++21eeOEFZs6cSfXq1Tl37hznzp0jIeHvvZPGjRvH77//zokTJ9iyZQsDBgwgLi6O4cOHF/yPFnGAe1pVoWZ5Xy4lpvHZ78ccM2mX58EnEC4chi2fAdCrRi86VO5Ami2NyZsna28wERERkXxyaQHbvn07YWFhhIWFATB27FjCwsJ46aWXgIyNl6+Wsauujt+xYwdz584lLCyM3r17Zx6fNm0aaWlpDBgwgEqVKmW+3n333cwxZ86cYfDgwYSGhnLXXXfh4eHB5s2bqVatmhN+tUj+uZlNPHdrPQC+XH+CqNjk/E/qXRq6T8p4//tbEBeFYRi80PYFvMxebDu3jcVHF+f/PCIiIiIlmGHXf9LOk7i4OAICAoiNjdXzYOISdrudgZ9vYtvJywxsGcLbA3LenPyG2Gwwswec2QaN74b+XwIwa+8spuyYgr+HPz/f8TPlvMvl/1wiIiIixcSNdINi+QyYSElgGAbP964PwMIdZzh4zgF705lM0PtdwIA9C+HkBgDua3Af9crWIy4tjre3vZ3/84iIiIiUUCpgIkVYWNUy9GlcCbsd3lx60DGTVm4GLe/PeL/kabBacDO5MbHdREyGiSUnlvBH5B+OOZeIiIhICaMCJlLEPd0zFHezwdpDMfxx9IJjJu36IniXhej9sC3jNsSGgQ25t/69ALyy+RWSLEmOOZeIiIhICaICJlLEVQ/05d42GQvIvLH0ADabAx7r9CkL3V7OeL/mdYg/D8DjzR6nkm8lIhMi+XT3p/k/j4iIiEgJowImUgw80bU2fp5u7I2M4+fdZx0zadhQqBwGqXGwMqOM+bj78ELbFwCYvW82686sc8y5REREREoIFTCRYqBcKU8e7VwLgHeWHSLFYs3/pCYz9J6S8X73PDi9GYCbQ27m7rp3Y8fOs+ue5UTsifyfS0RERKSEUAETKSZG3lSDSgFeRF5J5utNpxwzaUiLjCthAEvGgS2j2I1vPZ7mFZqTYElg1OpRxKU5YAVGERERkRJABUykmPByNzO2e10APlp9hCtJaY6ZuNtE8AqAc3tg+0wA3M3uTOk8hSDfIE7GneS5dc9htTngqpuIiIhIMacCJlKM3NU8hHpBfsSlpPPJmqOOmdQ3MGNVRIDVr0BixkqLgd6BfNDlAzzNnqyPXM9Huz5yzPlEREREijEVMJFixGwyeK5XPQBmbzxFxCUHLRXf8gEIagwpsbByYubHDcs1ZFL7SQDM2DuD30785pjziYiIiBRTKmAixUynuuW5qXYgaVYb7y4/5JhJ/7kgx66v4cyOzEN9avbh/kYZGze/+MeLHLh4wDHnFBERESmGVMBEihnD+Psq2E/hZ9lzJtYxE1dtA02HZLxf8lTmghwAT4Y9SYfgDqRYU3hyzZNcTL7omHOKiIiIFDMqYCLFUKPgAO4MCwbg9SUHsNsdsDkzQPdJ4OkPZ3dlXAn7i9lk5u2b36aafzWiEqN46vensNgsjjmniIiISDGiAiZSTD3Voy4ebiY2Hb/I2kMxjpm0VAXo8nzG+xUvweWTmYf8Pfz5sMuH+Lr7suP8Dt7a+pZjzikiIiJSjKiAiRRTIWV8uL99dQDeWHoAq81BV8FaPQTBLTIW5Jh/H1iSMw/VLF2TNzu+iYHB/EPzWXh4oWPOKSIiIlJMqICJFGOPda5NgLc7h88n8MOOM46Z1OwGA+eAT2DG3mC/jIV/3OLYuUpnngh7AoDXt7zOruhdjjmviIiISDGgAiZSjAX4uPNE19oATFlxiKS0dAdNHAIDZoJhgt1zYfuMLIcfbPwgPar1IN2Wzpg1YziXeM4x5xUREREp4lTARIq5oe2qEVLGm/NxqczccMJxE9fsBN0mZrxf+hxEbM08ZBgGr3R4hbpl6nIx5SJPrnmSlPQUx51bREREpIhSARMp5jzdzDzdMxSAz34/zoWEVMdN3n4UNOgHNgssGAYJ0ZmHfNx9+LDrh5T2LM3+i/uZuGmi41ZjFBERESmiVMBESoC+TSrTJCSAhNR0Plx1xHETGwb0+wQCQyE+ChbeD9a/l58PLhXMe53fw2yY+fX4r8zeN9tx5xYREREpglTAREoAk+nvzZnnbjnN8ZgEx03u6QeDvgEPPzi1AVa8nOVwq6BWPNPqGQDe3/k+f0T+4bhzi4iIiBQxKmAiJUT7WoF0rVeBdJudd5Ydcuzk5evCnZ9mvN/8Cez5PsvhwfUGc1edu7DZbTy97mlOxZ1y7PlFREREiggVMJES5Lle9TAZsHTvOXacuuTYyev3hZvGZLz/+Qk4vz/zkGEYTGgzgablmxKfFs+o1aNISHPgVTgRERGRIkIFTKQEqVvRj4EtqwDw+pKDjl8Uo+uLULMzWJIyNmlOic085GH24P3O71PBuwLHY48zfv14bHabY88vIiIiUsipgImUMGO618Xb3cyOU5dZtu+8Yyc3maH/TAioApeOwaJHwfZ3ySrvU54PunyAh8mDtWfWMi18mmPPLyIiIlLIqYCJlDAV/b14qGMNAN767SAWq4OvQvmWg4FzwOwJh5bAhilZDjcu35iX22cs1PH5n5+z/ORyx55fREREpBBTARMpgR7uVItyvh6cuJDId1tPO/4Ewc2hz7sZ71e/BkdXZjl8e63bGdZgGAAv/PEChy45eFEQERERkUJKBUykBCrl6cbobnUA+GDlERJS0x1/kubDoMUIwA7fj4TLJ7McHtNiDO0qtSM5PZkn1zzJ5ZTLjs8gIiIiUsiogImUUPe0rkrNQF8uJqbx+e/HCuYkvd6G4BaQciVjUQ5LcuYhN5Mb73R6h5BSIUQmRDLu93FYbJbc5xIREREpBlTAREood7OJZ27N2Jx5+vrjnI9LcfxJ3DwzngfzCYRze+CXsfCPlRcDPAP4qOtH+Lj5sPXcVqZsn3KNyURERESKPhUwkRKsZ8OKtKxWhhSLjfdXHC6YkwSEwICZYJhg91zYPiPL4dplavN6x9cB+PbAtyw6sqhgcoiIiIgUAipgIiWYYRiM710fgAXbIzh8Pr5gTlSzE3SbmPF+6XMQsTXL4Vuq3sJjTR8D4JXNr7A7ZnfB5BARERFxMRUwkRKuRbUy9GoUhM0Oby49WHAnaj8KGvQDmwUWDIOE6CyHH2n6CLdUvQWLzcKYNWOITorOZSIRERGRoksFTER4umcobiaD1Qej2XjsQsGcxDCg3ycQGArxUbDwfrD+veiGyTDx2k2vUbt0bWKSYxi9ZjSp1tSCySIiIiLiIipgIkLN8qUY0qYqkHEVzGaz/8s38sjTDwZ9Ax5+cGoDrHg5y2Ffd18+7PIh/h7+7Lmwh8mbJmO3F1AWERERERdQARMRAEbdUodSnm78eSaW//15tuBOVL4u3PlpxvvNn8Ce77McruJfhXc7vYvJMPHzsZ/59sC3BZdFRERExMlUwEQEgMBSnjzaqSYA7yw7RGq6teBOVr8v3DQm4/3PT8D5/VkOt6vcjnEtxwHw7vZ32XR2U8FlEREREXEiFTARyTTypppU9PfkzOVkvt50qmBP1vVFqNkZLEkZmzSnxGY5fF/9+7i91u1Y7VbG/T6OiLiIgs0jIiIi4gQqYCKSydvDzFPdQwH4aPVRYpMs//KNfDCZof9MCKgCl47BokfBZss8bBgGL7V7icaBjYlLi2PUmlEkWZIKLo+IiIiIE6iAiUgW/VuEULdiKWKTLUxbe7RgT+ZbDgbOAbMnHFoCG6ZkOexp9uT9zu8T6B3I0StHeX7D89jstlwmExERESn8VMBEJAuzyWB8r4zNmb/aeJIzlwv4qlNwc+jzbsb71a/B0ZVZDlf0rcj7nd/H3eTOqtOr+PzPzws2j4iIiEgBUgETkWw6h5anfa1ypKXbmLL8cMGfsPkwaDECsMP3I+HyySyHm1VoxottXwRgWvg0Vp1eVfCZRERERAqACpiIZGMYf18FW7Qrkr2Rsf/yDQfo9TYEt4CUKxmLcliSsxy+s86dDKk3BIDn1z/P0csFfHukiIiISAFQARORHDUOCaBfs8oAvLH0QMFviOzmmfE8mE8gnNsDv4yF/3fOca3G0TqoNUnpSYxaM4rYVCcUQxEREREHUgETkVyN6xGKh9nEH0cv8vvhmII/YUAIDJgJhgl2z4XtM7Icdje5826ndwkuFUxEfARP//406bb0gs8lIiIi4iAqYCKSqyplfRjevhoAby49iNVWwFfBAGp2gm4TM94vfQ4itmY5XMarDFO7TMXbzZtNUZt4f8f7BZ9JRERExEFUwETkmv7bpTb+Xm4cPBfPjzvPOOek7UdBg35gs8CCYZAQneVwaNlQXu3wKgBz9s/hf8f+55xcIiIiIvmU7wKWmprqiBwiUkiV9vHgia51AJiy/DDJadaCP6lhQL9PIDAU4qNg4f1gzXqrYY/qPXi4ycMATNw4kb0X9hZ8LhEREZF8uuECtmzZMkaMGEGtWrVwd3fHx8cHPz8/OnXqxGuvvcbZs2cLIqeIuNDQdtUILu3NubgUZv5xwjkn9fSDQd+Ahx+c2gArX8425L/N/kvnkM6k2dJ4cvWTxCQ54Tk1ERERkXy47gK2ePFiQkNDGT58OCaTiaeffpoff/yRZcuWMWPGDDp16sTKlSupWbMmjz76KDEx+ouQSHHh5W7m6Z6hAHy69hgXE5x05bt8Xbjz04z3mz6GPd9nOWwyTLzR8Q1qBtQkOjmaMWvHkGZNc042ERERkTww7Ne5tnTr1q158cUX6dOnDyZT7r0tMjKSqVOnUrFiRZ566imHBS1s4uLiCAgIIDY2Fn9/f1fHESlwNpud2z/ZwN7IOEa0r87E2xs67+QrJ8KG98HdBx5cBRUbZDl8Ku4Ug38dTHxaPHfVuYuJ7SZiGIbz8omIiEiJdiPd4LoLmGSlAiYl0cajFxjy5RbcTAYrx3aieqCvc05ss8I3d8HxtVC2Fjy8BrwCsgz5I/IPHlv1GDa7jefbPM/geoOdk01ERERKvBvpBnlahGPy5MkkJSVl+zw5OZnJkyfnZUoRKQLa1w6kc2h50m123vrtoPNObDJD/5kQUAUuHYNFj4LNlmVIh+AOjGk+BoC3tr7FtnPbnJdPRERE5DrlqYBNmjSJhISEbJ8nJSUxadKkfIcSkcJrfK/6mAxYuvccP+xw0rL0AL7lYOAcMHvCoSWwYUq2IcMbDqdPzT5Y7VbGrh1LZEKk8/KJiIiIXIc8FTC73Z7j8xW7d++mbNmy+Q4lIoVXaJAfT95SF4AJi/dw6Fy8804e3Bz6/FW8Vr8GR1dmOWwYBhPbTaR+2fpcSb3Ck6ufJMmS/Wq9iIiIiKvcUAErU6YMZcuWxTAM6tatS9myZTNfAQEBdO/enYEDBxZUVhEpJJ7oWpuOdQJJsdh47NsdJKam//uXHKX5UGgxArDDDw/C5ZNZDnu5efFh1w8p61WWQ5cP8eIfL6JHXUVERKSwuKFFOGbPno3dbueBBx7ggw8+ICDg74fgPTw8qF69Ou3atSuQoIWNFuGQku5iQip9PtzAubgUbm9aman3NHPeyoPpqfBVL4jcAUGNYeQKcPfOMmTn+Z2MXD6SdFs6o8JG8VCTh5yTTUREREqcAl8F8ffff6dDhw64ubnlOWRRpwImAttPXmLQF5ux2uy8ekcj7mtbzXknjz0Dn3eCpAvQdAjcMQ3+XwFceHghkzdNxsDgo64f0alKJ+flExERkRKjQFZBTExMzHzfqVOnfy1f/xwvIsVTy+plee7WegBM/t9+9pyJdd7JA0JgwEwwTLB7LmyfkW3I3XXvZlDoIOzYeXb9sxy/ctx5+URERERycN0FrHbt2rz++uucPXs21zF2u50VK1bQq1cvPvzwQ4cEFJHC7cGONejeoCJpVhuPzd1BbJLFeSev2Qm6Tcx4v/Q5iNiabcizrZ6lRcUWJFoSGbVmFHFpcc7LJyIiIvL/XPctiIcOHeKFF17g559/plmzZrRs2ZLKlSvj5eXF5cuX2b9/P5s2bcLd3Z3x48fz8MMPYzabCzq/y+gWRJG/xSZbuO2j9URcSqZ7g4p8MbSF854Hs9th4XDY/xP4VYJH1kGpClmGXEy+yOBfBxOVGEWH4A580vUTzKbi+79PIiIi4lwF+gzYmTNnWLBgAevXr+fkyZMkJycTGBhIWFgYPXv2pHfv3phMeVrdvkhRARPJas+ZWPp/upE0q40Jvevz0M01nXfy1HiYfgtcOATVboJhP4E5623SBy4eYNjSYaRYU3ig0QOMaTHGeflERESkWCvwRThEBUwkJ99sPsULi/diNhnMf7gtLas7cV/AC0fgiy6QFg/tHoeer2UbsvTEUp5Z9wwAb3V8i941ezsvn4iIiBRbBV7Axo4dm/NkhoGXlxe1a9emX79+xXpTZhUwkezsdjtPfhfOz7vPEuTvxa+jbqJcKU/nBTjwP5h/X8b7/jOg8YBsQz7Y8QEz9s7A0+zJ7F6zaViuofPyiYiISLFU4AWsS5cu7Ny5E6vVSmhoKHa7nSNHjmA2m6lXrx6HDh3CMAw2bNhAgwYN8vxDCjMVMJGcJaamc/vHGzgWk0jHOoHMur81ZpOTngcDWDkRNrwP7j7w4CqomPV/g6w2K0+sfoL1kesJ8g3iuz7fUc67nPPyiYiISLFTIMvQ/1O/fv3o1q0bZ8+eZceOHezcuZPIyEi6d+/O4MGDiYyM5Oabb2bMGD1jIVLS+Hq6Me3eFni5m1h/5AIfrz7q3ABdX4SancGSlHE1LCXr0vhmk5m3bn6L6v7VOZd4jrFrx2KxOnHlRhERESnR8nQFLDg4mBUrVmS7urVv3z569OhBZGQkO3fupEePHly4cMFhYQsTXQETubYfdpzhqYW7MQz4ZmQbOtQOdN7JEy/CF50gNgJCe8Ogb+H/LQ50PPY49/56LwmWBAbWHciL7V50Xj4REREpVgr8ClhsbCzR0dHZPo+JiSEuLmOPndKlS5OWlpaX6UWkGOjfIoR7WlXBbocnv9vF+bgU553ctxwMnANmTzi0BDZMyTakZkBN3rr5LQwMFhxewIJDC5yXT0REREqsPN+C+MADD7Bo0SLOnDlDZGQkixYtYuTIkdxxxx0AbN26lbp16zoyq4gUMRNvb0j9Sv5cSEjjibm7SLfanHfy4ObQ56/itfo1OLoy25CbQ25mVPNRALyx5Q12nN/hvHwiIiJSIuWpgH3++efccsst3HPPPVSrVo2qVatyzz33cMstt/DZZ58BUK9ePb788kuHhhWRosXL3cy0e5tTytONrScv8e7yw84N0HwotBgB2OGHB+HyyWxDRjYaya3VbyXdns7YtWOJSohybkYREREpUfK1D1hCQgLHjx/HbrdTq1YtSpUq5chshZqeARO5fkv2RPHYtzsBmDG8JbfUr+i8k6enwle9IHIHBDWGkSvA3TvLkCRLEsN/G87BSwepX7Y+s3vNxtvNO5cJRURERLIq8GfAripVqhRNmjShadOmJap8iciN6d24EiPaVwdg7ILdRFxKct7J3TwzngfzCYRze+CXsfD//ruTj7sPU7tMpYxnGQ5cOsDLG19Ge9SLiIhIQchXARMRuV7P965PsyqliU228PjcnaSmW5138oAQGDATDBPsngvbZ2QbUrlUZaZ0noKb4cbSE0v5at9XzssnIiIiJYYKmIg4hYebiU/ubU5pH3d2n4nl9V8PODdAzU7QbWLG+6XPQcTWbENaBbXi2dbPAvDBjg/YELnBiQFFRESkJFABExGnCS7tzXsDmwIwe9MpfvnzrHMDtB8FDfqBzQILhkFC9u00BoUOon+d/tix88zvz3Ay9qRzM4qIiEixpgImIk7VtV5FHutcC4DnftjD8ZgE553cMKDfJxAYCvFRsPB+sKb/vyEGE9pMIKxCGPGWeEatGUVCmhMzioiISLGmAiYiTje2e13a1ChLQmo6j327k+Q0Jz4P5ukH93wLHn5wagOsfDnbEHezO+91fo8KPhU4EXuC59Y/h83uxD3MREREpNhSARMRp3Mzm/hocBiBpTw5eC6el3/e69wAgXXgzk8z3m/6GPZ8n32IdyAfdvkQT7Mnv5/5nY93fezcjCIiIlIsqYCJiEtU8Pfiw8HNMBmwYPsZFm6PcG6A+n3hpjEZ739+As7vzzakYWBDXm6XcYVs+p7p/HbyN2cmFBERkWJIBUxEXKZ9rUDGdq8LwIs/7eXguTjnBuj6ItTsDJYkmH8fpMRmG9K3Vl9GNBwBwEt/vMShS4ecm1FERESKFRUwEXGpxzrXplPd8qRYbDz2zU4SUtP//UuOYjJD/5kQUAUuHYNFj4It+7Neo5uPpn3l9iSnJzNq9Sgup1x2XkYREREpVlTARMSlTCaD9wc1o1KAF8cvJPLcD39it9udF8C3HAycA2ZPOLQENkzJNsRsMvP2zW9T1a8qZxPP8tTvT2GxWZyXUURERIoNFTARcbmyvh58PKQ5biaDX/6M4uvNp5wbILg59PmreK1+DY6uzDYkwDOAD7t+iI+bD9vObeOdbe84N6OIiIgUCypgIlIotKhWhud61QPglV/2szviinMDNB8KLUYAdvjhQbh8MtuQWqVr8WbHNwGYd3AePx750akRRUREpOhTARORQmPkTTW4tWEQFqud/87dSWySk2/z6/U2BLeA5MsZi3JYkrMN6VK1C/9t9l8AXtn8CuHR4c7NKCIiIkWaSwvYunXr6Nu3L5UrV8YwDBYvXnzN8VFRUQwZMoTQ0FBMJhOjR4/OcdwPP/xAgwYN8PT0pEGDBixatCjbmGnTplGjRg28vLxo0aIF69evd8AvEpH8MAyDt+9uQtWyPpy5nMxTC8Ox2Zz4PJibZ8bzYD6BcG4P/DIWcnge7eEmD9O9WnfSbemMXjOac4nnnJdRREREijSXFrDExESaNm3Kxx9f3wanqamplC9fngkTJtC0adMcx2zatIlBgwYxdOhQdu/ezdChQxk4cCBbtmzJHDN//nxGjx7NhAkT2LVrFx07dqRXr16cPn3aIb9LRPLO38udafc2x8PNxMoD0Uxff9y5AQJCYMBMMEywey5sn5FtiMkw8WqHV6lTpg4XUy4yes1oUtJTnJtTREREiiTD7tTlxnJnGAaLFi3ijjvuuK7xnTt3plmzZnzwwQdZPh80aBBxcXEsXbo087Nbb72VMmXKMG/ePADatGlD8+bN+fTTTzPH1K9fnzvuuIM33njjus4fFxdHQEAAsbGx+Pv7X9d3ROT6zd1ymucX7cFsMpj3UFta1yjr3AB/TIUVL4HJHe5fAlVaZxtyJv4M9/x6D7GpsfSt2ZfXbnoNwzCcm1NERERc7ka6QbF7BmzTpk306NEjy2c9e/Zk48aNAKSlpbFjx45sY3r06JE5JiepqanExcVleYlIwRncugp3NKuM1WbniXk7uZCQ6twA7UdBg35gs8CCYZAQnW1IiF8I73Z6F7Nh5n/H/8fX+792bkYREREpcopdATt37hwVK1bM8lnFihU5dy7jGY0LFy5gtVqvOSYnb7zxBgEBAZmvKlWqOD68iGQyDIPX7mxM7QqlOB+XyujvwrE683kww4B+n0BgKMRHwcL7wZp9k+i2ldrydKunAZiyYwobz+b+H3JEREREil0BA7LdAmS327N9dj1j/mn8+PHExsZmviIiIhwXWERy5Ovpxqf3Nsfb3cyGoxf4cNUR5wbw9IN7vgUPPzi1AVa+nOOwIfWGcEftO7DZbTz9+9NExOl/H0RERCRnxa6ABQUFZbuSFR0dnXnFKzAwELPZfM0xOfH09MTf3z/LS0QKXp2Kfrx+VyMAPlx9hHWHY5wbILAO3PnX86KbPoY932cbYhgGL7Z9kSaBTYhLi2PUmlEkWhKdm1NERESKhGJXwNq1a8eKFSuyfLZ8+XLat28PgIeHBy1atMg2ZsWKFZljRKRwuTMshMGtq2K3w+j54ZyLdfKKg/X7wk1jMt7//ASc359tiIfZg/e7vE957/IcvXKU59c/j81uc25OERERKfRcWsASEhIIDw8nPDwcgBMnThAeHp65HPz48eMZNmxYlu9cHZ+QkEBMTAzh4eHs3//3X4aefPJJli9fzltvvcXBgwd56623WLlyZZY9w8aOHcuXX37JzJkzOXDgAGPGjOH06dM8+uijBf6bRSRvXu7bgAaV/LmUmMbjc3disTq53HR9EWp2BktSxibNKbHZhlTwqcAHXT7A3eTO6ojVfLb7M+dmFBERkULPpcvQr127li5dumT7fPjw4cyaNYsRI0Zw8uRJ1q5dm3ksp+e0qlWrxsmTJzP//P333/PCCy9w/PhxatWqxWuvvcZdd92V5TvTpk3j7bffJioqikaNGvH+++9z8803X3d2LUMv4nynLiZy24cbiE9N5+Gba/J87/rODZB4Eb7oBLERENobBn0Lpuz/Heunoz/xwh8vAPB+5/fpVq2bc3OKiIiIU91INyg0+4AVNSpgIq7x294oHv1mJwBfDG1Bj4ZBzg0QuRNm3grWVOj6Atz8dI7D3tr6Ft8c+AZvN2++6f0NdcvUdW5OERERcZoSvQ+YiBRvtzaqxMibagAwbuFuIi4lOTdAcHPoMyXj/erX4OjKHIc91fIp2gS1ITk9mVGrR3El5YrzMoqIiEihpQImIkXOs7fWI6xqaeJS0nns252kWKzODdB8KLQYAdjhhwfh8slsQ9xMbrzb6V2CSwUTmRDJuHXjSLdl30dMREREShYVMBEpcjzcTHwypDllfNzZExnLa78ecH6IXm9DcAtIvpyxKIclOduQ0l6l+bDrh3i7ebMlagtTtk9xfk4REREpVFTARKRIqlzam/cHNQPg682n+Hn3WecGcPOEgXPAJxDO7YFfxkIOj9TWLVOX1296HYBvDnzDT0d/cm5OERERKVRUwESkyOocWoHHu9QG4Lkf/uRodIJzAwSEwICZYJhg91zYPiPHYd2qdePRphnbXEzaNIktUVucmVJEREQKERUwESnSxnSvS7ua5UhKs/LYtztITnPy82A1O0G3SRnvlz4HEVtzHPafpv+hW9VuWGwWHl/1ONvObXNiSBERESksVMBEpEgzmwymDm5GeT9PDp9P4IXFe3H67hrtn4AGd4DNAguGQUJ0tiEmw8RbN79Fx+COpFhT+O+q/7Lj/A7n5hQRERGXUwETkSKvgp8XH94ThsmAH3aeYeH2M84NYBjQ72MIDIX4KFh4P1izr3joYfbg/S7v06FyB5LTk/nPyv+wK3qXc7OKiIiIS6mAiUix0K5WOZ7qEQrAiz/tZf/ZOOcG8PSDe74FDz84tQFWvpzzMLMnH3T5gHaV2pGcnsyjKx4lPDrcuVlFRETEZVTARKTY+E+nWnQJLU9quo3/zt1JfIrFuQEC68Cdn2a83/Qx7Pk+x2Febl5M7TqVNkFtSEpP4j8r/8OemD1ODCoiIiKuogImIsWGyWTw3sBmBJf25sSFRJ77YY/znwer3xduGpPx/ucn4Pz+HId5u3nz0S0f0SqoFQmWBB5Z8Qj7LuxzYlARERFxBRUwESlWyvh68PGQMNzNBr/uiWL2xpPOD9H1RajZGSxJGZs0p8TmOMzbzZuPu35M8wrNibfE89CKh9h/MefCJiIiIsWDCpiIFDthVcswvld9AF5bcoBdpy87N4DJDP1nQkAVuHQMFj0KNluOQ33cfZjWbRphFcKIT4vnoeUPcfDSQefmFREREadRARORYun+DtXp1SgIi9XO43N3cSUpzbkBfMvBoK/B7AmHlsCGKbkPdfdl2i3TaFq+KXFpcTy0/CEOXTrkxLAiIiLiLCpgIlIsGYbBWwOaUL2cD5FXkhm7YDc2m5OfB6scBn3+Kl6rX4OjK3MdWsqjFJ92+5TGgY25knqFh5Y/xJHLR5wUVERERJxFBUxEii1/L3c+ubc5Hm4mVh+M5rN1x5wfovlQaDECsMMPD8Llk7kO9fPw47Pun9GwXEMup17mweUPcuyKCzKLiIhIgVEBE5FirWHlACbf3hCAd5cdYvPxi84P0ettCG4ByZczFuVITch1qL+HP593/5z6ZetzKeUSI5eN5HjscSeGFRERkYKkAiYixd6gVlW4q3kwNjuMmreLmPhU5wZw84SBc8AnEM7tgW8HQGp8rsMDPAP4ovsXhJYJ5WLKRR5c9iAnY086L6+IiIgUGBUwESn2DMPg1TsaUbdiKaLjU3nyu11Ynf08WEAIDFkAngFwehN8fWeuy9MDlPYqzfQe06lTpg4xyTGMXDaS03GnnRhYRERECoIKmIiUCD4ebky7tzk+HmY2HrvI1JWHnR8ipAUM/xm8y8CZbTCnX8Ztibko41WGL3t8Se3StYlOjuaBZQ8QER/hxMAiIiLiaCpgIlJi1K7gxxt3NQbgozVH+f1wjPNDVG4Gw/8HPuXg7C6Y3RcSc38uraxXWab3mE7NgJqcTzrPyGUjiUyIdF5eERERcSgVMBEpUfo1C+beNlWx22H0d7s4eyXZ+SGCGsPwX8C3fMYzYbP7QkLuZTDQO5AZPWdQ3b86UYlRjFw2krMJZ50YWERERBxFBUxESpwXb2tAo2B/LidZeHzuTixWm/NDVGwAI5ZAqSCI3gez+kD8uVyHXy1h1fyrEZkQychlIzmXmPt4ERERKZxUwESkxPFyNzNtSAv8vNzYefoKby096Jog5evC/UvAPxguHMooYXG5X9mq4FOBGT1mUMWvCmcSzvDAsgc4n3jeiYFFREQkv1TARKREqlrOh3fvbgrAlxtO8NteF11NKlcLRvwKAVXg4lH4qjdcyX2hjYq+FZnZcybBpYKJiI9g5PKRxCS54Fk2ERERyRMVMBEpsXo2DOKhjjUAePr73Zy6mOiaIGVrZFwJK10NLp+AWb3h8slchwf5BmWWsFNxp3hg2QNcSL7gvLwiIiKSZypgIlKiPXNrPVpUK0N8SjqPfbuTFIvVNUFKV4X7l0LZWnDlNHzVBy4ey3V45VKVmdFzBpV8K3Ey7iQjl43kYnLuqymKiIhI4aACJiIlmrvZxMdDwijr68G+s3FM/mW/68IEBGfcjhhYF+LOZDwTduFIrsODSwUzo+cMKvpU5HjscR5c/iCXUi45MbCIiIjcKBUwESnxKgV488GgZhgGzN1ymsW7XLjPln+ljBJWvj7ER2U8Exad+yIhVfyqMLPnTCp4V+DolaM8uPxBLqfkvrmziIiIuJYKmIgIcHPd8jzRtQ4Azy/aw9HoeNeFKVUBRvwCFRtDYnTGlbBze3MdXtW/KjN6zqC8d3mOXD7CwyseJjY11omBRURE5HqpgImI/OXJW+rQoXY5ktKs/OebnSSlpbsujG8gDP8ZKjWDpAsw+zY4G57r8OoB1fmy55eU8yrHwUsHeWj5QyphIiIihZAKmIjIX8wmgw8GhVHBz5Mj0Qm8sGgvdrvddYF8ysKwnyC4JSRfhjm3Q+SOXIfXDKjJjJ4zKOtVlgOXDvDIikeIS4tzYmARERH5NypgIiL/UN7Pk48Gh2E2Gfy4K5LvtuW+J5dTeJeGoYugShtIiYU5d0DE1lyH1ypdiy97fEkZzzLsu7iPR1c8SnyaC2+nFBERkSxUwERE/p82NcsxrkcoAC//vI+9kS6+lc/LH+77Eap1gNQ4+PpOOLUx1+F1ytRheo/plPYszZ4Le3h05aMkpCU4MbCIiIjkRgVMRCQHj9xck1vqVSAt3cZ/5+4kLsXi2kCepeDehVCjE6QlwDf94cS6XIeHlg1leo/p+Hv482fMnzy26jESLS7aaFpEREQyqYCJiOTAZDKYMrApwaW9OXUxiWcW/una58EAPHxhyHyodQtYkuDbu+HoqlyH1ytbj+k9puPn4ceu6F08tvIxkixJTgwsIiIi/58KmIhILkr7ePDJvc1xNxv8tu8cX/1x0tWRwN0b7pkLdW+F9BSYNxgOL891eINyDZjefTp+7n7sjN7J46sfJzk92YmBRURE5J9UwERErqFZldK80KcBAK8vOcDO04Vgk2N3Lxj4NdS7Dayp8N0QOPhrrsMbBjbks+6fUcq9FNvObeOJVU+ohImIiLiICpiIyL8Y1q4afRpXIt1m5/Fvd3I5Mc3VkcDNA+6eBQ3uAJsFFgyD/T/lOrxJ+SZ82u1TfNx82HJuC0+ufpKU9BSnxRUREZEMKmAiIv/CMAze7N+YGoG+nI1NYcyCcGw2Fz8PBmB2h/4zoPHdYEuHhffDnu9zHd6sQjM+7fYp3m7ebIraxOi1o0m1pjoxsIiIiKiAiYhcBz8vd6bd2xxPNxNrD8Xw6e/HXB0pg9kN7vwcmg4BuxV+fAh2f5fr8OYVmzPtlml4u3nzR+QfjFkzhjRrIbiiJyIiUkKogImIXKf6lfx5pV8jAKYsP8TGYxdcnOgvJjP0+wSaDwO7DRY9Cju/znV4y6CWfHLLJ3iZvVgfuZ6n1j6FxeriZfZFRERKCBUwEZEbMLBVFQa0CMFmh1HzwomOLyTPUZlMcNtUaPUgYIefH4ftM3Md3iqoFR/d8hGeZk/WnlnLuN/HYbGphImIiBQ0FTARkRv0Sr9GhFb040JCKqPm7SLdanN1pAwmE/R+F9r8J+PPv4yBLZ/nOrxtpbZ82OVDPEwerI5YzbPrnlUJExERKWAqYCIiN8jbw8y0+5rj62Fm8/FLvL/ysKsj/c0w4NY3oP2ojD8vfQY2fpzr8PbB7ZnadSruJndWnFrBc+ueI92W7qSwIiIiJY8KmIhIHtQqX4o3+zcB4JM1x1hzKNrFif7BMKD7ZOg4LuPPyyfA+vdyHX5T8E180OUD3ExuLD+1nOfXP68SJiIiUkBUwERE8qhv08oMa1cNgDHzw4m8Uog2NzYMuOVF6Px8xp9XTYK1b+U6/OaQm3m/8/u4mdxYenIpL/zxAlab1UlhRURESg4VMBGRfJjQpz5NQgK4kmThv9/uJC29kDwPdlXnZ+GWlzLer30dVr8K9pz3MOtcpTPvdnoXN8ONX4//yksbX1IJExERcTAVMBGRfPB0M/PJkOb4e7kRHnGFN5cedHWk7Do+BT1ezXi/7h1Y+XKuJeyWqrfwdqe3MRtmfj72MxM3TcRmL2SlUkREpAhTARMRyacqZX2YMrAZADP/OMHSPVGuDZST9k9Ar7cz3v8xFZY9n2sJ616tO2/e/CZmw8zio4uZvGmySpiIiIiDqICJiDhA9wYVeeTmmgA88/2fnLyQ6OJEOWjzCPT5azGOzdNgyTiw5Vysbq1+K6/f9Domw8QPR37gtc2vYc+lsImIiMj1UwETEXGQcT1DaVW9DPGp6Tz27U5SLIXw+alWI+H2jwEDtn0Jv4zOtYT1rtmbVzu8ioHBgsMLeH3L6yphIiIi+aQCJiLiIO5mEx8Nbk45Xw/2R8Ux6X/7XB0pZ82Hwp2fgWGCnbPh58chl8U2+tbqyysdXsHA4LtD3/HWtrdUwkRERPJBBUxExIGCAryYek8YhgHztkbw484zro6Us6b3wF3TwTBD+Lew6BGw5rz3V7/a/ZjUfhIA3x74lne2v6MSJiIikkcqYCIiDnZTnUCevKUOABMW7eXw+XgXJ8pF4wEwYCaY3GDPQvjxQbBachx6Z507ebndywB8vf9r3t/xvkqYiIhIHqiAiYgUgCe61qFjnUCSLVYe+3Yniak5X11yuYZ3wMA5YHKHfYtg4QhIT8tx6IC6A3ix7YsAfLXvK6bunKoSJiIicoNUwERECoDZZPD+oGZU9PfkaHQCzy/aU3jLSr0+cM9cMHvCwV9gwTBIT81x6MDQgTzf5nkAZuydwcfhHxfe3yUiIlIIqYCJiBSQwFKefDykOWaTwU/hZ5m79bSrI+Wubg8YPA/cvODwUvhuCFiScxw6uN5gnmv9HABf/PkFn+7+1JlJRUREijQVMBGRAtSqelme6RkKwKSf97M3MtbFia6h9i0wZAG4+8DRlTDvHkhLynHovfXv5emWTwPw6e5P+Wz3Z85MKiIiUmSpgImIFLCHb65Jt/oVSbPa+M+3O7iYkPPtfYVCzU5w7/fg7gvH18LcgZCakOPQYQ2HMbbFWAA+Cf+EL/d86cSgIiIiRZMKmIhIATMMgyl3NyWkjDcRl5IZ9MVmouNSXB0rd9U7wNBF4OEHJ9fDN/0hJS7Hofc3up8nmz8JwNSdU5m5d6Yzk4qIiBQ5KmAiIk4Q4OPOnAdaE+TvxdHoBAZ+vomzV3J+xqpQqNoGhv0EngEQsRm+uQuSr+Q49MHGD/JE2BMAvL/jfWbvm+3EoCIiIkWLCpiIiJPULF+KBY+0I6SMNycvJjHw801EXMr5GatCIaQFDP8ZvMvAmW3w9R2QdCnHoQ83eZjHmj4GwLvb3+Wb/d84MaiIiEjR8X/t3Xd0VNX6xvHvzKRXSIAECIRQQu8dBEERBLsigih2wXIRuSjitaH+9Cper71jQaQI2AVpSu9IKKEFSEJNIJT0Puf3x2BibkAJJOdMwvNZaxZknz0z77DOgnnY+7xHAUxExET1Q/2YObI7DUL9OHgymyEfrmbfsTNfY+UW6rSDO34Ev1A4vAmmXAuZx8849YF2DzCyzUgAXln/CtN2TDOxUBERkcpBAUxExGR1q/kyc2R3GtX050hqDrd8tIa45HSryzq78NZw58/gXwuStsIXV0PGsTNOfajdQ9zb+l4AXl73MjN3zjSzUhEREbenACYiYoGwIB9mjuxOs/BAjqXncstHa9h++MyNLtxCreauEBYQDke3w+dXQXpSqWk2m43R7UdzV6u7AHhx7YvM2j3L7GpFRETclgKYiIhFagR4M+P+brSuG8yJzDyGfbyGzQdOWV3W2dWMhrvmQlBdSNkFnw2C1EOlptlsNh7t8CgjWowA4PnVz/Nt3LdmVysiIuKWFMBERCxUzc+Lr+7rSof61UjNzue2T9ayIeHMjS7cQmgjVwgLrg8n9sLng+DU/lLTbDYb4zqN47bmtwHw7Kpn+X7P92ZXKyIi4nYUwERELBbk48mUe7rSJSqE9NwCRny6jtV7z9zowi1UbwB3/ez69WQCfHaV69f/YbPZeLzz4wxrNgwDg6dXPs2Pe380uVgRERH3ogAmIuIGArw9+OKuLvRqUoOsvELu/GwdS3efudGFW6hWH+6cCyGNIHW/azvi8b2lptlsNiZ0mcAtTW/BwOCplU/x876fLShYRETEPSiAiYi4CV8vBx+P6MTlzWqRW+Dkvi82sGh7stVlnV1wXdd2xBrRkHbIFcKO7S41zWaz8WTXJ7mpyU04DSdPrniSX+J/saBgERER6ymAiYi4ER9PB+/f1pGBrcLJK3QyaupG5m49YnVZZxcY7uqOWKsFZCS5uiMe3VFqmt1m55nuz3BD4xtwGk6eWP4ECxIWWFCwiIiItRTARETcjJeHnbeHtee6dnUocBo8PO13vttUutug2wioBXf85LpfWOZRVwhL2lpqmt1m57kez3Fto2spNAoZv2w8ixMXW1CwiIiIdRTARETckIfDzutD2nFzxwicBjz6dQwz15fuNug2/ENhxA9Qux1kHYcvroHDMaWm2W12nu/xPFc3vJoCo4BxS8fx2/7fTC9XRETEKgpgIiJuymG38cpNbbitW30MA8bP2cqXqxOsLuvs/EJgxPdQtxNkn4Qp18LBjaWmOewOXuz5IgOjBlJgFDB26ViWHlhqQcEiIiLmUwATEXFjdruNF65rxT2XRAHw9PexfLJ8n8VV/QXfanD7t1CvG+SkwpTrYP/aUtMcdgcvXfISAxoMoMBZwKNLHmX5weXm1ysiImIyBTARETdns9l46qrmPNinEQAv/ryDd36Ns7iqv+ATBLfNgchLIC8dpt4ICStLTfOwe/Byr5e5IvIK8p35jPltDKsOrbKgYBEREfMogImIVAI2m43HBjRl7BXRALy2YDf/WbALwzAsruwsvANg+Cxo2AfyMuCrwbCv9DZDT7snr/R+hcvrX06eM4/Rv41m9eHV5tcrIiJiEgUwEZFKwmazMfryJkwY2AyAt3/dw8vzdrpvCPPyg2EzoHE/yM+CaUNgT+muh552Tyb1nkSfen3ILcxl9K+jWXdknQUFi4iIVDwFMBGRSmbkpY147poWAHy0bB/P/RCL0+mmIczTF4ZOg+iBUJAD04fC7vmlpzk8+c+l/6F3RG9yCnN4+NeHWZ+03oKCRUREKpYCmIhIJXRnzyheuqE1Nht8sTqRJ7/dSqG7hjAPbxgyBZpdDYV5MGM47Py51DQvhxev93mdnnV7kl2QzUOLH+L35N8tKFhERKTiKICJiFRSt3atz2uD22K3wYz1Bxg3azMFhU6ryzozDy+4+XNoeQM48+HrERD7Xalp3g5v3uz7Jt1rdye7IJsHFj1AzNEYs6sVERGpMApgIiKV2E0dI3hzaHscdhvfbjrEIzNiyHfXEObwhBs/gdZDwFkAs++GrbNLTfN2ePPWZW/RtXZXsgqyGLVoFFuObbGgYBERkfKnACYiUsld07YO7w3vgKfDxs9bj/DgV7+TW1BodVln5vCAGz6AdsPBKIRv7oOY6aWm+Xj48PZlb9M5vDOZ+ZmMXDhSK2EiIlIlWBrAli1bxjXXXEOdOnWw2Wx89913f/ucpUuX0rFjR3x8fGjYsCEffPBBieN9+vTBZrOVelx11VVFc5577rlSx8PDw8v744mImGZAy3A+GtEJbw87C7cnc/+UjeTku2kIszvg2negwx1gOOG7B+D3KaWm+Xr48s5l79AxrCMZ+RncM/8eft5X+toxERGRysTSAJaZmUnbtm155513zml+fHw8gwYNolevXmzatIknn3yS0aNHM2fOnKI533zzDUeOHCl6bNu2DYfDwc0331zitVq2bFli3tatW8v1s4mImK1v01p8emdnfD0dLN19jLs+W09mboHVZZ2Z3Q5XvwGd7wMM+OEfsH5yqWl+nn68d/l79K3XlzxnHk8sf4J3Nr2D03DTbZYiIiJ/w8PKNx84cCADBw485/kffPAB9evX54033gCgefPmbNiwgddee42bbroJgJCQkBLPmTFjBn5+fqUCmIeHh1a9RKTK6dm4Bl/c3YW7P1/P6n3HuePTdXx2V2cCfTytLq00ux0GTXJdG7bmPfh5LBTmQ7dRJab5efrxRt83eOP3N/hs22d8uOVDEtISeLHni/h4+FhUvIiIyPmpVNeArV69mv79+5cYGzBgABs2bCA/P/+Mz5k8eTJDhw7F39+/xHhcXBx16tQhKiqKoUOHsm/fvr9879zcXNLS0ko8RETcUZeoEL68pwtBPh5sSDzJbZPXkZp15r8jLWezwYCXoOcjrp9/GQ+r3i41zW6zM7bjWJ7v8Twedg/mJ8zn7vl3cyzrmMkFi4iIXJhKFcCSkpIICwsrMRYWFkZBQQEpKSml5q9bt45t27Zx7733lhjv2rUrU6ZMYf78+Xz88cckJSXRo0cPjh8/ftb3fvnllwkODi561KtXr3w+lIhIBWhfvzrT7utGdT9PNh84xbCP13A8I9fqss7MZoN+E6H3Y66fFzwFy/9zxqk3NLmBj674iGDvYLambGXYz8PYeWKnicWKiIhcmEoVwABsNluJnw3DOOM4uFa/WrVqRZcuXUqMDxw4kJtuuonWrVvTr18/fv7ZdVH3F198cdb3nTBhAqmpqUWPAwcOXOhHERGpUK3qBjPj/u7UCPBi+5E0hn60hqPpOVaXdWY2G1z2FPT9l+vnxc/Dkn+DUfrm0p3DOzNt0DQaBDUgOSuZEfNG8Nv+30wuWERE5PxUqgAWHh5OUlJSibGjR4/i4eFBaGhoifGsrCxmzJhRavXrTPz9/WndujVxcXFnnePt7U1QUFCJh4iIu2saHsiM+7sTFuRN3NEMhn64hiOp2VaXdXaXPg6XP+v6/ZKX4dcXzxjC6gfVZ+qgqXSr3Y3sgmwe+e0RPt/2edF/yomIiLirShXAunfvzsKFC0uMLViwgE6dOuHpWfIC86+//prc3Fxuu+22v33d3NxcduzYQe3atcu1XhERd9C4VgBfj+xO3Wq+7EvJZMiHqzlwIsvqss6u11jo/3+u3y9/DRY+c8YQFuwdzHv93mNI9BAMDP6z8T88t/o58gvd9Ho3ERERLA5gGRkZxMTEEBMTA7jazMfExLB//37Ate1vxIgRRfNHjRpFYmIiY8eOZceOHXz66adMnjyZcePGlXrtyZMnc/3115daGQMYN24cS5cuJT4+nrVr1zJ48GDS0tK44447KuaDiohYLDLUn69HdScy1I8DJ7K55cPVxKdkWl3W2fV4GAZOcv1+1Vvwy4QzhjBPuydPdXuKJ7o8gd1m55u4bxi5aCSpuakmFywiInJuLA1gGzZsoH379rRv3x6AsWPH0r59e5555hkAjhw5UhTGAKKiopg7dy5LliyhXbt2vPDCC7z11ltFLej/sHv3blasWME999xzxvc9ePAgw4YNo2nTptx44414eXmxZs0aIiMjK+iTiohYr241X74e2Z1GNf05nJrDLR+uJi453eqyzq7r/XD1f12/X/s+zL4bckvXa7PZGN58OG9f9jb+nv6sT1rP8LnDSUhNMLdeERGRc2AztGH+vKSlpREcHExqaqquBxORSiUlI5fbPlnLzqR0Qv29mHpvV5rXduO/xzZNhR8fAWcBhDaGIVMgrOUZp+4+uZt/LP4HhzMPE+gVyOt9Xqdb7W4mFywiIhebsmSDSnUNmIiIXLgaAd5Mv68breoGcTwzj2Efr2HrQTfestf+NrhzLgTVheN74OPL4Pcvz7glMbp6NNOumkbbmm1Jz0vngYUPMGv3LAuKFhEROTMFMBGRi1B1fy++urcb7etX41RWPrd+vIaNiSetLuvs6neFkcuhcT8oyIEfHobvHoS80texhfqGMnnAZAZFDaLAKOD51c/z6vpXKXQWWlC4iIhISQpgIiIXqWBfT768pytdokJIzy3g9slrWbPv7Dekt5x/KNw6Cy57Gmx22DwNPr4cju0qNdXb4c2/e/2bh9s9DMCX279k9G+jycx348YjIiJyUVAAExG5iAV4e/DFXV24pHENsvIKufOzdSyPO2Z1WWdnt0PvcTDiBwgIg2M74KO+sOXrUlNtNhsj245k0qWT8HZ4s+zgMm6fdzuHMw5bULiIiIiLApiIyEXO18vBJ3d0om/TmuTkO7nniw0s3pFsdVl/LaoXjFoBUb0hPxO+uc/VqCM/p9TUKxtcyWcDPqOGbw3iTsYx7OdhbD622YKiRUREFMBERATw8XTw4e2dGNAyjLwCJ6OmbuSXbUesLuuvBdSC27+DS8cDNtj4OUzuB8f3lpraumZrpl81nabVm3Ii5wR3/3I3c/fNNbtiERERBTAREXHx8rDzzq0duKZtHfILDR6atonvYw5ZXdZfszug75Nw2xzwC4WkrfDhpRD7Xamp4f7hTBk4hT71+pDnzGP88vG8G/MuuhuLiIiYSQFMRESKeDrsvHFLOwZ3jKDQaTBmZgxfbzhgdVl/r/Hlri2J9btDXjrMugPmPg4FuSWm+Xn68UafN7ir5V0AfLD5Ax5f9jg5BaW3LoqIiFQEBTARESnBYbfx6k1tuLVrfQwDHp+9halrEq0u6+8F1YE7foSej7h+XvchfHolnCxZu8PuYGynsTzf43k8bB78kvALd8+/m5TsFAuKFhGRi40CmIiIlGK32/i/61txV88GADz13TYmr4i3tqhz4fCEK56HYTPBpxoc/h0+7AU7S1/vdUOTG/io/0cEewezNWUrw34exq4TpVvai4iIlCcFMBEROSObzcYzV7fggT6NAHjhp+28+9sei6s6R02vhFHLoW5HyEmFGcNgwdNQmF9iWufwzkwbNI0GQQ1Iykzi9nm3s+TAEktKFhGRi4MCmIiInJXNZuPxAU15tF80AJPm7+L1hbsrR+OKavXhrl+g24Oun1e9BZ9fBaklG4vUD6rP1EFT6Vq7K9kF2Yz+dTRfxH5ROT6jiIhUOgpgIiLyl2w2G4/0a8L4K5sB8NbiOP79y87KEVA8vODKl2HIFPAOggNrXVsS9ywqMS3YO5j3+73PzdE3Y2Dw2obXmLh6Ivn/s2ImIiJyoRTARETknDzQpxHPXN0CgA+X7mPij9srRwgDaHEdjFwK4W0g6zhMHQy/vgjOwqIpnnZPnu72NOM7j8duszMnbg6jFo0iNTfVwsJFRKSqUQATEZFzdvclUfzfDa0A+HxVAk9+uw2ns5KEsJCGcM9C6HQ3YMCySTDlOkhPLppis9m4rcVtvH3Z2/h5+LEuaR3D5w4nITXBsrJFRKRqUQATEZEyGd41ktdubovdBtPX7Wfc7M0UFDqtLuvcePrA1f+FmyaDpz8kLIcPLoH4ZSWm9Y7ozZeDvqSOfx0S0xIZPnc4a4+stahoERGpShTARESkzAZ3jOCNoe1x2G188/shxsyMIb+yhDCA1oPh/iVQqwVkHnWthC2dBM7izxBdPZqvrvqKNjXbkJaXxqiFo5i9e7Z1NYuISJWgACYiIufl2rZ1ePfWDng6bPy05QgPffU7uQWFf/9Ed1EzGu5dDO1uA8MJv70IXw2GzOIbMtfwrcGnAz5lYNRACowCJq6eyKT1kyh0VqLPKSIibkUBTEREztuVrcL56PZOeHnYWbA9mZFfbiQnvxKFEy8/uP5duO5d8PCFvYvhg16wf03RFG+HN6/0eoWH2j0EwJTtU3jkt0fIzM+0qmoREanEFMBEROSC9G1Wi0/v6IyPp50lu45x9+frycorsLqssml/G9y3GEKbQPph+GwQrHwLTnd5tNlsjGo7ikmXTsLb4c3Sg0u5fd7tHM44bHHhIiJS2SiAiYjIBbukSQ2m3N0Vfy8Hq/Ye545P15GeU8nuoRXWEu7/DVoNBqMQFj4N04dB1omiKVc2uJLPBnxGqE8ocSfjGPbzMDYf22xh0SIiUtkogImISLnoEhXCl/d2JdDHg/UJJ7l98jpSsytZCPMOhJs+cXVKdHjD7nnw4aVwcGPRlNY1WzP9quk0rd6UEzknuPuXu5kXP8/CokVEpDJRABMRkXLToX51pt/XjWp+nsQcOMWtH6/hRGae1WWVjc3mulfYvQuhehSk7odPB8CaD4q2JNYOqM2UgVPoU68Pec48Hl/2OO/FvFd5bkwtIiKWUQATEZFy1apuMDPu70aNAC9iD6cx7KM1HEvPtbqssqvdFkYuhebXgjMffhkPX4+AnFQA/Dz9eKPPG9zZ8k4A3t/8PuOXjSenIMfCokVExN0pgImISLlrFh7EjPu7Exbkza7kdG75aDVJqZUwmPgEw5ApcOUrYPeEHT+4tiQecV335bA7+GenfzKxx0Q8bB7MS5jHPfPvISU75W9eWERELlYKYCIiUiEa1wrg65HdqVvNl33HMhny4WoOnsyyuqyys9mg2yi4+xcIrgcn4+GTK2DDZ0VbEm9sciMf9f+IYO9gtqRsYdjPw9h1YpfFhYuIiDtSABMRkQoTGerPzJHdqB/ix/4TWdzy4RoSUirp/bMiOsHIZRB9JRTmwk9j4Jv7ITcDgM7hnflq0Fc0CGpAUmYSt8+7nSUHllhZsYiIuCEFMBERqVAR1f34emR3Gtb059CpbIZ8uJo9RzOsLuv8+IXA0OnQbyLYHLD1a/i4LxzdAUBkUCRTB02la3hXsguyGf3raL6I/ULNOUREpIgCmIiIVLjwYB9m3t+dpmGBHE3PZehHq9mZlGZ1WefHbodLxsCdP0NgbUjZDR/1hZhpAAR7B/P+Fe8zOHowBgavbXiNiasnku+sZC35RUSkQiiAiYiIKWoGejP9/m60rBNESkYeQz9aw7ZDqVaXdf4iu8OoFdDoMijIhu8egO8fgrwsPO2ePNPtGR7v/Dh2m505cXN4YOEDpOZW4s8rIiLlQgFMRERME+LvxbR7u9GuXjVOZeUz7OM1/L7/pNVlnT//GjB8NvT9F9jssGkqfNIPUuKw2Wzc3uJ23r7sbfw8/FibtJbhc4eTkJpgddUiImIhBTARETFVsJ8nX97Thc4NqpOeU8Dtn6xl7b7jVpd1/uwOuPRxuP078K8FR2Phoz6wdTYAvSN6M2XgFGr71yYxLZHhc4ez7sg6S0sWERHrKICJiIjpAn08+eLuLvRsHEpmXiF3fLaOFXGV/N5ZDS+FUcsh8hLIy4A598BPYyE/h6YhTZl21TTa1GxDWl4aIxeOZM7uOVZXLCIiFlAAExERS/h5eTD5js70bVqTnHwnd3+xnt92HrW6rAsTGA4jvode41w/b5gMn/aHE/HU8K3BpwM+ZWDUQAqMAp5b/RyvrX+NQmehtTWLiIipFMBERMQyPp4OPri9I/1bhJFX4OT+Lzfwy7Ykq8u6MA4PuPxpGD4HfEPgyGb48FLY8SPeDm9e6fUKD7Z7EIAvtn/BI789QmZ+Jb03moiIlJkCmIiIWMrbw8G7wztwdZva5BcaPDTtd37YfNjqsi5ck36uLYn1ukJuKsy8DX6ZgK0wnwfaPsCk3pPwdniz9OBSRswbwZGMI1ZXLCIiJlAAExERy3k67Lw5tD03dqhLodNgzIxNzN540OqyLlxwhOt+YT3+4fp5zXvw2UA4dYAro67k0wGfEuoTyu6Tuxn28zC2HNtibb0iIlLhFMBERMQtOOw2XhvclmFd6uM0YNyszUxbu9/qsi6cwxP6vwhDp4FPMBzaAB/2gt3zaVOzDdOvmk509WiO5xznrl/uYl78PKsrFhGRCqQAJiIibsNut/HSDa24s0cDAJ78diufrYy3tqjy0uwqGLkM6rSH7JMwbQgseo7avjWZMnAKfSL6kOfM4/Flj/N+zPsYhmF1xSIiUgEUwERExK3YbDaevaYFIy9tCMDEH7fz/pK9FldVTqo3gLvnQ5eRrp9X/Be+uAb/7DTe6PsGd7S4A4D3Nr/H+OXjySnIsa5WERGpEApgIiLidmw2G09c2YxHLm8CwCu/7OTp77aRk18FWrZ7eMOgV+Hmz8ErEPavgg8uwRG/lHGdx/Fc9+fwsHkwL34e98y/h5TsSn5/NBERKUEBTERE3JLNZuPRK6IZf2UzAL5ck8h176xkd3K6xZWVk5Y3wMilENYaslLgyxvht5e5qfH1fHjFhwR5BbElZQu3/nwru07ssrpaEREpJwpgIiLi1h7o04jP7+pMjQAvdiWnc83bK/hyTWLVuEYqtBHcuxA63gkYsPTf8OUNdAlswLSrptEgqAFHMo8wYt4Ilh5YanW1IiJSDhTARETE7fVpWot5j/Tm0uia5BY4efq7bdw3ZSMnMvOsLu3CefrCNW/CDR+Bpx/EL4UPLiHyxAGmDppK1/CuZBVk8Y9f/8EXsV9UjeApInIRUwATEZFKoWagN5/d2Zmnr26Bl8POoh3JDHxzGav2VJFrpNreAvf9BjWbQUYyfHENwes+4f3L32Vw9GAMDF7b8BoTV08k35lvdbUiInKebIb+K+28pKWlERwcTGpqKkFBQVaXIyJyUdl2KJXRMzax71gmNhuM7N2If/aPxtNRBf5fMS8TfhoLW2a4fm58BcYNH/Jlws+8tuE1DAy6hnflP33+Q7B3sLW1iogIULZsoAB2nhTARESslZVXwAs/7WD6OtfNmttGBPPm0PY0qOFvcWXlwDBg05cw9zEoyIGgCLj5M5aSzePLHierIIsGQQ145/J3iAyKtLpaEZGLXlmyQRX4r0IREbkY+Xl58PKNrXl/eAeCfT3ZfDCVq95azpyNByv/dVI2G3QYAfcuhpBGkHYQPhvIpQe3MWXgFGr71yYhLYFbf76V9Unrra5WRETKQAFMREQqtYGtazPvkV50iQohM6+Qf87azJiZMaTlVIHrpMJbwf1LoOWN4CyA+U/SdMHzTLvsfdrUaENaXhr3L7ifObvnWF2piIicI21BPE/agigi4l4KnQbv/baHNxbHUeg0qBfiy5tD29OhfnWrS7twhgHrP4H5T0JhHlSLJOemj3lm3xzmJcwD4I4Wd/Box0dx2B0WFysicvHRNWAmUAATEXFPGxNP8siMTRw8mY3DbuPRfk14oE9jHHab1aVduMOb4Os74FQiOLww+v8fH3gX8N7m9wHoE9GHV3q/gp+nn8WFiohcXHQNmIiIXLQ6RlZn7iO9uLZtHQqdBq8t2M2tH6/h8Klsq0u7cHXaw8hl0OxqKMzDNu8xHohbx6vdJ+Jl92LJwSWMmDeCIxlHrK5URETOQgFMRESqnCAfT94c2o7/3NwWfy8Ha+NPMPDN5fyyrQoEE99qcMtUGPAS2D0g9lsG/vIin3b+F6E+oew6uYthPw9jy7EtVlcqIiJnoAAmIiJVks1m46aOEfw8uhdtIoJJzc5n1NTfmfDNFrLyCqwu78LYbND9IbjrF1eL+hN7aTv7AaZHDia6ejTHc45z9/y7+SX+F6srFRGR/6FrwM6TrgETEak88gqcvL5wNx8u24thQKOa/rw1rD0t61SBGxlnnYBvR0LcAgAy29zM+EAPlh5eCcB9re/jgXYP4Gn3tLJKEZEqTU04TKAAJiJS+azck8KjM2M4mp6Ll8PO+IHNuLtnA2y2St6gw+mElW/Ary+A4aSwZlP+27ofX8T/CECr0Fa83OtlGgQ3sLRMEZGqSgHMBApgIiKV04nMPB6fvYVFO5IB6NO0JpMGt6VmoLfFlZWDhBUw+x7ISAJPP37peR/PH1lEel46vh6+jOs0jpujb678gVNExM0ogJlAAUxEpPIyDIOpaxJ58ecd5BY4qRHgzX+GtOXS6JpWl3bhMo7CnHshfikASa2u5yk/g7XHNgHQO6I3E3tMpIZvDSurFBGpUhTATKAAJiJS+e1KSmf09E3sSk4H4N5LonjsyqZ4e1Tymxk7C2HZJFjyb8DA6R3EV20H8cbxDeQ586juXZ3nejzHZfUvs7pSEZEqQQHMBApgIiJVQ05+IS/N3cGU1YkAtKwTxFvD2tOoZoDFlZWDgxtg7mNw+HcA4sKimVAzlF2ZhwC4scmNPN75cfw9/a2sUkSk0lMAM4ECmIhI1bJoezKPzd7Myax8fD0dPHtNC27pXK/yXy/ldELMVFg0EbJSyAPeadyJzwuPYWAQERDBy71epl2tdlZXKiJSaSmAmUABTESk6klOy2Hs1zGs3HMcgEGtw3n5hjYE+1WBFu7Zp2DJy7DuYzAK2eAfxL9q1+VwYSZ2m517Wt2jdvUiIudJAcwECmAiIlWT02nw0fJ9vDZ/FwVOgzrBPrwxtD1dokKsLq18JMfC3MchcQXpNhsv167Hj6cbQLYIbcHLvV6mYXBDa2sUEalkFMBMoAAmIlK1bT5wikdmbCLheBZ2GzzctzGjL2+Ch8NudWkXzjAg9htY8DSkHWK+ny/Ph4WRhhMfhw9jO41laNOhlX/7pYiISRTATKAAJiJS9WXkFvDs97HM+f0gAB3qV+PNoe2pF+JncWXlJC8Tlv8HVr1NMoU8U7MGq3xdy2E96/bkhR4vUNOvCrTmFxGpYApgJlAAExG5eHwfc4invt1Gem4Bgd4e/N+Nrbm2bR2ryyo/x/fCLxNwxs1nelAA/w2pTq7NRjXvajzb/Vn6RfazukIREbemAGYCBTARkYvLgRNZPDJjE7/vPwXA4I4RPHdtSwK8PawtrDztng/zxrM34wATatZgh7cXANc1uo4nujxBgFcVaM0vIlIBFMBMoAAmInLxKSh08tbiON75bQ9OAxqE+vHWsPa0iahmdWnlJz8HVr9D/vL/8F6AJ5ODgzBsNur6hfNS71foENbB6gpFRNyOApgJFMBERC5ea/cd59GZMRxOzcHDbmPcgKbc36shdnsValqRehAWPM3ve37myZqhHPL0wAbc3fJuHmr/MJ4OtasXEfmDApgJFMBERC5uqVn5PPHNFuZtSwLgksY1eH1IW2oF+VhcWTmLX07GvMf4tzOZ7wNdWxCbB9Tn5cvfolG1RhYXJyLiHhTATKAAJiIihmEwc/0BJv64nez8QkL8vXj1pjb0axFmdWnlq7AANkxm0apXmBjswymHA2/sPNr2AYa1vR+7rQq05hcRuQAKYCZQABMRkT/sOZrB6Omb2H4kDYAR3SN5clBzfDwdFldWzjKOcWzhkzyd9Bsr/XwB6OEXwfMDPiYsKMLi4kRErKMAZgIFMBER+bPcgkJe/WUXk1fEA9A0LJC3hrWnaXigxZWVP+PgBmbM/wev29PIsdsJMuCZ5ncyoOs/rS5NRMQSCmAmUAATEZEzWbLrKONmbSYlIw9vDztPXdWc27pFYrNVoQYdAE4n+9a+zYTYD9l+eqXvGnt1Jgz4gMBaLSwuTkTEXApgJlAAExGRszmWnsu4WZtZuvsYAP2ah/Hq4DaE+HtZXFn5y89M4YO59/FJZhxOm406BYX8X90BdLr8JfD0tbo8ERFTKICZQAFMRET+itNp8NmqBF6Zt5O8QidhQd78d0g7ejSuYXVpFSJm57dMWPM8B20F2AyDO3NtPHzJ83i1uB6q2uqfiMj/UAAzgQKYiIici9jDqYyevom9xzKx2WBk70b8s380no6q1zkwMy+DVxc8xDfHfwegaW4e//ZpROOBb0DNaGuLExGpQApgJlAAExGRc5WVV8ALP+1g+rr9ALSNCObNoe1pUMPf4soqxuJ9c5m48hlOOnPxchqMOZXG8Ba3Y790PPjo30wRqXoUwEygACYiImU1b+sRnvhmK6nZ+fh7OXj+ulbc2KFu1WvQAaRkp/DMknEsP7oRgK7ZObyYZSP88uehzS3aligiVYoCmAkUwERE5HwcPpXNmJkxrIs/AcB17erwwvWtCPLxtLiy8mcYBrN2z+K1da+Q7cwjsNDJ08dPMDCkNQyaBLXbWl2iiEi5UAAzgQKYiIicr0KnwXu/7eGNxXEUOg0iqvvy5tD2dIysbnVpFSIhNYEJy8ez7fh2AAZlZPKv4ycJ6nAnXPY0+IVYW6CIyAVSADOBApiIiFyojYkneWTGJg6ezMZhtzHm8iY82LcxDnvV256X78znoy0f8fGWjyg0nIQXFPB/x47TxeYHlz0FHe8Cu8PqMkVEzosCmAkUwEREpDyk5eTz1Lfb+GHzYQC6RIXwxi3tqFOtat5Da/OxzUxYPoED6QewGTAiLY3RJ07hFd4aBk6CyO5WlygiUmYKYCZQABMRkfJiGAbf/H6IZ77fRmZeIcG+nrxyU2uubFXb6tIqRFZ+FpM2TGL27tkANMkv5N/JR4nOz3c16LjieQgMt7hKEZFzpwBmAgUwEREpbwkpmTwyYxObD6YCMKxLPZ6+ugV+Xh4WV1YxlhxYwrOrnuVEzgk8sfHI8ZPcnpaG3SsALn0cuj4AHl5Wlyki8rfKkg0svQvksmXLuOaaa6hTpw42m43vvvvub5+zdOlSOnbsiI+PDw0bNuSDDz4ocfzzzz/HZrOVeuTk5JSY99577xEVFYWPjw8dO3Zk+fLl5fnRREREyqxBDX9mjerBA30aYbPB9HUHuObtFcQeTrW6tArRp14fvrn2G/pE9CEfg9dCq3FfZCOSCrNh4TPwfg/Ys8jqMkVEypWlASwzM5O2bdvyzjvvnNP8+Ph4Bg0aRK9evdi0aRNPPvkko0ePZs6cOSXmBQUFceTIkRIPHx+fouMzZ85kzJgx/Otf/2LTpk306tWLgQMHsn///nL9fCIiImXl5WFn/JXNmHpPV2oFerP3WCY3vLuKySviqYqbVkJ9Q3nrsrd4tvuz+Hr4ss6ez40NGvJzSDgcj4OpN8H0W+FkgtWlioiUC7fZgmiz2fj222+5/vrrzzpn/Pjx/PDDD+zYsaNobNSoUWzevJnVq1cDrhWwMWPGcOrUqbO+TteuXenQoQPvv/9+0Vjz5s25/vrrefnll8+pXm1BFBGRinYiM4/HZ29h0Y5kAPo0rcmkwW2pGehtcWUVY3/afiYsn8CWlC0ADPSuw7/iNhBcWAAOb7hkDPQcA15+ltYpIvK/Ks0WxLJavXo1/fv3LzE2YMAANmzYQH5+ftFYRkYGkZGRREREcPXVV7Np06aiY3l5eWzcuLHU6/Tv359Vq1ad9b1zc3NJS0sr8RAREalIIf5efDyiIy9c1xJvDztLdh1j4JvLWbLrqNWlVYj6QfX5YuAXPNjuQRw2B/NyD3NTdGvWRHWBwlxY+gq82wW2fw/u8f/HIiJlVqkCWFJSEmFhYSXGwsLCKCgoICUlBYBmzZrx+eef88MPPzB9+nR8fHzo2bMncXFxAKSkpFBYWHjG10lKSjrre7/88ssEBwcXPerVq1fOn05ERKQ0m83G7d0b8MPDl9A0LJCUjFzu/Gw9L/y0ndyCQqvLK3cedg8eaPsAXw78ksigSJJzjnMfSbzabSi5QRGQegC+HgFTroOjO60uV0SkzCpVAAPXP0R/9scOyj/Gu3Xrxm233Ubbtm3p1asXX3/9NdHR0bz99tt/+zr/O/ZnEyZMIDU1tehx4MCB8vg4IiIi56RpeCDfP9yTEd0jAZi8Ip4b3l3FnqMZFldWMVrXbM3XV3/NkOghAHyZvIqhDRuzq9t9ru2I8Uvhg54w/1+Qo10pIlJ5VKoAFh4eXmqV6ujRo3h4eBAaGnrG59jtdjp37ly0AlajRg0cDscZX+d/V8X+zNvbm6CgoBIPERERM/l4Onj+ulZ8MqIT1f082X4kjWveXsGMdfurZIMOP08/nu7+NO9e/i6hPqHsSd3H0GOL+XTA4xRGDwRnAax+B97uCDHTwOm0umQRkb9VqQJY9+7dWbhwYYmxBQsW0KlTJzw9Pc/4HMMwiImJoXZt180svby86NixY6nXWbhwIT169KiYwkVERMpRvxZh/DKmNz0bh5KdX8gT32zloWm/k5qV//dProR6R/Tmm+u+oW+9vhQ4C/jvji+4J8SHwzd9DKGNIfMofPcAfDoADsdYXa6IyF+yNIBlZGQQExNDTEwM4GozHxMTU9QOfsKECYwYMaJo/qhRo0hMTGTs2LHs2LGDTz/9lMmTJzNu3LiiORMnTmT+/Pns27ePmJgY7rnnHmJiYhg1alTRnLFjx/LJJ5/w6aefsmPHDh599FH2799fYo6IiIg7Cwvy4cu7uzJhYDM87Dbmbk1i4JvLWBd/wurSKkSITwhv9n2TiT0m4uvhy8bkjdy09b/8OOApjMufA09/OLgOPuoDPz4CmcetLllE5IwsbUO/ZMkS+vbtW2r8jjvu4PPPP+fOO+8kISGBJUuWFB1bunQpjz76KLGxsdSpU4fx48eXCE6PPvoo33zzDUlJSQQHB9O+fXuee+45unfvXuI93nvvPV599VWOHDlCq1at+O9//0vv3r3PuXa1oRcREXex5eApRk/fRMLxLOw2eLhvY0Zf3gQPR6Xa6HLODqQd4MkVTxJzLAaA/pH9eabVfQQvfQ22znJN8qkGlz0FHe8Ch4dltYrIxaEs2cBt7gNW2SiAiYiIO8nILeC5H2KZvfEgAB3qV+PNoe2pF1I175lV4Czg022f8n7M+xQYBdTyrcULl7xAj3xg7uOQvNU1Maw1DHoVInWZgYhUHAUwEyiAiYiIO/ph82H+9c1W0nMLCPT24OmrW3BTxwgc9rN3+q3MYlNieWL5EySkJQAwvPlwxrR9GJ/N0+HXFyHnlGti65vhiuchqI5ltYpI1aUAZgIFMBERcVcHTmTxyIxN/L7/FADNwgMZf2Uz+jSt+Ze3XKmssguyeX3D68zYNQOARsGNeLnXyzT3qQW/vgAbPwcM13Vilz4G3R4ED29LaxaRqkUBzAQKYCIi4s4KCp18ujKed37dQ1pOAQDdGoYwYWBz2tarZm1xFWTFoRU8vfJpUrJT8LB78FC7h7ir5V04kra4tiUeXOeaGNIIBr4KTfpZW7CIVBkKYCZQABMRkcrgVFYe7/62hy9WJZJX6LpP1tVtavPYgKZEhvpbXF35O5lzkudXP8+i/YsA6FCrA/93yf8R4V8HtsyEhc+42tYDNB0EA16CkCgLKxaRqkABzAQKYCIiUpkcPJnF6wt2823MIQwDPB02hneN5B+XNSY0oGptxzMMg+/3fs+/1/2bzPxM/D39mdBlAtc2uhZbbjosfQXWfuC6kbPDG3qOhkvGglfVbFgiIhVPAcwECmAiIlIZbT+cxr9/2cmy3ccACPD2YGTvhtzTKwo/r6rVrv1g+kGeXPEkm45uAuCKyCt4utvTVPepDsd2wbzHYd8S1+SgCBjwIrS4HqrgdXIiUrEUwEygACYiIpXZyj0pvDxvB9sOpQFQK9CbMf2iGdIpokrdP6zQWchnsZ/xbsy7FDgLqOFbgxd6vsAldS8Bw4AdP8L8f0HqftcTonq7rg+r1dzawkWkUlEAM4ECmIiIVHZOp8GPWw7z2oJdHDiRDUCjmv48fmUz+rcIq1IdE3cc38ETy59gX+o+AIY2HcrYTmPx9fCFvCxY+QaseAMKc8HmgM73urYmBkdYWreIVA4KYCZQABMRkaoit6CQr9bs5+1f4ziZlQ9Ax8jqPDmoGR0jQyyurvzkFOTwxu9v8NWOrwCICo7i5V4v0zK0pWvCyQTXatjOn1w/2z2g9RDo+QjUamZN0SJSKSiAmUABTEREqpq0nHw+XLqXySviycl3dUzs3yKMx69sRuNaARZXV35WHVrFUyuf4lj2MTxsHjzQ7gHubnU3HvbT18Dt/Q2WvQaJK4qfFH0l9BwDkd0tqVlE3JsCmAkUwEREpKpKSs3hjUW7+XrDAZwGOOw2hnSqx6P9mlAryMfq8srFqZxTvLDmBRYkLgCgXc12vNTrJeoF1iuedHCDa2vijp+A01+X6nV1rYhFDwR71blWTkQujAKYCRTARESkqotLTueVX3axaEcyAL6eDu7tFcX9vRsS6ONpcXUXzjAMftr3Ey+tfYmM/Az8PPx4ossTXN/4+pLXv6XEwaq3YfN0KMxzjdWIhh6joc0Q8KhabfxFpOwUwEygACYiIheL9QkneGnuDjbtPwVAiL8Xoy9rzK1dI/HyqPyrQIczDvPkiifZmLwRgMvqXcazPZ4lxOd/rn9LT3LdP2z9ZMh1dY8ksDZ0exA63gk++j4gcrFSADOBApiIiFxMDMNgfmwSr/6yi30pmQBEhvoxrn9Trm5Tu9J3TCx0FvLF9i94e9PbFDgLCPEJ4aF2D3FjkxuLrw37Q04abPwMVr8HGUmuMe9g6Hw3dH0AAsPM/wAiYikFMBMogImIyMUov9DJzPUHeGNRHCkZuQC0iQjmiYHN6NGohsXVXbidJ3YyYfkE9pzaA0Djao15rPNj9KjTo/TkglzY8jWsegtSdrvGHF7Qdphre2KNxiZWLiJWUgAzgQKYiIhczDJzC/hkeTwfLdtLZl4hAH2a1uSJgc1oFl65/13Md+bz9a6veS/mPdLyXFsNe9XtxbjO42gY3LD0E5xO2D3PdR+xg+tOD9qg+dXQ81GI6Gha7SJiDQUwEyiAiYiIwLH0XN7+NY5pa/dT4DSw2eDG9hGM7R9N3Wq+Vpd3QVJzU/lg8wfM2DmDAqMAh83BkKZDeLDtg1TzqXbmJyWudnVO3P1L8ViDXq7OiY37QSXfqikiZ6YAZgIFMBERkWLxKZm8Nn8XP289AoCXh527ejTgwT6NCfar3B0T41PjeX3j6yw5sASAQK9ARrUZxbBmw/B0nOWzHd0BK9+CrV+Ds8A1VqulK4i1uhHO9jwRqZQUwEygACYiIlJazIFTvDx3B2vjTwAQ7OvJQ30bMaJ7A3w8HRZXd2HWHFnDpPWT2H3Sdb1XZFAkYzuOpW+9vmdvQpJ6ENa8Dxs/h7wM11hwPej+MHS4Hbz8zSleRCqUApgJFMBERETOzDAMftt1lH/P28nuZFfoqFvNl7FXRHN9+7o47JV3G16hs5Dv9nzH25ve5njOcQC6hHfhsc6P0Syk2dmfmH3S1b5+7QeQecw15lsdutzvevhX/gYmIhczBTATKICJiIj8tUKnwZzfD/L6gt0kpeUA0Cw8kCcGNuPS6JqVunV9Zn4mn2z9hCmxU8hz5mHDxvWNr+cf7f9BTb+aZ39ifrbrhs4r34KT8a4xD19ofxt0fwhCosz5ACJSrhTATKAAJiIicm5y8gv5bGUC7y3ZQ3qO63qoHo1CmTCwOa0jgi2u7sIcyjjEGxvf4JcEV9MNXw9f7m19LyNajMDHw+fsT3QWwo4fXJ0Tj8S4xmx2aHmD6zqx2m0rvHYRKT8KYCZQABMRESmbk5l5vPvbHqasTiSv0AnANW3r8Fj/ptQP9bO4ugsTczSGSesnsSVlCwDh/uGM6TCGQVGD/nqlzzAgfhmsfBP2Li4eb9gXLhkDUZeqc6JIJaAAZgIFMBERkfNz4EQW/1mwi+9iDgPg6bAxvGsk/7isMaEB3hZXd/6chpN58fN44/c3SMpMAqBNjTY81vkx2tVq9/cvcGSL66bO274Bw3VvNWq3c62ItbgO7JW7iYlIVaYAZgIFMBERkQuz7VAqr/yyk+VxKQAEeHsw6tKG3HNJQ3y9Km/YyC7IZkrsFCZvm0x2QTYAAxsMZEzHMdQJqPP3L3AyAVa/C79/CaefT/UG0OMf0G44eFbu+6uJVEUKYCZQABMRESkfy+OO8e95O4k9nAZArUBvxl4RzeCOEXg47BZXd/6OZR3j7U1v892e7zAw8HZ4M6LFCO5pfQ/+nufQfj7zOKz7CNZ96OqiCOBfE7qOhE73gF9IxX4AETlnCmAmUAATEREpP06nwQ+bD/Pagl0cPOla9WlcK4DxVzajX/Nalbpj4o7jO5i0YRLrk9YDEOoTyj/a/4PrG1+P41y2FeZlwqapsOodSN3vGvP0h453QvcHITii4ooXkXOiAGYCBTAREZHyl1tQyNQ1+3n71zhOZeUD0LlBdZ4Y2JyOkdUtru78GYbBrwd+5fUNr7M/3RWimlZvymOdH6Nr7a7n9iKF+RD7Hax8A5K3ucbsHtD6ZugxGsJaVEjtIvL3FMBMoAAmIiJScVKz8/lg6V4+XRFPboGrY+KVLcN57MqmNKoZYHF15y+/MJ9pO6fx4eYPSc9PB6BPvT78s+M/aRDc4NxexDBgz2JXEEtYXjzeZICrc2L97uqcKGIyBTATKICJiIhUvCOp2fx34W5mbzyI0wCH3cbQzvV4pF8TagX+xX223NzJnJO8v/l9vt71NYVGIR42D4Y2G8qotqMI9i7DvdEObXS1sN/+A3D6K11EZ+g5BpoOAnvlvYZOpDJRADOBApiIiIh5dien88q8nSzeeRQAPy8H9/ZqyP29GxLg7WFxdedv36l9vLbhNZYfcq1kBXsH80DbBxjSdAieds9zf6Hje10t7GOmQ2Guayy0CfQcDW1uAY/K295fpDJQADOBApiIiIj51u47zsvzdhJz4BQAof5ePNKvCcO61MezEndMXHVoFZM2TGLPqT0ANAhqwLhO4+gd0btsDUjSk2HtB7B+MuSmusYCwqHbA9DpLvApw+qaiJwzBTATKICJiIhYwzAM5m1LYtL8XcSnZALQINSPxwY0Y1Dr8ErbMbHAWcA3cd/wbsy7nMg5AUC32t14rPNjRFePLtuL5abDxs9h9XuQ7rrhNd5B0OluVxgLDC/f4kUucgpgJlAAExERsVZ+oZMZ6/bz5uI4UjLyAGhbrxoTBjajW8NQi6s7f+l56Xy89WOmbp9KvjMfu83OjU1u5KF2D1HDt0bZXqwgD7bOcl0nlrLLNebwgrZDXZ0TazQp/w8gchFSADOBApiIiIh7yMgt4ONl+/h4+T6y8goBuKxZLcZf2Yym4YEWV3f+DqQf4L8b/8vCxIUA+Hv6c2/re7m9xe14O8p4TZfTCXHzYcUbcGDN6UEbNLvK1bCjXufyLF3koqMAZgIFMBEREfdyND2HtxbHMX3dAQqdBnYb3NQhgrH9o6kd7Gt1eedtY/JGXl3/KtuPbwegbkBdxnQcw4DIAee33XL/GteK2K65xWORPV1BrMkVamEvch4UwEygACYiIuKe9h3LYNL8XczblgSAt4edu3pG8UCfRgT7lqGzoBtxGk5+2vcTb258k6PZrk6Q7Wu157FOj9G6Zuvze9GjO2HV27BlJjhdN72mVgvo+Qi0ugkclfPPSsQKCmAmUAATERFxb7/vP8m/5+5kXYKroUU1P08e7tuY27tH4u3hsLi685OVn8UXsV/wWexnZBdkA3BVw6sY02EM4f7n2Vgj9RCsfR82fAZ5Ga6xoAjo/hB0GAHelffG1yJmUQAzgQKYiIiI+zMMg8U7jvLKLzuJO+oKF3Wr+TJuQDTXta2L3V45t9slZybz1qa3+GHvDwD4OHy4o+Ud3N3qbvw8/c7vRbNPwYbJsOYDyHStsuFTDbrcB11GQkDNcqldpCpSADOBApiIiEjlUVDoZM7vB3l94W6S01w3Km5RO4gnBjajd3TlDRaxKbG8uv5Vfj/6OwA1fWsyusNorm10LXbbed4XLT8HNk93bU88sdc15uED7W+D7g9DSFQ5VS9SdSiAmUABTEREpPLJzivk05XxfLBkL+m5BQBc0rgGTwxsRqu6lfMmxYZhsDBxIa9vfJ1DGYcAaB7SnMc6P0bn8AvobugshJ0/uTonHnYFPGx2aHG96zqxOu0utHSRKkMBzAQKYCIiIpXXicw83vl1D1+uSSC/0PVV6Lp2dRjXvyn1Qs5zC5/FcgtzmbZjGh9t+YiMfNd2y8vrX84/O/6TekH1zv+FDQMSVsDKN2DPouLxhn1cQaxhX3VOlIueApgJFMBEREQqvwMnsnhtwS6+jzkMgJfDzm3dInn4ssaE+HtZXN35OZ59nPdi3mN23GychhMPuwfDmw3n/rb3E+R1gd9Zkra5WthvmwOG655r1G7rCmLNrwOHx4V/AJFKSAHMBApgIiIiVce2Q6m8PG8HK/ccB8DX08H17etwW7dIWtapnFsT407G8dqG11h1eBUA1b2r82C7BxkcPRgP+wUGpVP7YfW78PsUyM9yjVVv4LpGrM0Q8Kmcf2Yi50sBzAQKYCIiIlWLYRgsj0vh3/N2sv1IWtF4+/rVuL1bJINa18bHs3K1rzcMg+WHlvPahteIT40HoGFwQ8Z1GkeviF4X/gZZJ2Ddx7DuQ8hyhVc8fKDpQGg7DBpdpvuJyUVBAcwECmAiIiJVk2EYrIs/wZdrEvllWxIFTtdXpep+ngzpVI9bu9YnMtTf4irLJt+Zz+zds3kv5j1O5Z4CoGednozrNI7G1Rtf+BvkZcGmqa429sd2Fo/71YDWg6HtUKjdTteKSZWlAGYCBTAREZGq72h6Dl+vP8C0tfs5nJoDuDJE7yY1ub1bJH2b1cJRie4llpqbykdbPmLazmkUOAtw2BwMjh7Mg+0eJMQn5MLfwDDgyGbYMhO2zoLMY8XHajR1BbE2QyA44sLfS8SNKICZQAFMRETk4lFQ6OS3Xcf4ck0iy3YXh4q61Xy5tWt9hnSqR81AbwsrLJvEtERe3/A6vx74FYBAz0Dub3M/tza/FS9HOTUfKSyAvb/Clhmw82coyDl9wAZRvaDNUGhxLXgHls/7iVhIAcwECmAiIiIXp4SUTKat28/XGw5wKisfAE+HjStb1ea2rvXpEhWCrZJstVt3ZB2TNkxi5wnXtsGIgAjGdhpLv/r9yvcz5KTC9h9g8wxIXFE87uELza92hbGGfdRFUSotBTATKICJiIhc3HLyC/l5yxGmrk1k0/5TRePRYQHc1i2SG9rXJdDH/RtQFDoL+WHvD7y16S1SslMA6BjWkcc6P0bL0Jbl/4YnE2Hr17B5JhyPKx4PCIPWN7u2KYa3Lv/3FalACmAmUAATERGRP2w7lMpXaxP5btNhsvNd98fy83Jwffu63NY1khZ13P+7QlZ+FpO3TeaL2C/ILczFho1rGl3DIx0eoZZfrfJ/Q8OAw7+7VsW2zobsE8XHarWEtrdA6yEQVLv831uknCmAmUABTERERP5XWk4+32w8yJdrEtl7LLNovGNkdW7vFsnA1uF4e7h3K/sjGUd44/c3mBs/FwBfD1/uanUXd7a8E18P34p504I82LPIdb3YrnlQmOcat9kh6lJXS/vmV4NX5eo+KRcPBTATKICJiIjI2RiGwZp9J5i6JpH5scWt7EP8vRjSqR7Du9anXoifxVX+tS3HtvDq+lfZfGwzALX8ajGmwxiuangVdpu94t44+yTEfufqpLh/dfG4p7+raUebWyCqN9jdO8jKxUUBzAQKYCIiInIujqblMGP9Aaav28+RP7Wy7xNdk9u6RdKnqfu2sjcMg/kJ8/nvxv9yOPMwAK1CW/FY58foENah4gs4EQ9bvobN0+FkfPF4YB1oc7OreUdYi4qvQ+RvKICZQAFMREREyqKg0MninUeZuiaR5XEpReN/tLK/pXM9agS4Zyv7nIIcpu6YysdbPiarIAuA/pH9ebTjo0QEmnBPL8OAg+tdQWzbN5BzqvhYeBtX445WgyEwrOJrETkDBTATKICJiIjI+YpPyWTa2kS+3nCQ1OziVvYDW9Xm9u6RdIqs7pat7FOyU3hn0zt8E/cNBgaedk9ub3E797W+jwCvAHOKKMiF3fNdWxR3zwen688PmwMaXeYKY82uAs8Kul5N5AwUwEygACYiIiIXKie/kJ+2HOHLNYlsPnCqaLxpWCC3dXe1sg/wdr97Y+06sYtJ6yexNmktACE+ITzU7iFubHIjHnYT6806AdvmuMLYwfXF416B0OI6VxiL7An2CrxmTQQFMFMogImIiEh52nowlalrEvl+8yFy8p0A+Hs5uKFDXW7rFkmzcPf6vmEYBksPLuU/G/5DQloCAI2rNWZEixEMaDAAP0+Tm4yk7HEFsS0z4NT+4vHgetBmiOt6sZrR5tYkFw0FMBMogImIiEhFSM3KZ87vB5m6NpF9f2pl37lBdW7rFsmVrdyrlX1+YT4zd83k/c3vk5aXBoC/pz9XN7yawdGDaRbSzNyCnE44sMZ1f7HY7yA3tfhYnQ6nrxe7CfxrmFuXVGkKYCZQABMREZGKZBgGq/ceZ+raRObHJlN4upV9qL8XQzrX49Yu7tXKPjU3lTlxc5i9ezYH0g8UjbcKbcXg6MEMjBpo/qpYfg7snucKY3sWgbPANW73gMZXuG72HD0QPH3MrUuqHAUwEyiAiYiIiFmS03KYse4A09YlkpyWC7ha2fdtWovbu0XSO7qm27SydxpO1iWtY/bu2Szev5iC06HHz8OPqxpexeDowbQItaB1fMax09eLzYDDm4rHvYOh5fWumz3X7+b6gxUpIwUwEyiAiYiIiNkKCp0s2uFqZb9iT3Er+4jqvgzvGsmQThGEulEr++PZx/lh7w/M3j2b/enF12W1CG3B4OjBDIoahL+nv/mFHdvlWhXb8jWkHSwerxbputFz26EQ2sj8uqTSUgAzgQKYiIiIWGnfsQy+WrufWRsOkJbjWmXyctgZ1Dqc27tH0qG++7SyNwyD9Unrmb17Nov2LyL/dOt4Xw9fBkUN4ubom2kR2sL8ep1OSFwBm2fC9u8hL734WERnVxBreSP4hZhbl1Q6CmAmUAATERERd5CdV8iPWw4zdU0iWw4WN5xoFh7I7d0jub5dXfzdqJX9iZwT/Lj3R2bvnl3UPRGgeUjzolUx0+4p9md5WbBrrmtlbO9iMFydKLF7QvQAVxhr0h883GeFUdyHApgJFMBERETE3Ww+cIqpaxL5YfNhcgtcASLA24MbT7eyjw4LtLjCYoZhsCF5A7N3z2Zh4sISq2IDowYyuMlgWtVoZc0qXnoybJsNm6dD0tbicZ9qrg6KbYe6VsjcZIVRrKcAZgIFMBEREXFXp7LymL3xINPW7mdfSnEr+y5RIa5W9i3D8fJwn5sTn8o55bpWLG428anxReNNqzdlcPRgrmp4FYFeFoXH5O2uxh1bvob0I8XjIQ1d9xZrMwRCoqypTdyGApgJFMBERETE3RmGwaq9x/lydSILdxS3sq8R4MUtnesxrEt9Iqq7Tyt7wzD4/ejvzN49mwUJC8hz5gHg4/DhyqgrGRw9mDY12lizKuYshPhlri2KO36E/OJgS/3uruYdLW8A32rm1yaWUwAzgQKYiIiIVCZJqTlMX7efGev3F7Wyt9vgsma1uK1bJL2b1MTuJq3swXVfsT+uFduburdovEn1JgxuMpirG11NkJdF38FyM2DnT64wtm8JcPrrtMMbml7pamnfuB84PK2pT0ynAGYCBTARERGpjPILnSzansyXaxJZtfd40Xj9ED+Gd63PzZ3qEeLvZWGFJRmGweZjm5m1exbzE+aTW+gKjz4OH/o36M/N0TfTtmZb6zo+ph2GrbNcYezo9uJxv1BoNdh1s+c6HXS9WBWnAGYCBTARERGp7PYczeCrtYnM3niQ9D9a2XvYubp1bYZ3i6RD/Wpu08oeXKtiP+/7mVm7Z7Hn1J6i8cbVGjM4ejBXN7yaYO9ga4ozDFfDji0zXdeLZR4tPlYj2rVFsc0tUK2eNfVJhVIAM4ECmIiIiFQVWXkF/Lj5MF+uSWTbobSi8Ra1g7itWyTXtavjVq3sDcNgS8oWZu+ezS/xv5BTmAOAt8Ob/pH9GRw9mPa12lsXHgsLXFsTN0+HnT9DQXbxsQa9XEGsxXXgo++QVYUCmAkUwERERKSqMQyDzQdTmbomkR//1Mo+8E+t7Ju4USt7gLS8NObum8us3bPYfXJ30XjD4IYMjh7MNQ2voZpPNesKzElzNe3YPB0SVlB0vZiHDzS7ynW9WMO+4HCfgCtlpwBmAgUwERERqcr+aGU/dU0iCcezisa7RoVwe/dI+rdwr1b2hmGwLWUbs+NmMy9+HtmnV5287F5c0eAKBjcZTMewjtZuqTx1ALZ+DZtnQsqu4nH/WtBskOtGz1GXgrcFN6KWC6IAZgIFMBEREbkYOJ0GK/em8OXqRBbtSOZ0J3tqBHgzrIurlX2dar7WFvk/MvIymBvvWhXbeWJn0XiDoAYMjh7MtY2upbpPdesKNAw4vMl1vdjW2ZCVUnzM4QWRPaDxFa5AVqOJGnhUAgpgJlAAExERkYvN4VPZzFi3n+nrD3AsvbiV/eXNw7itWyS9Gtdwq1b2hmGw/fh2Zu2exdz4uUWrYp52T/pF9uPm6JvpFNbJ2lWxwnzYtxTiFkDcfDiZUPJ4tUhXEGvSHxpcAl7uc982KaYAZgIFMBEREblY5Rc6WRCbzNQ1iazeV7KV/aDWtRnQMoy2EdXcKoxl5me6VsV2zWLHiR1F45FBkQxuMphrG19LiE+IhRXiWhk7vhf2LHQFsoQVUJhXfNzDxxXCmvSHJldASEPrapUSFMBMoAAmIiIiAnuOpjN1zX7mbDxIem5B0XhYkDdXtAhjQMtwukaFutX1YrHHY5mzew4/7/uZrALX9W0edg/61e/H4OjBdA7vjN3mBvXmZUL8stOrYwsh9UDJ46GNi8NYZE/w8LamTlEAM4MCmIiIiEixrLwCFu04yoLYJJbsOkbGn8JYoI8HlzerxYCW4fSOruk2Le2z8rOYFz+PWbtnEXs8tmi8fmB9boq+iesaXUeob6iFFf6JYcCxna4gFrcA9q8GZ/GfMZ5+rgYeTa5wParVt67Wi5ACmAkUwERERETOLLegkFV7j7MgNomF25NJySjeRuflYad3kxr0bxHO5c1rERrgHqs2O47vYE7cHH7a9xOZ+ZmAa1XssnqXMTh6MF1rd3WPVbE/5KS57jX2x+pYRlLJ4zWbnw5j/aF+N3B4WlLmxUIBzAQKYCIiIiJ/r9BpsGn/SebHJjE/Npn9J4pb2ttt0KlBCANahtO/RRj1QqxvMJGVn8X8hPnM2j2LrSlbi8YjAiK4Kfomrm98PTV8a1hY4RkYBiRvKw5jB9aC4Sw+7hUIjfq4wljjKyCotmWlVlUKYCZQABMREREpG8Mw2JWczoLYZObHJhF7OK3E8Ra1g1xhrGUYzcIDre1OCOw6sYvZu2fz076fyMjPAMDD5kHf+n0Z3GQw3ep0c69VsT9kn4S9v7rC2J5FkHms5PHw1sWdFet20k2gy4ECmAkUwEREREQuzIETWSzc7gpj6xNOFN1jDFwdFfu3CGNAq3A61K+Ow8KOiln5WSxIXMCs3bPYcmxL0XjdgLrc1MS1KlbTr6Zl9f0lpxOOxBRfO3ZoI/CnP2ifYGh0+enVsX4Q4Kafw80pgJlAAUxERESk/JzIzGPRjmQWxCazPO4YuQXFW+hqBHjRr3kY/VuG0aNRDXw8HZbVufvkbubsnsOPe38kPT8dAIfNQZ96fRgcPZjutbvjsFtX39/KTIE9i11hbO9i12rZn9XpUNxZsU57cOfP4kYUwEygACYiIiJSMTJzC1ged4z5scks3pFMWk5xtz9/Lwd9mtaif8sw+jarRZCPNc0lsguyWZi4kFm7ZhFzLKZovI5/HW5sciPXN76eMP8wS2o7Z85C14pY3ALX48jmksf9Ql2rYk36Q6PLwM/i+6S5sUoTwJYtW8akSZPYuHEjR44c4dtvv+X666//y+csXbqUsWPHEhsbS506dXj88ccZNWpU0fGPP/6YKVOmsG3bNgA6duzISy+9RJcuXYrmPPfcc0ycOLHE64aFhZGU9D/dY/6CApiIiIhIxcsvdLJ23wnmxyaxYHsSyWm5Rcc8HTa6N6rBgJZhXNE8jFpBPpbUuOfkHubEzeH7vd+Tnle8KtY7ojeDowfTs05P914V+0N6kuuasbiFrmvIcv90jZ7NDhGdXU08mlwB4W3A7obXv1mk0gSwefPmsXLlSjp06MBNN930twEsPj6eVq1acd999zFy5EhWrlzJgw8+yPTp07npppsAGD58OD179qRHjx74+Pjw6quv8s033xAbG0vdunUBVwCbPXs2ixYtKnpth8NBzZrnvudVAUxERETEXE6nwZZDqSyITWJ+bBJ7j2UWHbPZoH29avRvGc6AluFE1fA3vb6cghwWJi5k9u7Z/H7096LxcP9wbmxyIzc0voFw/3DT6zovhflwYF1xZ8WjsSWPB4QVh7FGfV3Xkl3EKk0A+zObzfa3AWz8+PH88MMP7Nixo2hs1KhRbN68mdWrV5/xOYWFhVSvXp133nmHESNGAK4A9t133xETE3Pe9SqAiYiIiFhrz9EMFmxPYkFsMjEHTpU4Fh0WQP8WrjDWqm6Q6R0V957ay5y4Ofyw9wdSc1MBsNvs9K57elWsbk887JWo+2DqwT+tjv0G+cXhF5sD6neHJqe3K9Zq4UrEF5EqG8B69+5N+/btefPNN4vGvv32W4YMGUJWVhaenqX3AKenp1OrVi1mzZrF1VdfDbgC2KRJkwgODsbb25uuXbvy0ksv0bBhw7O+d25uLrm5xUveaWlp1KtXTwFMRERExA0kpeawcHsSC7Yns3rvcQr+1FKxTrAP/U/fa6xLVAgeDvO2zuUW5rIocRGzds9iY/LGovEwv7CiVbHaAZXsvlwFubB/dXFnxZTdJY8H1S2+CXTUpeAdYE2dJqqyASw6Opo777yTJ598smhs1apV9OzZk8OHD1O7dumT96GHHmL+/Pls27YNHx/XvuB58+aRlZVFdHQ0ycnJvPjii+zcuZPY2FhCQ0PP+N5num4MUAATERERcTOpWfn8tuso82OTWLLrGNn5hUXHqvl5clmzWgxoGU7vJjXx9TLv2qx9qfv4Zvc3fL/3e07lngJcq2I96/Ska+2uRAVH0TC4IXUC6rjn/cXO5mTC6TC2EOKXQUF28TG7J0T2KL7vWI0mVXJ1rEoHsLvuuosJEyYUja1cuZJLLrmEI0eOEB5eck/tq6++yr///W+WLFlCmzZtzvq6mZmZNGrUiMcff5yxY8eecY5WwEREREQqn5z8QlbEpbBgexKLdhzlRGZe0TEfTzu9m9RkQMtwLm9ei2p+XqbUlFeYx+L9i5m1exbrk9aXOu7t8KZBUIOiQBYVHEVUcBSRQZH4eFjTaOSc5WdDwsrizoon40serxZZHMYaXAJeftbUWc7KEsAq0cZTCA8PL9Wp8OjRo3h4eJRauXrttdd46aWXWLRo0V+GLwB/f39at25NXFzcWed4e3vj7e19/sWLiIiIiOl8PB30axFGvxZhFBQ62Zh4kvmxrps/HzqVzYLtySzYnozDbqNrVAj9W4TRv2U4dar5VlhNXg4vBkYNZGDUQBJSE5gXP4+4U3HEp8aTmJZIbmEuu07uYtfJXSWeZ8NG3YC6JYJZw2oNiQqKoppPtQqrt0w8fU9fC9YPeBWO7y0OYwkr4FQirP/Y9fDwcYWwP+47FnL2y4Gqkkq1AjZ+/Hh+/PFHtm/fXjT2wAMPEBMTU6IJx6RJk3jxxReZP38+3bp1+9v3zs3NpVGjRtx///0888wz51SvmnCIiIiIVF6GYbD9SBrzY5NZEJvEzqT0Esdb1w1mQEtXGGtSK8C0Jh4FzgIOZRwiPjWefan7iE+NL/r9Hy3uzyTEJ4QGQQ2KAlnDaq6AVtu/tvtsZ8zLdG1R/KOzYuqBksdDGxeHscie4FF5Fj8qzRbEjIwM9uzZA0D79u15/fXX6du3LyEhIdSvX58JEyZw6NAhpkyZAhS3oR85ciT33Xcfq1evZtSoUSXa0L/66qs8/fTTTJs2jZ49exa9V0BAAAEBrgsAx40bxzXXXEP9+vU5evQoL774IkuXLmXr1q1ERkaeU+0KYCIiIiJVR+LxTBZud62MbUg8yZ+/IUfV8Kd/yzD6twinfb1q2O3mX8NkGAbHc46XCGR//JqUefZ72fo4fGgQ3KBoG+MfK2eRQZF4OywMOIYBx3YVr47tXw3O4htu4+nnauDR5HSr+2r1rav1HFSaALZkyRL69u1bavyOO+7g888/58477yQhIYElS5YUHVu6dCmPPvpo0Y2Yx48fX+JGzA0aNCAxMbHUaz777LM899xzAAwdOpRly5aRkpJCzZo16datGy+88AItWrQ459oVwERERESqpmPpuSze4QpjK/ccJ6/QWXSsZqA3V7QIY0DLcLo3DMXLw/rVpaz8LOLTTgezU/tISEtg36l9JKYnUvDnUPMndpudugF1i7cy/ulas2BvC+7plZMG+5a4wtieRZB+pOTxms2Lw1i9buBhzvV656rSBLDKTAFMREREpOrLyC1gya6jLIhN5redR0nPLQ40gd4e9G1Wi/4tw+jTtBYB3u7VXqHAWcDB9INn3M6YkZ9x1ueF+ISUCmYNgxsS5h9mznZGw4DkbcVbFQ+sBaM4BOMVCI36uLYrNr4Cgqxv468AZgIFMBEREZGLS16Bk9X7jjM/NomF25M5ll7cIdvLw84ljWvQ/3TDjxoB7nv9kmEYpGSnlNrKGJ8aT3JW8lmf5+vhW6o7Y8PghtQPqo+XowJXpLJPwt5fIW4R7FkImcdKHh8XBwG1Ku79z4ECmAkUwEREREQuXk6nwaYDp1gQm8T82CQSjmcVHbPZoFNkdQa0DKd/i3Dqh1aeVuuZ+ZkkpCaUCmb70/ZTYJx5O6PD5iAiMIKooKiibYx/dGgM8irn78lOJxyJKb4JdGEejFpevu9xHhTATKAAJiIiIiLgWlGKO5pxOowls/VQaonjzcIDXWGsZRgtageZ1lGxPOU788+6nTEzP/Oszwv1CS3ZmfH0r2F+YeXz51CQ5xbXgymAmUABTERERETO5NCpbBbGJrFgezJr409Q6Cz+uh1R3Zf+LcIZ0DKMTg1CcFjQUbE8GYbBsexjZ9zOeDTr6Fmf5+vhW6ozY8PghtQPrI+nw9PET1A+FMBMoAAmIiIiIn/nZGYei3ceZUFsEsvijpGTX9xMIsTfi37Na9G/RTjdG4Xi72ZNPC5URl6GqyPjH8Hs1D7i0+I5kHbgL7cz1gusR4PgBqUagQR6BZr8Cc6dApgJFMBEREREpCyy8wpZFneM+bFJLN5xlNTs/KJjDruNVnWD6RoVQucGIXRuUJ1qftZvrasI+c58DqQfIP5UPPFpp4NZquv3f7WdsaZvzZLXmJ0OZuW2nfECKICZQAFMRERERM5XfqGT9fEnWLA9mUU7kjl4MrvUnGbhgXQ5Hci6RoVQK8jHgkrNYxgGR7OOltjKmJCa4NrOmH327Yxrb12Ln6e1jU4UwEygACYiIiIi5eXgySzWJ5xgXfxJ1sUfZ++x0itBDUL9/hTIQqkX4mv5yo9Z0vPSi7oz/rkJSIGzgHk3zbO6PAUwMyiAiYiIiEhFScnIZX38CdYlnGBd/Am2H0njf7+1hwf5uAJZlGuFrHHNAOyVvKlHWRU6C3HYHVaXoQBmBgUwERERETFLanY+vyeeLApkWw6eIr+w5Nf46n6edG4QQpco16NF7SA8HHaLKr64KICZQAFMRERERKySnVfIpgMnWRd/gvUJJ9iYeLJEh0UAfy8HHRuE0KVBdbpEhdImIhgfT+tXi6oiBTATKICJiIiIiLvIK3Cy7XCqK5Cd3rqYnlOy1buXh5129arR5fQqWYfI6gRUsdb3VlEAM4ECmIiIiIi4q0Knwa6k9NONPU6wNv4EKRm5JeY47DZa1Qkq2rbYuUEI1f2rZuv7iqYAZgIFMBERERGpLAzDID4lk3V/auxxptb3TcMC6Rzl2rLYpUEI4cFVu/V9eVEAM4ECmIiIiIhUZodOZZfotLjnaEapOZGhfkUrZF2jQqgf4nfRtL4vCwUwEyiAiYiIiEhVkpKRy4Y/7kWWcJzth9Nw/k9SqBXoXRTGukSF0qTWxdf6/kwUwEygACYiIiIiVVl6Tj4bE12dFtfFn2DzGVrfV/PzpFPkH4EshJZ1Ls7W9wpgJlAAExEREZGLSU5+IZv2nypq7LEx8STZ+YUl5vh5OegYWb2o02LbetUuitb3CmAmUAATERERkYtZfqGTbYdSiwLZuvgTpP1v63uHnbb1gk/fHDqUjlW09b0CmAkUwEREREREijmdBruSXa3v154OZMfSS7a+t9ugZZ0/Apmr9X1IFWh9rwBmAgUwEREREZGzMwyDhONZrD99H7J1Ccc5cKJ06/smtQKKAlmXqBBqB/taUO2FUQAzgQKYiIiIiEjZHEnNLtquuC7+BHFnaH1fL8SXLg1C6RoVQueoEBqEun/rewUwEyiAiYiIiIhcmBOZeSWuIYs9nFqq9X3NP7W+79wghKZhgW7X+l4BzAQKYCIiIiIi5Ss9J5/f959iXfxxV+v7A6nkFTpLzAn29aRzg+pFN4huXTfY8tb3CmAmUAATEREREalYOfmFbD5wyrVCluBqfZ+VV9z63maDmGf6E+zraWGVZcsGVa8HpIiIiIiIVAk+ng66Ngyla8NQwNX6fvvhNNadbuyRlVdgefgqK62AnSetgImIiIiICJQtG1i7WVJEREREROQiogAmIiIiIiJiEgUwERERERERkyiAiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJApiIiIiIiIhJFMBERERERERMogAmIiIiIiJiEgUwERERERERkyiAiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJApiIiIiIiIhJFMBERERERERMogAmIiIiIiJiEgUwERERERERkyiAiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJApiIiIiIiIhJFMBERERERERMogAmIiIiIiJiEgUwERERERERkyiAiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJApiIiIiIiIhJPKwuoLIyDAOAtLQ0iysREREREREr/ZEJ/sgIf0UB7Dylp6cDUK9ePYsrERERERERd5Cenk5wcPBfzrEZ5xLTpBSn08nhw4cJDAzEZrNZWktaWhr16tXjwIEDBAUFWVqLVA46Z6SsdM5IWemckbLSOSNl5U7njGEYpKenU6dOHez2v77KSytg58lutxMREWF1GSUEBQVZfvJJ5aJzRspK54yUlc4ZKSudM1JW7nLO/N3K1x/UhENERERERMQkCmAiIiIiIiImUQCrAry9vXn22Wfx9va2uhSpJHTOSFnpnJGy0jkjZaVzRsqqsp4zasIhIiIiIiJiEq2AiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJAlgl8d577xEVFYWPjw8dO3Zk+fLlfzl/6dKldOzYER8fHxo2bMgHH3xgUqXiLspyznzzzTdcccUV1KxZk6CgILp37878+fNNrFbcQVn/nvnDypUr8fDwoF27dhVboLidsp4zubm5/Otf/yIyMhJvb28aNWrEp59+alK14g7Kes589dVXtG3bFj8/P2rXrs1dd93F8ePHTapWrLRs2TKuueYa6tSpg81m47vvvvvb51SW778KYJXAzJkzGTNmDP/617/YtGkTvXr1YuDAgezfv/+M8+Pj4xk0aBC9evVi06ZNPPnkk4wePZo5c+aYXLlYpaznzLJly7jiiiuYO3cuGzdupG/fvlxzzTVs2rTJ5MrFKmU9Z/6QmprKiBEjuPzyy02qVNzF+ZwzQ4YMYfHixUyePJldu3Yxffp0mjVrZmLVYqWynjMrVqxgxIgR3HPPPcTGxjJr1izWr1/Pvffea3LlYoXMzEzatm3LO++8c07zK9X3X0PcXpcuXYxRo0aVGGvWrJnxxBNPnHH+448/bjRr1qzE2MiRI41u3bpVWI3iXsp6zpxJixYtjIkTJ5Z3aeKmzvecueWWW4ynnnrKePbZZ422bdtWYIXibsp6zsybN88IDg42jh8/bkZ54obKes5MmjTJaNiwYYmxt956y4iIiKiwGsU9Aca33377l3Mq0/dfrYC5uby8PDZu3Ej//v1LjPfv359Vq1ad8TmrV68uNX/AgAFs2LCB/Pz8CqtV3MP5nDP/y+l0kp6eTkhISEWUKG7mfM+Zzz77jL179/Lss89WdIniZs7nnPnhhx/o1KkTr776KnXr1iU6Oppx48aRnZ1tRslisfM5Z3r06MHBgweZO3cuhmGQnJzM7Nmzueqqq8woWSqZyvT918PqAuSvpaSkUFhYSFhYWInxsLAwkpKSzvicpKSkM84vKCggJSWF2rVrV1i9Yr3zOWf+13/+8x8yMzMZMmRIRZQobuZ8zpm4uDieeOIJli9fjoeH/im52JzPObNv3z5WrFiBj48P3377LSkpKTz44IOcOHFC14FdBM7nnOnRowdfffUVt9xyCzk5ORQUFHDttdfy9ttvm1GyVDKV6fuvVsAqCZvNVuJnwzBKjf3d/DONS9VV1nPmD9OnT+e5555j5syZ1KpVq6LKEzd0rudMYWEht956KxMnTiQ6Otqs8sQNleXvGafTic1m46uvvqJLly4MGjSI119/nc8//1yrYBeRspwz27dvZ/To0TzzzDNs3LiRX375hfj4eEaNGmVGqVIJVZbvv/pvSzdXo0YNHA5Hqf8dOnr0aKmU/4fw8PAzzvfw8CA0NLTCahX3cD7nzB9mzpzJPffcw6xZs+jXr19FlilupKznTHp6Ohs2bGDTpk08/PDDgOvLtWEYeHh4sGDBAi677DJTahdrnM/fM7Vr16Zu3boEBwcXjTVv3hzDMDh48CBNmjSp0JrFWudzzrz88sv07NmTxx57DIA2bdrg7+9Pr169ePHFF91qRUOsV5m+/2oFzM15eXnRsWNHFi5cWGJ84cKF9OjR44zP6d69e6n5CxYsoFOnTnh6elZYreIezuecAdfK15133sm0adO0v/4iU9ZzJigoiK1btxITE1P0GDVqFE2bNiUmJoauXbuaVbpY5Hz+nunZsyeHDx8mIyOjaGz37t3Y7XYiIiIqtF6x3vmcM1lZWdjtJb+qOhwOoHhlQ+QPler7r0XNP6QMZsyYYXh6ehqTJ082tm/fbowZM8bw9/c3EhISDMMwjCeeeMK4/fbbi+bv27fP8PPzMx599FFj+/btxuTJkw1PT09j9uzZVn0EMVlZz5lp06YZHh4exrvvvmscOXKk6HHq1CmrPoKYrKznzP9SF8SLT1nPmfT0dCMiIsIYPHiwERsbayxdutRo0qSJce+991r1EcRkZT1nPvvsM8PDw8N47733jL179xorVqwwOnXqZHTp0sWqjyAmSk9PNzZt2mRs2rTJAIzXX3/d2LRpk5GYmGgYRuX+/qsAVkm8++67RmRkpOHl5WV06NDBWLp0adGxO+64w7j00ktLzF+yZInRvn17w8vLy2jQoIHx/vvvm1yxWK0s58yll15qAKUed9xxh/mFi2XK+vfMnymAXZzKes7s2LHD6Nevn+Hr62tEREQYY8eONbKyskyuWqxU1nPmrbfeMlq0aGH4+voatWvXNoYPH24cPHjQ5KrFCr/99ttffjepzN9/bYahNVwREREREREz6BowERERERERkyiAiYiIiIiImEQBTERERERExCQKYCIiIiIiIiZRABMRERERETGJApiIiIiIiIhJFMBERERERERMogAmIiLyJ8899xzt2rWzugwREamiFMBEROSiYbPZ/vJx5513Mm7cOBYvXmx6bUuWLMFms3Hq1CnT31tERMzjYXUBIiIiZjly5EjR72fOnMkzzzzDrl27isZ8fX0JCAggICDAivJEROQioBUwERG5aISHhxc9goODsdlspcb+dwvinXfeyfXXX89LL71EWFgY1apVY+LEiRQUFPDYY48REhJCREQEn376aYn3OnToELfccgvVq1cnNDSU6667joSEhDPWlZCQQN++fQGoXr160WqciIhUPQpgIiIif+PXX3/l8OHDLFu2jNdff53nnnuOq6++murVq7N27VpGjRrFqFGjOHDgAABZWVn07duXgIAAli1bxooVKwgICODKK68kLy+v1OvXq1ePOXPmALBr1y6OHDnCm2++aepnFBERcyiAiYiI/I2QkBDeeustmjZtyt13303Tpk3JysriySefpEmTJkyYMAEvLy9WrlwJwIwZM7Db7XzyySe0bt2a5s2b89lnn7F//36WLFlS6vUdDgchISEA1KpVq2g1TkREqh5dAyYiIvI3WrZsid1e/H+WYWFhtGrVquhnh8NBaGgoR48eBWDjxo3s2bOHwMDAEq+Tk5PD3r17zSlaRETckgKYiIjI3/D09Czxs81mO+OY0+kEwOl00rFjR7766qtSr1WzZs2KK1RERNyeApiIiEg569ChAzNnzqRWrVoEBQWd03O8vLwAKCwsrMjSRETEYroGTEREpJwNHz6cGjVqcN1117F8+XLi4+NZunQpjzzyCAcPHjzjcyIjI7HZbPz0008cO3aMjIwMk6sWEREzKICJiIiUMz8/P5YtW0b9+vW58cYbad68OXfffTfZ2dlnXRGrW7cuEydO5IknniAsLIyHH37Y5KpFRMQMNsMwDKuLEBERERERuRhoBUxERERERMQkCmAiIiIiIiImUQATERERERExiQKYiIiIiIiISRTARERERERETKIAJiIiIiIiYhIFMBEREREREZMogImIiIiIiJhEAUxERERERMQkCmAiIiIiIiImUQATERERERExiQKYiIiIiIiISf4fBJ1W0N0T6VgAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_66_4.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Assume that all function definitions from the example program using Autograd\n",
     "# are located here.\n",
@@ -1895,45 +1753,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 457.256\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.00310113\n",
-      "The max absolute difference between the solutions is: 0.000464088\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
@@ -2276,60 +2096,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost: 457.256\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Final cost: 0.00310113\n",
-      "The max absolute difference between the analytical solution and DNN Autograd: 0.000464088\n",
-      "The max absolute difference between the analytical solution and numerical scheme: 0.00266858\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_91_3.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 1000x1000 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad, elementwise_grad\n",
@@ -2995,58 +2762,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/core/fromnumeric.py:3208: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
-      "  return asarray(a).size\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Initial cost:  41.05505310046363\n"
-     ]
-    },
-    {
-     "ename": "KeyboardInterrupt",
-     "evalue": "",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36m<cell line: 129>\u001b[0;34m()\u001b[0m\n\u001b[1;32m    140\u001b[0m num_iter \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m250\u001b[39m\n\u001b[1;32m    141\u001b[0m lmb \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.01\u001b[39m\n\u001b[0;32m--> 143\u001b[0m P \u001b[38;5;241m=\u001b[39m \u001b[43msolve_pde_deep_neural_network\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_hidden_neurons\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnum_iter\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mlmb\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    145\u001b[0m \u001b[38;5;66;03m## Store the results\u001b[39;00m\n\u001b[1;32m    146\u001b[0m g_dnn_ag \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mzeros((Nx, Nt))\n",
-      "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36msolve_pde_deep_neural_network\u001b[0;34m(x, t, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m    118\u001b[0m \u001b[38;5;66;03m# Let the update be done num_iter times\u001b[39;00m\n\u001b[1;32m    119\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(num_iter):\n\u001b[0;32m--> 120\u001b[0m     cost_grad \u001b[38;5;241m=\u001b[39m  \u001b[43mcost_function_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mP\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m \u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mt\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    122\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m l \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(N_hidden\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m    123\u001b[0m         P[l] \u001b[38;5;241m=\u001b[39m P[l] \u001b[38;5;241m-\u001b[39m lmb \u001b[38;5;241m*\u001b[39m cost_grad[l]\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m     20\u001b[0m     \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     21\u001b[0m \u001b[38;5;124;03m    Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m     22\u001b[0m \u001b[38;5;124;03m    positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;124;03m    arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m     24\u001b[0m \u001b[38;5;124;03m    should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 25\u001b[0m     vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     26\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m     27\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     28\u001b[0m                         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m      9\u001b[0m     start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m     end_value, end_node \u001b[38;5;241m=\u001b[39m  \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m      9\u001b[0m     start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m     end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     14\u001b[0m     subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "Input \u001b[0;32mIn [9]\u001b[0m, in \u001b[0;36mcost_function\u001b[0;34m(P, x, t)\u001b[0m\n\u001b[1;32m     78\u001b[0m g_t \u001b[38;5;241m=\u001b[39m g_trial(point,P)\n\u001b[1;32m     79\u001b[0m g_t_jacobian \u001b[38;5;241m=\u001b[39m g_t_jacobian_func(point,P)\n\u001b[0;32m---> 80\u001b[0m g_t_hessian \u001b[38;5;241m=\u001b[39m \u001b[43mg_t_hessian_func\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpoint\u001b[49m\u001b[43m,\u001b[49m\u001b[43mP\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     82\u001b[0m g_t_dt \u001b[38;5;241m=\u001b[39m g_t_jacobian[\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m     83\u001b[0m g_t_d2x \u001b[38;5;241m=\u001b[39m g_t_hessian[\u001b[38;5;241m0\u001b[39m][\u001b[38;5;241m0\u001b[39m]\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:78\u001b[0m, in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     75\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m     76\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mhessian\u001b[39m(fun, x):\n\u001b[1;32m     77\u001b[0m     \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mReturns a function that computes the exact Hessian.\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m---> 78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mjacobian\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:61\u001b[0m, in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     59\u001b[0m jacobian_shape \u001b[38;5;241m=\u001b[39m ans_vspace\u001b[38;5;241m.\u001b[39mshape \u001b[38;5;241m+\u001b[39m vspace(x)\u001b[38;5;241m.\u001b[39mshape\n\u001b[1;32m     60\u001b[0m grads \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(vjp, ans_vspace\u001b[38;5;241m.\u001b[39mstandard_basis())\n\u001b[0;32m---> 61\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39mreshape(\u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstack\u001b[49m\u001b[43m(\u001b[49m\u001b[43mgrads\u001b[49m\u001b[43m)\u001b[49m, jacobian_shape)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m     84\u001b[0m     \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m     85\u001b[0m     \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m     86\u001b[0m     \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m     arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m     89\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m     90\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:88\u001b[0m, in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m     83\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mstack\u001b[39m(arrays, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m):\n\u001b[1;32m     84\u001b[0m     \u001b[38;5;66;03m# this code is basically copied from numpy/core/shape_base.py's stack\u001b[39;00m\n\u001b[1;32m     85\u001b[0m     \u001b[38;5;66;03m# we need it here because we want to re-implement stack in terms of the\u001b[39;00m\n\u001b[1;32m     86\u001b[0m     \u001b[38;5;66;03m# primitives defined in this file\u001b[39;00m\n\u001b[0;32m---> 88\u001b[0m     arrays \u001b[38;5;241m=\u001b[39m [array(arr) \u001b[38;5;28;01mfor\u001b[39;00m arr \u001b[38;5;129;01min\u001b[39;00m arrays]\n\u001b[1;32m     89\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m arrays:\n\u001b[1;32m     90\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mneed at least one array to stack\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:14\u001b[0m, in \u001b[0;36mmake_vjp.<locals>.vjp\u001b[0;34m(g)\u001b[0m\n\u001b[0;32m---> 14\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mbackward_pass\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mend_node\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:21\u001b[0m, in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m node \u001b[38;5;129;01min\u001b[39;00m toposort(end_node):\n\u001b[1;32m     20\u001b[0m     outgrad \u001b[38;5;241m=\u001b[39m outgrads\u001b[38;5;241m.\u001b[39mpop(node)\n\u001b[0;32m---> 21\u001b[0m     ingrads \u001b[38;5;241m=\u001b[39m \u001b[43mnode\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43moutgrad\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     22\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m parent, ingrad \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(node\u001b[38;5;241m.\u001b[39mparents, ingrads):\n\u001b[1;32m     23\u001b[0m         outgrads[parent] \u001b[38;5;241m=\u001b[39m add_outgrads(outgrads\u001b[38;5;241m.\u001b[39mget(parent), ingrad)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:67\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     65\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnum 0 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     66\u001b[0m     vjp \u001b[38;5;241m=\u001b[39m vjpfun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 67\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (\u001b[43mvjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mg\u001b[49m\u001b[43m)\u001b[49m,)\n\u001b[1;32m     68\u001b[0m \u001b[38;5;28;01melif\u001b[39;00m L \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m2\u001b[39m:\n\u001b[1;32m     69\u001b[0m     argnum_0, argnum_1 \u001b[38;5;241m=\u001b[39m argnums\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:423\u001b[0m, in \u001b[0;36mmatmul_vjp_1.<locals>.<lambda>\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m    421\u001b[0m A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[1;32m    422\u001b[0m B_meta \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mmetadata(B)\n\u001b[0;32m--> 423\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: \u001b[43mmatmul_adjoint_1\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mg\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mA_ndim\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mB_meta\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:410\u001b[0m, in \u001b[0;36mmatmul_adjoint_1\u001b[0;34m(A, G, A_ndim, B_meta)\u001b[0m\n\u001b[1;32m    408\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:  \u001b[38;5;66;03m# We need to swap the last two axes of A\u001b[39;00m\n\u001b[1;32m    409\u001b[0m     A \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mswapaxes(A, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m2\u001b[39m, A_ndim \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n\u001b[0;32m--> 410\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmatmul\u001b[49m\u001b[43m(\u001b[49m\u001b[43mA\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mG\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    411\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m B_is_vec:\n\u001b[1;32m    412\u001b[0m     result \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39msqueeze(result, anp\u001b[38;5;241m.\u001b[39mndim(G) \u001b[38;5;241m-\u001b[39m \u001b[38;5;241m1\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:45\u001b[0m, in \u001b[0;36mprimitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     43\u001b[0m     argnums \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(argnum    \u001b[38;5;28;01mfor\u001b[39;00m argnum, _   \u001b[38;5;129;01min\u001b[39;00m boxed_args)\n\u001b[1;32m     44\u001b[0m     ans \u001b[38;5;241m=\u001b[39m f_wrapped(\u001b[38;5;241m*\u001b[39margvals, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 45\u001b[0m     node \u001b[38;5;241m=\u001b[39m \u001b[43mnode_constructor\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mf_wrapped\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mparents\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     46\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m new_box(ans, trace, node)\n\u001b[1;32m     47\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:36\u001b[0m, in \u001b[0;36mVJPNode.__init__\u001b[0;34m(self, value, fun, args, kwargs, parent_argnums, parents)\u001b[0m\n\u001b[1;32m     33\u001b[0m     fun_name \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mgetattr\u001b[39m(fun, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124m__name__\u001b[39m\u001b[38;5;124m'\u001b[39m, fun)\n\u001b[1;32m     34\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     35\u001b[0m                               \u001b[38;5;241m.\u001b[39mformat(fun_name, parent_argnums))\n\u001b[0;32m---> 36\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvjp \u001b[38;5;241m=\u001b[39m \u001b[43mvjpmaker\u001b[49m\u001b[43m(\u001b[49m\u001b[43mparent_argnums\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mvalue\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:77\u001b[0m, in \u001b[0;36mdefvjp.<locals>.vjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m     74\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mNotImplementedError\u001b[39;00m(\n\u001b[1;32m     75\u001b[0m             \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mVJP of \u001b[39m\u001b[38;5;132;01m{}\u001b[39;00m\u001b[38;5;124m wrt argnums 0, 1 not defined\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(fun\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m))\n\u001b[1;32m     76\u001b[0m     vjp_0 \u001b[38;5;241m=\u001b[39m vjp_0_fun(ans, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m---> 77\u001b[0m     vjp_1 \u001b[38;5;241m=\u001b[39m \u001b[43mvjp_1_fun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mans\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     78\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: (vjp_0(g), vjp_1(g))\n\u001b[1;32m     79\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_vjps.py:422\u001b[0m, in \u001b[0;36mmatmul_vjp_1\u001b[0;34m(ans, A, B)\u001b[0m\n\u001b[1;32m    420\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmatmul_vjp_1\u001b[39m(ans, A, B):\n\u001b[1;32m    421\u001b[0m     A_ndim \u001b[38;5;241m=\u001b[39m anp\u001b[38;5;241m.\u001b[39mndim(A)\n\u001b[0;32m--> 422\u001b[0m     B_meta \u001b[38;5;241m=\u001b[39m \u001b[43manp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mmetadata\u001b[49m\u001b[43m(\u001b[49m\u001b[43mB\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    423\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;01mlambda\u001b[39;00m g: matmul_adjoint_1(A, g, A_ndim, B_meta)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:61\u001b[0m, in \u001b[0;36mnotrace_primitive.<locals>.f_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     58\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(f_raw)\n\u001b[1;32m     59\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf_wrapped\u001b[39m(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m     60\u001b[0m     argvals \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmap\u001b[39m(getval, args)\n\u001b[0;32m---> 61\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf_raw\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margvals\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/numpy/numpy_wrapper.py:148\u001b[0m, in \u001b[0;36mmetadata\u001b[0;34m(A)\u001b[0m\n\u001b[1;32m    146\u001b[0m \u001b[38;5;129m@notrace_primitive\u001b[39m\n\u001b[1;32m    147\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmetadata\u001b[39m(A):\n\u001b[0;32m--> 148\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m _np\u001b[38;5;241m.\u001b[39mshape(A), _np\u001b[38;5;241m.\u001b[39mndim(A), _np\u001b[38;5;241m.\u001b[39mresult_type(A), _np\u001b[38;5;241m.\u001b[39miscomplexobj(A)\n",
-      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import jacobian,hessian,grad\n",
@@ -3681,7 +3397,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
index 67a50bdf0..0300f86fa 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb
@@ -624,18 +624,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_35_0.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmath\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -907,22 +909,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_51_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import math\n",
@@ -1221,30 +1208,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "inputs = (n_inputs, pixel_width, pixel_height, depth) = (1797, 8, 8, 1)\n",
-      "labels = (n_inputs) = (1797,)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1200x1200 with 5 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_67_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# import necessary packages\n",
     "import numpy as np\n",
@@ -1296,45 +1260,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.\n",
-      "  warnings.warn(\"JAX on Mac ARM machines is experimental and minimally tested. \"\n"
-     ]
-    },
-    {
-     "ename": "AttributeError",
-     "evalue": "module 'jaxlib.pocketfft' has no attribute 'pocketfft'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [4]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m datasets, layers, models\n\u001b[1;32m      2\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlayers\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Input\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmodels\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Sequential      \u001b[38;5;66;03m#This allows appending layers to existing models\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 51\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/__init__.py:30\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     32\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/v1/__init__.py:47\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m layers\n\u001b[1;32m     46\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg\n\u001b[0;32m---> 47\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     48\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m logging\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lookup\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/__init__.py:9\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m constants\n\u001b[0;32m----> 9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m experimental\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Interpreter\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpHint\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m authoring\n\u001b[1;32m      9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01manalyzer\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ModelAnalyzer \u001b[38;5;28;01mas\u001b[39;00m Analyzer\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpResolverType\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/authoring/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental.authoring namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compatible\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/authoring/authoring.py:43\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m\n\u001b[1;32m     42\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[0;32m---> 43\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m convert\n\u001b[1;32m     44\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmetrics\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m converter_error_data_pb2\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/convert.py:29\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msix\u001b[39;00m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite_constants\n\u001b[0;32m---> 29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m util\n\u001b[1;32m     30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wrap_toco\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconvert_phase\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Component\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/util.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     47\u001b[0m \u001b[38;5;66;03m# Jax functions used by TFLite\u001b[39;00m\n\u001b[1;32m     48\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;66;03m# pylint: disable=unused-import\u001b[39;00m\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 51\u001b[0m   \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_computation \u001b[38;5;28;01mas\u001b[39;00m _xla_computation\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m:\n\u001b[1;32m     53\u001b[0m   _xla_computation \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/__init__.py:116\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     40\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconfig\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     41\u001b[0m   config \u001b[38;5;28;01mas\u001b[39;00m config,\n\u001b[1;32m     42\u001b[0m   enable_checks \u001b[38;5;28;01mas\u001b[39;00m enable_checks,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     51\u001b[0m   numpy_rank_promotion \u001b[38;5;28;01mas\u001b[39;00m numpy_rank_promotion,\n\u001b[1;32m     52\u001b[0m )\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mapi\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     54\u001b[0m   ad,  \u001b[38;5;66;03m# TODO(phawkins): update users to avoid this.\u001b[39;00m\n\u001b[1;32m     55\u001b[0m   checkpoint \u001b[38;5;28;01mas\u001b[39;00m checkpoint,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    114\u001b[0m   xla_computation \u001b[38;5;28;01mas\u001b[39;00m xla_computation,\n\u001b[1;32m    115\u001b[0m )\n\u001b[0;32m--> 116\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mexperimental\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmaps\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m soft_pmap \u001b[38;5;28;01mas\u001b[39;00m soft_pmap\n\u001b[1;32m    117\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mversion\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m __version__ \u001b[38;5;28;01mas\u001b[39;00m __version__\n\u001b[1;32m    119\u001b[0m \u001b[38;5;66;03m# These submodules are separate because they are in an import cycle with\u001b[39;00m\n\u001b[1;32m    120\u001b[0m \u001b[38;5;66;03m# jax and rely on the names imported above.\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/experimental/maps.py:26\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wraps, partial, partialmethod\n\u001b[1;32m     24\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01menum\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Enum\n\u001b[0;32m---> 26\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m numpy \u001b[38;5;28;01mas\u001b[39;00m jnp\n\u001b[1;32m     27\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m core\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linear_util \u001b[38;5;28;01mas\u001b[39;00m lu\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/__init__.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2018 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     17\u001b[0m \n\u001b[1;32m     18\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m fft \u001b[38;5;28;01mas\u001b[39;00m fft\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg \u001b[38;5;28;01mas\u001b[39;00m linalg\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01minterpreters\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mxla\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m DeviceArray \u001b[38;5;28;01mas\u001b[39;00m DeviceArray\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/fft.py:17\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2020 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     14\u001b[0m \n\u001b[1;32m     15\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 17\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     18\u001b[0m   ifft \u001b[38;5;28;01mas\u001b[39;00m ifft,\n\u001b[1;32m     19\u001b[0m   ifft2 \u001b[38;5;28;01mas\u001b[39;00m ifft2,\n\u001b[1;32m     20\u001b[0m   ifftn \u001b[38;5;28;01mas\u001b[39;00m ifftn,\n\u001b[1;32m     21\u001b[0m   ifftshift \u001b[38;5;28;01mas\u001b[39;00m ifftshift,\n\u001b[1;32m     22\u001b[0m   ihfft \u001b[38;5;28;01mas\u001b[39;00m ihfft,\n\u001b[1;32m     23\u001b[0m   irfft \u001b[38;5;28;01mas\u001b[39;00m irfft,\n\u001b[1;32m     24\u001b[0m   irfft2 \u001b[38;5;28;01mas\u001b[39;00m irfft2,\n\u001b[1;32m     25\u001b[0m   irfftn \u001b[38;5;28;01mas\u001b[39;00m irfftn,\n\u001b[1;32m     26\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m     27\u001b[0m   fft2 \u001b[38;5;28;01mas\u001b[39;00m fft2,\n\u001b[1;32m     28\u001b[0m   fftfreq \u001b[38;5;28;01mas\u001b[39;00m fftfreq,\n\u001b[1;32m     29\u001b[0m   fftn \u001b[38;5;28;01mas\u001b[39;00m fftn,\n\u001b[1;32m     30\u001b[0m   fftshift \u001b[38;5;28;01mas\u001b[39;00m fftshift,\n\u001b[1;32m     31\u001b[0m   hfft \u001b[38;5;28;01mas\u001b[39;00m hfft,\n\u001b[1;32m     32\u001b[0m   rfft \u001b[38;5;28;01mas\u001b[39;00m rfft,\n\u001b[1;32m     33\u001b[0m   rfft2 \u001b[38;5;28;01mas\u001b[39;00m rfft2,\n\u001b[1;32m     34\u001b[0m   rfftfreq \u001b[38;5;28;01mas\u001b[39;00m rfftfreq,\n\u001b[1;32m     35\u001b[0m   rfftn \u001b[38;5;28;01mas\u001b[39;00m rfftn,\n\u001b[1;32m     36\u001b[0m )\n\u001b[1;32m     38\u001b[0m \u001b[38;5;66;03m# Module initialization is encapsulated in a function to avoid accidental\u001b[39;00m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;66;03m# namespace pollution.\u001b[39;00m\n\u001b[1;32m     40\u001b[0m _NOT_IMPLEMENTED \u001b[38;5;241m=\u001b[39m []\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/numpy/fft.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01moperator\u001b[39;00m\n\u001b[1;32m     17\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lax\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_client\n\u001b[1;32m     21\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mutil\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m safe_zip\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/lax/__init__.py:332\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    299\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (_reduce_sum, _reduce_max, _reduce_min, _reduce_or,\n\u001b[1;32m    300\u001b[0m                   _reduce_and, _reduce_window_sum, _reduce_window_max,\n\u001b[1;32m    301\u001b[0m                   _reduce_window_min, _reduce_window_prod,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    306\u001b[0m                   _upcast_fp16_for_computation, _broadcasting_shape_rule,\n\u001b[1;32m    307\u001b[0m                   _eye, _tri, _delta, _ones, _zeros, _dilate_shape)\n\u001b[1;32m    308\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcontrol_flow\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    309\u001b[0m   associative_scan \u001b[38;5;28;01mas\u001b[39;00m associative_scan,\n\u001b[1;32m    310\u001b[0m   cond \u001b[38;5;28;01mas\u001b[39;00m cond,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    330\u001b[0m   while_p \u001b[38;5;28;01mas\u001b[39;00m while_p,\n\u001b[1;32m    331\u001b[0m )\n\u001b[0;32m--> 332\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    333\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m    334\u001b[0m   fft_p \u001b[38;5;28;01mas\u001b[39;00m fft_p,\n\u001b[1;32m    335\u001b[0m )\n\u001b[1;32m    336\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mparallel\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    337\u001b[0m   all_gather \u001b[38;5;28;01mas\u001b[39;00m all_gather,\n\u001b[1;32m    338\u001b[0m   all_to_all \u001b[38;5;28;01mas\u001b[39;00m all_to_all,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    355\u001b[0m   xeinsum \u001b[38;5;28;01mas\u001b[39;00m xeinsum,\n\u001b[1;32m    356\u001b[0m )\n\u001b[1;32m    357\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mother\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    358\u001b[0m   conv_general_dilated_patches \u001b[38;5;28;01mas\u001b[39;00m conv_general_dilated_patches\n\u001b[1;32m    359\u001b[0m )\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lax/fft.py:145\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    143\u001b[0m batching\u001b[38;5;241m.\u001b[39mprimitive_batchers[fft_p] \u001b[38;5;241m=\u001b[39m fft_batching_rule\n\u001b[1;32m    144\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m pocketfft:\n\u001b[0;32m--> 145\u001b[0m   xla\u001b[38;5;241m.\u001b[39mbackend_specific_translations[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcpu\u001b[39m\u001b[38;5;124m'\u001b[39m][fft_p] \u001b[38;5;241m=\u001b[39m \u001b[43mpocketfft\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpocketfft\u001b[49m\n",
-      "\u001b[0;31mAttributeError\u001b[0m: module 'jaxlib.pocketfft' has no attribute 'pocketfft'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from tensorflow.keras import datasets, layers, models\n",
     "from tensorflow.keras.layers import Input\n",
@@ -1673,7 +1599,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
index 23ad81342..58b249e1d 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb
@@ -60,40 +60,19 @@
    },
    "outputs": [
     {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.\n",
-      "  warnings.warn(\"JAX on Mac ARM machines is experimental and minimally tested. \"\n"
-     ]
-    },
-    {
-     "ename": "AttributeError",
-     "evalue": "module 'jaxlib.pocketfft' has no attribute 'pocketfft'",
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 7>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n\u001b[0;32m----> 7\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mtf\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m datasets, layers, models\n\u001b[1;32m      9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mkeras\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlayers\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Input\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 51\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/__init__.py:30\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     32\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/v1/__init__.py:47\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m layers\n\u001b[1;32m     46\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg\n\u001b[0;32m---> 47\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     48\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m logging\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lookup\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/__init__.py:9\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m constants\n\u001b[0;32m----> 9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m experimental\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Interpreter\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpHint\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m authoring\n\u001b[1;32m      9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01manalyzer\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ModelAnalyzer \u001b[38;5;28;01mas\u001b[39;00m Analyzer\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpResolverType\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/authoring/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental.authoring namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compatible\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/authoring/authoring.py:43\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m\n\u001b[1;32m     42\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[0;32m---> 43\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m convert\n\u001b[1;32m     44\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmetrics\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m converter_error_data_pb2\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/convert.py:29\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msix\u001b[39;00m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite_constants\n\u001b[0;32m---> 29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m util\n\u001b[1;32m     30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wrap_toco\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconvert_phase\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Component\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/util.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     47\u001b[0m \u001b[38;5;66;03m# Jax functions used by TFLite\u001b[39;00m\n\u001b[1;32m     48\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;66;03m# pylint: disable=unused-import\u001b[39;00m\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 51\u001b[0m   \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_computation \u001b[38;5;28;01mas\u001b[39;00m _xla_computation\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m:\n\u001b[1;32m     53\u001b[0m   _xla_computation \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/__init__.py:116\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     40\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconfig\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     41\u001b[0m   config \u001b[38;5;28;01mas\u001b[39;00m config,\n\u001b[1;32m     42\u001b[0m   enable_checks \u001b[38;5;28;01mas\u001b[39;00m enable_checks,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     51\u001b[0m   numpy_rank_promotion \u001b[38;5;28;01mas\u001b[39;00m numpy_rank_promotion,\n\u001b[1;32m     52\u001b[0m )\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mapi\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     54\u001b[0m   ad,  \u001b[38;5;66;03m# TODO(phawkins): update users to avoid this.\u001b[39;00m\n\u001b[1;32m     55\u001b[0m   checkpoint \u001b[38;5;28;01mas\u001b[39;00m checkpoint,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    114\u001b[0m   xla_computation \u001b[38;5;28;01mas\u001b[39;00m xla_computation,\n\u001b[1;32m    115\u001b[0m )\n\u001b[0;32m--> 116\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mexperimental\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmaps\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m soft_pmap \u001b[38;5;28;01mas\u001b[39;00m soft_pmap\n\u001b[1;32m    117\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mversion\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m __version__ \u001b[38;5;28;01mas\u001b[39;00m __version__\n\u001b[1;32m    119\u001b[0m \u001b[38;5;66;03m# These submodules are separate because they are in an import cycle with\u001b[39;00m\n\u001b[1;32m    120\u001b[0m \u001b[38;5;66;03m# jax and rely on the names imported above.\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/experimental/maps.py:26\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wraps, partial, partialmethod\n\u001b[1;32m     24\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01menum\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Enum\n\u001b[0;32m---> 26\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m numpy \u001b[38;5;28;01mas\u001b[39;00m jnp\n\u001b[1;32m     27\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m core\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linear_util \u001b[38;5;28;01mas\u001b[39;00m lu\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/__init__.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2018 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     17\u001b[0m \n\u001b[1;32m     18\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m fft \u001b[38;5;28;01mas\u001b[39;00m fft\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg \u001b[38;5;28;01mas\u001b[39;00m linalg\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01minterpreters\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mxla\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m DeviceArray \u001b[38;5;28;01mas\u001b[39;00m DeviceArray\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/fft.py:17\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2020 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     14\u001b[0m \n\u001b[1;32m     15\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 17\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     18\u001b[0m   ifft \u001b[38;5;28;01mas\u001b[39;00m ifft,\n\u001b[1;32m     19\u001b[0m   ifft2 \u001b[38;5;28;01mas\u001b[39;00m ifft2,\n\u001b[1;32m     20\u001b[0m   ifftn \u001b[38;5;28;01mas\u001b[39;00m ifftn,\n\u001b[1;32m     21\u001b[0m   ifftshift \u001b[38;5;28;01mas\u001b[39;00m ifftshift,\n\u001b[1;32m     22\u001b[0m   ihfft \u001b[38;5;28;01mas\u001b[39;00m ihfft,\n\u001b[1;32m     23\u001b[0m   irfft \u001b[38;5;28;01mas\u001b[39;00m irfft,\n\u001b[1;32m     24\u001b[0m   irfft2 \u001b[38;5;28;01mas\u001b[39;00m irfft2,\n\u001b[1;32m     25\u001b[0m   irfftn \u001b[38;5;28;01mas\u001b[39;00m irfftn,\n\u001b[1;32m     26\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m     27\u001b[0m   fft2 \u001b[38;5;28;01mas\u001b[39;00m fft2,\n\u001b[1;32m     28\u001b[0m   fftfreq \u001b[38;5;28;01mas\u001b[39;00m fftfreq,\n\u001b[1;32m     29\u001b[0m   fftn \u001b[38;5;28;01mas\u001b[39;00m fftn,\n\u001b[1;32m     30\u001b[0m   fftshift \u001b[38;5;28;01mas\u001b[39;00m fftshift,\n\u001b[1;32m     31\u001b[0m   hfft \u001b[38;5;28;01mas\u001b[39;00m hfft,\n\u001b[1;32m     32\u001b[0m   rfft \u001b[38;5;28;01mas\u001b[39;00m rfft,\n\u001b[1;32m     33\u001b[0m   rfft2 \u001b[38;5;28;01mas\u001b[39;00m rfft2,\n\u001b[1;32m     34\u001b[0m   rfftfreq \u001b[38;5;28;01mas\u001b[39;00m rfftfreq,\n\u001b[1;32m     35\u001b[0m   rfftn \u001b[38;5;28;01mas\u001b[39;00m rfftn,\n\u001b[1;32m     36\u001b[0m )\n\u001b[1;32m     38\u001b[0m \u001b[38;5;66;03m# Module initialization is encapsulated in a function to avoid accidental\u001b[39;00m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;66;03m# namespace pollution.\u001b[39;00m\n\u001b[1;32m     40\u001b[0m _NOT_IMPLEMENTED \u001b[38;5;241m=\u001b[39m []\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/numpy/fft.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01moperator\u001b[39;00m\n\u001b[1;32m     17\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lax\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_client\n\u001b[1;32m     21\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mutil\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m safe_zip\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/lax/__init__.py:332\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    299\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (_reduce_sum, _reduce_max, _reduce_min, _reduce_or,\n\u001b[1;32m    300\u001b[0m                   _reduce_and, _reduce_window_sum, _reduce_window_max,\n\u001b[1;32m    301\u001b[0m                   _reduce_window_min, _reduce_window_prod,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    306\u001b[0m                   _upcast_fp16_for_computation, _broadcasting_shape_rule,\n\u001b[1;32m    307\u001b[0m                   _eye, _tri, _delta, _ones, _zeros, _dilate_shape)\n\u001b[1;32m    308\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcontrol_flow\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    309\u001b[0m   associative_scan \u001b[38;5;28;01mas\u001b[39;00m associative_scan,\n\u001b[1;32m    310\u001b[0m   cond \u001b[38;5;28;01mas\u001b[39;00m cond,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    330\u001b[0m   while_p \u001b[38;5;28;01mas\u001b[39;00m while_p,\n\u001b[1;32m    331\u001b[0m )\n\u001b[0;32m--> 332\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    333\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m    334\u001b[0m   fft_p \u001b[38;5;28;01mas\u001b[39;00m fft_p,\n\u001b[1;32m    335\u001b[0m )\n\u001b[1;32m    336\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mparallel\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    337\u001b[0m   all_gather \u001b[38;5;28;01mas\u001b[39;00m all_gather,\n\u001b[1;32m    338\u001b[0m   all_to_all \u001b[38;5;28;01mas\u001b[39;00m all_to_all,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    355\u001b[0m   xeinsum \u001b[38;5;28;01mas\u001b[39;00m xeinsum,\n\u001b[1;32m    356\u001b[0m )\n\u001b[1;32m    357\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mother\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    358\u001b[0m   conv_general_dilated_patches \u001b[38;5;28;01mas\u001b[39;00m conv_general_dilated_patches\n\u001b[1;32m    359\u001b[0m )\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lax/fft.py:145\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    143\u001b[0m batching\u001b[38;5;241m.\u001b[39mprimitive_batchers[fft_p] \u001b[38;5;241m=\u001b[39m fft_batching_rule\n\u001b[1;32m    144\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m pocketfft:\n\u001b[0;32m--> 145\u001b[0m   xla\u001b[38;5;241m.\u001b[39mbackend_specific_translations[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcpu\u001b[39m\u001b[38;5;124m'\u001b[39m][fft_p] \u001b[38;5;241m=\u001b[39m \u001b[43mpocketfft\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpocketfft\u001b[49m\n",
-      "\u001b[0;31mAttributeError\u001b[0m: module 'jaxlib.pocketfft' has no attribute 'pocketfft'"
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Start importing packages\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
     }
    ],
@@ -1916,7 +1895,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
index 38a0fb505..0ff8d6a7b 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter2.ipynb
@@ -748,13 +748,13 @@
       " [2 4 5]\n",
       " [3 5 6]]\n",
       "test U\n",
-      "[[-2.22044605e-16 -7.49932427e-16 -8.23408962e-16]\n",
-      " [-7.49932427e-16  0.00000000e+00  4.77954956e-17]\n",
-      " [-8.23408962e-16  4.77954956e-17  2.22044605e-16]]\n",
+      "[[ 4.44089210e-16 -4.69484813e-16 -6.67314874e-16]\n",
+      " [-4.69484813e-16 -4.44089210e-16 -1.54041041e-16]\n",
+      " [-6.67314874e-16 -1.54041041e-16  1.11022302e-16]]\n",
       "test VT\n",
-      "[[ 3.33066907e-16 -7.32066545e-17  3.32714903e-16]\n",
-      " [-7.32066545e-17  0.00000000e+00 -1.82997013e-16]\n",
-      " [ 3.32714903e-16 -1.82997013e-16 -3.33066907e-16]]\n",
+      "[[ 2.22044605e-16  3.78156479e-17  1.85278920e-16]\n",
+      " [ 3.78156479e-17  0.00000000e+00 -6.33166055e-17]\n",
+      " [ 1.85278920e-16 -6.33166055e-17 -1.11022302e-16]]\n",
       "[[0. 0. 0.]\n",
       " [0. 0. 0.]\n",
       " [0. 0. 0.]]\n"
@@ -1798,10 +1798,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.003788445263115483\n",
-      "3.859628021353642\n",
-      "[[0.93725291 2.8143782 ]\n",
-      " [2.8143782  9.64008343]]\n"
+      "0.015836015068980684\n",
+      "4.146630977737321\n",
+      "[[0.88786042 2.4773343 ]\n",
+      " [2.4773343  7.74767365]]\n"
      ]
     }
    ],
@@ -1845,10 +1845,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.07783152589039466\n",
-      "2.06282378894371\n",
-      "[[1.         0.66124684]\n",
-      " [0.66124684 1.        ]]\n"
+      "0.07636331150360104\n",
+      "1.4231233000637726\n",
+      "[[1.         0.68477696]\n",
+      " [0.68477696 1.        ]]\n"
      ]
     }
    ],
@@ -1902,33 +1902,14 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[-0.15499979 -0.6924788 ]\n",
-      " [-0.50456256 -2.98248681]\n",
-      " [ 1.97264311  4.4533029 ]\n",
-      " [ 0.03286166 -0.27108228]\n",
-      " [-0.97421755 -3.08891672]\n",
-      " [-0.3744637   0.62223681]\n",
-      " [ 1.18655084  4.67392051]\n",
-      " [-0.51719273 -1.14648903]\n",
-      " [-0.51793145 -1.51975002]\n",
-      " [-0.14868784 -0.04825655]]\n",
-      "          0         1\n",
-      "0 -0.155000 -0.692479\n",
-      "1 -0.504563 -2.982487\n",
-      "2  1.972643  4.453303\n",
-      "3  0.032862 -0.271082\n",
-      "4 -0.974218 -3.088917\n",
-      "5 -0.374464  0.622237\n",
-      "6  1.186551  4.673921\n",
-      "7 -0.517193 -1.146489\n",
-      "8 -0.517931 -1.519750\n",
-      "9 -0.148688 -0.048257\n",
-      "          0         1\n",
-      "0  1.000000  0.929612\n",
-      "1  0.929612  1.000000\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'pandas'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[7], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m\n\u001b[1;32m      3\u001b[0m n \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m10\u001b[39m\n\u001b[1;32m      4\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mnormal(size\u001b[38;5;241m=\u001b[39mn)\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pandas'"
      ]
     }
    ],
@@ -1967,47 +1948,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0         1         2         3         4         5         6         7   \\\n",
-      "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.079729  0.074983  0.077280  0.078995  0.080168  0.068546  0.070577   \n",
-      "2   0.0  0.074983  0.071314  0.073127  0.075035  0.076519  0.065106  0.067183   \n",
-      "3   0.0  0.077280  0.073127  0.080979  0.082487  0.083517  0.075422  0.077387   \n",
-      "4   0.0  0.078995  0.075035  0.082487  0.084199  0.085447  0.076612  0.078725   \n",
-      "5   0.0  0.080168  0.076519  0.083517  0.085447  0.086942  0.077411  0.079671   \n",
-      "6   0.0  0.068546  0.065106  0.075422  0.076612  0.077411  0.072522  0.074203   \n",
-      "7   0.0  0.070577  0.067183  0.077387  0.078725  0.079671  0.074203  0.076007   \n",
-      "8   0.0  0.072638  0.069315  0.079368  0.080867  0.081977  0.075887  0.077825   \n",
-      "9   0.0  0.074671  0.071455  0.081315  0.082991  0.084282  0.077536  0.079615   \n",
-      "10  0.0  0.060425  0.057463  0.068676  0.069583  0.070161  0.067515  0.068912   \n",
-      "11  0.0  0.062197  0.059245  0.070486  0.071501  0.072183  0.069129  0.070625   \n",
-      "12  0.0  0.064048  0.061113  0.072365  0.073497  0.074293  0.070797  0.072398   \n",
-      "13  0.0  0.065974  0.063066  0.074310  0.075569  0.076491  0.072515  0.074230   \n",
-      "14  0.0  0.067967  0.065101  0.076313  0.077711  0.078771  0.074276  0.076112   \n",
-      "\n",
-      "          8         9         10        11        12        13        14  \n",
-      "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.072638  0.074671  0.060425  0.062197  0.064048  0.065974  0.067967  \n",
-      "2   0.069315  0.071455  0.057463  0.059245  0.061113  0.063066  0.065101  \n",
-      "3   0.079368  0.081315  0.068676  0.070486  0.072365  0.074310  0.076313  \n",
-      "4   0.080867  0.082991  0.069583  0.071501  0.073497  0.075569  0.077711  \n",
-      "5   0.081977  0.084282  0.070161  0.072183  0.074293  0.076491  0.078771  \n",
-      "6   0.075887  0.077536  0.067515  0.069129  0.070797  0.072515  0.074276  \n",
-      "7   0.077825  0.079615  0.068912  0.070625  0.072398  0.074230  0.076112  \n",
-      "8   0.079786  0.081728  0.070305  0.072122  0.074007  0.075958  0.077970  \n",
-      "9   0.081728  0.083834  0.071659  0.073585  0.075587  0.077666  0.079814  \n",
-      "10  0.070305  0.071659  0.063876  0.065268  0.066700  0.068170  0.069669  \n",
-      "11  0.072122  0.073585  0.065268  0.066742  0.068261  0.069823  0.071420  \n",
-      "12  0.074007  0.075587  0.066700  0.068261  0.069873  0.071534  0.073236  \n",
-      "13  0.075958  0.077666  0.068170  0.069823  0.071534  0.073300  0.075115  \n",
-      "14  0.077970  0.079814  0.069669  0.071420  0.073236  0.075115  0.077050  \n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -3552,31 +3493,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[2. 2.]\n",
-      "Training MSE for OLS\n",
-      "3.0\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_252_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "%matplotlib inline\n",
     "\n",
@@ -3655,231 +3572,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[2. 2.]\n",
-      "Training MSE for OLS\n",
-      "3.0\n",
-      "[1.99995    1.99980002]\n",
-      "[ 0.50001525 -0.99953475]\n",
-      "[1.99993978 1.99975913]\n",
-      "[ 0.50001525 -0.99944272]\n",
-      "[1.99992746 1.99970988]\n",
-      "[ 0.50001525 -0.99933188]\n",
-      "[1.99991263 1.99965056]\n",
-      "[ 0.50001525 -0.99919837]\n",
-      "[1.99989476 1.99957911]\n",
-      "[ 0.50001524 -0.99903755]\n",
-      "[1.99987324 1.99949306]\n",
-      "[ 0.50001524 -0.99884384]\n",
-      "[1.99984732 1.99938942]\n",
-      "[ 0.50001524 -0.99861053]\n",
-      "[1.9998161  1.99926459]\n",
-      "[ 0.50001523 -0.9983295 ]\n",
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-      "[ 0.50001523 -0.99799099]\n",
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-      "[1.99967865 1.99871521]\n",
-      "[ 0.50001521 -0.99709215]\n",
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-      "[ 0.50001521 -0.99650061]\n",
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-      "[1.99918546 1.9967458 ]\n",
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-      "[ 0.50001063 -0.69695259]\n",
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_254_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import os\n",
     "import numpy as np\n",
@@ -3965,33 +3658,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 2.03099776 -0.17917768  5.18029127]\n",
-      "Training MSE for OLS\n",
-      "0.009163470508352218\n",
-      "Test MSE OLS\n",
-      "0.008675369724975977\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_256_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import os\n",
     "import numpy as np\n",
@@ -5019,31 +4686,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 1.0169643   0.27924636 -1.4087793   1.03308408  0.        ]\n",
-      "Test MSE OLS\n",
-      "0.9582286166520774\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter2_322_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -5147,313 +4790,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
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-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -5828,7 +5165,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
index 91b2e9d92..0a619c4d9 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter3.ipynb
@@ -489,10 +489,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Runtime: 0.101292 sec\n",
+      "Runtime: 0.085891 sec\n",
       "Jackknife Statistics :\n",
       "original           bias      std. error\n",
-      " 99.9618        99.9518        0.148771\n"
+      " 99.8321        99.8221         0.15031\n"
      ]
     }
    ],
@@ -912,12 +912,19 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Bootstrap Statistics :\n",
-      "original           bias      std. error\n",
-      " 99.9169   14.873        99.9169        0.147934\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtime\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m time\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
     }
    ],
@@ -972,22 +979,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_51_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# the histogram of the bootstrapped data (normalized data if density = True)\n",
     "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n",
@@ -1172,32 +1164,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Error: 0.013121574062587286\n",
-      "Bias^2: 0.012073649469946107\n",
-      "Var: 0.0010479245926411787\n",
-      "0.013121574062587286 >= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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nfd0X39LSQnFxMYWFhWzbto3f/va3XHrppXzrW99i8eLFAIwZM4b29nb+/Oc/c/jwYV544QX++te/upxn5MiR1NfX89FHH1FeXk5jYyMjRowgLCzMPG7lypU88sgjAa3r888/53e/+x0HDhzgL3/5C//973+5/fbbAbjwwgs55ZRTuPrqq9m2bRtbtmxh8eLFnHPOOcyYMaPTP4uRI0eyfv16CgsLKS8vB/RamTVr1pCfn8+2bdv4+OOPuyR4BEHwjGF2Niol2qU2JNOPC6tN1bj3zV0yj0boMkGLkfr6enbs2MGOHTsAyM/PZ8eOHWYdwn333WdeSAGuuuoqkpOTue6668jLy2P9+vX8/Oc/5/rrr/dawNpb9HVf/OrVq8nMzGTkyJHMnz+fTz75hKeeeop33nnHrK+YOnUqTz75JI8//jiTJ0/mpZdeYunSpS7nmT17NjfddBNXXnklqamp/O53vyM1NZUVK1bw3//+l9zcXB577DGeeOKJgNb1f//3f3z11VdMmzaNRx55hD/84Q9cdNFFAKa3TGJiImeffTYXXngho0eP5tVXX+3Sz+Lhhx/myJEjjBkzhtTUVABsNhu33norEydOZP78+YwfP57ly5d36XkEQeiIsw28M0ZHTaGXyMjTH3/jc5CezKMRAkXRgpkPje5rcd5553XY/sMf/pAVK1Zw7bXXcuTIEZc2z3379vGzn/2Mzz//nOTkZK644goeffTRgMVIbW0t8fHx1NTUdEjZNDc3k5+fz6hRo4iI6Fw6ZfXuIh56N88lzJgZH8GShblDri9+5MiR3HHHHS4dPAOB7ngfCMJQ5b43d/LylmPcdv5J3DVvvLn9uY1HWLJyDxdNSudv17hGPm2qxvRH1lLd5H+q75++N5VLpw7r9nUL/R9f129ngm7tPffcc/GlX5zNugwmTJjA2rVrg32qXkP64gVBGMq4d9IYGDUjnroOt+RXBiREoOt1dwdK6lh/oIwfzh5JqFWmmAxGetxnZKAgffGCIAwFbKrW4cbL8BjpmKbx7sIaaJdhQlRol+vulryzh02HK8iMj+SSU4ZWtHqoIGJEcOHIkSN9vQRBEHoITynp9Nhwyuv1dv9RdsMzA0OMlNe30tJuIzzE4RUUaLTjutmjuhRl1jSNPSdqAMgrqhExMkiReJcgCMIQwFsLbond0CwxKpTocNf708SoUCJC9ctEsdtxRjeiL+IirMwYmdglI7SS2hZqm/XBod+U1PvZWxioSGREEARhAKJpGrXN7cRHhvrd19foC4OGVlsH23dFUciKj+RweQOF1U3kJDsiJ0Y34k0vbvP+vBpc/c8vzO870xhwoKTO/P83pSJGBisSGREEQRiA3PvGLqY89AG7jtf43dff6AuA1nbVYwtupr2915PXyPzJmZwzLqXD9rAQ/dLS0OJqZNgZIzRnMXK0ooHmto7miMLAR8SIIAjCAOOro5W8ulV3Qd5+rMrv/l0ZfZEV772IVdM09hfr0YpfXDSeP31vKi/dcDpxEZ6D7p0xQnMWI6rmMGgTBhciRgRBEAYQqqrx8HuOoZRVDf7ba7sy+sJwYT3hIbKyq7CG4tpmosKsXH/mKC6dOgyLRTELYj0RrBHafnudiDH66pvSOh97CwMVqRkRBEEYQLy78wRfH6s2v69q9D/40ig2La5p9lo3khQd5rEFN8v0GukYGflgTwkA545LIaLgMzi6gcSiGq63NrBfHcHn2sno8qNjN00g0RpV1Thoj4zMyEnkyyNVUsQ6SJHIyBDgwQcfZOrUqX29DEEQukhzm43frd4PwDB7xCIQMeJr9IXBbeeN8diC68tr5IO8YgDmHX4cXrgU1v+eCd/8nQdCX+LFsKVkUgEoXGddxRmWPCw4JnUHEq0prG6iodVGqFVhbm464Jq2EQYPIkb6kGuvvRZFUVAUhdDQUEaPHs3dd99NQ4PkRAVhKGFTNTYdqvDbAvuvDfkUVjeRFR/BzeeOAaCywb8YAb3Y9JkfnEqGl3bcZ9Yf9lhYmuWlgPVIeQMHSuoJoZ3zbJ93OE5RIFmpBeBsy25eCXuUDeG3Md+yJeABpEZKZnRKDLmZ+uT3g9JRMyiRNI2BaoOjG6G+BGLSIWc2WKz+j+si8+fP59///jdtbW189tln3HjjjTQ0NPDMM8+47NfW1kZoqP8WPkEQBhaBzsYqq2th+ScHAbhnwQRi7UWivgbVuTN/ciaqCrf8p2M7bmltCze/uI1nrp7C/Jh887MwM2MmAHUt7dQ2txEXoX8Ord2jC5fTLfuIVzzfQMUpDaBBDXpLcAaVLA9dxtenjg7ICM0ojh2XEcvYdN0d9oi9oyYitOc/n4XeQyIjAHkrYdlkeO5b8MYN+r/LJuvbe5jw8HAyMjLIzs7mqquu4uqrr+btt982UyvPPvsso0ePJjw8HE3TqKmp4cc//jFpaWnExcVx/vnn8/XXX7uc87HHHiM9PZ3Y2FhuuOEGmpsDq6QXBKF38WZE5qkF9sm1B2hotTElO4GFp2SREBUGBB4ZAT0C88j/8jw+pgEXWbYw7Y2zXT4Lo5+ZSnyYHqkxoiP1Le288+U3AMyzbPX6fPHoIqVG08WIRdEjJtP2PA6H1sGu1yH/M/1m0APf2FMy49JiSIsNJy4iBFWD/HKJHg82RIzkrYTXFkPtCdfttUX69l4QJM5ERkbS1qbf6Rw8eJDXXnuNN954gx07dgBwySWXUFxczKpVq/jqq6849dRTueCCC6is1CvTX3vtNZYsWcJvfvMbtm7dSmZmJsuXL+/V1yAIgn98GZE5t8C221Re2HSEV78sAODXl0zEYlFIsouR6gBqRgx8+Y1cZNnC8tBlpGoVrg/UFpHZpj/3iZomPswrYd6Tn7K7XCWMVuZZfYgRe8SklihzmwJQW6jXmPi5+dtviJGMWBRFYWx6LCB1I4ORoS1GVBusvgd8fRysvterau9utmzZwn/+8x8uuOACAFpbW3nhhReYNm0ap5xyCp988gm7du3iv//9LzNmzGDs2LE88cQTJCQk8PrrrwOwbNkyrr/+em688UbGjx/Po48+Sm5ubq+sXxCEwPFnRGa0wH7v75v59Tt7UDW4ckY2M0bqtRaJdjHS0GqjpT2wzyjvHSwaS0KfB/TohftjwxRdoCx5Zzc3Pr+VEzXNZMcq/Dv092Qq3lt03SMjXvFw82dTNbM+ZJxdhIyzp2o81Y18U1LH0vf30tja7vu5hH7J0BYjRzd2jIi4oOkK/ujGHlvCe++9R0xMDBEREcyaNYuzzz6bP//5zwDk5OSQmppq7vvVV19RX19PcnIyMTEx5ld+fj6HDh0CYO/evcyaNcvlOdy/FwSh7wnUiGzr0SpCrQq//lYuj11+srk9NiLErLsItG7EuYPFgkoGusg4WTlMllLpQYjoZNrFSEFlE1aLwk3njOGD/7uQOQm+vULi7JERo2bEOx1v/goqG2lpVwkPsTAiSY+snJTmPTJy75u7+Nunh3lre6Gf5xL6I0O7gLW+pHv36wTnnXcezzzzDKGhoWRlZbkUqUZHu/4Bq6pKZmYm69at63CehISEHlujIAjdT6BGZJnxEfxj8QwmD4t32W6xKCREhlLR0EplQyvpcf7PZ/iNTKlbzwOhz/Obth/wPzWZb1s3+DxumuUgL9rmMiVZZenV55CbFac/sOB38No1Xo8LODICuNz8jTrLFBwnpenRkE2HKiiv14f6uXuNnKhu4qujuhOtJ9t6of8ztMVITHr37tcJoqOjOemkkwLa99RTT6W4uJiQkBBGjhzpcZ+JEyeyefNmFi9ebG7bvHlzdyxVEIRuJBAjsshQC2vuOJs4L8PwEqPDqGhopSrAIlYrKs+P/oiT8v4CQImWCEC64ttS/nLrZ5xu2UvW5f/GYggRgNxFcMUL8O5t0NTxHEbNSGBixI795u9AsS5GYsJDOPPxj11SWofLG3j360IWThkGwP92Ogp9y+xTiIWBxdBO0+TMhrgsvNsAKRA3TN+vH3DhhRcya9YsLrvsMtasWcORI0fYuHEjv/rVr9i6VS8iu/3223n22Wd59tlnOXDgAEuWLGHPnj19vHJBENwJxIjskUsnexUigFnEWhVImiZvJfx+DGP3/gXF3tVSgqsY8T4tRmF4fDiWkXM6PpS7CH5+CK55B87+OUxYBOG6YDEjI37TNE7Yb/4O2OtCvvBSW/Ozl3eY3Ubv7XKIESN6IgwshrYYsVhh/uP2b9w/Duzfz3+sV/xGAkFRFFatWsXZZ5/N9ddfz7hx4/je977HkSNHSE/X/4CvvPJKHnjgAe655x6mT5/O0aNHufnmm/t45YIgeMKXEVlCVCjfmZHt8/iEKF2oVPrrqMlbqadTnKIXmgYlWgIAaejbPYuiAD4LLVYYcy6c/yv43gtwzxH44XvEn38HALWR2bB4JcRmdniWfDWD1bYZaJrrzd/+4lrfrwm92+hIeYOLPX6ZiJEBiaJpWmCjE/uQ2tpa4uPjqampIS4uzuWx5uZm8vPzGTVqFBERgeVgO5C3Uu+qcS5mjRum//HlLurCyoXeolveB4LQR9hUjS35lZTWNbPjWDX//vwI509I49lrT/N53L1v7OSVL4/xf3PH8bMLxnreSbXprbNuxfrVWjRTW/4BwP7wxYQrXrpQuvBZmF/ewHlPrCM6zMqeh+c7rBQAIw7z3ZYH+FKbwNKQf/L9q66D3EW02VQm/Hp1QJN9vz9zBC9vKSApOozKhlYy4yPYdN8FQa9V6Bl8Xb+dGdo1Iwa5i2DCJX3iwCoIgmC1KMwakwzA5sN658rEzFi/x5nGZ74iI166Bo16kUTqOgqRi36rfw528bMw3p5iami10WZTCc1dBFc873LzV6ClAfA76w0sGDmPBHSr+UCECMBn35QBcNXMETz9yUHK61vQNA1F8e/wKvQfRIwYWKww6qy+XoUgCEOcvCK9cNOYxeKLpGj9Yu+ztddLN6DX4tW4YXD6Td1yMxYX4bjE1Da1kRwT7nLzp9WVUPlKJKhQ1aLwxAf7efSykzkQxGTe41V6u/EPzsjh6U8O0mbTqGlqM4WaMDAY2jUjgiAI/Qibqpm1ErlZ3kPaBgFZwnvpBjTESJq7GOnGOrkQq4WYcF2Q1DY7RV/sN3/14y6lzTHIl5e+KGB3YY3pvBoZavVa3AsQE66vc/aYZDLiI8xIjBSxDjxEjAiCIPQT8ssbaG5TiQqzkpMU5Xf/gCzhza5BV0pxj4xY4LvPdXudnCEQapo6Rm+qGvRtkaFWFk3JQtPggXd2m4LskpMzAO/dRkYm51un6AMFU2PDASiV9t4Bh4gRQRCEfkJekX4RnpARiyWAqbaJ0QF007h0DTow0zT2Thq+82+YdFlwCw6AOB9ixFh3UnQY9188kagwK9sKqvlwbykAi6YO89htFGrVfzaNrTZCLAoXTdJFS0qMLs7Ea2TgMWhqRgZAU5DQg8jvXxgM5J3QxcjETP8pGnDMp6lu8OMzYpqT3Q5NuoW70dabHtYK332hxzoH4yP1y4xHMdKgi4ak6DAy4iO47YKxPPb+PrN4dVx6LBnxEczNzTC7jdJiI3hr+3Fe23ocgDPHppjpqlS7q215feDDA4X+wYAXI4Z9emNjI5GRkX28GqGvaG3VP3ysVumAEgYue4sCrxcB/SIOUNfSTmu7SliIj2C3UTh6ZAPkf0bJlnFQA2mXPwa5HdM43YWvNE2lXUQl2l/H9XNG8drWYxwuayAuIoT0OD3tYkVlliUPrCVgSWdPmmO93zrF8X+JjAxcBrwYsVqtJCQkUFqqh/WioqKkpWuIoaoqZWVlREVFERIy4N/SwhDGSNPkBhgZiYsIxaLotRPVja2k+ZtPY7HC6HNg9DmUbvkIaCY93n9tSlcwxEitx5oRe5rGbt4WFmLhkUsn88Nnt3Dm2BT9s9yDD9TY8HOBHxNmtTA311Gga9SMSAHrwGNQfHJnZOj5QkOQCEMPi8XCiBEjRIgKA5ayuhbK6lpQFBif4d9jBOzD8qJ0s6+qxjb/YsSOqmpmkWdGgMd0Fl+RkQpDjESHm9vmnJTChnvO191lTZM01zTsrOYNLLRMZsq0M8zzA6TE6OeRyMjAY1CIEUVRyMzMJC0tjba2wEZpC4OLsLAwLBapxxYGLkaKZlRKNFFhAX40qzYSQtupBCoPbYW0swNqy61sbKVd1VAUR2qjp4iLsIsRD14oZmQk2nX+TkZ8hO4cu/oePE3MCVPa+XPYX6DgLVAvNl+zERkRMTLwGBRixMBqtUrNgCAIAxIjRRNo8Sp73ob//R9JNbdymPFUr/4NfHGL3jnjpxi1pFYfPJcSE06ItWdFfHyU/24ao2bEBS/OsQ40qC3U97MbVqbGSJpmoCK3koIgCP2AvcHUi3zwa/jvD6GxnARFNwir1GL1i/dri/X0hg9Ka/WLtVEg2pOYNSPNngpYdTGS7EmMeHGO9bWfERmpaGhFDdBOXugfiBgRBEHoBxhtvX7FyO63YeNT5rdJdjFSjVFnosHqe/U0hxeMyEh6bM8PlfTlM2KkaRI9Wbd7cY71tV9SdBiKojvZVvmbZCz0K0SMCIIg9CI2VWPToQre2VHIpkMV2FSN5jYbh8r0eSw+23pVG6y6y2VTIvpxlZpT0auRvvBCiT0yEmjBa1fw2drrZHrWAdM51ltRuqLP0cmZbW4JtVpMYVMmqZoBxaCqGREEQejPrN5dxEPv5lFU02xuy4yP4NrZOaianq5Ii/WROjm6ERorXDYl2iMjVVqM674+0hwldfbISC+madzFSLtNNbd5rBkxnGNfW4wuSJzTLnaB4mGOTmpMOJUNrZTVtTAho5tehNDjSGREEAShF1i9u4ibX9zmIkQAimuaWfr+fkAvXvXZnu5BYBiRkSrc2oF9pDlKjTRNL0ZG6prbTWdVgOqmNjQNFAUSIkM9H5y7CK54HuIyXbfHZenbPRTqpsTqwkaKWAcWQYuR9evXs3DhQrKyslAUhbfffjvgYz///HNCQkKYOnVqsE8rCIIwYLGpGg+9m+ehSdX1fn9Cph9/EQ8Cw2NkJCrFJX3hTkkfFLAC1DkVsRr1IvGRob47enIXwR274YfvweX/0v+9Y5fXjqFU8RoZkAQtRhoaGpgyZQpPP/10UMfV1NSwePFiLrjggmCfUhAEod/hqfbDG1vyKztERDwR5q/N1sMEXqOA1SUycskffPqNFNsjI2m9UMAaarUQFaavxTlVU2m6rwbgc2Kx6u27J39H/9fHa3O4sEoB60Ai6JqRBQsWsGDBgqCf6Cc/+QlXXXUVVqs1qGiKIAhCf8Nb7ceShbnMn5zZYf/SOv9CBCA2ws9HsksdhS5+Eow0jVHAOvs2n9N3222qmcLojTQN6NGPxlabRzHisV6kC4gL68CkV2pG/v3vf3Po0CGWLFkS0P4tLS3U1ta6fAmCIPQHfNV+3PziNlbvLupwTKARiMnD4v3vZNZR6BESIzJSSzTN314B8x7xeXh5fSuaBlaL4tnfowcwXVidxYivTpouIC6sA5MeFyPffPMN9957Ly+99FLAQ8yWLl1KfHy8+ZWdnd3DqxQEQfBPILUfD72b1yFlM3NUEpnxEV6bVAFCLAqzx6QEtpDcRayeu5ZbQh9mSesPzWc/+91Yj2LImRIzRROOxdI7s5wcw/LazW1VwaRpgiBFXFgHJD0qRmw2G1dddRUPPfQQ48aNC/i4++67j5qaGvPr2LFjPbhKQRCEwPBX+6EBRTXNbMmvdNlutSgsWZgLeHfNmD85A2uA4mD17iJufulrVtWdxLvabPOspXUtXqMzBqYY6aUUDXg2PqvooTSNREYGJj0qRurq6ti6dSs//elPCQkJISQkhIcffpivv/6akJAQPv74Y4/HhYeHExcX5/IlCILQ1wRa++Fpv/mTM3nmB6fqQ+DcUID7Lp4Y0Ll9RWcMPEVnDErsF+l0X34m3Ywnr5EqX1bwXcCIjFQ2ttJuU7v13ELP0aOmZ3Fxcezatctl2/Lly/n44495/fXXGTVqVE8+vSAIQrcSaO2Ht/3mT85kbm4GW/IrKa1rZt3+Mt7aXsiZY1MYlhAZ0LmDic7MGpPc4fHe9Bgx8CRGKht9GJ51gaToMCwKqJpeJNubESCh8wQtRurr6zl48KD5fX5+Pjt27CApKYkRI0Zw3333UVhYyPPPP4/FYmHy5Mkux6elpREREdFhuyAIQn/HqP0ormn2GJlQgIz4CGaOSvJ6DqtFYdaYZGyqxmPv7wPgytMCr4sLJjpTWN3E6t3FfOfU4cRHhWJTNXYdrwGgpV3FpmoBp4a6gkcx0qBHaJKivRiedRKrRSE5JpyyuhZK61pEjAwQgk7TbN26lWnTpjFt2jQA7rrrLqZNm8YDDzwAQFFREQUFBd27SkEQhH6Ar9oP4/slC3MDusCv/6aMoppmEqNCmZsb4FA4govOLF21l0fey+P/PfM5L2w6wpmPf8y6A2UAvLb1GGc+/rHfgtfuID5Sv++tdUnT2CMj3VzAClLEOhAJWoyce+65aJrW4WvFihUArFixgnXr1nk9/sEHH2THjh2dXK4gCELf4q32IyM+gmd+cKpHnxFPvPalXph/2bRhhId4N/Fyx19njoLueXLayEQ2HdLn2Bwua+DX7+wJqh25O4mP8hQZMWpGur92RYpYBx4yKE8QBCFI3Gs/0mL11Iy/iIhN1diSX8nhsno+yNPnzFwxw56iUW36ILz6Et32PWe2R6dRIzpz84vbOoyPM1iyMJejlY1UNLQSFmJBVTXaPRS0auji5aF385ibG3g3T7C4p2maWm00tdkASOzmNA1ASoxM7h1oiBgRBEHoBEbtR6B4cm0NtSocrWhgYtU6WH0P1J5wHBCXpbutepjBMn9yJn+56lR+9c5uM8IAEB5i4U/fm8r8yZm8vEVPl49JjWZvUZ3XdfkreO0O3E3PDMOzUKtCTHj3X4ZMS/g6sYQfKMjUXkEQhB7Gm2trm03j7f/8Fe21xa5CBKC2SLd9z1vp8XyP/C/PRYgAZCVEmmkiw+tkRFJUQGsMtDC2M5imZ/ZBeabhWXSY7ynFncQclieRkQGDiBFBEIQexJcviILKA6HPo/nydF19r57CseNN2ADklzeY9R+GGJme472zx5meHJrncGBtQ1U1x1yaHiheBefIiIiRgYKIEUEQhB7Ely/I6ZZ9ZCmVPj6INagt1GtJCNzwrKCikcLqJkIsCt+fmR1QwauvduSuYjiwqhrUt7Y7Jvb20GwciYwMPESMCIIg9CC+0h8XKl8FdpJ6vdjVn+EZ6PUfr3yp14tMGhZPbERot7Ujd5aIUCvhIfrlpqaxrccm9hqkSDfNgEPEiCAIQg/iLf2hoPL/QjYEdpIY3Yck0LqO7QXVAJxuj3Z0VztyV3DuqKlq7BkreAMjMlLT1EZLu83P3kJ/QLppBEEQehBvrq2nW/aRrHjvcjGJStHbfAm8ruNoRYP+3CMdqZfOtiN3F/GRoZTWtVDb1OYYktdDNSPxkaGEWBTaVY2K+layArTaF/oOiYwIgiD0IM6urc6kUR3YCU65wvQb8Wd4BpAQFcqJmmYUBU4b6VoHYrQjXzp1GLPGJPeaEAG3yEgP14xYLIq4sA4wRIwIgiD0MEaaJDLUYWJWSkJgB4+/2PyvLzt6c/f0WPNfw/m0P+AsRnq6gBUgJdZufCZ1IwMCESOCIAi9wPzJmZyUFgPA9XNGcvt1P0SLy8K7rFAgbpiZonE+j6f6D6NAdG9RLUCPdsd0Bk81Iz0pRsyOGhEjAwKpGREEQegFbKrGgRK9RmRxdjkjm/fCqdfCuqXQwdjdLlDmP+bREt5T/cdrW4/x1vZCapvbgf4nRuI8REZ6qmYEnLxG3NI0hiV/X9TNCN4RMSIIgtALHKlooKVdJZJWRrx1KSh28RGZCCjQVOnYOS5LFyIerOAN3O3oP9pb4vL4zJH9U4xUN7VR1ag7sfZomsZDZMSTJX9mfARLFub2SkeR4B0RI4IgCL3Avi8/BqyMUwqwKE5RkKZqQINz74fkMT6H5PnC2bNjVEo0aXE956jqC2+RByNNc7yqCZt9aF9PDMkzcERG9CiM4VzrbhhnTC7urRZnwTMiRgRBEHoa1cb+LR8AC5hoKXB70D47d9tzcMeuoEWIgXPKo6+iIr4iD4YYOVKutx3HhIcQHtK51xoIzpERX861vTW5WPCNFLAKgiD0NOufYG9rKgDjlWMednC1fe8MiU6dM6f1Qb2It5k5RuThUKleL3O8qhHo2agIOCIjZfUtfp1rnScXC32DiBFBEIROYFM1Nh2q4J0dhWw6VGGmHjqg2uCL5ezTRgAwQXGPjDhRX+L9MT84p2lO72Ux4i/yAPDa1uOAPp8GICk6vEfXlGYXIyeqmyiobAjomJ6cXCz4RtI0giAIQbJq5wl+9c5uKhvazG1eCyGPbqS+sZljWhoAEyyeIiN27LbvnSEnOQpFgVHJ0QxP7F3H0UAiD4brqkFSD3ugjEyOZnRqNIfLGsg74XC6taAy07KPNKopJYEt6gRU+315T04uFnwjYkQQBCEIlq7K42/r8ztsL/JWCFlfwn4tG4AMKkhU6j2fODKpg6dIMGTGR/LOrXNIiQlHUXq37qEzEYWeGpJnYLEoXDd7JL9+Zw+fHiglIy6cqfWf8UDo82QpjnTMCS2Jh9sW83Xs2f2uHXooIWkaQRCEAFm1s8ijEDHQ0AshXVI2MensU3UxMt5XVOT0mzpdvGpwyvCEPpnD0pmIQlIPeowYfPvU4cRGhHCkopEbckpZHrqMDFzrQjKoZHnoMpafelyKV/sQESOCIAgBYFM1fvXObr/7dSiEzJnNvtCJgI96kcgkOPvu7lhmn+BvZo4CZMSFE2Z1XHKSYnpejESHh/C903QhuH5fMYoC7nrDooCiKEzb87he39NJ6prbKKpp6spyhzQiRgRBEAJgS36l6RzqD5e0hcXK/lg9/TLRW2Rk4Z+6HBXpS3zNzDG+f3DRJOIiHZUBvREZAVg8ayQWBT5rG89BdZjHfZRu6Gb6/j82c+7v18lgvk4iYkQQBCEAgqmLcE5baJrG3lq9WHN8rNs54obBFS/4dFodKHibmZMRH2HW0RgurNDzNSMG2UlRzB2uRzz+bbvI986d7GZSVY29RXW0tKum5b9BwF1XQxwpYBUEQQiAQOsikqJDXQohT9Q0U9fcTohFYcwda6Bws37R66TTan/G08wc59kv8U5iJLmXxAjAdVNjWXOskTdtZ/GLkFdJULy0+naym6m6qc0UGSeqHYJT7OcDRyIjgiAIAWDURfjj0UsnuxRC7i/Wp+ielBZDWFgojDoLTv6O/u8gEiIGxsycS6cOY9aYZJefRXwfREYATj/jLCaGFNJMOK/YzvOwh+cJyYHinJopqtbrRvyZwK3eXdSp5xqsiBgRBEEIAKMuwle/xazRSVx8SpbLtr1Feth+QkZsD65uYOAsRnqrZgRAsYZw3Uw9EvF8+zzaNedLn+8JyYHgLEZO1DQFZALXoetqiCNiRBAEIUCMuoj0OFf30Ogw/SKWV1RHTWOby2P7inUxMj4jzue5h0JtgSFGLIqrMOkNFi24mOQIjROk8KE63fFAXBZc8XyX6naMYXygp2nEfj54pGZEEAQhCOZPzmRseiwX/OFTwkIsPHfdTKbnJLLwzxvYX1LHX95ex/0n15g1IfuK9DTNhEzvkZGhUltgCJDEqDAsvezpERFq5f/NGM0/N+Tz6Um/YP6ptd1Wt1Ne5xQZqW4KuNhZ7OcdSGREEAQhSCrsd8JZ8RHMGpNMWIiFeydXA/DPnc3c/PJONj77C5r/OJXDZXpkZKKXyMhQqi0wxUgv1os4M2NkIgDbqyK6tW7HJU1T3URqTGBzd8R+3oGIEUEQhCAx7miNybDkreTcDYu5wvoJKhbeV0/nqrZfcUHZ/2HTFOLDtA6pHQhswNxgqi0wxEhv1os4MzVbFyMHSupoaGnvtvNWOKVpGlptTMyM82sClxkfIfbzTogYEQRBCJIye1g+LTZCd+1cfQ+KovG70H+wJuwXXG39kCiaKSQVgPHaYRRN7XCeoVZbcM74VM4YncQPZuX0yfNnxEeQEReBqsGuwhrXB1Ub5H8Gu17X/w3CjdXd6KykrtmvCdyShbliP++E1IwIgiAESaldjKTGhuuunbUnzMfGW47zG8uz3BPyMm/YzmadOoUbeB+OTtPTAi7nGVq1BWmxEbzy41l9uoap2Qms3lPMjmPVnDE6Wd+YtxJW3+PyeyQuC+Y/HlBhq7sYKapuNoud3WuBMgZhLVB3IGJEEAQhSEprncSIF9fOOKWJ60LWcB1r9A0e9gu0ZkBqC7qPqSPsYqSgWt+QtxJeWwzuybLaIn17AJ02RjdNSkwY5fWtFNq9RvyZwAkOJE0jCIIQJGX1RpomPHDXTg/7BTJgTmoLupdp2QkA7DhWbabYOggRcGxbfa/PlI2maWZk5ORh8QAuA/N8mcAJDkSMCIIgBElprR52T4uL0FtD47LoWB1g4N3dM5ABc1Jb0L2cPDweq0WhuLaZ4rwNrqmZDvgfoFff0k5Lu2o/dwLgagkvBEbQYmT9+vUsXLiQrKwsFEXh7bff9rn/m2++ydy5c0lNTSUuLo5Zs2axZs2azq5XEAShzzEKWFNjwvXW0PmP2x/xIil8uHsGMmBO6D6iwkIYl657vuw4WhHYQT4G6BkpmqgwK2NSowG9vVcIjqBrRhoaGpgyZQrXXXcdl19+ud/9169fz9y5c/ntb39LQkIC//73v1m4cCFffPEF06ZN69SiBaGvsKma5H+HOG02lcpG/QKUVr0dKsr0FMx3V6CtuQ/F6U5bi8tCmf+Y35oDqS3oXaZmJ7C3qJbttbHMD+QAH6m4CnuKJiUmnKyESEC3hBeCI2gxsmDBAhYsWBDw/suWLXP5/re//S3vvPMO7777rogRYUAxVFwyBd9U1LeiaWDFRtKrl4Ki1xY0RaTzcNs15LdGkEY1pSRwrHkKv1ZPDuiCZ9QWCD3PtOwEXt5SwI7aaJoiMwhvLMaT7lM1aInKINLHAL1yU4yEmWKkuKYZVdV63WV2INPrNSOqqlJXV0dSkveCrJaWFmpra12+BKEvGUoumYJvSr/+AIAUarAojsLHiKYSftP+BPHUs1KdzWY1lxO1bfL+6IdMHZEAwK7CWpa0LgZ04eGM8f1DbYux+bhUlpmdNOGkx4ZjUaDNpnVo9xV80+ti5A9/+AMNDQ1cccUVXvdZunQp8fHx5ld2dnYvrlAQXBlqLplDDZuqcfkzG7l+xZdomp/foWqj7NO/A5CmVLs8pCh6hcjS0H9iQS9olPdH/2RMagwx4SE0ttp4rWEqN7fdQTGuN8jFJHNz2x28Uj+Vpav28vf1hzyey5hLkxwTTojVQnqcXvtzwoeZndCRXvUZefnll3nwwQd55513SEtL87rffffdx1133WV+X1tbK4JE6DOCccmUMPvAo6imia+OVgF6MaJp8e6J/M8obdE/Nt3FCOiCJIl6TrfksUmdDMj7oz9itSicMjyejYf0AtY16kzWtsxgpmWfmWLbok5Atd+v/2tDPhpw8cmZDE+McjlXRYNRzKxb3GfGR1BU08yJ6iam2tuIBf/0mhh59dVXueGGG/jvf//LhRde6HPf8PBwwsMDGzQkCD3NUHPJ7C36SzFwdWOb+f9vSut8i5GvnqWUBABSPYgRg1lKHpuY7LJN3h/9i6nZCaYYAVCxsFnN9bivEdM6Ut7YQYyU19nTNPb3TVZCJNsKql06avrLe70/0yti5OWXX+b666/n5Zdf5pJLLumNpxSEbkNcMruf/lQMXNXoGHJ2sLSe2WNSPO+o2uDgR5Rp3wUgjWrvJ/VwnZH3R/9i2gh9aF6IRcGmah7TsACRoRaa2vS0W355PWeOdX1/lDt10wCOjhq710h/eq/3Z4KuGamvr2fHjh3s2LEDgPz8fHbs2EFBQQGgp1gWL15s7v/yyy+zePFi/vCHP3DGGWdQXFxMcXExNTU1nk4vCJ3CpmpsOlTBOzsK2XSoolvz8+KS2b30t2LgKufISEm99x2PboTWekq1BMB3ZGST0x22vD/6J0YKxRAi3v6+DSEC8Nj7+zq8Pw0xkhytp2my7H4xRTVN/e693p8JWoxs3bqVadOmmW25d911F9OmTeOBBx4AoKioyBQmAH/7299ob2/n1ltvJTMz0/y6/fbbu+klCEOd1buLOPPxj/n+PzZz+ys7+P4/NnPm4x932x+6uGR2H/2xGLjaKTLyTWmd9x3txlf+xEi9Fs4Xquv7Rd4f/Y/U2HCGJUSiAXdcOLaD6RyABZUwHGK1obW9g4ioqHdN02TaIyOF1U397r3enwk6TXPuuef6rDhfsWKFy/fr1q0L9ikEIWCMOw/3d6Rx59FdDpYygbN76I/FwFUNjovNwVIfkRG78VWZXYx4KmAF+Fv7t8zCR3l/9G+mjkigsLqJUKuFDfecz5b8Soprmnjkf3s5rWkDt4S8w6WtvzH3H60UMU45zkPvRjA3N4M2m0pdSzvglKaJ18VIQUUj1U1tHZ/UjhQ2uyJTe4UBi7+7bAX9zmNubka33JWKS2bX6Y/FwM41I+X1rVQ2tJJkD7m7kDMbLTaLsuYEwLMY0SKTmH31Y5zU0CbvjwHAtOwE/reziB3Hqk3TuU2HKjitaQPPhC5jrW06ALE0UEc0J7Rk1obezS11sCV/KtlJuvAIs1qIi9Avp1kJeoTFlxBxRgqbdWRQnjBgCeYuu7uQCZxdI9AiztSYcP63s4hjlY09vCLXNA34iI5YrNSc/zithAK66ZkrCsrCPzFrbJq8PwYIU50m+BoR/9LaBpaEPg/ALm00AHMt27Bio5lwSklgSegLlNY2mHNpUmLCUBT9d50UHUZ4SOCXVils1hExIgxY+uNdtuCbQIuBVQ1u/c827n9rV4+vybmAFXzXjZRlnQdAvNJIhOJ0XNwwuOJ5vzNohP7F5GHxhIdYKKtrIa9Id/o+qXEXWUolFgW+1sYAcKrlAMOVMgAKyCBLqeCkxl3mXJrkGEc7uKIoZkdNUnSoFL4HiIgRYcAiLbcDj0CLgQ+U6IKgJ6afundeGWma0Sn6xFVfHTWldrfNtNQ0+OF7cPm/9H/v2CVCZAASEWrl3PGpAKzeXQzAxFg9GqdpsFPVIyNTLIcZoZQCcFRNN/dznkvjTKa9GHbRlCxACt8DQcSIMGDp6ZbbnmwX7gztNpUn1x5g06EAx573U4xiYPfuhYz4CLPguMCenqlrbu/W5/bUebXnhH5HfNpI/X3iq4jViLKlxobDqLPg5O/o/1qs3bpOofdYYC8uXrVL75CxxGYAcFRLp4YYwmhlvFLASEUXK0e0DHO/cqe5NM4YkZHU2Ai/73VBRwpYhQGLcZd984vbUMClkLWrdx790ajoi/xKnvroG97fVcTau87pkzV0F/6KgY/1gBjx1nlliMyIUP3ezGeaxoiM+HJpFQYU509MI8xq4VBZA9+U1DE2ZzbEZbGjahQAucpRwhQbOYre2n1US9fTcjmzKdu1D3C09RoYXiOF1U3cet5JUvgeABIZEQY0gdxlB0t/NSoy7soPlzfQ0m7rkzV0J76KgY/axUhTm412m+rtFAHjq/PKwLgzLqltocZLJ0RprV2MxEnqb7AQFxHKWXZX1VW7ivUo1/zHzRTNVIs+IM9FjMx/DCxWKhr0yEiyW/eVERkpsqcZpfDdPxIZEQYcmqaZlevQvS23vd0uHAyVdj8Mm6qRX97AhIy4Xn3+3kJVNZcumvqWdhKiPLTaBoG/zivQR8EnRYdR2dDKwdI6pud0TO8ZNSOpMRIZGUzMn5zBR/tKeX93EbdfOBZyF/F1kgXK4BTLYQBGGmIkZCTaxEtQcEzsdZ9nlOlmCS/4RyIjwoDi92v2cdpvPmR/sWsovbvuPPqiXThQqhocLagHfNmWD3DK6ltoaXdEQ7ojVRNoR5WRfvFWxGqmaeJEjAwm5uamE2JR2Fdcx+GyetpsKnuq9TqgKd/+OVz+L7Kv+SuKAnVtCpX2v0X3uTQGw+xeIydqur8Ae7AiYkQYUKzeXUx5fSu/W72vR87fn9uFK51ty0t82JYPcArcvEW6Q4wE2lEVH6l7iKw/UOaxYNmlgFUYNCREhZkuqO/vLuZASR3NbSqx4SGMmnIOnPwdIsaeTYY9PWekEY00jbsYybS7sNY1t1PXHJj52VBHxIgwYNA0zYxafLSvlO0FVd12bqNzJtCLfF+0C7tGRgavGDla4S5Guv5h7q/zCsCi6EXCAKt2F3ucbyQFrIOXi0/W68ve313EzuO6od3Jw+OxOEVZc5KjADha0UC7TTXbwpPdWnujw0NMYesvPSjoiBgRBgx1Le00tjoKN59ce6Bbzuvc7vn0J4d87tuXRkWVDc6Rke5P03gr2uxteiIy4svfxMA9EOJesNzcZqPWvpZU8a4ZdMzLTceiwO7CWt7beQKAKXaHVoORyboXzZGyeir3foam6SI2MaJja3emU0eN4B8RI8KAodh+hxERaiHEovDZN+UB12548wzx1jnjib42KnKeoXKkons7ap7fdIQpD33A/3ae6HNvFXcL+PqW7mnv9dZ55Q33yapGVCQ8xDGHRBg8JMeEc/ooPVXz+UHdy2fK8HiXfXLsYqTg89coe+1nACRp1VifOhnyVrrsO8zsqJHISCDIX5QwYDAEw8jkaE7NSeQ/XxTwxAf7efXHZ7h017jjzTPk15dM5JH/7fXZ7ulMX09grXSaLqtqcLisgYmZ3dNRs/WInvL6xRs7aWhxiJy+8FY5WtEAQIhFoV3VujXn7t559eqXx9hoN5GzoDLTso/t6km0EIaCiobFLFgOs88bSY0N9/l+EwYuF5+cwabDDlNB98hITtMewMqR1jgqQvS/vRSlBmqL4LXFLiMBMo0iVomMBIRERoQBg9Gznxkfwc/OP4mwEAtb8ivNuxhP+PIMueU/2wOKiPz0vJN4+UdnsOGe8/tMiGiaZkZGhifqd1zdWTdinMtZiEDfeKsUVOq/57HpsQBmaqS7cO68MoajnaQcY0v4zbwS9ijTLXr67/6Ql7jIsgXQC1fL7MWrUi8yeLloUgaGzkyNDTcLVgFQbeTs/BOge42Uo0dNUpRazDja6ntB1f+Gssz2XhEjgSBiRBgwGMIhIz6SzPhIrpo5AoA/rN1vXlSc8ecZEihj02P63KiotrndTJkY9SrdVTdiUzWvFujuqYqeprG13WyXzLVHfbrbEt6Zsjpd4C22riVF0QXZWKVQf0xL4JnQZVxk2UJabIRjLo3Uiwxa0uIimJGTCMCU4QmuEbCjG8lp3A1AJXHkq/qNiWN6swa1hXB0I+CoL9lbHPxNQ38bRdEbiBgRBgxGzYhRGHbLeWOICLWwvaCadfvLOuwfiNFVIPSHi4/RSRMdZmVyln5H5su2PBi25FfS7uPDrje9VYzi1ehwK/Utenqmp1ojbapGTYUe8UnEIcZOsouRg9owAB4Ke4GZOfFmzYi09Q5ubjhzFCEWhcumZbk+UF9CjNJsio+vtLGAPU3jth84Zh3tK66l2qneyx+e5id56uwabIgYEQYMRbVGZEQXB2mxESyeNRKA363Z3+HuoateIP1pxLfhMZIYHcY4e/qiuyIjxbWBhZF7w1vl7e26EGhosbFmj/6h/sa2453+IFZVjfve3Mm/NuR3eGzLoTLiNH1IXqLi+FmOsxwH4BttOBYFMqjAemyTwwpexMigZv7kTL75zQK+dYqbGInRp/Xm2Afm7VBPAjyIEft+qbHhnJQWg6bB5sOBCfn+OoqiNxAxInSKvggjFtvdDLPshkIAN50zhriIEPYW1fLql8dc9u+OiEZ/GfFtREaSosMYlx4D6B01zW1d76iJCQsNaL+ejhCt3l3EXz893GF7c5va6Q/i/SV1vLzlGL9fs69DKs925HNqNd03IkFxRJmMNM1xLYVGzS486ktMMSbuq4MfjwXK9gF6xoyaRvS/h2RqjaPMAXoGZ4zWb2Q2H/Y/aTuQtHJvpUv7AhEjQtD0VRjRUTPiuCgmRYdxx4XjAHjig/3UNDpC+v6MrozIx/KrTiU6zNUnwKLA01dN6zcjvg2PkcSoMFJjw4mLCDE7arrKyJQon4/3RoTI+CD2RWc+iIvt0bTmNtUc926QSjXV6FEm58hIklJHMjVoWDis2X//MemU1UuaZkhjH6CXYyl12axHRuyfMvYBegazRusD+AIRI/15FEVvIGJECIpVO4u4qQ/CiPUt7WYho7tPxDWzchibFkNlQyt//NBhhObL6MrZM+TiUzK5MFcPrX7rlExi7Rf6iNCORkZ9RaVTZERRFEeqphvqRqoavddk9Ja3Sk99EJfWOs7pbj6VkT2aNru7gXPNCDjqRl61ncvr1gW8XTWSwir9+P5QQyT0EbmLGHnGt102pSo1EJfl0tZrcPpoo26kzsVB2RP9eRRFbyBiRAiYVTtP8NOXt3l8rKfDiEbxamxECDHhrvY4oVYLSxZOAuCFzUd57ctjZvpobm6GR6OrjPgInvnBqWbko8J+13zBxDSumJENwH+3Hu/219FZzJoR+/Tasd1YN1LZ0GL+311vuP+ceoqe+iA26jwAjle5mqnVpp4KQBitRNLi8phRN/KCbR53N1zDHa/tNEWbpGmGNjlTznL5PuWKp+COXR2ECOgza8am6WnVL/J9R0cCFbmDVQyL6ZkQEKt3F3HLf7b73Mf57tUYOtVduHfSuHPm2BSmZsez41gNv3hjp7ndMO3acM/5ptFVWqyecnC+0zc7JWIi+O6MOP61IZ+P9pVQUd9Ccj8YF++oGdHrO4y6ke7wGnFOX0SFhfCPxTO8/px6ip76IC5xEi9GZAPVBkc3Un20FIjQoyJuL/E662oqtVgaEiegJo9D0zRUTWP6iMRBezEQAmNksmta85uwXFKx4C2OesboZL4prWfz4Uqfot5IKxfXNHusG1HQbw76Q0F9TyBiRPBLIPl8Z3oijFhkL17NcCpedWb17iJ2HKvpsN1IH/m7uzdHgceGMSEjjlOGx7PzeA1v7zjBDWeO6oZX0DUM99XEaD0y4kjTdEdkxCFGGlrbOWN0Uq87jM4clURabLjp5eGJztStuEZGmnTL7tX3QO0JqmwnA/eRaG2CyCRocqSARsW085dLZsCky4J9KcIgZ/PhChQc0eBrnt3i06l41phkXth81G/diJFWvvnFbS7nh74fRdEbSJpG8Euwfh2B3DlqmkZFfUvAKR0zMhLX8dy+xFIg6aN2m2qmQVLtUZDvTh8OwH+3HvNoqNbbGO6rSUaaxh76PdoNHTUV9Y4LtqbpxZ69jdWi8IMzRvjcpzMfxCVO4qbw2BHdsrtWH4JWhf4zTNBqUJoq4dz74fJ/wQ/fQ7n7gAgRoQNG6637J4KvmjlDQO8rrnMR/p7wNj+pt9KlfYlERgS/BBPp8Hf32tJuY9WuIlZ8foSvj9dw0zljuHfBBL/ndfcYcSaY4kdP6aPKhlY0Tb8gGjUZi6YM45H/7WVfcR17TtQyeVh8h+N6E+fWXtA7OuIjQ6lpauNwWQO5WZ2fUVPh9gHZ0NpOZFjvF+8aUa+wEAut7a6CaOm3J3fqg7jMqYD1eHEJhDouI9WavZOGOkCBbc/puX9L/ylcFvoP/lpvFeCRlbuYG/UN1oZS3W8kZzYpMeGMS4/hQEk9XxyuYMHJvt/H7vOTejNd2peIGBH8EkyO3Nvda0V9Cy9sPsqLmwvMlAjA2rzigMRIsTGXpn4P5Jfovfz2i0ZpXbM55CyNag5qmeRpI3EvBPAmqozUQHJ0GBb72uOjQrloUgbvfn2CN7Yd73MxYkRuDDGid9TE8OWRKr4preuaGHFreW1ssWEPGvQqBRV6gel3pw/nW6dkUVrXzP1v7aKhxWa6WQaDqmouaZ9CWzxaCObsETMyotTjYuU96iwPZxOGOv5ueuZZtrCk5Xmszzt1fMVlwfzHOWP0aA6U1LM5ADECjvlJQwlJ0wh+MQqrfGFRYPlV3sOIV//zC5Z9+A3l9S2kx4Vz87ljADhc3kCDtxHxqg3yP4PV91F0UC+ezdj2JDz3LVg22RzZPaFqHRvCb+OVsEd5KuxpVoX/ko/D7mIMhS6n85ZtMetF3ApVF56iv5Y1u4v7NFXTblOpaXKtGQFHR01Xi1jdQ8cNrT03C8YXhhV8TnKUOcjOiFR1ZlheVWOri819A5FUO6msak3/v0tbr93KWxDc8RUhvsiyhWdCl5GBW+u5fZrvrDDdzC9QJ9ahiIgRwS/Ofh3eePr707j4FM9CpLG1nX32YVF/vHIKG+45n3vmTyAtNhxN02c3dCBvpS44nvsWbF5OkU2PTGQq9j9mY2T3B79m3Ke3kqG4/pGPtpTwYfjP+U3IPwlDv9j+47OO7p7g6KRJcTOzOntcKlFhVk7UNPP18Y7Fsb1FTVObKaQSIh1uqUbdyIEutvdWNLgWjTb2sRgZkeToVoiN0F9vZ4blldiLV1MiNFKoBqBQSzEfrzLSNE7uq4aVtyC44y1CbEFlSejz+v87BIXtwy33PALojsAvbT46ZIbfBYOIESEg5k/O5O554zpsz4yP4K8/OJWL3ec4OHGkXL/IJESF8v+mDSfUqr/tJtlTC3tOOIkR1QbrHofXrjELDZu0MNMp0yE6NP1r09MoaB7fyIoCV4d8zKqw+wHIO1FNy6r79WiL6ij6NFpbU90iIxGhVs6bkAbA+304E8IoXo2PDCXE6nilRkeNt4m7gaCqmhkZSYnRoxANLYEXxN784ldc9pfPu0XAOMRItLkt1u4pU98JMWLcyaa2n2C4og9SPO4sRow0DfV4svIWBGe8OTrPtOwjS6n0IEQMNJLrDxBj0cXxL9/ePWSG3wWDiBEhYNzbav9y1alsuOd85k/O9Dmr5kiFbllujNQ2MOow9hTaxUjeSvjjJFj3W5f9ijW9XiCKZuJwNa5C89/5MUY5QSTNaFgo3PxGhzSPIzIS1uHYBZMzAH2A29vbj3fbHU1RTRO7CwOLthhtvUnRrusbm971jprqpjaMlzMsUY9IBCosKupbeH93MTuOVfPmtkL/B/igrrnNFEXZSY73WWxEiPl4sBhtvelqGcOUcgCOa6nm42aaxqgZcbPyFgRnvDk6p9mjbv5IVV2jt0Nh+F0wiBgRAuZohesclJzkKKwWxe+smvxy/bhRKa5ixIiM7D5RowuD1xZDXcc/zCK7GMlQKumM/YWiQLb9zviYpkc6qD2hP1/eSrNmxD0yAnq9Bugh/zte/brb7miuX7GVy/7yeYefqSccc2lcB9qlxoSTEBWKqsGhss5FRwz31biIEOLtKaBAIyP7ix3pjX9/no/aBZF2rFIvUE6KDjNTM+AsRjqTprEPtlOqzMiIS5oGpzTNGbd4dNAUBGc8td6WkhDQsaGK63t4KAy/CwYRI0LAHKlwjUqU1bUENPL6SLnnyMikLD0ycqCkjtb37wePTXNQjC5GMpXOF385xEiq6wOr76XcCOe71Yys3l3Ena9+3XE9XbyjKa1tZm9RLe2qxt4iD/UyblS5ddIYKIpi1o10NlVjpKiSY8LNYYGBRkb2OxXOHipr4LOD5Z1aA0BBpf4eca4XAYgxxIi3ImcfGJ006VQz3EdkJIF6GH9x8IsWhiTzJ2ey4Z7zeflHZ/Cn703l9ut+iBaXheZlJKeqwQktmW+0YR0eG+zD74JBxIgQMAX2u3ijdbektjmgkddGZMR9OuzwxEjiIkJos2l8U+P9rWhERjIVDw6GSmBv4WxFn7R53EWM6O2cZVXVgGtkpCfHeW8rqDL/f7yqyceeOs4Te90xUisf7i3pVArJOHdydBhRYfqFv6HVERnxlX4zIiMRofrv4N+f5wf13M54Kl4F5wLW4NM0ZmQkUjPFiBEZadOs1KE/V2JcjNSKCEFhtN5eOnUYs8amsWPSvfaRAa77Gd8/1HaNl8o2ncE6/C4YRIwIAWNERibb0yvbC6oDMhszLMvdIyOKopj+GHvUkV7PY9SMZLq3zaHArJ8GtHbjYtQhMgKUN+oX35Sa3bDrdcj/jC2HynpsnPdXRx1i5Fhlo489ddwNzwxW7y7iw7xiAN79uqhTKSTDfTUpOozocHtkxB6F8Jd+Mzqkfnb+WBQF1u0v63SExrsYCTJNY7SD73qd0nL9d54249IONSPV6O9FBZX4+Q9IrYjQaWyqxi3bhnNz2x1mFNegmGRubruDNepMn+eQeUdieiYESHVjq+l1cWpOIl8frzHnxfjDOG6kW80IwOSseDYfriRPy/F6vKNmxCkyEjdMLzjMXQTDT4N3b4OmKi9ngOFmZCTNZXubZqWqRY/0pK68GhT9Yjo1Ip2LLN/3+yHy+cGyoN0RXcRIIJERY2KvkxjxZ0sdqHW04b6aHBPuEhnxd/6/XD2Nb+xpmnm56WwvqObDvSWs2JjPo5ed7Pd53TlqF7ojkrsQGXGaOwNQ2vwUkEJaJAy7fCm8DLVEU6tFmu6rcWEK1skLg16vIBgYZmhFzGRtywzTfLGUBLaoE1B93PMP9uF3wRB0ZGT9+vUsXLiQrKwsFEXh7bff9nvMp59+yvTp04mIiGD06NH89a9/7cxahT7EiIqkx4Wbd68t7f47WQySosPMAklnJg2zF7FaxtNhdKqdYk13IsyMaNcLDX/4nuvI7txF8PND+myRyESP5/BcM6JQEaHPQwmhnXgcxaQRzaU8E7qMiyxbfL6upz85xPRH1vKnDw8ElCJpbrOxu9BRJxJUZMSepunOFJLhvpocHWbWjNS3tPs9/5KVe2hotRFmtTAyJZrr54wE4I2vCqlpDD6lYqSrshPdxIjR2uuvZsQogLYLEVVTKLMXFqZ/fAfRoY4C4MIL/kLV/L8AkBjbUSALQjA4p1hULGxWc1mpzmazmouKBQsqZ1jyWGTZaN4UwdAYfhcMQYuRhoYGpkyZwtNPPx3Q/vn5+Vx88cWcddZZbN++nfvvv5/bbruNN954I+jFCn2H0fWRkxxtFnqqmuax795AwWHS5T5228AoYt2rjUTVFDwJEiNNk3Hd8zB/qW7X7R5Wt1jh3Ht0UfLD93TREuWwUzZqRiqJo0ELtz+PRpmqi6FkarEojsuvggYK/Cb0WS61bGC6sh9vBbbVTW388cNvmP7oWr8pkt2FNbTaVELsHz7Hq5r8urtWNrq6rwYzi8cfhuFZckwYUfYL/7HKRr/nL6vTRczo1GhCrRZmjUlmQkYsTW02XvmywO/zupxP0zhht/sfluDaPh5Qmka16RERp99PFTG02QO/KdTA6nsZnqifuzDlTKriJwKQ4KEORxCCwVeK5SLLFhd36NusbwGQQvWQGH4XDEGLkQULFvDoo4/y7W9/O6D9//rXvzJixAiWLVvGxIkTufHGG7n++ut54okngl6s0HcYxmUjk6PMQs/y+laPfffO3589Ti8Y9JSiARidEk14iIWGdoUjC56DONc/zJbYEZRjd19NCOAu1mLVxcr8pXD3N6YwiYuOIt5u+31cS9VnRpx7P+XN9hSN0tHzwwKkKLX8KWw5b4Q/xGnKfvtr8xwRqm5s89tlY6RozhybgqJAU5utw6A6dxw1I7qwC7TYLZD9jMhIklNkpLYp8MjGhAw93aEoCtfPGQXAcxuPmC3RgVDZ0EpLu4qiQHq8a0dTQA6sRzeaERGDUi0BgGRqCFPaobaQYWH6e/h4VSPVRuorqmO0ThCCwZsZmieLeKMIP0mpY8OiehEiTvR4AeumTZuYN2+ey7aLLrqIrVu30tbm+UOvpaWF2tpaly+hb3GOjBi26WV1LX5HXoda9QvcqGTPQiLEamFipr2INXIG3LFbFxD2Ue6lP9wIQHiIhYRgLxxuwmR4iv48x877s57mSR5DmaYLnRQPYsSdhdZNAJys5HtN32j4TpEYYmTW6GQy4vSfmb9UTZVbN02gxW6B7Fdhuq+Gm5GRYBpyxmc4BvQtmppFUnQYJ2qa+SAv8BkvRhQmJSac8BDXiFdAkREP3jQlmp6uS1Mc9TnDw/XoS2F1E1VGtEkiI0IX8WSG5s0i3rAnKNKSsb53h4sT9FCnx8VIcXEx6emu8x7S09Npb2+nvNyzL8HSpUuJj483v7Kzs3t6mYIfnF1UjTRNfUs7ja3tHfruX/7RGaYzq3mcl8gIuNnCGwLi5O/AqLMoqtMvGpnxESidcTwzsFjJTteLV4+FjdKfJyadMnvUJVWp9nuKi6xfArBTG8PDIc/yl5BlzLLsxuIWKfGWItE0zWzrnZ6TaNZH+CpibW1XTY8No5vG252YgYL+8wqkKM5s7Y1xREZCrIrf8xtppvEZjsFzEaFWrjxN/1tdvbvY73MbGCmaLA/DGGPC/Tiw5q2E1fd12FxqipFqc9uwJH2tx6uaTO8WSdMI3YH7TZk3i3gjMlJHFHWNTbBeMgQGvdLa634RMXLk3i4u9913HzU1NebXsWPHenyNgm+Mboec5Chiw0MID9HfOuX22gGXvvsxyWZB1hEv7qvOGHUje050jE4YHTvukZfOYNiMG26f5MymLFQ3IkrBf2QkXalmkqJ7aWzSTuaSkC28HPZbdobfwM+sb7iIEk8pkoLKRsrrWwm1KkweFs9w+3qOV3mPjBjpBIsCcfaUhTdbaufvAymKs6mai6Ga0U3T2GrzeX4NvV4IXCMjALn2KFexj5oTd0wx4lYvAo7X3NKu0upeMG0UrTZ2vKkxXDHTlSqMuTPDRuuvqbC6ieoGIzIiaRqhe3C+Kbt7drzHfaKVFuLshfLFWhJsfEqiI3Z6XIxkZGRQXOx6l1RaWkpISAjJyckejwkPDycuLs7lS+g76prbzHB+TnIUiqKY0ZGyeu8XnVq347zhHBlxL+Y0QviZ8R0vVMGSnWREIuwXf4uV8vQ5gOeaEU+cZdkFwHqbo301Rmnh/0Lf4OvwH7HA8gXgOUVipGgmD4snItTKcCMyUumIjLibjBlW9YlRYVicxIW/9FggueiqxlZzGnBSlKvPiK/z//qSiaia3uniHs1It6eeimsDFyO+fseGAyu4RUc8FK06Y6ZpjLkh8x9juKfISLRERoTuw7gpmzFpotd9jOhIkZYErfUSHbHT4z4js2bN4t1333XZ9sEHHzBjxgxCQ+WuZCBgREVSYhxzQ1Jjwzle1WR2Vbig2uDoRo4cLQUiSHGbN+LO+IxYrBaFyoZWimubXS5Kxh12t0RGzIu/IxJRbkkBKkmJsoDvOlJAFyN/tS1ig3oymobLrJxYpYnloX/iRetlzBzV0V7cECPTRyTa1+MaGVm9u4iH3s1z6WQxilYTPVw050/OZG5uBve/tYtXvzzG2WNT+Pd1MwNuEzSKVxOi9GnA7g6sxvm35FdSWtdMWqye+nlvp14sOi4jtkN0M8NJjGiaFlBqrdCMjHT8HVstClFhVhpbbdS3tJNsuOR6KFp1xihgTQ9vg+88D7mLGGYvzK1saOWEPeImkRGhR8iZDZEJ0FTd4aFMpZL92giK7JYFfPEMnH33kDfeCzoyUl9fz44dO9ixYwegt+7u2LGDggK9ne++++5j8eLF5v433XQTR48e5a677mLv3r08++yz/Otf/+Luu+/unlcg9DiOFI0j1WJ01JTZ79xN8lbqE3Gf+xb5H/0DgJGt+80JuZ6ICLWaM1b2FLoWKxtpmsxuECNma6dTO60xsTf1ij/phbPf/gdEpXg9x3TLASJooZREDmjDPe7zA/VtrGvu1Z1AnUKwphjJsYuRJIc48jbjx5jY6w2rRWHWaP1Drc2mBeVXYLb12oWOGRlxmk3jKf1m2MCPt3fSOJMWp78vWttV0+zOH8Zr9pSmAaci1sYW012V/E99ntOIjKROX2T60cRHhprnOlCsd1ZJAavQI1iscPotHh8yIiMnDDHSVKWL6yFO0GJk69atTJs2jWnTpgFw1113MW3aNB544AEAioqKTGECMGrUKFatWsW6deuYOnUqjzzyCE899RSXX355N70Eoac5YnbSOFItqU4dNSZuxlNHtQwARqoF5oRcb+Q6T/C1Y1M10168prGty5MtjbRIXUu7eaE0BsWlxkXqhbOnXAHf+iPeDNgilDZOt+wF4DO1o9OootiP/OKv8Ny34I+TYN3j1G173byIu4uRwuomHly5x0vCQedYZaPX129cxE8E6Ihr4DA803+XRmSkzaZ1rM9wwngdEzyIkYhQq9n1FGiqpqjat+A0omq1Ly3Wf6Zv3ADrf+/znGVGZCTZtYjX8DFptbceB92hJQiBcvbdENaxVs7oqHGxjq8PvPtssBK0GDn33HPRNK3D14oVKwBYsWIF69atcznmnHPOYdu2bbS0tJCfn89NN93UHWsXegmzrTfJKTLiLkY85PCPqLoYGaXYa4ZW3+u1WMsoYt1dWMumQxU8/O4eTvvNhxwq05/7D2sPBD13xZ3IMCsp9ojOscomWtptpihJcRqSR+4iuOJ5iPTcjXKWZTfgWYx0oK4I1v2WHW/9EQ3ItlSQdvwDQE9phFgU2mwaxbUtPk/T0q56NTEzLuJFNc2oQQg2504agKgwR5jYOTriXsdizKQZl95RjIBTqiaAItZ2m2qKFq+REVV/vvoG/261AJoGpdhrRsad5vLYcDeHV4mMCD2GxQqzb++wORO3yAhATHqH/YYaMptG8IthBe88dbeDGPGQw883IiNKMcaEXI5u1CMQbhhFrJ/sK+HDvZ7vEoKdu+KJ7KRIyutbOFbVaF6EQ61KR6v63EUw4RK9uGzzcmiuNh86y7ITgC/UibRoIYQr/oe4faWNA2A6e+G1Z+CK57HmLiIrIZKCykYUVE73M9PCm4lZRnwEiqKnRioaWs3fjT+ch+TpPwcLYSEWWttVGlptJER5rmMx8BQZAb2IdV9xHaV+BJb+mlpQNf134Dw12US1EVN7ABhvTtn1RxWxpvtqalzHSdHOiBgRepSz79ZrQpzmZpmRES0JvdMrS6ZGI1N7hQBwNjwz6FAzsn9Vh+OOuIgRO17CkUao3ubjxj7YuSuecC5iNYRUSky450JLw2L+F4f1uTd2xinHSaOKZsL5Sh0X0PMa+023HNA32KNERrvxr0JeNC2jXwl7lK/Cb+I26xuk2LtBzlF2cFL9No+RpVCrhXR7947RJhsIzkPyDAyvkcaWdq91LAabD1d43J5urxsJJE1j1ASlx0W4dAuZHN1IXLv+QV6nBdZRVRI9HtBFVliI60ecsxgJD7EQGTa0iwaFHsZihYVPuWxydNPYIyPzHxvyxasgYkTwQ1OrjRL7He5IDzUj5XUt+gVy56sux9Vo0VSh3zm7iBEP4UibqvG7NfsDWk8wc1c8YXqNVDWabbN+IwmGKLniBYhMRFHgTHuLbyCpGpumsEM9CYBTLd/gHCXKRh/gV4fbHbtSz12hbzDRotdfXRqykUkf/gB+P8a19ka1Qf5nZNqtzk9UNRAozkPyDIy6kbpm78PyDLyJwowg2nsLq+0pGqODSrXBoXXw8aPw0aNweB2xiv7a6vEhRs76ucO1d9FLAKR5+L06z76RqIjQK+Qu0j874rIAR2SknkhqL3veMfBziCNpGsEnBfY22PjIUBe3SqPGoqyuBe3TJ1AaXe+SjRRNGlVEK/boSVSKx3Ckv8Fvngh0Pos7Rs2A3pbsiIwEhJG6yf+Ms955nTdL4TP1FO7hVZ+HfaMNp44oomlivOJk4FdXxPCi9cACjmtpHo+ttI+6T0Svm6CpCl67Rv9wA71Op/YEWa0/YzuzOLHyIQj5VkAfcO41I+DoqPnqaJXf34khCmeNcfULSrfXsJQGEhkx23rDYd3jsPFP0OoqqGK4GoA6zTXlUq1F8/9aH2aWZQ+/HX2Omf4r2ar/jA3PE2eca0akeFXoNYzPjqMbiaovIf51qGmB4szzEBctHYmMCD5x2MC7XgiMaEKrTaV23Z86HucpRXPKFR7DkZ0RFoHOZ3HHOU1jRkYCFSOgr3/Mucz5kW5UtEfLoULzXDthsEMdA8AUyyFCFKculYYyslsP6etRUz0eW2U/d5JS5/rAytt0UWKv0xlmtAs2hfrtXDIob3CtGQFHZKSkC8P4Ao6MqDaKjh0GIDPvWVj32w5CBDAjI7VuNSNfqBPJ1zJ52XY+xQmnmtsNkekxMpIokRGhj3AadZGZqP9dB5NWHeyIGBG8YlM11h/Q0wjR4SEuIfmIUKvp2WAMm3Mm3+iksTiJkfEdjcAgOGERzNwVT2SbFuxNlBqRkdjgL0ppsRFMyIhFw8Krk/7GwTGL0fDsB1qo6UJjtGJ0Aun25ESnMlzRf77HNc9ipNKe6krCTYw0V7l828G7wEfnknlupyF5BkbNSErVDs6w5BFCO7Msu7kr5DXutLxGCK7Fup5+d6YLa42HAlZ7WonV98ETYynM0/0VslTvXVKx6B/Y7pGRfE0vYtaw8Od1h81uH6OLx1NkJDEq1OwaSoyWyIjQNxgdcMGMTRjsSJpG8Ih7F8XGQxWc+fjHLFmYa3aypIbbqGvW3S5PwrWTpkNkJG6Y14pxY/BbcU2zzxqFYOaueCMrIRKLorfK7ivSL/BBRUacyE6MZF9xHb/bBr9jPhdZkng47AXScU1ZFdvbTDOUSsermP8YRCaSrZQCUEQybZqVUMUhIJq0MJrR15boHhlxf10uYsR35xJAm02l2j651oyM5K0k6theYDJx+/7LK2EfY9MUrIr+WynVEvhjyxVYULnJ8g7vxFzBzJx4XVzUl+j1QDmzTRFQ0dBCW1sbocc36y3Oh9bBgf+5uFIaRXzG+j0Ri+eakfyQ0Rja6KUvCnjpC72+JtSq/4wbWtqxqa5GcIqiMCwhkm9K62VIntBnZJreQCJGDESMCB0wuijchYFLa63lS1IbDnGYcebkW2ecxYgGKD4qxo3Bbze/uM0cxOaJjPgIFzHUGUKtFjLjIymsbmJnYTUAKQG2wjqzencRa/eWumxbo87kw+YZnGbZx31nJjAlqhK2raC4XI/ipFOlF7HNf0zPIas2UuOiCS9rpYUwirRkRiiOcxpRkTDaiMb3h9YwRR8W5+Jd4MNIyZjNoij2dIXdsC66/WYAGtEFhcXpt7Ff1R1nRyrF/CLsv9ylrsL6hzCXtkXiski+6HFCLCG0qxply84iq2Gv13UUafrPJtOXGFGMyEikXqiaNgFi0vnqTRs0d0zrtNlbsv698Qir9xR3eM8MT9TFiFjBC32FMdOpSNI0JpKmEVywqZrXLgpj27q3n0V77RpSVf0CUu4hTXNE07tmRirFPNn2HVarp3XYxxlvg9mSokO5Yc5IXv7RGWy45/wuCREDo26guU2v3wg2MmL8jDw+hoUv1Fxu+no0trN/ge22XRyNOgWAlhk3Ybttp6O41GJFWfC4mao55paqqXIqXnXuPNY8/HKMyEIZibRo9nsMH0ZKRidNYlQYVlTTsC5K0UVPgz0i4/y8+7URgN7aDBDS3uAqRABqi7D8dzFpofp5iuu8W8I3a6FU2IVsIJGROqJg9Dlw8new5ZzJ4XL/nUNFdgHtbJY3Y6QugCZneZ6sKgg9TYa9eyyYgZKDHYmMCC7462xRUPlF23JQIFWpBhzW2wZVWgw16LNmwmllue0y0t7NY25uhs/0irfBbJ1NyXgjOzHKpTU42MiIv5+R0X789McHeeXLAop0R3t+tRn+svdT1zv13EVkZ73HocKOYsTspHFK0Wiafv4aYoinAcUuEROpIxw9wlKsJZMTH+LTSMmlrdfJsM6IwDRqHestCu1RlxznomSPr14hvbWAE4w1Z8R4wkjRRNFMPN6Fhdnaq8SYr2nd/lKCsZp56N08zp+QzldHqxiWEMFfrjqVeZMyAj+BIHQjRmSkQwGrfcioc9pzqHiQiBgRXPDX2XKr9W2SFP3q6hAjrneYRltvBhU83v59bFi8toG6Ywxm60mMIlaDgFt77QTa/fPHDw902ObJRTY7eyQUHuX4iMugaodZU2H4tDh30lQRw31tNwLw17A/gT2xpSh6quawlsUJLZmc+ff5/BAzh+TFhEF9obk9Cn17Ax3FSIWmNyGmKrUdHnNF0+tjNPyIEUeKxtdw3xijgNWaYL6mvCJ/a3BejS4Oz1j6kVm0C3oRYVfTfoLQGTKcRjiY063zVpqt+iZxWTD/8SHhRSJpGsEFX50tFlSuD1ltfp+KPtSujASX/Yx6kRZCWaPONLd31hsEOs5H6crQvGwnr4mwEAtxEcFp8s62FYNnF1nDFfRY3FT4+WE2zFnBba0/5Y/t3wagXIvjqbbL+H7r/cxo+Str1JmsUWfy5cxlEOe4kJpFrDPv9/vh5TIkzymdE614j4xU2h0RkvyKEUhX9PRNsea966lQS3FZtzdiI3WxWN+umLN3Wtq8D/LzhrMQAYcw7Mq8I0HoDJn2NE1jq43a5vYOQ0ZNaosCbtUf6EhkRHDBV2fLTMs+Eu1REfAeGdlqtz6vcrPz6exF3NN8lK7c1RrTckGvF/FoBe+DQLt/vOHsIjtrTLK5nmOVjWCxYh19Nis/cnR6HNBG8KRtRIfz2MYvhPnXmGHdzK1xsL+NE1ET/K7BxfAsZ4p+B1ZbRBSuNSPOlNsjI8kELkZ8Rkbw0UkTFgNjLoDTbiB22CxYshZNg4bWdmIjQumOzJ2eUNKFob8UoiB0J5FhVhKjQqlqbKOoqoF4tyGjDuzv0tX36qZpgzhlI5ERwQWjs8UTF1q2unyfqtgjI041IzZNYbVtpst+XfEG8TYfpSt3tc7zSTrTSePrZxTM5cyIFJlGbFV6OsIQO95w+Xk6GSllDR8JwIka/xX6Fc6GZxarHgoG0y230UeaJtn+e/eOQoZdqJbgXYwYnT9GJ01zWCKccQv88D24twCufB5Gn0NEeBhhVv2jqq5Z7+U1hjfqz9Z5ujpeQBA6i1HEWvTNto4RERecWvUHMSJGhA7Mn5zJ8qunuXzIX2TZwg1OKRpwiJFK4rBp+t5btfFmOB+65g0SSGdPZ4bmpcdFmF4UqTGd85owu3/iXMVMRnwEd144NqBzGJEio4alrK6F5jZbQGLH08/TmLtyotp/OsxM0xj1MrmL4IrniYrSz9Fgpmn051A1xaxhSfbpeaLvnz75HMB3msYQIwdtWXyv9Vds/+4WmL9UF1dud4AxEY6ZOQD59k6am84Z3aEDqzN0JYUoCJ3BbO+t8Cfu7XgYRjqYEDEieGTysAQ0IMSi8IfvTOKphFc67JNELQoqKhYqiEMD3rbNcdknIz7CpVgzGALtWgn2rtZqUcwLt98heT6YPzmTz++9wLQ///UlE9lwz/n89PyxZMZHeL1jd48UxUeGEhOuX2yf33SETYcqmJubwdi0mA7H+vp5ZpliJJDISMcheeQuIvryvwDQGH+SHqH4VSksXkntuO/Qbs/qJtnTNFpkEkS6RT7isuCK50k/X/crKcGzGKnSYtitjgLgPW02R2NPZeYYzy60gOn2W9fchqZpphj5zvThbLjnfF7+0RlcNjWrw3FJAbqsdqUOSBA6Q2aC3YW1vePfuUc2Lx/UtSNSMyJ4ZM8J/YIzPiOWy5OPQWPHds4QRSWZOsqJp0xLIIVaPgk/HxrhR2eN4vwJ6V1qzQ30brUzd7XZSVEcqWgMupPGHatFYWx6DMW1zcRHhZmv1TBxc8dTZGPNnmKa23Tn1d+u2gfotuwNrfq2Ry+bTGxEiN9WZ+PD7UR1k6NC3wuVnsQIEBWhf99giXa4t44+h7eLRsCuPKzY+HnbTZSSwLGwKfx6YS7zY/I7tCJmtOgRjAYtgrrvv8vhg3t5Z+NOKrU4ikniC3UCmtO9kL/ImSlGWtopq2+hvqUdi6L/Ho0OrDNGJ7HnRC3flNbz3enD+fapw5mek8g5v//Ea32Pgi7wOjteQBA6i1HEeoJUe82Wr1QNDPbaEYmMCB4xWidzM+N8OnmmOBWx7sj9BcWNCtFhVv5v3nhmjUnuUlFgoHernbmrnWk3vpqanRD0se4YUZbjVY46BiONY6SDDNwjG0ZNTLtbqskQIhefnMEPzsjh0qnD/P48s+wfbg1Ghb4PjCGByW5pqmj7oLzGFoct/erdRTxoN3mzYWWlOpvNai4natu4+aWvWd1wEpz8HZf0SnR4CLH2aE9J4qlMueQnzPz+r/gi9kI2q7kuQuSp7031GzmLDdcjHHXN7Rwu06MiwxOjCA9xfCgrisJjl5/Md6cP59cLc5k1JpmwEIuZ8nL/yXXHeAFB6CxGXVhRbbNZs+WbwV07IpERwSN59sjIpKw4n06eqUoN+zS9iHWj7TSglQsmphMR2nXl7q9rxd9drU3VvBqo/fT8k/j+6SO6HBkBhxgprHJNj8yfnEli1B5K61q4e944puckuazBV02MwfaC6g7zVbwRGWYlKTqMyoZWTlQ3ER/pOUXR2q6atRfJ0a6v3xgi19Da7rJGT/jrRkmPj6CutJ6S2mZOSotxMbXbcayKx1fvJzEqlEVTh/n8XYFzzUgbDfaoy6iU6A5rmp6TxPQc1/eDIQzdO7K6Y7yAIHQWZ68Rchfpxdubl/s9Tq05MSijCCJGBI/sNSIjWfGQM8Js/XRvP0ulGoDS8BGsOqZfyBZM7h5nS18za/zd1fprB1YUpVuECMBwp0nAzrTZVMrsEYgrTsvuEMHxVxMD+gfVH9ceYM5JKQGlvDLjI0wxMjHTUUjc2q6y9UglH+8r5eP9+vwbq0XpIFii7dGM5jbVFAiB1u24m9Wlx4VzsLTeZTKpkVJpamu3rzcyoNZtI02zp7CW4lr95zwyuaMY8UZvufsKQqAYkcyiarvx2fiLAxIj1W/fzdGSZqZd9MOeXmKvMhgFltBFqhtbKbQXQU5o2Q173oJTr8VxL+zA6Kj5NGYBx6uaiAy1cu74tG5bi7eZNb4KOXuiHdgXwxL01txCt8LRsroWNE0vAk6J7ih8Aq11efqTg3z/H5s58/GP/a7dvYhVVTWWrzvI9EfWctU/v+CfG/I5XNZAiEXhmjNysLhdjI3ICEBja3uX6naM6b0lHh4zOn5CLIrH31VRTTM3vbiNVTv1PHqVvcblP1sK+HifPsvnre3Hg/pdGkIokJSXIPQ0xmdaU5uNmqY2yJmNFpeF5qdZPUGrZcrG29i+5rneWGavIZERoQNGvcgISzlxr1zleCAyCdBchqOlRmpQD1tK9D+gc8enEhnWvcVVwdzV+msH7gmTK8O35ER1k0tKxRiClR4X0eGiD8HXuniykndnmNNo8qqGVu56bQef7Ncv3snRYZw7Po3zJ6Rx1rgU4iI6pnHCQyxYLQo2VaOx1daluh2jy6jEQ2SlyO6FcrCs3mea6qcvb+eGY9Xma3Cmtrnd789DEPorEaGOtGpRTTObDzewrvEH/Fb7HRq4GPuVagnE0UCE0oZFAVWDzE0PYbvgaqwhg+MyPjhehdCt5G3fBFjI5bDrA4YIOfd+SB4DMemkVo+EV3eauyw4uWcuCoHOrOlKWqGzpMdFEGJRaFc1SuuazSp54yKcHuc5HRSsk2sgYirL3lGz8WA5K3ecoLC6ifAQCw9fOonvTs/2KIqcURSFqDArdc3tNLS0m2v09jP1VbdjREY8TSY1IiONrbYOjzmjavCPz/J97iMOqsJAxUirvvf1CZavO4TGVKosd/Db0H8RqrXzrm0Wr9nO5WvtJC60fMU/w/4A6EIlgwr2fLGGSXMu6eNX0T1ImkZwRbWRt1tvSc21HHV70H7J3PYcTPp/MOosUuMcbqZhIRbOn9B9KZrO0JPtwN6wWhSzrda5iNW4gBvixNNx3jo9vOHPW8V4rq+P11BY3cTI5CjeumUOV542wq8QMTA7alo7b8AGTmma2pYOjwXihRII4qAqDGSMjpoXNh81b0jWqDO5tOURZrYs55ftN/K1dhIA69VTaNNco85NVYUMFkSMCK4c3Uheiy4ochV3MQLu7WVpTqZhZ49NNc27+oqebAf2haO913GRLXFK03jDW02MP7yJKee5OwsmZ7DyZ2eSmxXncV9vRIXbO2rsXSvzJ2eabpHO+DO0M15TiYfIiL/C3WARB1VhIGLcPLi34h8njWbCGasc51chLxJDI62Eclhz/VuLTBzWa2vtaSRNI7jQXFPCQU13ssy1HPG+o917xLkjpbu6aLpCV9uBO8vwxCig0qWI1UhPZMT77tpxron5/GAZT39yyO/zeRNTpwyL56fnnUR2UiRXzMgOeggguEZGDFra9Sm5j337ZCLDrAF1oxjpqdK6FpdaGlXVzJqR1Nhwyuo6Rk6CRRxUhYGIEVHtiMY/Qp/gfGU7Vgustp3GVm08e7UcxnMcVYNSJZkJp1/Uq+vtSSQyIrhwsDWFdkJIoI5MfIS+7d4j8ZGhjE6NJiUmnAsnevcj6S18pT560uTKk/GZcfef4SVN44xRE3Pn3PFBWcm7Y7Eo3H3ReK48bUSnhAh49hqpbNS7Wc6fmBZwN0pqTDgWRT/eGMwHUN7QQptNQ1HgQS8poEDpyhBGQehrvA/EVHjddg6KvVjVSJnnqTkY/ohFs5YMmuJVEDEiuJGHPi8k13IUz9cyBeKG6bbf6AWP79w6hw/uPJv4qMDmgPQ0nWkH7irDEr2naTJ8pGnc6Ssx5YzhNWK4sFY3tqLZPwCTogIfLBhitZiRs5IahxgxilfTYyO45JQsll81jc68HHFQFQY6c8akMCkrjojQjpfiNepMbm67g2KSmGhPme/VRlCqJPP17KcGnc/I4JFVQreQV1wPwCTlKHizGpv/mMtshFgPLaJ9TW+bXBntvUYBq6ZpptlXMGIE+t4x1D0yYgzVS4gKJcQa3P1LRnwEpXUtFNc2czLxAByt0O3cjRD1xadk8TQKt/zH+yyfq2Zm89KWYx3OLQ6qwkAmLS6C/912lumNBK6fuB+oM1nbMoOfTmyEvbAz5BRS7ssj48SXsOt1l3lQAx0RI4ILhg187qwFcOAT1+FNcVm6EMld1EerC45A24G7g+FOxmeaplHd2GbWWaR5ae31RV86hrrXjJhzbKIDj4oY6LUcNWb9jE3V+Ounesv49BGOib8Xn5LJXy3eBdick1JcxMjffjCdC3PTJSIiDAr83YCcOz6Npx9YTU0rVD51NmkN+x0Hx2Xps20GyOeyN0SMCCaqqjkG5M04Fy7erXfNuE1kFTqSER+BRdELPcvqW6io16MJSdFhnZ7T05tiyhn3bhpzwm8n7PON4t1Suxh5besx9hbVEhcRwi3nneSyry8Bpqp6jYmmQVxECPMmpXe6JkYQ+iP+bkBGx2kcrFHYUxtBmvNHSm0RvLYYrnh+QAsSESOCybGqRupb2gkLsTA6NRosFscYecEnYSEW0uN0c7DCqiaqm9qA4FM0/QH3yIghrDoTGTFef3FNM7XNbTyxRr+ju/3CcSR5OJ83AWaxKMSEh1DX3M6o1BgRIsKgxOsNiGpjYvMODjKNvdoIzuNrpwftdoir74UJlwzYG0YpYBVMjBTN+PRYQoOsDRCc6kaqm0z31WD9Q/oD7pGRCiNNExO8GEm1+9DsKqzh/jd3UdHQyujUaBbPygn6XLH2wtrRHqb1CsKg5uhGcm37AMhTR3rYQfd/sh35vFeX1Z3IFUcw2WPUi2QGZ5Il6DgbnxWZVvADT4x0iIwYaRoPw/58sXp3EY+/r3+A7iuu472d+lC7BZMzOiV2jULpUSJGhKFGfYlLR403HvqP/2Ga/RURI4LJZwfLAZiSndC3Cxmg6MZnekeN0dbr3Ueg/9Khm8ZI0wQRGTG6Ayob2zo89pdPDnXqAzMlVn/+cekxQR8rCAOamHRyLQUA5GuZNGme/xYPNEb3yGTy3qBTYmT58uWMGjWKiIgIpk+fzmeffeZz/5deeokpU6YQFRVFZmYm1113HRUVFZ1asNCRw2X1vLKlAFX1Pm6tsqGVVbuKvO5zorqJr49VoyhwYW7fzpcZqDi8Rhod7qsDMTLi5jNSGWRkxNfkZHAM+7P5eL964v6LJ3Lvggn9wlxPEHqVnNmkxkWRQg0qFvZr2S4PaxqUa3FsVccBnfv76muCFiOvvvoqd9xxB7/85S/Zvn07Z511FgsWLKCgoMDj/hs2bGDx4sXccMMN7Nmzh//+9798+eWX3HjjjV1evKBz/1u7uPfNXbzy5TGv+/z8v19zy0vbeG7TEY+Pr9lTDMCMnMQuW2vbVI1Nhyp4Z0chmw5VDLg/is5ipGkKq5tMj5H0QRAZKbe7p3oqOPVEMJOTg2FSVjw3nTMmaK8TQRjwWKwoCx5noj06sld1TdUoCqQotawPv4N5li0Dcnhk0H/VTz75JDfccAM33ngjEydOZNmyZWRnZ/PMM8943H/z5s2MHDmS2267jVGjRnHmmWfyk5/8hK1bt3Z58QK02VS2F1QD8MqXngXh8apGPt5fCsB/vihA0zqKg9W7dTFy0aSuzZdZvbuIMx//mO//YzO3v7KD7/9jM2c+PnDzmMEw3MmFtXgAp2nMyIhbN01KgGmavpicLAiDntxF5E6cBECe5rkAPINKngldxkWWLXyRX8GPn9/qMi+rPxOUGGltbeWrr75i3rx5LtvnzZvHxo0bPR4ze/Zsjh8/zqpVq9A0jZKSEl5//XUuueQSr8/T0tJCbW2ty5fgmf3Fdaa51s7jNew5UdNhn9e2HjftvL8prWebXbwYlNe38OURXUXP78KwO6NOwP2uuLimecDmMYMhyx4ZaWy1UW2vlRiIBaxmZKSlnTabSo29TTlQn5G+mpwsCIOdiZNPBWCnOhpPAWfDA3BJ6At8vLeED/JK+Pun/gdv9geCEiPl5eXYbDbS011ztunp6RQXF3s8Zvbs2bz00ktceeWVhIWFkZGRQUJCAn/+85+9Ps/SpUuJj483v7Kzs73uO9TZedxVfLzmlqqxqRr/3apvM+7SX3WLoKzNK0HV4ORh8WYRZrD4qhMwtg3EPGYwRIRazVZWgMhQK3ERA8/Kx7mbpspeL2JRICEyMNt/Y3JyZ4f9CYLgmdwsvdPxoDaMjtOrdCwKpFPJ4VL9Jv6jfaUeo+H9jU4lX90NhzRN82pClJeXx2233cYDDzzAV199xerVq8nPz+emm27yev777ruPmpoa8+vYMe+1EEOdr49VAzBluD73463thTS3OUa/rz9QRlFNMwlRofz+O1MAePfrIuqaHV0ORoom2KiIc23Iis/ze6ROYKBh1I2AfsEdiOZcps9Iaztl9Y56EUuA1uv9YdifIAxGRqdEE2bRaCCSY1qq1/32a9nU2z/ij1c1cbC0vpdW2HmCEiMpKSlYrdYOUZDS0tIO0RKDpUuXMmfOHH7+859zyimncNFFF7F8+XKeffZZioo8h+3Dw8OJi4tz+RI88/XxagBuPncMwxIiqW1uN8UFwMtb9CjIt6cNZ85JyYxOjaapzWZ6PtQ0tbHxkN7SG0y9iHttyCP/2xvQcYO9TsCoG4GBmaIBR2RE0xwTdoP1GOmLycmCMNgJsVoYn6TfLHirGwH4yt5VY/DRvtIeXVd3EJQYCQsLY/r06axdu9Zl+9q1a5k9e7bHYxobG7FYXJ/GatV/mAMhdNSfaWxt50BJHQDTRiTy3enDAXj6k4NsOlRBUXWT+Sb83sxsFEXhe6fpKS+j8+bjfSW02TTGpsVwUlpg/g3eakMCYbDXCWQ5RUasFmVApqUinWbpFFQ2AoF30jgzf3ImG+45n5d/dAZ/+t5UXv7RGWy453wRIoLQBSaM0P9+8lTPYkTVYL16CuCoIfl47yATIwB33XUX//znP3n22WfZu3cvd955JwUFBWba5b777mPx4sXm/gsXLuTNN9/kmWee4fDhw3z++efcdtttzJw5k6ysrO57JUOQPSdqUTVIjwtne0EV/7FHQQ6W1vP9f2zmvCfWYVM1po1IYFx6LADfPnU4IRaFr49Vs7eoNugUjT8PCW8MhTqB1buLeGWLox5nw8HyAdlJZLEoZhHrMbsY6YwVPDhmbVw6dRizxiRLakYQusDq3UWsySsB9MiI+72O8f1n6sku3289Wkl1Y2tvLbNTBC1GrrzySpYtW8bDDz/M1KlTWb9+PatWrSInR1dpRUVFLp4j1157LU8++SRPP/00kydP5rvf/S7jx4/nzTff7L5XMUQx6kUy4iO4+cVtlNa1uDzebO+y2VdcZ14QU2LCmZurp9RWfH6ETw+UAYGnaPx5SHhiKNQJGNGi2uZ2l+0DtZMoyp6qMcRISicm9gqC0H24f8Z8rk6mGNebu2KSubb1FzTj+veqavDJ/rJeW2tnULQBkCupra0lPj6empoaqR9x4mcvb+fdr08QGx5CXUu73/3/as/Vr9tfyrX//tLcnp0UyfqfnxdQseU7Owq5/ZUdQa0zMz6CJQtzB2143qZqnPn4x15FmoIuGDfcc/6AEWPn/P4TjlY0MjYthm9K67lr7jhuu2BsXy9LEIYk3j5jFFROt+wjjWpKSWCLOgHVS4xhzphkXvrRGb2xXBcCvX4PvL5DwcSIjAQiREBvrZ2bm8FZY1PJio/ghP2NPX9SRsBdH4HWfPz6komkxIaTFqunZgbKRbgzBOM46nE8eD/EjIxUdS1NIwhC1/H2GaNhYbOaa35vQSWdSkpIIoMKSkk0xcn2Y9W021TTwdimamzJr6S0rrlffE6LGBmgVDa0msWFgeJ8QfzujGz+9NE3QHAtvYaHRHFNs8e6ESMKcO2cUYNagDgzGB1Ho+01I81teqov2G4aQRC6j0A+Oy6ybGFJ6PPc0Ho3JVoSD4S+wFTLQZa0LmatNpPGVhvbj1Vz2sgkVu8u4qF381wETl9HsGXIwwBlp72l15PduIKKFRspVHOGJQ8LqvmY8aa+4rRsYsJDGJMazbTsxICfVzwkOjIYHUejwl3vUyQyIgh9h7/PjossW3gmdBlRWhP7NH1uzQzLATKo5G9hy8gJ0f2dPtpb2m+dskWMDFC+PqY7r55uj1QYXGTZwufht7Et/Cd8Hn4br4Q9yobw27jIsgVwvKmHJUTy4V3n8MbNswM2szIQDwlXBqPjqBEZMUjuRGuvM0N1eKIgdAe+PmMUVJaEPg/A19pYNCyMUEpIU6rN1t6fhf8P0K0c+qtTtqRpBihGZGRKdgLzJ2dw84vbmGdXx+DoLwfH8KT7Q3/BzFEXO7Z3YYjb/MmZzM3N6Fc5x77CiBbd/OI2FHD5Qx+o0SKjZsQg0Lk0nuiPIWFBGEj4+owJo510qrAosFUdD8AM5YD5uEWBC9vXY1Wu4UCJbyfWvqxvk8jIAETTNNN5VRcjmTxz9RQeCtPVsfs1zzE86XmsTimbriIeEg4GW7QoOtwRGQm1Kp2esdNfQ8KCMNDw9hnTQhgfq9MA2KrpzqszLPtd9klQGpieYiNQ+qK+TSIjAwD3qufhiZGU17cSYlHIzdRbpeZXvARUepudhEWByKZiOLoRRp3Ve4sfQgymaJFzZCQpOqxTM3b8DU9UcHR4DcSfkSD0Nu6fMWvzSnhvZxH/ts3nXMvXbFdPAuA0NzECcP7oKLaUtXTY7om+qG8TMdLP8RTiTojSp6dOyIwlItQKeSth3W8DO2F9SU8sU7BjRIsGOs41I0md7KQZjC3PgtDXOH/GzBiZxPu7i9moTuZN21k0E0489YxRTjgdoUBcFuefMYPHvvjc57mNbsi+qG+TNE0/xluIu7pRH8eYGBUGqg1W3xP4SWM8DzQUBGecu2lSOtlJMxhbngWhPzEsIZKLJumf6Y+2/wDQu2gsihGPtEcc5z/GmPR4wqyOS35/64YUMdJPCWQGzM7j1diOfA61J3zs5UTcMMjxPNBQEJxxjox0tpNmMLY8C0J/4/o5owCoIwqA6c4pmrgsuOJ5yF2E1aIwPEkf5HnHBSf1u/o2SdP0UwKZAVPT1M6hw4cY53MvJ+Y/Bhar//2EIY9zZKSzaZpADfIGUsuzIPQ3puckcvKweHYV6nYPp118A8RepkfBc2a7fOaPSIricFkD6fGRbLjn/H5V3yZipJ8ScIhbSwhMjJx7P+Qu6tKahKGDS2TER5rGl6X0YGx5FoT+hqIoXDdnJHe99jVhVgsnn3Y2hHq+6cxJ0qMnRysa+119m4iRfkqgoWvryDmwKwtqi8BbUiduGJx9d/ctThj0OHfTeKsZCcQ/xGhHdN8vQ3xGBKHbWDgli53HaxiTFqM3NXhhRHI0AAWVDb21tIARMdJP8RfiBrur55hUmP84vLYYvN1/SnpGCBJnnxFPaRqjuNr9vWn4hzjnngdTy7Mg9EdCrRYeXDTJ734j7JGRYOea9QZSwNpP8TUDxsAMcecu0ouU4tzuMp2KlwQhGJwjI+5pGn/+IdDRUloM8gSh78lJdqRpNK1/jWSQyEg/xluIOzrMyh+umOIa4s5dBBMu0U3N6ks8Fi8JQqA4R0ZS3CIj4h8iCAOT7ERdjNQ1t1Pd2EZiF2dOdSciRvo5Roh71a4ibntlO5oGb986h7HpsR13tljFXVXoFmLCvUdGxD9EEAYmkWFW0mLDKa1roaCyUcSIEBxWi8I3JXVoGswanexZiAhCNxIbEcrd88YRYrUQHe76MSH+IYIwcMlJjqK0roWjlY1MyU7o6+WYiBgZALTZVF758hgAV58xoo9XIwwVfnr+WI/bxT9EEAYu2UlRfHmkioKK/tVRIwWsA4CP9pZSWtdCSkwY83Iz+no5whDHV3G1+IcIQj9DtUH+Z7Drdcj/jJxE3YW1v3XUSGRkAPCfL44C8N0RDYQd+1wKU4U+R/xDBGEAkLcSbfU9KE4jQ0aEXQJczdEKESOCDyrqWwgNsRAXoU/mLfhiJeu/0YXH9w/+HA6X6i278x+Xll2hTxH/EEHox+StRHttMRqaSwQzu/kAAAUlFX2zLi+IGOlHvLOjkDtf3YGqQWxECMMi21CrTwDZnGXZyQhLqb5jbZFuciYeIkIf098spQVBAFQbTe/+nHBNw/3eYKRSAkBxo0ZzSysR4f2jo0bESB/hPtPDalH4+X93YvhE1TW3s69ZAbIB+IH1Q6ejNUCB1ffq3iKSshEEQRDs2I58TmRTsUfHzGRqiaaJBiIp2PM54049r/cX6AERI32Ap5keFgVUDebmpvPkFVMozvuc4289QKGWQpTSwjzLVrezaFBbqJucibeIIAiCYMfXNHdFgWyllH1aDlsOnGDcqb26NK+IGOllvM30MCIi3zolg9iIUGJDyxlr/dr/CetLun2NgiAIwsDF3zT3HKWEfVoOBxpjem1N/pDW3l7E10wPg8fe36/P9IhJD+ykge4nCIIgDAmsI+dwQktC9XKxGaHo9YelocN6cVW+ETHSi/ib6QFQUtPIvk2roK4IolLwPiZPgbhhepuvIAiCINiZOSaVp0JvBOggSFRNT9MAtNn6z7A8SdP0Iv5mdVxk2cKS0OfJWlvp50x2gTL/MSleFQRBEFywWhTOvex6bvlPKw+EPk8WjmtKMcmstOk3sf3J+EzESC/ia1bHRZYtPBO6LLATxWXpQkTaegVBEAQPzJ+cCVfdxHdXziG7/mvSqKaUBI7FTOEn88ey9Z08CiobUVUNSz/wBhIx0ot4m+lhQWVJ6PP6/729J6JSYP5SiM0UB1ZBEATBLw5jwukuxoSqpvHQu3tpaVcpq28hPa7vh1pKzUgv4jzTw5mZln1kKZXehQhAY7kuREadJUJEEARBCAjDmPDSqcOYNSYZq0Uh1GohK0EXIP3FFl7ESC9jzPSIDHX86NOoDuxgaeMVBEEQuoERSVEAHO0n03tFjPQB8ydnMiZN7+++/syR/OSSADtipI1XEARB6AZGJEUDcKyfFLGKGOkDVFXjYGk9ANecMZJJs+brRanSxisIgiD0MLb2diLqCgDYuf8gtvb2Pl6RiJE+4VhVI81tKuEhFj1UZrHqU3iBjoJE2ngFQRCE7mH7mucof3Qcpx1cBkD1iW8of3Qc29c816fr6pQYWb58OaNGjSIiIoLp06fz2Wef+dy/paWFX/7yl+Tk5BAeHs6YMWN49tlnO7Xg7samamw6VME7OwrZdKhCdz/tYQ6U6FGRMakxjnHruYv0Kbxxma47x2XJdF5BEAShy2xf8xxTNt5GqlbBCPv03mNaGqlaBVM23tangiTo1t5XX32VO+64g+XLlzNnzhz+9re/sWDBAvLy8hgxYoTHY6644gpKSkr417/+xUknnURpaSnt/SAs5GlgXWZ8BEsW5uo92j3EgZI6AMZnxLo+kLtIn8J7dKNerBqTLm28giAIQpextbeTtekhQLeQGIHuwlpBPI1EEE0zIzf9EtsFV2MN6X3Xj6AjI08++SQ33HADN954IxMnTmTZsmVkZ2fzzDPPeNx/9erVfPrpp6xatYoLL7yQkSNHMnPmTGbP7tv6B2Ngnbs9e3FNMze/uI3Vu4t67LkNMTI2tBx2vQ75n4Fq0x+0WPX23ZO/I228giAIQrew74s1pFNhWkjEKU0kol+LjmrpKAokUseW5+7vk/UFJUZaW1v56quvmDdvnsv2efPmsXHjRo/HrFy5khkzZvC73/2OYcOGMW7cOO6++26ampq8Pk9LSwu1tbUuX92Jr4F1xraH3s3rsZTNgaOFAIzb/ht44wZ47luwbDLkreyR5xMEQRCGNk1VhR22OadqDCYce6lPClqDEiPl5eXYbDbS011bTNPT0ykuLvZ4zOHDh9mwYQO7d+/mrbfeYtmyZbz++uvceuutXp9n6dKlxMfHm1/Z2dnBLNMv/gbWaUBRTTNb8v3NiAme9t0rOVSl/6LHK8ccD9QWwWuLRZAIgiAI3U5kYscJvcb03qOa45qeSD37vljTa+sy6FQBq6K4dnxomtZhm4GqqiiKwksvvcTMmTO5+OKLefLJJ1mxYoXX6Mh9991HTU2N+XXs2DGP+3UWfwPrgt0vYFQbR1c9QSuhRNLMMKXc6UF7FGb1vY6UjSAIgiB0AxNOv4hqol225dgjI0edIiMA4YdW9dq6DIISIykpKVit1g5RkNLS0g7REoPMzEyGDRtGfHy8uW3ixIlomsbx48c9HhMeHk5cXJzLV3fia2BdZ/YLmKMb+aYuDICxSiEWxT0NpEFtoV7AKgiCIAjdhDUkhOOp57tsuzrkIz4Mu5sHQl5w2T7m8Iu9HqUPSoyEhYUxffp01q5d67J97dq1XgtS58yZw4kTJ6ivrze3HThwAIvFwvDhwzux5K5jDKzzYTFGZrw+UKhbqS9hv6a/5nEWz0IM4MChg73aaiwIgiAMfnLnLHT5PlOp5CTLCSKUto4793KUPug0zV133cU///lPnn32Wfbu3cudd95JQUEBN910E6CnWBYvXmzuf9VVV5GcnMx1111HXl4e69ev5+c//znXX389kZGR3fdKgsB5YJ0XizGWLMx1eIB0FzHpHFDtYkTxLkYe+Lic21/Zwff/sZkzH/+4Rzt7BEEQhKGBJT4roP0U6PUofdBi5Morr2TZsmU8/PDDTJ06lfXr17Nq1SpycnIAKCoqoqCgwNw/JiaGtWvXUl1dzYwZM7j66qtZuHAhTz31VPe9ik5gDKzLiHdNxWTER/DMD07tGZ+RnNl8o4wCYKwHMaJqcEJLZos6wdzWG63GgiAIwhAgZzbEZXnsJPVILw5nVTRN6/d5gNraWuLj46mpqen2+hGbqrElv5LSumbSYvXUjK+IiKpqXP/cl7TbNFZcdxoh1sD1XGu7Su6vV9GuKXwefptLAasKoMHNbXewRp3pcpyCLpI23HN+90drBEEQhKFD3kp47ZrA9v3he7rfVRcI9Po95GfTWC0Ks8Ykc+nUYcwak+z3Yn+orJ51+8vYcLCcD/KCU41HKhpo1xRiQjWy4sJcHivWkj0KEejZVmNBEARhCJG7CL77HKqPy7+qQVNkRq8OZx3yYiRYthVUmf9fsfFIUMeazquZiSh37tZV5+X/YsOcFZzZ8iePQsSZbm81FgRBEIYctomX8kvrXaiaLjycMb5/qG0xtl6UCCJGgmR7QbX5/y35lewtCtwd9kCxLkbGpcW62L5bR5/tU6UadHursSAIgjDk2JJfycsNp3Jz2x0U49o1WowepX+lfmqvRuN7fxrOAMcQIykx4ZTXt/DcxiM8dvkpAR1rTOsd5zYgz2g1Lq5p9lhYZNSMdHursSAIgjDkMKLsa9SZrG2ZwUzLPtKoppQEtqgTzJvj3ozGS2QkCOqa2zhQqkc3Hr50EgBv7yikurE1oOONY8elx7hs77NWY0EQBGHI4RxlV7GwWc1lpTqbzWquS5S+N6PxIkaC4OtjNWgaDE+MZMHkDCZmxtHcpvLql/7t6pvbbBwpbwBgXHpsh8f7pNVYEARBGHL0mfGnDyRNEwTb7cWr00YkoigK187O4Z43dvH8pqPceNZon5GLw2UNqBrER4aSFhvucZ/5kzOZm5sRVKuxIAiCIASDEY2/+cVtKOBSHtBX0XgRI0Gw/Vg1AKeOSADg0qnDWPr+Pgqrm/hwbwkXTcoA4Otj1Tz2/j52Fdagahqqppm27uPSY7wOFQRHq7EgCIIg9BRGNP6hd/NcpthnxEewZGFur0fjRYwEiKZpLpERgIhQK1eels3fPj3McxuPMGV4Ar9bvZc3t5/wep4LJnoeKCgIgiAIvUl/isaLGAmQoxWNVDW2ERZiITfT4SJ3zRk5/GP9YTYequC8339IU7v+S7zc8ik/CllFdGw8nHMPlnFzCQ+xkBLjOUUjCIIgCL1Nf4nGixgJEMPsbHJWHGEhjrrf4YlRXDgxnQ/ySmhqV5iu7OeB0BeYYjkMgNZwHGXVYoh5Xne+EwRBEATBBREjAWL4ixgpGmd+ffF4Yg7/j3Ntm1ho2YRzSYiChoaCsvpemHCJbnYmCIIgCIKJiJEA2X7MqBdJ6PBYdt0OnuRJ8KIzFDTHOOYuDh0SBEEQhMGG+IwEQFOrjb1FumHZqR4iI2pdcUDnCXQ/QRAEQRhKiBgJgJ3Hq7GpGulx4WQ6m5KpNsj/jMID2wM6z966qB5aoSAIgiAMXCRN44RN1Ty2OBn+ItOydbMzVBt8+jvY9DS01pNtP17TwJOFiKrpw4cORp3MpF57NYIgCIIwMBAxYmf17qIO5i+ZdvMXh79IAuSthLdvgtYGj+dxFySOcczXcG1cdE8tXxAEQRAGLCJG0IXIzS9u6zAxt7immZte3EZchP5jmqbugdeu8XoeRdHFiMs5SObhtmvYGXu2TN0VBEEQBA8MeTFiUzUeejevgxABh19/bXM7IRaFk7/6pd/zGVGRp9ovY6M6mS/t45ifkam7giAIguCRIV/AuiW/0iU1443RkY1E1hcEfN6D6nA2q7mkxUfJ1F1BEARB8MGQj4yU1vkXIgCnN38GoYGf94rzZvD90WfI1F1BEARB8MOQFyNpsRFeH5ugHGWqcohKYrjeujrwk0alcOYFi8RtVRAEQRACYMiLkZmjksiMj6C4ptmlbsSCyrNhvyeDSoIObFz8BxEigiAIghAgQ75mxGpRWLIwt8P2mZZ9ZCmdECKzb4PJl3XL2gRBEARhKDDkxQjA/MmZPPODUwmzOn4caVQHdQ4tPBa++xzMe6SbVycIgiAIgxsRI3bmT84kOSYMgDsuHMtPLpkd0HFvtM/h+633c6b2LKu103tyiYIgCIIwKBExYqel3UZxrd5Z84Mzcpg0az7EZQGe8zSqBie0ZH7efjOb1MmcqG3j5he3sXp3US+uWhAEQRAGPiJG7ByrbELTIDrMSnJ0mF6AOv9x+6OugsTZ4l21/wiN4teH3s3DpnqyUBMEQRAEwRMiRuwcq2wEIDspSh+GB5C7CK54HuJcDcuKSebmtjtYo8502a4BRTXNbMmv7I0lC4IgCMKgYMi39hocrdAH3+UkR7k+kLsIJlwCRzeydc9enthYwxa7xbs3AjVSEwRBEARBxIjJUXtkJCfZw2RdixVGnUWbmsvmDZv9nsuXkZogCIIgCK5ImsZOQYUuRkYkRXndxzBI82Y9ogCZ8REynVcQBEEQgkDEiB1HZMS7GHE2SHMXJMb3S2Q6ryAIgiAEhYgRQFU1CuxiZERDHux6HfI/A9XWYV/DIC0j3jUVkxEfIdN5BUEQBKETSM0IUFrXQmu7ihUbWW/9P1DsIiQuS2/vzV3ksv/8yZnMzc1gS34lpXXNpMVGyHReQRAEQegknYqMLF++nFGjRhEREcH06dP57LPPAjru888/JyQkhKlTp3bmaXuMo9s+AGCYUk6o4hQNqS2C1xZD3soOx1gtCrPGJHPp1GHMGpMsQkQQBEEQOknQYuTVV1/ljjvu4Je//CXbt2/nrLPOYsGCBRQUFPg8rqamhsWLF3PBBRd0erE9gmrj6MbXAchRStwetJuXrb7XY8pGEARBEISuE7QYefLJJ7nhhhu48cYbmThxIsuWLSM7O5tnnnnG53E/+clPuOqqq5g1a1anF9sjHN1IQaM+k2aEUuphBw1qC+Hoxt5dlyAIgiAMEYISI62trXz11VfMmzfPZfu8efPYuNH7xfrf//43hw4dYsmSJQE9T0tLC7W1tS5fPUZ9CUe1dMCbGHHsJwiCIAhC9xOUGCkvL8dms5Genu6yPT09neLiYo/HfPPNN9x777289NJLhIQEVi+7dOlS4uPjza/s7OxglhkcMekUaGmApzSN636CIAiCIHQ/nSpgNWe32NE0rcM2AJvNxlVXXcVDDz3EuHHjAj7/fffdR01Njfl17NixziwzMHJmU4DejjvCoxhRIG4Y5Mzu8IhN1dh0qIJ3dhSy6VCFDMgTBEEQhE4QVGtvSkoKVqu1QxSktLS0Q7QEoK6ujq1bt7J9+3Z++tOfAqCqKpqmERISwgcffMD555/f4bjw8HDCw8ODWVqnqW1VqdJ0C/gRSpnbo3aBNf8x3RLeidW7i3jo3TyKahxzaDLjI1iyMFe8RgRBEAQhCIKKjISFhTF9+nTWrl3rsn3t2rXMnt0xchAXF8euXbvYsWOH+XXTTTcxfvx4duzYwemnn9611XcDhg18SoRGTHyi64NxWfrUXjefkdW7i7j5xW0uQgSguKaZm1/cxurdRT26ZkEQBEEYTARtenbXXXdxzTXXMGPGDGbNmsXf//53CgoKuOmmmwA9xVJYWMjzzz+PxWJh8uTJLsenpaURERHRYXtfcdQuRrLTEuGm3XrXTH2JXiOSM7tDRMSmajz0bh6eEjIaeizloXfzmJubId4jgiAIghAAQYuRK6+8koqKCh5++GGKioqYPHkyq1atIicnB4CioiK/niP9iaOVDQDkJEWZ03l9sSW/skNExBkNKKppZkt+JbPGJHfnUgVBEARhUNIpO/hbbrmFW265xeNjK1as8Hnsgw8+yIMPPtiZp+0RjhkzaZKjA9q/tM67EOnMfoIgCIIw1Bnyg/KMNE1Okvdpvc6kxUb43ymI/QRBEARhqCNixBAj/7+9e4+Nsl7zAP6d6WXKpTNcepkWsFTUIlQMtJYOoYBAaxE5BRNB5HSHYIwQwRRN3AKJQLKGQgTWDVA0shijQlfbeiBgpSf2gkuRQoZQnIDusUD30FKL9GJZQNpn/xg7OsylM0Nnhnfm+0nehP76e2eep0+gD++8v9870r1mJCN5BPRa542GCpZVNRnJIwYiPCIioqAXsk/t7ekVnPifNlzt+D8AwKhhg9w6r9Lcglt3HT+npu921Y0LJvDmVSIiIjeF5JWRivPNmL71G+T/5ynI78tiFu35736X5PYt6W2/+ZvD7w8bHIHiv07hPiNEREQeCLlmxNEeIYNwCxm/VuGjzz5BRcP/OjzP1ZLePppwNbIn6Ac4YiIiouAWUs3IvQ3F46pLAIDp6vP4j8hdOBj5b5hcOgM93//N7tz+lvQCQEvnbZxq/GWAoyYiIgpuIdWM/LmheEZ9Cga1GYDtA/Ji5TrUnxsB8yGbc7mkl4iIyDdCqhnpaxTU6MXGiI+tT+t9SNVqnWO977SiEOj940ZVLuklIiLyjZBqRvoahQz1BSSqfsHa8FLsiNiDLHWDzTwVBOj8p2Vr+N9lJI9Agi4KztbIcEkvERGRd0KqGelrKOLQDgCYqL6M58O+RbK6xfEJv/7x8U2YWoWNCyYAgF1DwiW9RERE3gupZqSvoWjFMPdOGBoPwHLja90/ruP23V4UzH0M8fdseqbXRXFJLxERkZdCbtOz3NQEYOlSXCstttys6vBChgrQJgJJ01BxvhmbD5ttVtLotRqsnfsoxsYMQVy05aMZXhEhIiLyTkhdGemT+8RoxLywEyqVCuLsQ5fcIlSYW+32JAGAa5238e9//xGacDUM40ayESEiIroPIdmMAEDYxDyoFn8Mlfaej1a0icDij9EzfoHTTc76xjYfNqOn19U2aERERNSfkPuYxsaEvwDj51tWzfx6zXKPSNI0QB2GU/+47nKTMwHQ3HELpxp/gWHcSP/FTEREFGRCuxkBAHUYkJxlN8xNzoiIiPwjZD+m6Q83OSMiIvIPNiNOcJMzIiIi/2Az4gQ3OSMiIvIPNiMu5KYmoPivU6DXcZMzIiIiX+ENrP3ITU1A9gQ9TjX+gtauW9zkjIiIaICxGXFDmFrF5btEREQ+ErrNSG+Pw/1FiIiIyL9CsxkxHwIq/hXovPrHmDYRyN1q2QiNiIiI/Cb0bmA1HwL+619sGxEA6Gy2jJsPBSYuIiKiEBVazUhvj+WKiKsnzlQUWuYRERGRX4RWM3L5hP0VERsCdP7TMo+IiIj8IrSakV+vDew8IiIium+h1YwMjR/YeURERHTfQqsZSZpmWTXj6okz2lGWeUREROQXodWMqMMsy3cBOH3iTG4R9xshIiLyo9BqRgDLPiKLPwa09zxXRptoGec+I0RERH4VmpueTfgLMH4+d2AlIiJ6AIRmMwJYGo/krEBHQUREFPJC72MaIiIieqCwGSEiIqKA8qoZ2bNnD5KTkxEVFYW0tDQcP37c6dyysjJkZ2cjNjYWWq0WBoMBX3/9tdcBExERUXDxuBkpKSlBQUEBNmzYAJPJhKysLMybNw9XrlxxOL+2thbZ2dk4evQozpw5g6effhoLFiyAyWS67+CJiIhI+VQi4uipcU5NnToVU6ZMQXFxsXXs8ccfx8KFC7Flyxa3XmPixIlYsmQJ3n77bbfmd3Z2QqfToaOjA1qt1pNwiYiIKEDc/f3t0ZWRO3fu4MyZM8jJybEZz8nJwYkT7j1crre3F11dXRgxYoTTObdv30ZnZ6fNQURERMHJo2akra0NPT09iI+3fXZLfHw8Wlpa3HqN7du3o7u7G4sXL3Y6Z8uWLdDpdNZjzJgxnoRJRERECuLVDawqle1W6iJiN+bIgQMHsGnTJpSUlCAuLs7pvHXr1qGjo8N6NDU1eRMmERERKYBHm57FxMQgLCzM7ipIa2ur3dWSe5WUlODll1/G559/jrlz57qcq9FooNFoPAmNiIiIFMqjZiQyMhJpaWmorKzEokWLrOOVlZXIy8tzet6BAwewYsUKHDhwAPPnz/c4yL57bHnvCBERkXL0/d7ud62MeOjgwYMSEREh+/btE7PZLAUFBTJkyBC5dOmSiIgUFhZKfn6+df5nn30m4eHhsnv3bmlubrYe7e3tbr9nU1OTAODBgwcPHjx4KPBoampy+Xve46W9gGXTs23btqG5uRmpqanYuXMnZsyYAQBYvnw5Ll26hOrqagDArFmzUFNTY/caRqMRH330kVvv19vbi6tXryI6Otqte1Pc1dnZiTFjxqCpqSlolwwzR+UL9vyA4M8x2PMDmGMw8EV+IoKuri4kJiZCrXZ+m6pXzUiwCIX9S5ij8gV7fkDw5xjs+QHMMRgEMj8+m4aIiIgCis0IERERBVRINyMajQYbN24M6mXEzFH5gj0/IPhzDPb8AOYYDAKZX0jfM0JERESBF9JXRoiIiCjw2IwQERFRQLEZISIiooBiM0JEREQBFXLNyDvvvINp06Zh8ODBGDZsmFvniAg2bdqExMREDBo0CLNmzcL333/v20Dvw40bN5Cfnw+dTgedTof8/Hy0t7e7PGf58uVQqVQ2R2Zmpn8C7seePXuQnJyMqKgopKWl4fjx4y7n19TUIC0tDVFRUXj44Yexd+9eP0XqPU9yrK6utquVSqXChQsX/Bix+2pra7FgwQIkJiZCpVLhyy+/7PccpdXQ0xyVVsMtW7bgqaeeQnR0NOLi4rBw4UJcvHix3/OUUkdv8lNaDYuLizFp0iRotVpotVoYDAZ89dVXLs/xZ/1Crhm5c+cOXnjhBaxatcrtc7Zt24YdO3Zg165dqK+vh16vR3Z2Nrq6unwYqfdeeuklnD17FhUVFaioqMDZs2eRn5/f73m5ublobm62HkePHvVDtK6VlJSgoKAAGzZsgMlkQlZWFubNm4crV644nN/Y2Ihnn30WWVlZMJlMWL9+PV5//XWUlpb6OXL3eZpjn4sXL9rU69FHH/VTxJ7p7u7Gk08+iV27drk1X4k19DTHPkqpYU1NDV577TWcPHkSlZWVuHv3LnJyctDd3e30HCXV0Zv8+iilhqNHj0ZRURFOnz6N06dPY/bs2cjLy3P6H2u/18+zx+QFj/3794tOp+t3Xm9vr+j1eikqKrKO3bp1S3Q6nezdu9eHEXrHbDYLADl58qR1rK6uTgDIhQsXnJ5nNBolLy/PDxF6JiMjQ1auXGkzNn78eCksLHQ4/6233pLx48fbjL366quSmZnpsxjvl6c5VlVVCQC5ceOGH6IbWACkvLzc5Rwl1vDP3MlRyTUUEWltbRUAUlNT43SOkuvoTn5Kr6GIyPDhw+XDDz90+D1/1y/krox4qrGxES0tLcjJybGOaTQazJw5EydOnAhgZI7V1dVBp9Nh6tSp1rHMzEzodLp+462urkZcXBwee+wxvPLKK2htbfV1uC7duXMHZ86csfnZA0BOTo7TXOrq6uzmP/PMMzh9+jR+++03n8XqLW9y7DN58mQkJCRgzpw5qKqq8mWYfqW0Gt4Ppdawo6MDADBixAinc5RcR3fy66PEGvb09ODgwYPo7u6GwWBwOMff9WMz0o+WlhYAQHx8vM14fHy89XsPkpaWFsTFxdmNx8XFuYx33rx5+PTTT/HNN99g+/btqK+vx+zZs3H79m1fhutSW1sbenp6PPrZt7S0OJx/9+5dtLW1+SxWb3mTY0JCAj744AOUlpairKwMKSkpmDNnDmpra/0Rss8prYbeUHINRQRvvPEGpk+fjtTUVKfzlFpHd/NTYg0bGhowdOhQaDQarFy5EuXl5ZgwYYLDuf6uX/iAv2IAbNq0CZs3b3Y5p76+Hunp6V6/h0qlsvlaROzGfMndHAH7WIH+412yZIn1z6mpqUhPT0dSUhKOHDmC559/3suoB4anP3tH8x2NP0g8yTElJQUpKSnWrw0GA5qamvDuu+9ixowZPo3TX5RYQ08ouYarV6/GuXPn8O233/Y7V4l1dDc/JdYwJSUFZ8+eRXt7O0pLS2E0GlFTU+O0IfFn/YKiGVm9ejVefPFFl3PGjh3r1Wvr9XoAli4xISHBOt7a2mrXNfqSuzmeO3cO165ds/vezz//7FG8CQkJSEpKwo8//uhxrAMlJiYGYWFhdlcIXP3s9Xq9w/nh4eEYOXKkz2L1ljc5OpKZmYlPPvlkoMMLCKXVcKAooYZr1qzBoUOHUFtbi9GjR7ucq8Q6epKfIw96DSMjI/HII48AANLT01FfX4/33nsP77//vt1cf9cvKJqRmJgYxMTE+OS1k5OTodfrUVlZicmTJwOwfM5fU1ODrVu3+uQ9HXE3R4PBgI6ODpw6dQoZGRkAgO+++w4dHR2YNm2a2+93/fp1NDU12TRg/hYZGYm0tDRUVlZi0aJF1vHKykrk5eU5PMdgMODw4cM2Y8eOHUN6ejoiIiJ8Gq83vMnREZPJFNBaDSSl1XCgPMg1FBGsWbMG5eXlqK6uRnJycr/nKKmO3uTnyINcQ0dExOlH8X6vn09ui32AXb58WUwmk2zevFmGDh0qJpNJTCaTdHV1WeekpKRIWVmZ9euioiLR6XRSVlYmDQ0NsnTpUklISJDOzs5ApNCv3NxcmTRpktTV1UldXZ088cQT8txzz9nM+XOOXV1d8uabb8qJEyeksbFRqqqqxGAwyKhRowKe48GDByUiIkL27dsnZrNZCgoKZMiQIXLp0iURESksLJT8/Hzr/J9++kkGDx4sa9euFbPZLPv27ZOIiAj54osvApVCvzzNcefOnVJeXi4//PCDnD9/XgoLCwWAlJaWBioFl7q6uqx/zwDIjh07xGQyyeXLl0UkOGroaY5Kq+GqVatEp9NJdXW1NDc3W4+bN29a5yi5jt7kp7Qarlu3Tmpra6WxsVHOnTsn69evF7VaLceOHRORwNcv5JoRo9EoAOyOqqoq6xwAsn//fuvXvb29snHjRtHr9aLRaGTGjBnS0NDg/+DddP36dVm2bJlER0dLdHS0LFu2zG752Z9zvHnzpuTk5EhsbKxERETIQw89JEajUa5cueL/4B3YvXu3JCUlSWRkpEyZMsVmuZ3RaJSZM2fazK+urpbJkydLZGSkjB07VoqLi/0csec8yXHr1q0ybtw4iYqKkuHDh8v06dPlyJEjAYjaPX1LIO89jEajiARHDT3NUWk1dJTbvf9OKrmO3uSntBquWLHC+m9MbGyszJkzx9qIiAS+fiqR3+9IISIiIgoALu0lIiKigGIzQkRERAHFZoSIiIgCis0IERERBRSbESIiIgooNiNEREQUUGxGiIiIKKDYjBAREVFAsRkhIiKigGIzQkRERAHFZoSIiIgCis0IERERBdT/A5AXg33lDaS1AAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_65_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1263,110 +1230,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 0\n",
-      "Error: 0.32149601703519115\n",
-      "Bias^2: 0.3123314713548606\n",
-      "Var: 0.009164545680330616\n",
-      "0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912\n",
-      "Polynomial degree: 1\n",
-      "Error: 0.08426840630693412\n",
-      "Bias^2: 0.0796891867672603\n",
-      "Var: 0.004579219539673834\n",
-      "0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
-      "Polynomial degree: 2\n",
-      "Error: 0.10398646080125037\n",
-      "Bias^2: 0.10077114273548984\n",
-      "Var: 0.0032153180657605116\n",
-      "0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036\n",
-      "Polynomial degree: 3\n",
-      "Error: 0.06547790180152352\n",
-      "Bias^2: 0.062082386342319454\n",
-      "Var: 0.0033955154592040923\n",
-      "0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355\n",
-      "Polynomial degree: 4\n",
-      "Error: 0.06844519414009445\n",
-      "Bias^2: 0.06453579006728322\n",
-      "Var: 0.003909404072811221\n",
-      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 5\n",
-      "Error: 0.05227921801205679\n",
-      "Bias^2: 0.04818727730430286\n",
-      "Var: 0.004091940707753925\n",
-      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n",
-      "Polynomial degree: 6\n",
-      "Error: 0.03781367141738902\n",
-      "Bias^2: 0.03365768507152769\n",
-      "Var: 0.0041559863458613296\n",
-      "0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902\n",
-      "Polynomial degree: 7\n",
-      "Error: 0.027609773491022394\n",
-      "Bias^2: 0.022999498260366198\n",
-      "Var: 0.004610275230656182\n",
-      "0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238\n",
-      "Polynomial degree: 8\n",
-      "Error: 0.017355848195593312\n",
-      "Bias^2: 0.010331721306655165\n",
-      "Var: 0.007024126888938144\n",
-      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
-      "Polynomial degree: 9\n",
-      "Error: 0.026605727637184558\n",
-      "Bias^2: 0.010018312644139219\n",
-      "Var: 0.016587414993045335\n",
-      "0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554\n",
-      "Polynomial degree: 10\n",
-      "Error: 0.021592704588021178\n",
-      "Bias^2: 0.010516485576646504\n",
-      "Var: 0.01107621901137467\n",
-      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
-      "Polynomial degree: 11\n",
-      "Error: 0.07160048164232538\n",
-      "Bias^2: 0.014436800088896381\n",
-      "Var: 0.05716368155342902\n",
-      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
-      "Polynomial degree: 12\n",
-      "Error: 0.11547777218876518\n",
-      "Bias^2: 0.016285782696017142\n",
-      "Var: 0.09919198949274803\n",
-      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 13\n",
-      "Error: 0.2284246870217162\n",
-      "Bias^2: 0.01975416527168255\n",
-      "Var: 0.20867052175003364\n",
-      "0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_66_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1460,49 +1324,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "============================\n",
-      "Underfitting vs. Overfitting\n",
-      "============================\n",
-      "\n",
-      "This example demonstrates the problems of underfitting and overfitting and\n",
-      "how we can use linear regression with polynomial features to approximate\n",
-      "nonlinear functions. The plot shows the function that we want to approximate,\n",
-      "which is a part of the cosine function. In addition, the samples from the\n",
-      "real function and the approximations of different models are displayed. The\n",
-      "models have polynomial features of different degrees. We can see that a\n",
-      "linear function (polynomial with degree 1) is not sufficient to fit the\n",
-      "training samples. This is called **underfitting**. A polynomial of degree 4\n",
-      "approximates the true function almost perfectly. However, for higher degrees\n",
-      "the model will **overfit** the training data, i.e. it learns the noise of the\n",
-      "training data.\n",
-      "We evaluate quantitatively **overfitting** / **underfitting** by using\n",
-      "cross-validation. We calculate the mean squared error (MSE) on the validation\n",
-      "set, the higher, the less likely the model generalizes correctly from the\n",
-      "training data.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1400x500 with 3 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_68_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"\n",
     "============================\n",
@@ -1585,149 +1407,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:   1\n",
-      "Mean squared error on training data: 439230.69504801\n",
-      "Mean squared error on test data: 481979.17861098\n",
-      "Degree of polynomial:   2\n",
-      "Mean squared error on training data: 115822.95008046\n",
-      "Mean squared error on test data: 123711.53703498\n",
-      "Degree of polynomial:   3\n",
-      "Mean squared error on training data: 9011.85263220\n",
-      "Mean squared error on test data: 10913.84780262\n",
-      "Degree of polynomial:   4\n",
-      "Mean squared error on training data: 303.47610036\n",
-      "Mean squared error on test data: 426.30787294\n",
-      "Degree of polynomial:   5\n",
-      "Mean squared error on training data: 3.80354994\n",
-      "Mean squared error on test data: 5.98822371\n",
-      "Degree of polynomial:   6\n",
-      "Mean squared error on training data: 3.66204648\n",
-      "Mean squared error on test data: 8.14812206\n",
-      "Degree of polynomial:   7\n",
-      "Mean squared error on training data: 0.47075725\n",
-      "Mean squared error on test data: 2.00607783\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:   8\n",
-      "Mean squared error on training data: 0.04912436\n",
-      "Mean squared error on test data: 0.21596432\n",
-      "Degree of polynomial:   9\n",
-      "Mean squared error on training data: 0.02522069\n",
-      "Mean squared error on test data: 0.08576932\n",
-      "Degree of polynomial:  10\n",
-      "Mean squared error on training data: 0.02511518\n",
-      "Mean squared error on test data: 1.20015436\n",
-      "Degree of polynomial:  11\n",
-      "Mean squared error on training data: 0.01640891\n",
-      "Mean squared error on test data: 1.35533773\n",
-      "Degree of polynomial:  12\n",
-      "Mean squared error on training data: 0.00813803\n",
-      "Mean squared error on test data: 0.17446471\n",
-      "Degree of polynomial:  13\n",
-      "Mean squared error on training data: 0.00759119\n",
-      "Mean squared error on test data: 1.08131003\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  14\n",
-      "Mean squared error on training data: 0.00472199\n",
-      "Mean squared error on test data: 0.81333804\n",
-      "Degree of polynomial:  15\n",
-      "Mean squared error on training data: 0.00410478\n",
-      "Mean squared error on test data: 92.09172409\n",
-      "Degree of polynomial:  16\n",
-      "Mean squared error on training data: 0.00315593\n",
-      "Mean squared error on test data: 234.38533185\n",
-      "Degree of polynomial:  17\n",
-      "Mean squared error on training data: 0.00242999\n",
-      "Mean squared error on test data: 1271.35771826\n",
-      "Degree of polynomial:  18\n",
-      "Mean squared error on training data: 0.00228742\n",
-      "Mean squared error on test data: 108.27092910\n",
-      "Degree of polynomial:  19\n",
-      "Mean squared error on training data: 0.00156376\n",
-      "Mean squared error on test data: 1371.99051150\n",
-      "Degree of polynomial:  20\n",
-      "Mean squared error on training data: 0.00137818\n",
-      "Mean squared error on test data: 1887.86252988\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  21\n",
-      "Mean squared error on training data: 0.00118508\n",
-      "Mean squared error on test data: 14859.69908626\n",
-      "Degree of polynomial:  22\n",
-      "Mean squared error on training data: 0.00092647\n",
-      "Mean squared error on test data: 876.51191552\n",
-      "Degree of polynomial:  23\n",
-      "Mean squared error on training data: 0.00085889\n",
-      "Mean squared error on test data: 5594.60815105\n",
-      "Degree of polynomial:  24\n",
-      "Mean squared error on training data: 0.00084705\n",
-      "Mean squared error on test data: 1277.61702282\n",
-      "Degree of polynomial:  25\n",
-      "Mean squared error on training data: 0.00079129\n",
-      "Mean squared error on test data: 128664.31650694\n",
-      "Degree of polynomial:  26\n",
-      "Mean squared error on training data: 0.00076905\n",
-      "Mean squared error on test data: 19003.94822514\n",
-      "Degree of polynomial:  27\n",
-      "Mean squared error on training data: 0.00068946\n",
-      "Mean squared error on test data: 2379.66219404\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  28\n",
-      "Mean squared error on training data: 0.00062595\n",
-      "Mean squared error on test data: 4082.19983530\n",
-      "Degree of polynomial:  29\n",
-      "Mean squared error on training data: 0.00060705\n",
-      "Mean squared error on test data: 3250.17647619\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_69_6.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -1920,22 +1600,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_75_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -2046,30 +1711,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_77_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -2216,18 +1858,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'\\n#Model training, we compute the mean value of y and X\\ny_train_mean = np.mean(y_train)\\nX_train_mean = np.mean(X_train,axis=0)\\nX_train = X_train - X_train_mean\\ny_train = y_train - y_train_mean\\n\\n# The we fit our model with the training data\\ntrained_model = some_model.fit(X_train,y_train)\\n\\n\\n#Model prediction, we need also to transform our data set used for the prediction.\\nX_test = X_test - X_train_mean #Use mean from training data\\ny_pred = trained_model(X_test)\\ny_pred = y_pred + y_train_mean\\n'"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"\n",
     "#Model training, we compute the mean value of y and X\n",
@@ -2615,43 +2246,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "True beta: [2, 0.5, 3.7]\n",
-      "Fitted beta: [2.08376632 0.19569961 3.97898392]\n",
-      "Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n",
-      "MSE with intercept column\n",
-      "0.004113634617443139\n",
-      "MSE with intercept column from SKL\n",
-      "0.004113634617443147\n",
-      "Manual intercept: 2.083766322923899\n",
-      "Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n",
-      "Sklearn intercept: 2.0837663229239043\n",
-      "Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n",
-      "MSE with Manual intercept\n",
-      "0.00411363461744314\n",
-      "MSE with Sklearn intercept\n",
-      "0.004113634617443131\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_112_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -2843,116 +2438,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Beta values for own Ridge implementation\n",
-      "[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02\n",
-      "  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02\n",
-      " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
-      " -9.80609616e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02\n",
-      "  2.64742912e-02  1.63249532e-02 -5.01831251e-05 -2.15098090e-02]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 1.03032441e+00  6.28336218e-02 -6.24175744e-01  5.21169159e-02\n",
-      "  2.80847477e-01  2.12552073e-01  8.13220608e-02 -1.69634577e-02\n",
-      " -6.50846112e-02 -7.38962192e-02 -5.94226022e-02 -3.50227564e-02\n",
-      " -9.80609615e-03  1.08299273e-02  2.41882037e-02  2.93492130e-02\n",
-      "  2.64742912e-02  1.63249532e-02 -5.01831207e-05 -2.15098090e-02]\n",
-      "MSE values for own Ridge implementation\n",
-      "4.3632959215700067e-07\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "4.363295916323784e-07\n",
-      "Beta values for own Ridge implementation\n",
-      "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471\n",
-      "  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
-      " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565\n",
-      "  0.02976145  0.04543942]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 1.03630548 -0.01963611 -0.37900111 -0.07062318  0.12182967  0.16343471\n",
-      "  0.13003291  0.07490892  0.02365049 -0.01449782 -0.03814292 -0.04909093\n",
-      " -0.05009826 -0.04389027 -0.03279636 -0.01866537 -0.00289724  0.01348565\n",
-      "  0.02976145  0.04543942]\n",
-      "MSE values for own Ridge implementation\n",
-      "5.194042827197027e-06\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "5.1940428268204826e-06\n",
-      "Beta values for own Ridge implementation\n",
-      "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007\n",
-      "  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499\n",
-      "  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
-      " -0.01708852 -0.01708781]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 1.04220758 -0.10931453 -0.17641709 -0.06020587  0.02208512  0.05789007\n",
-      "  0.06491736  0.05785343  0.04537385  0.03196357  0.01969145  0.00934499\n",
-      "  0.00107405 -0.00526348 -0.00992331 -0.01318643 -0.01531845 -0.01655318\n",
-      " -0.01708852 -0.01708781]\n",
-      "MSE values for own Ridge implementation\n",
-      "2.0940821989643363e-05\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "2.094082198961999e-05\n",
-      "Beta values for own Ridge implementation\n",
-      "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361\n",
-      "  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985\n",
-      "  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387\n",
-      "  0.00249435  0.00105081]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 1.01219292 -0.06043581 -0.10391807 -0.05651951 -0.01898855  0.00312361\n",
-      "  0.01463049  0.01975848  0.02123176  0.02068067  0.01905883  0.01691985\n",
-      "  0.01458337  0.01223198  0.00996754  0.00784393  0.00588657  0.00410387\n",
-      "  0.00249435  0.00105081]\n",
-      "MSE values for own Ridge implementation\n",
-      "0.0003153514830957865\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "0.00031535148309580783\n",
-      "Beta values for own Ridge implementation\n",
-      "[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02\n",
-      " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
-      " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
-      " -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04\n",
-      "  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 8.38916861e-01  1.31276579e-01  8.97497404e-03 -1.72271878e-02\n",
-      " -2.11744554e-02 -1.91492986e-02 -1.57201944e-02 -1.23002365e-02\n",
-      " -9.30466214e-03 -6.81048318e-03 -4.78184120e-03 -3.15130074e-03\n",
-      " -1.84923989e-03 -8.13661243e-04  7.46984697e-06  6.56636616e-04\n",
-      "  1.16805821e-03  1.56912044e-03  1.88168312e-03  2.12318726e-03]\n",
-      "MSE values for own Ridge implementation\n",
-      "0.015072388895177157\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "0.0150723888951771\n",
-      "Beta values for own Ridge implementation\n",
-      "[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427\n",
-      " 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728\n",
-      " 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987\n",
-      " 0.0036237  0.003301  ]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[0.37396662 0.14174745 0.0764924  0.04892055 0.03447512 0.02586427\n",
-      " 0.02024962 0.01633913 0.01347916 0.0113104  0.0096208  0.00827728\n",
-      " 0.00719176 0.00630331 0.00556826 0.0049544  0.00443743 0.0039987\n",
-      " 0.0036237  0.003301  ]\n",
-      "MSE values for own Ridge implementation\n",
-      "0.26409315307910036\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "0.26409315307910025\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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rLBYLwcHBFZpdREREivdH2k42BZy/fFKsdZTJaZyZdgQoNzeXzZs3Ex0d7bQ9Ojqa9evXl2gfdrudkydPUrduXaftp06dIiwsjMaNG3P77bcXOEJ0uZycHLKyspxuYq79+/djsVhITU0tcszKlSuxWCycOHHimuUSEZGSW54wHcMCHU5406iF+RdAvZRpBejIkSPk5+cTFBTktD0oKIiMjIwS7ePf//43p0+f5t5773Vsa9WqFfHx8SxZsoR58+bh7e1Njx492LNnT5H7mThxIgEBAY5bSEhI2d5UJTd06FAsFgsjR44s8Njjjz+OxWJxusr74cOHeeyxxwgNDcXLy4vg4GBiYmJITk52jGnSpEmhc67++c9/FpmjT58+jnGenp40b96cuLg4cnJyHGNCQkJIT0+nXbt25fPmy6io93fxdjXXJevTpw9jx44tt6wiIpWNbY8NAKvfTeYGKYTp5wG69CKRAIZhFNhWmHnz5vHKK6+wePFiGjRo4NjerVs3unXr5rjfo0cPOnXqxPTp05k2bVqh+4qLi2PcuHGO+1lZWdW2BIWEhDB//nzeeOMNfHx8gPOXOpg3bx6hoaFOYwcNGkReXh4fffQRzZo14/fff+frr7/m2LFjTuMmTJjAiBEjnLZd6WrtI0aMYMKECeTm5pKSksLDDz8M4Pjq093dvVJ8jZmSkuK4Wvr69esZNGgQu3fvdpxi/eIV10VExJk9/xzLPH4FwBpxn8lpCjLtCFBgYCDu7u4FjvYcPny4wFGhyy1YsIBhw4bx6aefcttttxU71s3NjYiIiGKPAHl5eTkuDFrcBUKrg06dOhEaGsqiRYsc2xYtWkRISIjTPKoTJ06wdu1aJk2aRN++fQkLC6NLly7ExcXRv39/p33WqlWL4OBgp1vNmjWLzeHr60twcDChoaEMGjSIqKgoli9f7ni8sK/AEhISuOGGG/Dx8aFv377s37+/wH7fe+89QkJC8PX1ZeDAgUyZMoXatWs7jfnyyy8JDw/H29ubZs2a8eqrr3Lu3LlCc9avX9/xni5+1dqgQQPHtl27dtGrVy98fHwICQlh9OjRnD592vH8GTNm0KJFC7y9vQkKCuLuu+8Gzh+NW7VqFW+++abjaFJh70dEpKra9PV/OOJj4J8DkdHDzI5TgGkFyNPTk/DwcJKSkpy2JyUl0b179yKfN2/ePIYOHcrcuXML/CIujGEYpKamOq6OXREMw+B07mlTbmW5lu3DDz/M7NmzHfc//PBDHnnE+dwMfn5++Pn58cUXXzh9NVURtm7dyrp165yuBn+5AwcOcNddd9GvXz9SU1MZPnw4zz//vNOYdevWMXLkSMaMGUNqaipRUVG89tprTmOWLVvGAw88wOjRo9mxYwezZs0iPj6+wLiS+OGHH4iJieGuu+5i27ZtLFiwgLVr1/Lkk08CsGnTJkaPHs2ECRPYvXs3iYmJ9OrVC4A333yTyMhIRowY4VipWF2POoqIa7IlzwEgKvs6PLx9TU5TkKlfgY0bN44hQ4bQuXNnIiMjeffdd0lLS3PMUYmLi+PgwYPMmXP+Q5w3bx4PPvggb775Jt26dXMcPfLx8SEgIACAV199lW7dutGiRQuysrKYNm0aqampvP322xX2Ps7kncFvol+F7b84p+JOUdOz+KMtlxsyZAhxcXGOoyzr1q1j/vz5rFy50jGmRo0axMfHM2LECGbOnEmnTp3o3bs3f/7zn2nf3vk6Ls899xwvvPCC07alS5cWOz9mxowZvP/+++Tl5ZGbm4ubm1ux/4zeeecdmjVrxhtvvIHFYqFly5b88MMPTJo0yTFm+vTpWK1Wnn76aQBuuOEG1q9fz9KlSx1jXnvtNZ5//nkeeughAJo1a8b//d//8eyzz/Lyyy9f8bO71L/+9S/uu+8+xzyeFi1aMG3aNHr37s0777xDWloaNWvW5Pbbb6dWrVqEhYU5jrIFBATg6enpOBImIlLd2E6kQG2IDbvV7CiFMrUADR48mKNHjzJhwgTHhNeEhATCwsIASE9Pdzon0KxZszh37hxPPPEETzzxhGP7Qw89RHx8PHD+q5tHH32UjIwMAgIC6NixI6tXr6ZLly7X9L1VZoGBgfTv35+PPvoIwzDo378/gYGBBcYNGjSI/v37s2bNGpKTk0lMTGTy5Mm8//77TpOln3nmGaf7ANddd12xGe6//37Gjx9PVlYWkyZNwt/fn0GDBhU5fufOnXTr1s1pflhkZKTTmN27dzNw4ECnbV26dHEqQJs3byYlJcXpiE9+fj7Z2dmcOXMGX9+S/1/K5s2b+fnnn/nkk08c2wzDwG63s2/fPqKioggLC6NZs2bExsYSGxvLwIEDS/UaIiJV0ZEDu9l4cfl77JMmpymc6ZOgH3/8cR5//PFCH7tYai669AhFUd544w3eeOONckhWcr4evpyKO3VNX/PS1y6LRx55xPFVTXFHXry9vYmKiiIqKoqXXnqJ4cOH8/LLLzsVnsDAQK6//vpSvX5AQIDjOR9//DFt27blgw8+YNiwwr8nLslXfYVNoL/8eXa7nVdffZW77rqrwPNLe7JMu93OY489xujRows8FhoaiqenJ99//z0rV65k+fLlvPTSS7zyyiukpKQUmJckIlKdLP9qGoYFbsz0pnHLCLPjFMr0AlQdWCyWUn8NZbbY2Fhyc3MBiImJKfHz2rRpwxdffFGuWTw8PPjb3/5GXFwcf/nLXwo9QlLY63733XdO91u1asXGjRudtm3atMnpfqdOndi9e3epC1thOnXqxPbt24vdV40aNbjtttu47bbbePnll6lduzbffPMNd911F56eno4VZiIi1Uniz4lQC6y+7a882CSmXwtMzOHu7s7OnTvZuXMn7u7uBR4/evQot9xyCx9//DHbtm1j3759fPbZZ0yePJkBAwY4jT158iQZGRlOt9KeTPK+++7DYrEwY8aMQh8fOXIke/fuZdy4cezevZu5c+cWOEI4atQoEhISmDJlCnv27GHWrFnYbDano0IvvfQSc+bM4ZVXXmH79u3s3LmTBQsWFJjDVBLPPfccycnJPPHEE6SmprJnzx6WLFnCqFHnz3a6dOlSxxy0X3/9lTlz5mC322nZsiVw/hxDGzZsYP/+/Rw5cgS73V7qDCIilY09/xyJ7vsAsHb+i8lpiqYC5MKKW/Lv5+dH165deeONN+jVqxft2rXjxRdfZMSIEbz11ltOY1966SUaNmzodHv22WdLlcXT05Mnn3ySyZMnc+pUwa8TQ0NDWbhwIV9++SUdOnRg5syZ/OMf/3Aa06NHD2bOnMmUKVPo0KEDiYmJPPXUU05fbcXExLB06VKSkpKIiIigW7duTJkyxTHvrDTat2/PqlWr2LNnDz179qRjx468+OKLjhWHtWvXZtGiRdxyyy20bt2amTNnMm/ePNq2bQvA008/jbu7O23atKF+/fpFXgNPRKQq+f7bufzha1ArB3rEPmp2nCJZjLKso67msrKyCAgIIDMzs0BByM7OZt++fY4r2EvlNmLECHbt2sWaNWvMjlJl6WdeRErj/ybcykvGNww80ZBFbxy6pq9d3O/vy2kOkFQrr7/+OlFRUdSsWRObzcZHH31U5NdqIiJS/mzHNkIdsIYVf6Jis6kASbWyceNGJk+ezMmTJ2nWrBnTpk1j+PDhZscSEXEJxw7tZUPA+WkMsTFPXGG0uVSApFr59NNPzY4gIuKyli99E7sbtM30IqR1V7PjFEuToEVERKRcJP6UAIDV50aTk1yZClAZae64uAr9rItISTgtfw//s8lprkwFqJQuXrDzzJkzJicRuTYu/qwXd7FaEZHUVQv43deOXy7cbH3M7DhXpDlApeTu7k7t2rU5fPgwAL6+vgUuvyBSHRiGwZkzZzh8+DC1a9cu9ISZIiIX2dbFA3DrmWA8fcy5QHhpqACVwcWrd18sQSLVWe3atXXFehG5ItvRDeeXv4feYnaUElEBKgOLxULDhg1p0KABeXl5ZscRqTAeHh468iMiV3Q8fR/JAScBiI0u/ALnlY0K0FVwd3fXLwcREXF5SV9Nw+4GrTM9CWvbw+w4JaJJ0CIiInJVbLuWAmD1rvzL3y9SARIREZEyM+x2Et1+AcDa6V6T05ScCpCIiIiU2dY1n5FR007NXOhpHWl2nBJTARIREZEys635EIBbzgThVbP4K7BXJipAIiIiUma2I98BYG3c1+QkpaMCJCIiImVy4vdfWR+QBUBs1F9NTlM6KkAiIiJSJiuWTiPfDVpmedK0fS+z45SKCpCIiIiUiW3XlwBYPduanKT0VIBERESk1Ay7nUTLXgCsHe8xOU3pqQCJiIhIqf2wbhGHatrxzYVe/arW/B9QARIREZEysK3+AIC+Zxrg7Vfb3DBloAIkIiIipWb7IxkA63W9TU5SNipAIiIiUipZf/zGOv9MAKxRVePq75dTARIREZFSWbF0Gufc4YYsD5p16GN2nDJRARIREZFSse1YAkCsZxuTk5SdCpCIiIiUmGG3Y2MPANYOd5ucpuxUgERERKTEticv5qCfHe886N2vas7/ARUgERERKQXbqvcB6Hu6Pj7+dU1OU3YqQCIiIlJitsPrAbA2qlrX/rqcCpCIiIiUyMmjh1jrfwIA621V7+zPl1IBEhERkRL5eul08tzh+iwPru94q9lxrooKkIiIiJSIbfsXAFg9WpsbpByoAImIiMgVGXY7NuP88vfY9neZnObqqQCJiIjIFe347ksO+OXjdQ769H/C7DhXTQVIRERErijxwvL3Pqfq4RsQaHKaq6cCJCIiIldk+30dANaGVXv5+0UqQCIiIlKsU8cyWFPrOADWWx4zOU35UAESERGRYn3z1XRya0CzkzVo0SnK7DjlQgVIREREimX78QsArDVaY3GrHtWherwLERERqRCG3Y4tfzcAse3uNDdMOVIBEhERkSLtSkng11r5eJ6Dvv2fNDtOuVEBEhERkSIlfnt++Xvvk3WpWaeByWnKjwqQiIiIFMmWsQYAa3BPk5OULxUgERERKdTp44dZVesYANZbHjU5TflSARIREZFCffvVW+TWgCYna9Cyc6zZccqVCpCIiIgUyvbD5wBY3VtWm+XvF1WvdyMiIiLl4vzy910AWNsNNDlN+VMBEhERkQJ+2ryMfbXOXVj+XvWv/n45FSAREREpwPbNuwD0PFkHv7rBJqcpf6YXoBkzZtC0aVO8vb0JDw9nzZo1RY5dtGgRUVFR1K9fH39/fyIjI1m2bFmBcQsXLqRNmzZ4eXnRpk0bPv/884p8CyIiItVO4sXl70E9TE5SMUwtQAsWLGDs2LGMHz+eLVu20LNnT6xWK2lpaYWOX716NVFRUSQkJLB582b69u3LHXfcwZYtWxxjkpOTGTx4MEOGDGHr1q0MGTKEe++9lw0bNlyrtyUiIlKlnck8wkq/owBY+44wOU3FsBiGYZj14l27dqVTp0688847jm2tW7fmzjvvZOLEiSXaR9u2bRk8eDAvvfQSAIMHDyYrKwubzeYYExsbS506dZg3b16h+8jJySEnJ8dxPysri5CQEDIzM/H39y/LWxMREamyEua+Sv89rxB6yp39k3KrzAqwrKwsAgICSvT727R3lJuby+bNm4mOjnbaHh0dzfr160u0D7vdzsmTJ6lbt65jW3JycoF9xsTEFLvPiRMnEhAQ4LiFhISU4p2IiIhUL7ZtCwGwWm6oMuWntEx7V0eOHCE/P5+goCCn7UFBQWRkZJRoH//+9785ffo09957r2NbRkZGqfcZFxdHZmam43bgwIFSvBMREZHqxZa3EwBrNbr6++VqmB3AYrE43TcMo8C2wsybN49XXnmFxYsX06CB88XZSrtPLy8vvLy8SpFaRESketqzOYm9/ufwyIdbqtHV3y9nWgEKDAzE3d29wJGZw4cPFziCc7kFCxYwbNgwPvvsM2677Tanx4KDg8u0TxEREQHb1zMBuDmrNrXqNTI5TcUx7SswT09PwsPDSUpKctqelJRE9+7di3zevHnzGDp0KHPnzqV///4FHo+MjCywz+XLlxe7TxERETkvMf3C8vcG1fv3pqlfgY0bN44hQ4bQuXNnIiMjeffdd0lLS2PkyJHA+bk5Bw8eZM6cOcD58vPggw/y5ptv0q1bN8eRHh8fHwICAgAYM2YMvXr1YtKkSQwYMIDFixezYsUK1q5da86bFBERqSLOZh3j25p/AGDtPdzkNBXL1KndgwcPZurUqUyYMIGbbrqJ1atXk5CQQFhYGADp6elO5wSaNWsW586d44knnqBhw4aO25gxYxxjunfvzvz585k9ezbt27cnPj6eBQsW0LVr12v+/kRERKqSVQkzyPaAxqfcaRs5wOw4FcrU8wBVVqU5j4CIiEh1MSbuJqZ5b2XE6Va8O3mn2XFKrUqcB0hEREQqF1vuDgCsbf5kcpKKpwIkIiIi7E39hj3+edTIh1v7jzI7ToVTARIRERFsSecvS9UjKwD/+o1NTlPxVIBEREQE26FVAFjrR5qc5NpQARIREXFx2adO/G/5e69hJqe5NlSAREREXNzqhHc46wHXnXLjxh53mR3nmlABEhERcXG2LZ8BEMv11fbq75dzjXcpIiIiRbLlbgfA2rr6L3+/SAVIRETEhe3btprd/rnUyIfbbq/+y98vUgESERFxYbakGQB0zwogoEGoyWmuHRUgERERF2b77VsAYgNd65qZKkAiIiIuKud0Ft/4HgbA2vMRk9NcWypAIiIiLmqNbSZnPKHhaTc69LzH7DjXlAqQiIiIi7J9/ykAsUZzl1n+fpFrvVsRERFxsGX/AIC11e0mJ7n2VIBERERc0K/b17EzIBd3O0TdPsbsONecCpCIiIgLsi17G4DITH9qB4WZnObaUwESERFxQbYD55e/W+u51vL3i1SAREREXEzO6Sy+9s0AILbHQyanMYcKkIiIiItZt+w9TntC0Bk3buo92Ow4plABEhERcTG2zfMBiM1vipt7DZPTmEMFSERExMXYzl5Y/t6yv8lJzKMCJCIi4kIO7NzA9oAc3OwQ1X+02XFMowIkIiLiQmzLpgPQLbMWdRs1NzmNeVSAREREXIjt128AsNbtYnISc6kAiYiIuIjcs6dY4ZsOgLXHUHPDmEwFSERExEWsX/Y+pzyhwRkLHfv82ew4plIBEhERcRG2TfMAiHHh5e8XqQCJiIi4CNuZbQBYW/QzOYn5VIBERERcwG+7U/ghIBs3O0S78PL3i1SAREREXEBi4lsAdMnyo17jFianMZ8KkIiIiAuw/boCAGvtCJOTVA4qQCIiItVcXvYZVngfAsDa3TWv/n45FSAREZFqbv2y98jygsCzFsJvud/sOJWCCpCIiEg1l7jp/NXfY/LCXH75+0UqQCIiItWc7VQqANYWVnODVCIqQCIiItXYoT3fs7V2NhYDYvqPMTtOpaECJCIiUo0l2s5f/T0isyaBIS1NTlN5qACJiIhUY7b9SQBYAzqbnKRyUQESERGpps7lZpPkdRAAa+QQk9NULipAIiIi1VTysvfJ9IZ6Zy10vkUF6FIqQCIiItWUbeNcAKLzQnH38DQ5TeWiAiQiIlJNJV5c/t481twglZAKkIiISDWU8cs2ttQ+C0BMv1Emp6l8VIBERESqocSEaQB0PuFLgyZtTU5T+agAiYiIVEO2X5YDYPUPNzlJ5aQCJCIiUs2cy81muddvAFi7PWBymspJBUhERKSa2ZA0mxPeBnXPWuhy21Cz41RKKkAiIiLVjG3DJwBE54Vo+XsRVIBERESqmcSTWwCIbRZtcpLKSwVIRESkGvl9349srn0GgNh+uvp7UVSAREREqpFlF5a/dzrhQ1DTdianqbxML0AzZsygadOmeHt7Ex4ezpo1a4ocm56ezn333UfLli1xc3Nj7NixBcbEx8djsVgK3LKzsyvwXYiIiFQOtl+WAWCt1cnkJJWbqQVowYIFjB07lvHjx7NlyxZ69uyJ1WolLS2t0PE5OTnUr1+f8ePH06FDhyL36+/vT3p6utPN29u7ot6GiIhIpZCfl8tyjwMAWLveb3Kays3UAjRlyhSGDRvG8OHDad26NVOnTiUkJIR33nmn0PFNmjThzTff5MEHHyQgIKDI/VosFoKDg51uIiIi1d3GFfEc8zGonW2ha9TDZsep1EwrQLm5uWzevJnoaOcZ6tHR0axfv/6q9n3q1CnCwsJo3Lgxt99+O1u2bCl2fE5ODllZWU43ERGRqsb23ccAROc0poanvvkojmkF6MiRI+Tn5xMUFOS0PSgoiIyMjDLvt1WrVsTHx7NkyRLmzZuHt7c3PXr0YM+ePUU+Z+LEiQQEBDhuISEhZX59ERERs9iyNgNg1fL3KzJ9ErTFYnG6bxhGgW2l0a1bNx544AE6dOhAz549+fTTT7nhhhuYPn16kc+Ji4sjMzPTcTtw4ECZX19ERMQMh/dvZ9OF5e8x1idNTlP51TDrhQMDA3F3dy9wtOfw4cMFjgpdDTc3NyIiIoo9AuTl5YWXl1e5vaaIiMi1ttz2FgA3nfChYfObzA1TBZh2BMjT05Pw8HCSkpKcticlJdG9e/dyex3DMEhNTaVhw4bltk8REZHKxvazDQCr303mBqkiTDsCBDBu3DiGDBlC586diYyM5N133yUtLY2RI0cC57+aOnjwIHPmzHE8JzU1FTg/0fmPP/4gNTUVT09P2rRpA8Crr75Kt27daNGiBVlZWUybNo3U1FTefvvta/7+REREroX8vFyWeZw/hYy1y30mp6kaTC1AgwcP5ujRo0yYMIH09HTatWtHQkICYWFhwPkTH15+TqCOHTs6/r5582bmzp1LWFgY+/fvB+DEiRM8+uijZGRkEBAQQMeOHVm9ejVdunS5Zu9LRETkWtr0zX846mMQkA2RMcPNjlMlWAzDMMwOUdlkZWUREBBAZmYm/v7+ZscREREp1iuv9OFVyyruzryOz6b8ZnYc05Tm97fpq8BERETk6tgyNwFgbRJlcpKqQwVIRESkCjtyYDcpAacBiIl9wuQ0VYcKkIiISBW2/KtpGBZof8Kb627obHacKkMFSEREpAqz7bmw/L1m0RcJl4JUgERERKooe/45ltXYD4A14i/mhqliVIBERESqqM3ffMIfvgb+OdA9ZoTZcaqUUhWgyZMnc/bsWcf91atXk5OT47h/8uRJHn/88fJLJyIiIkWyrf8IgNuyG+Hh7WtymqqlVAUoLi6OkydPOu7ffvvtHDx40HH/zJkzzJo1q/zSiYiISJFsJ1IAsIbdZnKSqqdUBejycybqHIoiIiLmOPrbHjYEnAIgNlZXfy8tzQESERGpgpISpmNYoF2mF41bRpgdp8pRARIREamCbD99BYDVp73JSaqmUl8M9f3338fPzw+Ac+fOER8fT2BgIIDT/CARERGpGPb8cyS67wPA2vnPJqepmkp1MdQmTZpgsViuOG7fvn1XFcpsuhiqiIhUZpu//pjOa4fglwtHXziJp4+f2ZEqhdL8/i7VEaD9+/dfTS4REREpB7Z18QDcdqahyk8ZaQ6QiIhIFWM7thEAa9gtJiepukpVgDZs2IDNZnPaNmfOHJo2bUqDBg149NFHnU6MKCIiIuXr2KG9fBdwfs6tNWaUyWmqrlIVoFdeeYVt27Y57v/www8MGzaM2267jeeff54vv/ySiRMnlntIEREROW9FwlvY3aBtphchrbuaHafKKlUBSk1N5dZbb3Xcnz9/Pl27duW9995j3LhxTJs2jU8//bTcQ4qIiMh5tl1LAYj1aWdykqqtVAXo+PHjBAUFOe6vWrWK2NhYx/2IiAgOHDhQfulERETEwZ5/jkS3XwCwdhpscpqqrVQFKCgoyLHEPTc3l++//57IyEjH4ydPnsTDw6N8E4qIiAgAW9d8RkZNOzVz4ebYx8yOU6WVqgDFxsby/PPPs2bNGuLi4vD19aVnz56Ox7dt20bz5s3LPaSIiIiAbc1sAG49E4xXTZ2n7mqU6jxAf//737nrrrvo3bs3fn5+xMfH4+np6Xj8ww8/JDo6utxDioiICNiOboA6YA3pa3aUKq9UBah+/fqsWbOGzMxM/Pz8cHd3d3r8s88+o1atWuUaUERERODE77+SHJAFgDXmCZPTVH2lKkCPPPJIicZ9+OGHZQojIiIihUta+ib5btA605Owtj3MjlPllaoAxcfHExYWRseOHSnFJcRERETkKiXuWgp+EOut5e/loVQFaOTIkcyfP59ffvmFRx55hAceeIC6detWVDYREREBDLudRMteAKwd7zE5TfVQqlVgM2bMID09neeee44vv/ySkJAQ7r33XpYtW6YjQiIiIhVk29r/cqimHd9c6NXvcbPjVAulvhiql5cXf/nLX0hKSmLHjh20bduWxx9/nLCwME6dOlURGUVERFyabfX5ubW3nGmg5e/l5KquBm+xWLBYLBiGgd1uL69MIiIicgnbke8AsDbW8vfyUuoClJOTw7x584iKiqJly5b88MMPvPXWW6SlpeHn51cRGUVERFxW5uE01gVkAmCN0tdf5aVUk6Aff/xx5s+fT2hoKA8//DDz58+nXr16FZVNRETE5a1YOp18N2iZ5UnT9r3MjlNtlKoAzZw5k9DQUJo2bcqqVatYtWpVoeMWLVpULuFERERcXeLOL8EPrJ5tzY5SrZSqAD344INYLJaKyiIiIiKXMOx2bOwBIPamQSanqV5KfSJEERERuTZ+XP85B/3s+ORB7/66/EV5uqpVYCIiIlJxbKs+AKDv6fp4+9U2N0w1owIkIiJSSdn+SAbA2qi3yUmqHxUgERGRSijrj99Y638CAGvUX80NUw2pAImIiFRCX381nXPu0CLLg+Y33WJ2nGpHBUhERKQSsu1YAoDVs43JSaonFSAREZFKxrDbSTTOL3+3drjb5DTVkwqQiIhIJbPjuy854JePdx701tXfK4QKkIiISCVjW/UeAH1OB+LjX9fkNNWTCpCIiEglY/t9PQDWhrr2V0VRARIREalETh49xBr/4wBYbx1pcprqSwVIRESkEvnmq7fIc4fmWTVoER5ldpxqSwVIRESkErH9+AUAVo/W5gap5lSAREREKgnDbsdm/ASAtb2u/l6RVIBEREQqiV0pCaT55eN1Dvro6u8VSgVIRESkkrB9e375e++T9fANCDQ5TfWmAiQiIlJJ2DLWAmBt2NPkJNWfCpCIiEglcOpYBqtrHQPAesujJqep/lSAREREKoFvv3qb3BrQ9GQNbgiPMTtOtacCJCIiUgnYfvwcAKt7Kyxu+vVc0Uz/hGfMmEHTpk3x9vYmPDycNWvWFDk2PT2d++67j5YtW+Lm5sbYsWMLHbdw4ULatGmDl5cXbdq04fPPP6+g9CIiIlfPsNux5e8GwHrjQJPTuAZTC9CCBQsYO3Ys48ePZ8uWLfTs2ROr1UpaWlqh43Nycqhfvz7jx4+nQ4cOhY5JTk5m8ODBDBkyhK1btzJkyBDuvfdeNmzYUJFvRUREpMx+2ryM/bXO4XkO+vZ/0uw4LsFiGIZh1ot37dqVTp068c477zi2tW7dmjvvvJOJEycW+9w+ffpw0003MXXqVKftgwcPJisrC5vN5tgWGxtLnTp1mDdvXolyZWVlERAQQGZmJv7+/iV/QyIiImUwddJAnsr+gtuO1yVp6lGz41RZpfn9bdoRoNzcXDZv3kx0dLTT9ujoaNavX1/m/SYnJxfYZ0xMTLH7zMnJISsry+kmIiJyrdjSz0//sAbfbHIS12FaATpy5Aj5+fkEBQU5bQ8KCiIjI6PM+83IyCj1PidOnEhAQIDjFhISUubXFxERKY0zmUdYVev8UR9r3xEmp3Edpk+CtlgsTvcNwyiwraL3GRcXR2ZmpuN24MCBq3p9ERGRkvp26Vvk1ICwk+60iuhndhyXUcOsFw4MDMTd3b3AkZnDhw8XOIJTGsHBwaXep5eXF15eXmV+TRERkbKy/bAIfMDq3lLL368h0z5pT09PwsPDSUpKctqelJRE9+7dy7zfyMjIAvtcvnz5Ve1TRESkIhh2O7ZzOwGwtrvT3DAuxrQjQADjxo1jyJAhdO7cmcjISN59913S0tIYOXIkcP6rqYMHDzJnzhzHc1JTUwE4deoUf/zxB6mpqXh6etKmTRsAxowZQ69evZg0aRIDBgxg8eLFrFixgrVr117z9yciIlKcPd8n8cuF5e+39B9ldhyXYmoBGjx4MEePHmXChAmkp6fTrl07EhISCAsLA86f+PDycwJ17NjR8ffNmzczd+5cwsLC2L9/PwDdu3dn/vz5vPDCC7z44os0b96cBQsW0LVr12v2vkREREoi8Zt3Aeh5sg5+dYNNTuNaTD0PUGWl8wCJiMi1YH2qPom1j/Avz/48HbfU7DhVXpU4D5CIiIgrO5t1jJU1jwBg7a3l79eaCpCIiIgJVn71FtkeEHLKnTbd7jA7jstRARIRETGBbetCAKyWFlr+bgJ94iIiIiaw5V1Y/t72TnODuCgVIBERkWvs5y1f87N/Hh75cOvtWv5uBhUgERGRayxxxUwAbs6qTa16jUxO45pUgERERK4x26FVAFgb6CoFZlEBEhERuYayT53g25p/ABDb6xGT07guFSAREZFraNVXb3PWA6475Ua77gPNjuOyVIBERESuIVvqfwGwouXvZtInLyIicg3ZcrcDYG3zJ5OTuDYVIBERkWvkl60r+ck/jxr5cNvto82O49JUgERERK4RW9IMAHpkBeBfv7HJaVybCpCIiMg1knjwwvL3+pEmJxEVIBERkWsg+9QJvvE9DEBsz4dNTiMqQCIiItfAGttMznhCo9NutL/5brPjuDwVIBERkWvAtuUzAGKN5lr+Xgnon4CIiMg1YMv+EQBrqztMTiKgAiQiIlLh9v+4ll0Bubjbtfy9slABEhERqWC2ZW8D0D3Tn9pBYSanEVABEhERqXCJv60EwBrYzdwg4qACJCIiUoFyTmfxtW8GANaeuvp7ZaECJCIiUoHWJs7itCcEn3ajQ897zI4jF6gAiYiIVCDb9wsAiLU30/L3SkT/JERERCqQ7ezF5e+3m5xELqUCJCIiUkHSdiSzIyAHNztE9dfy98pEBUhERKSC2Ja9BUBkZi3qNGxqchq5lAqQiIhIBbGlfQOAtV5Xk5PI5VSAREREKkDu2VP/W/7eY6i5YaQAFSAREZEKsC7xXU55QtAZN27qPdjsOHIZFSAREZEKYNs0H4CY/Ca4udcwOY1cTgVIRESkAtjObgPAekN/k5NIYVSAREREytmBnRv48cLy9+jbx5gdRwqhAiQiIlLOEi9c/b1rph91GzU3OY0URgVIRESknNl+XQGAtW4Xk5NIUVSAREREylFe9hlW+KQDYO3+kMlppCgqQCIiIuVo/bL3OOkFDc5Y6NT3PrPjSBFUgERERMqRLWUeADH5TbX8vRJTARIRESlHttNbAYi9PtbkJFIcFSAREZFycvCnTWyrnY3FgGhd/b1SUwESEREpJ4mJ56/+3iWzJoEhLU1OI8VRARIRESkntv0Xlr/XjjA5iVyJCpCIiEg5yMs+Q5L3QQCskQ+anEauRAVIRESkHHyX9CFZXhB41kLnW4eYHUeuQAVIRESkHNg2zgUgJi9My9+rABUgERGRcmA7lQpo+XtVoQIkIiJyldL3ppJa+ywWA2K0/L1KUAESERG5SokJ0wDonFmT+qGtTU4jJaECJCIicpVs+5IAsAaEm5xESkoFSERE5Cqcy80myevC8vduWv1VVagAiYiIXIXvln/ICW+DemctRNyq8/9UFSpAIiIiVyHxwvL36LxQ3D08TU4jJaUCJCIichVsJ78HwNpcy9+rEtML0IwZM2jatCne3t6Eh4ezZs2aYsevWrWK8PBwvL29adasGTNnznR6PD4+HovFUuCWnZ1dkW9DRERcUMYv2/i+9lkAoq1PmpxGSsPUArRgwQLGjh3L+PHj2bJlCz179sRqtZKWllbo+H379tGvXz969uzJli1b+Nvf/sbo0aNZuHCh0zh/f3/S09Odbt7e3tfiLYmIiAtZZpsOQPgJX4KatjM5jZSGqefqnjJlCsOGDWP48OEATJ06lWXLlvHOO+8wceLEAuNnzpxJaGgoU6dOBaB169Zs2rSJ119/nUGDBjnGWSwWgoODS5wjJyeHnJwcx/2srKwyviMREXEltr3LIACs/p3MjiKlZNoRoNzcXDZv3kx0dLTT9ujoaNavX1/oc5KTkwuMj4mJYdOmTeTl5Tm2nTp1irCwMBo3bsztt9/Oli1bis0yceJEAgICHLeQkJAyvisREXEV53KzWe71GwDWrg+YnEZKy7QCdOTIEfLz8wkKCnLaHhQUREZGRqHPycjIKHT8uXPnOHLkCACtWrUiPj6eJUuWMG/ePLy9venRowd79uwpMktcXByZmZmO24EDB67y3YmISHW3ccVHHPc2qJNtoWvUw2bHkVIy/XK1FovF6b5hGAW2XWn8pdu7detGt27dHI/36NGDTp06MX36dKZNm1boPr28vPDy8ipTfhERcU2JGz4BN4jOaazl71WQaUeAAgMDcXd3L3C05/DhwwWO8lwUHBxc6PgaNWpQr169Qp/j5uZGREREsUeARERESsuWtRkAa/MYk5NIWZhWgDw9PQkPDycpKclpe1JSEt27dy/0OZGRkQXGL1++nM6dO+Ph4VHocwzDIDU1lYYNG5ZPcBERcXmH929nU+0zAMRYR5mcRsrC1GXw48aN4/333+fDDz9k586dPPXUU6SlpTFy5Ejg/NycBx/832nFR44cya+//sq4cePYuXMnH374IR988AFPP/20Y8yrr77KsmXL+OWXX0hNTWXYsGGkpqY69ikiInK1liWcX/7e8YQPwc3am5xGysLUOUCDBw/m6NGjTJgwgfT0dNq1a0dCQgJhYWEApKenO50TqGnTpiQkJPDUU0/x9ttv06hRI6ZNm+a0BP7EiRM8+uijZGRkEBAQQMeOHVm9ejVdunS55u9PRESqJ9veRPAHa62OZkeRMrIYF2cRi0NWVhYBAQFkZmbi7+9vdhwREalE8vNyafCiN8d8DNaEv83Ntz9udiS5oDS/v02/FIaIiEhVkvL1HI75GNTOttAt+hGz40gZqQCJiIiUgu27/wAQlXMdNTx1maWqSgVIRESkFBIzLyx/bxplchK5GipAIiIiJfRH2k5SAk4DENtvtMlp5GqoAImIiJTQ8oTpGBbocMKbhs1vMjuOXAUVIBERkRKy7bEBYPW7ydwgctVUgERERErAnn+OZR6/AmCNuM/kNHK1VIBERERKYNPX/+GIj4F/DkRGDzM7jlwlFSAREZESsCXPASAq+zo8vH1NTiNXSwVIRESkBBJPbALA2uQ2k5NIeVABEhERuYKjv+1hQ8ApAGJjnzQ5jZQHFSAREZErWP7VNAwLtD/hzXU3dDY7jpQDFSAREZErsO1JACC2ZnuTk0h5UQESEREphj3/HInu+wCwdv6LyWmkvKgAiYiIFOP7b+fyh69BrRzoEfuo2XGknKgAiYiIFMO2/iMAbjvbUMvfqxEVIBERkWLYjm0EwBqm5e/ViQqQiIhIEY4d2utY/m61jjI5jZQnFSAREZEiJH01DbsbtMv0onHLCLPjSDlSARIRESmCbfdXAFh9tPy9ulEBEhERKcSly99jwwebnEbKmwqQiIhIIVJXLeB3Xzt+uXCz9TGz40g5UwESEREphG1dPAC3ngnG08fP3DBS7lSARERECmE7ugEAa+gtJieRiqACJCIicpnj6ftIDjgJgDVGV3+vjlSARERELrMiYTp2N2iT6UVom0iz40gFUAESERG5jG3XUgCsPu1MTiIVRQVIRETkEobdTqJlLwDWTlr+Xl2pAImIiFxi65rPSK9pp2Yu3Byr5e/VlQqQiIjIJWxrPgTgljNBeNX0NzmNVBQVIBERkUvYjnwHgLVxX5OTSEVSARIREbngxO+/sj4gCwBrzBMmp5GKpAIkIiJywddfvUW+G7TK9KRJu5vNjiMVSAVIRETkAtvOJQBYvbX8vbpTARIREeHC8nd+BsDa8R6T00hFUwESEREBkhPf46CfHd9c6GkdaXYcqWA1zA4gIiJyrR1P38emtQtI2fUNKcd+ZKPH7xyqaQeg75kGePvVNjegVDgVIBERqdbOZB5hy9rPSPlxOSmHt5DCIfb45/1vQO3zf7jZ4cYsb+Jue8WMmHKNqQCJiEi1kZd9hu0bviRly1dsPLiRlHO/8qN/NvkXJ3xccl7D5lk1iKAREfVvoku7GDr2uJuadRqYkluuPRUgERGpkgy7nZ+3fM3GlM9J+TWZlLN7+d7vJNkeFwb4/W9s8Gk3uuQ1IKJOWyJa9qVzj3up17iFKbmlclABEhGRKuHgT5tISV7Ixp9XkXJyN5t8jnPC2zj/oPeFGxCQDZ3P1iGiVku6NO9FROTdXNciHIub1v3I/6gAiYhIpXPs0F42rf2UlN0XJykfJv3CJGVqAHXO/9XrHHQ85UcX7+ZEhEYS0flPtOgUhZu7fr1J8fQTIiIipro4SXnjD8tI+SOVFA7xcxGTlNtleRNRI5Qu10UQcVN/2nUbgIe3rym5pWpTARIRkWsmL/sMP363mJTUr0g5uImN535lezGTlLtwHRH1byKiXbQmKUu5UgESEZEKYc8/d2GS8hekpJ2fpLzF71Shk5QbnnYjIq8BXeq2I6LlLXS++V7qNmpuSm5xDSpAIiJy1Qy7nYN7NpOS/F9S9q5h48ldbPI5TuaFicmXT1KOOFuXiFotiWjeky7d7+G6GzqbFV1clAqQiIiU2rFDe0lZM5+U3d+Scnw7Gz0Ok1HIJGXvvPOTlCN8mtMlrDsRnQdwfcdbNUlZTKefQBERKdbp44fZsu6/bPzxf5OU9/qf+9+A2uf/cHdMUg4j4rrOdOl4B2273qFJylIpqQCJiIhDXvYZflj/OSlbE0g5tImN+Wlsr5WNvZBJytdneRBBI7o06Hh+kvLN9+AbEGhKbpHSUgESEXFR9vxz7Pk+iY0pi89PUs75hdSaRU9S7pLXgIi67ejS6lY63zyYOg2bmpJbpDyoAImIuADDbue33SmkfLeQjXtXk3LqJzb5HifL68IAnws3oHa2hc5n69DFvxURzXsRETlIk5Sl2lEBEhGpho7+toeUtQtI+enCJGXPP/jd98IkZQ+cJil3OlXrf5OUI+7k+o636rIRUu2ZXoBmzJjBv/71L9LT02nbti1Tp06lZ8+eRY5ftWoV48aNY/v27TRq1Ihnn32WkSNHOo1ZuHAhL774Inv37qV58+a89tprDBw4sKLfioiIKU4fP8z3az8lZXsSGw9vIcUtnV9qFT1JuYtHEyIaRRDRsb8mKYvLMrUALViwgLFjxzJjxgx69OjBrFmzsFqt7Nixg9DQ0ALj9+3bR79+/RgxYgQff/wx69at4/HHH6d+/foMGjQIgOTkZAYPHsz//d//MXDgQD7//HPuvfde1q5dS9euXa/1WxQRKVe5Z0/xw/ovzk9STj8/SXlHrZz/TVIO+N/YFhcnKQd1IqJdDDf1GKRJyiIXWAzDMMx68a5du9KpUyfeeecdx7bWrVtz5513MnHixALjn3vuOZYsWcLOnTsd20aOHMnWrVtJTk4GYPDgwWRlZWGz2RxjYmNjqVOnDvPmzStRrqysLAICAsjMzMTf3//KTyihnNNZpO/bVm77k+IZdnv57MeobPspn39ly/PzOX8zsNvPYdgNp21Of9oL2XbJ3+32/EIeL9mfdvsl++Li9kvHXPg7BbfbjfzixzjuX77vS557cYzT2Mv35zzOfvn+i/kzM/ckm3J+IdXvNDmF/K9ro9NudMkLIqJuOyJa3aJJyuKSSvP727QjQLm5uWzevJnnn3/eaXt0dDTr168v9DnJyclER0c7bYuJieGDDz4gLy8PDw8PkpOTeeqppwqMmTp1apFZcnJyyMnJcdzPysoq5bspmS1rPiVyw4gK2beIVBOWy/686LJJyhFn6xDh34ou1/cmIvJuGrXodA1DilR9phWgI0eOkJ+fT1BQkNP2oKAgMjIyCn1ORkZGoePPnTvHkSNHaNiwYZFjitonwMSJE3n11VfL+E5Kzs3NHZ+8K4+rjCymHSe8Opf/DjF9P+X0OVa+PBYsgJtxPpvl4p9YLvn7xe2WQu+7Xf6Y03OvvN3twr2C4yyXjS34p9ul2yw49lRw/GXbLJZLnu+8zek5lqLvu1ncLnltS+HPsVjwdveiQ+POmqQsUk5MnwRtsTj/p9wwjALbrjT+8u2l3WdcXBzjxo1z3M/KyiIkJOTK4UupS/TDnIl+uNz3KyIiIqVjWgEKDAzE3d29wJGZw4cPFziCc1FwcHCh42vUqEG9evWKHVPUPgG8vLzw8vIq8nERERGpXkw7hurp6Ul4eDhJSUlO25OSkujevXuhz4mMjCwwfvny5XTu3BkPD49ixxS1TxEREXE9pn4FNm7cOIYMGULnzp2JjIzk3XffJS0tzXFen7i4OA4ePMicOXOA8yu+3nrrLcaNG8eIESNITk7mgw8+cFrdNWbMGHr16sWkSZMYMGAAixcvZsWKFaxdu9aU9ygiIiKVj6kFaPDgwRw9epQJEyaQnp5Ou3btSEhIICwsDID09HTS0tIc45s2bUpCQgJPPfUUb7/9No0aNWLatGmOcwABdO/enfnz5/PCCy/w4osv0rx5cxYsWKBzAImIiIiDqecBqqwq6jxAIiIiUnFK8/tb6yhFRETE5agAiYiIiMtRARIRERGXowIkIiIiLkcFSERERFyOCpCIiIi4HBUgERERcTkqQCIiIuJyVIBERETE5Zh6KYzK6uLJsbOyskxOIiIiIiV18fd2SS5yoQJUiJMnTwIQEhJichIREREprZMnTxIQEFDsGF0LrBB2u51Dhw5Rq1YtLBZLue47KyuLkJAQDhw4oOuMXYE+q5LTZ1Vy+qxKTp9V6ejzKrmK+qwMw+DkyZM0atQIN7fiZ/noCFAh3NzcaNy4cYW+hr+/v/4FKSF9ViWnz6rk9FmVnD6r0tHnVXIV8Vld6cjPRZoELSIiIi5HBUhERERcjgrQNebl5cXLL7+Ml5eX2VEqPX1WJafPquT0WZWcPqvS0edVcpXhs9IkaBEREXE5OgIkIiIiLkcFSERERFyOCpCIiIi4HBUgERERcTkqQJVATk4ON910ExaLhdTUVLPjVEp/+tOfCA0Nxdvbm4YNGzJkyBAOHTpkdqxKZ//+/QwbNoymTZvi4+ND8+bNefnll8nNzTU7WqX12muv0b17d3x9faldu7bZcSqVGTNm0LRpU7y9vQkPD2fNmjVmR6qUVq9ezR133EGjRo2wWCx88cUXZkeqlCZOnEhERAS1atWiQYMG3Hnnnezevdu0PCpAlcCzzz5Lo0aNzI5RqfXt25dPP/2U3bt3s3DhQvbu3cvdd99tdqxKZ9euXdjtdmbNmsX27dt54403mDlzJn/729/MjlZp5ebmcs899/DXv/7V7CiVyoIFCxg7dizjx49ny5Yt9OzZE6vVSlpamtnRKp3Tp0/ToUMH3nrrLbOjVGqrVq3iiSee4LvvviMpKYlz584RHR3N6dOnzQlkiKkSEhKMVq1aGdu3bzcAY8uWLWZHqhIWL15sWCwWIzc31+wold7kyZONpk2bmh2j0ps9e7YREBBgdoxKo0uXLsbIkSOdtrVq1cp4/vnnTUpUNQDG559/bnaMKuHw4cMGYKxatcqU19cRIBP9/vvvjBgxgv/85z/4+vqaHafKOHbsGJ988gndu3fHw8PD7DiVXmZmJnXr1jU7hlQhubm5bN68mejoaKft0dHRrF+/3qRUUt1kZmYCmPbfJxUgkxiGwdChQxk5ciSdO3c2O06V8Nxzz1GzZk3q1atHWloaixcvNjtSpbd3716mT5/OyJEjzY4iVciRI0fIz88nKCjIaXtQUBAZGRkmpZLqxDAMxo0bx80330y7du1MyaACVM5eeeUVLBZLsbdNmzYxffp0srKyiIuLMzuyaUr6WV30zDPPsGXLFpYvX467uzsPPvgghoucyLy0nxXAoUOHiI2N5Z577mH48OEmJTdHWT4vKchisTjdNwyjwDaRsnjyySfZtm0b8+bNMy2DLoVRzo4cOcKRI0eKHdOkSRP+/Oc/8+WXXzr9xyQ/Px93d3fuv/9+Pvroo4qOarqSflbe3t4Ftv/222+EhISwfv16IiMjKypipVHaz+rQoUP07duXrl27Eh8fj5uba/2/Tll+tuLj4xk7diwnTpyo4HSVX25uLr6+vnz22WcMHDjQsX3MmDGkpqayatUqE9NVbhaLhc8//5w777zT7CiV1qhRo/jiiy9YvXo1TZs2NS1HDdNeuZoKDAwkMDDwiuOmTZvG3//+d8f9Q4cOERMTw4IFC+jatWtFRqw0SvpZFeZib8/JySnPSJVWaT6rgwcP0rdvX8LDw5k9e7bLlR+4up8tAU9PT8LDw0lKSnIqQElJSQwYMMDEZFKVGYbBqFGj+Pzzz1m5cqWp5QdUgEwTGhrqdN/Pzw+A5s2b07hxYzMiVVobN25k48aN3HzzzdSpU4dffvmFl156iebNm7vE0Z/SOHToEH369CE0NJTXX3+dP/74w/FYcHCwickqr7S0NI4dO0ZaWhr5+fmOc3Fdf/31jn8vXdG4ceMYMmQInTt3JjIyknfffZe0tDTNJyvEqVOn+Pnnnx339+3bR2pqKnXr1i3w33pX9sQTTzB37lwWL15MrVq1HPPJAgIC8PHxufaBTFl7JgXs27dPy+CLsG3bNqNv375G3bp1DS8vL6NJkybGyJEjjd9++83saJXO7NmzDaDQmxTuoYceKvTz+vbbb82OZrq3337bCAsLMzw9PY1OnTqZtly5svv2228L/Rl66KGHzI5WqRT136bZs2ebkkdzgERERMTluN7kABEREXF5KkAiIiLiclSARERExOWoAImIiIjLUQESERERl6MCJCIiIi5HBUhERERcjgqQiIiIuBwVIBEpsT59+jB27FizYxTq6NGjNGjQgP379wOwcuVKLBZLhV/ctKyvEx8fT+3atUv1nIiICBYtWlSq54hI4VSARMQ06enp3HfffbRs2RI3N7ciy9XChQtp06YNXl5etGnThs8//7zAmIkTJ3LHHXfQpEmTig1tohdffJHnn38eu91udhSRKk8FSERMk5OTQ/369Rk/fjwdOnQodExycjKDBw9myJAhbN26lSFDhnDvvfeyYcMGx5izZ8/ywQcfMHz48GsV3RT9+/cnMzOTZcuWmR1FpMpTARKRMjl+/DgPPvggderUwdfXF6vVyp49e5zGvPfee4SEhODr68vAgQOZMmWK09c+TZo04c033+TBBx8kICCg0NeZOnUqUVFRxMXF0apVK+Li4rj11luZOnWqY4zNZqNGjRpERkYWmffo0aP85S9/oXHjxvj6+nLjjTcyb948pzF9+vRh1KhRjB07ljp16hAUFMS7777L6dOnefjhh6lVqxbNmzfHZrMV2P+6devo0KED3t7edO3alR9++MHp8fj4eEJDQx2fxdGjR50e37t3LwMGDCAoKAg/Pz8iIiJYsWKF0xh3d3f69etXILeIlJ4KkIiUydChQ9m0aRNLliwhOTkZwzDo168feXl5wPlCMHLkSMaMGUNqaipRUVG89tprpX6d5ORkoqOjnbbFxMSwfv16x/3Vq1fTuXPnYveTnZ1NeHg4S5cu5ccff+TRRx9lyJAhTkeSAD766CMCAwPZuHEjo0aN4q9//Sv33HMP3bt35/vvvycmJoYhQ4Zw5swZp+c988wzvP7666SkpNCgQQP+9Kc/OT6LDRs28Mgjj/D444+TmppK3759+fvf/+70/FOnTtGvXz9WrFjBli1biImJ4Y477iAtLc1pXJcuXVizZk3JPjwRKZop16AXkSqpd+/expgxY4yffvrJAIx169Y5Hjty5Ijh4+NjfPrpp4ZhGMbgwYON/v37Oz3//vvvNwICAord9+U8PDyMTz75xGnbJ598Ynh6ejruDxgwwHjkkUecxnz77bcGYBw/frzI99OvXz/j//2//+eU4eabb3bcP3funFGzZk1jyJAhjm3p6ekGYCQnJzu9zvz58x1jjh49avj4+BgLFiwwDMMw/vKXvxixsbFOrz148OAiP4uL2rRpY0yfPt1p2+LFiw03NzcjPz+/2OeKSPF0BEhESm3nzp3UqFGDrl27OrbVq1ePli1bsnPnTgB2795Nly5dnJ53+f2SslgsTvcNw3DadvbsWby9vYvdR35+Pq+99hrt27enXr16+Pn5sXz58gJHWNq3b+/4u7u7O/Xq1ePGG290bAsKCgLg8OHDTs+79Ou3unXrOn0WO3fuLPD13OX3T58+zbPPPkubNm2oXbs2fn5+7Nq1q0A+Hx8f7HY7OTk5xb5fESleDbMDiEjVYxhGkdsvFpPLS0pxzytOcHAwGRkZTtsOHz7sKCIAgYGBHD9+vNj9/Pvf/+aNN95g6tSp3HjjjdSsWZOxY8eSm5vrNM7Dw8PpvsVicdp28T2VZCXWpZ/FlTzzzDMsW7aM119/neuvvx4fHx/uvvvuAvmOHTuGr68vPj4+V9yniBRNR4BEpNTatGnDuXPnnObPHD16lJ9++onWrVsD0KpVKzZu3Oj0vE2bNpX6tSIjI0lKSnLatnz5crp37+6437FjR3bs2FHsftasWcOAAQN44IEH6NChA82aNSswaftqfPfdd46/Hz9+nJ9++olWrVoB5z+vSx+/fPzFfEOHDmXgwIHceOONBAcHO85pdKkff/yRTp06lVtuEVelAiQipdaiRQsGDBjAiBEjWLt2LVu3buWBBx7guuuuY8CAAQCMGjWKhIQEpkyZwp49e5g1axY2m63AUaHU1FRSU1M5deoUf/zxB6mpqU5lZsyYMSxfvpxJkyaxa9cuJk2axIoVK5zOGRQTE8P27duLPQp0/fXXk5SUxPr169m5cyePPfZYgSNLV2PChAl8/fXX/PjjjwwdOpTAwEDuvPNOAEaPHk1iYiKTJ0/mp59+4q233iIxMbFAvkWLFpGamsrWrVu57777Cj3KtGbNmgKTwkWk9FSARKRMZs+eTXh4OLfffjuRkZEYhkFCQoLj66IePXowc+ZMpkyZQocOHUhMTOSpp54qMFenY8eOdOzYkc2bNzN37lw6duxIv379HI93796d+fPnM3v2bNq3b098fDwLFixwmn9044030rlzZz799NMi87744ot06tSJmJgY+vTpQ3BwsKOglId//vOfjBkzhvDwcNLT01myZAmenp4AdOvWjffff5/p06dz0003sXz5cl544QWn57/xxhvUqVOH7t27c8cddxATE1PgSM/BgwdZv349Dz/8cLnlFnFVFqMsX8qLiJTBiBEj2LVrV4Us405ISODpp5/mxx9/xM2tev6/3TPPPENmZibvvvuu2VFEqjxNghaRCvP6668TFRVFzZo1sdlsfPTRR8yYMaNCXqtfv37s2bOHgwcPEhISUiGvYbYGDRrw9NNPmx1DpFrQESARqTD33nsvK1eu5OTJkzRr1oxRo0YxcuRIs2OJiKgAiYiIiOupnl+Ui4iIiBRDBUhERERcjgqQiIiIuBwVIBEREXE5KkAiIiLiclSARERExOWoAImIiIjLUQESERERl/P/AZaP27Xvhj1uAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_120_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -3042,138 +2528,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Beta values for own Ridge implementation\n",
-      "[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01\n",
-      "  2.18613217e-01  1.02054837e-01 -4.25617658e-04 -5.90475506e-02\n",
-      " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
-      "  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02\n",
-      "  2.02198703e-02 -3.46383925e-03 -3.63025821e-02]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[ 3.43579948e-02 -5.43330971e-01 -3.10141413e-03  2.47116868e-01\n",
-      "  2.18613217e-01  1.02054837e-01 -4.25617654e-04 -5.90475506e-02\n",
-      " -7.68534263e-02 -6.68929213e-02 -4.24906604e-02 -1.40927184e-02\n",
-      "  1.11482289e-02  2.88529063e-02  3.67047975e-02  3.38135733e-02\n",
-      "  2.02198702e-02 -3.46383925e-03 -3.63025821e-02]\n",
-      "Intercept from own implementation:\n",
-      "1.0330308045188872\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "1.0330308045183219\n",
-      "MSE values for own Ridge implementation\n",
-      "3.1392559591206444e-06\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "3.1392559585048734e-06\n",
-      "Beta values for own Ridge implementation\n",
-      "[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649\n",
-      "  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
-      " -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906\n",
-      "  0.04423486]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[-0.05807125 -0.29822833 -0.08551306  0.08156108  0.13679863  0.12333649\n",
-      "  0.08251519  0.03815288  0.00111756 -0.02498832 -0.04010697 -0.04566964\n",
-      " -0.04355837 -0.03562355 -0.02348765 -0.00848904  0.00831018  0.0260906\n",
-      "  0.04423486]\n",
-      "Intercept from own implementation:\n",
-      "1.041148729430595\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "1.041148729430523\n",
-      "MSE values for own Ridge implementation\n",
-      "1.96013048502692e-05\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "1.960130485007504e-05\n",
-      "Beta values for own Ridge implementation\n",
-      "[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251\n",
-      "  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499\n",
-      " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528\n",
-      " -0.01290947]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[-0.1416398  -0.14021063 -0.05383795  0.01367553  0.04784395  0.05796251\n",
-      "  0.05447415  0.044613    0.03267527  0.02098261  0.01066519  0.00217499\n",
-      " -0.00440346 -0.00917248 -0.01231917 -0.01405935 -0.0146081  -0.01416528\n",
-      " -0.01290947]\n",
-      "Intercept from own implementation:\n",
-      "1.0495569966278295\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "1.0495569966278269\n",
-      "MSE values for own Ridge implementation\n",
-      "5.4959161509377256e-05\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "5.495916150936645e-05\n",
-      "Beta values for own Ridge implementation\n",
-      "[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529\n",
-      "  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792\n",
-      "  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
-      " -0.00905423]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[-0.13535942 -0.08593216 -0.03568439 -0.0036367   0.01397146  0.02229529\n",
-      "  0.02503753  0.0245528   0.02228115  0.01908936  0.01549377  0.01179792\n",
-      "  0.00817631  0.00472512  0.00149311 -0.00149956 -0.00424967 -0.00676387\n",
-      " -0.00905423]\n",
-      "Intercept from own implementation:\n",
-      "1.0399676689527966\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "1.0399676689527975\n",
-      "MSE values for own Ridge implementation\n",
-      "7.571105947979352e-05\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "7.571105947979394e-05\n",
-      "Beta values for own Ridge implementation\n",
-      "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114\n",
-      " -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018\n",
-      "  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011\n",
-      "  0.00683964]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[-0.05100875 -0.04063602 -0.02723445 -0.01713366 -0.0100706  -0.00517114\n",
-      " -0.00174276  0.00068734  0.00243186  0.00369758  0.00462287  0.0053018\n",
-      "  0.00579953  0.006162    0.00642221  0.00660427  0.00672607  0.0068011\n",
-      "  0.00683964]\n",
-      "Intercept from own implementation:\n",
-      "0.999955585168597\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "0.999955585168597\n",
-      "MSE values for own Ridge implementation\n",
-      "0.0007698473260556344\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "0.0007698473260556325\n",
-      "Beta values for own Ridge implementation\n",
-      "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
-      " -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117\n",
-      " -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
-      " -0.00058016]\n",
-      "Beta values for Scikit-Learn Ridge implementation\n",
-      "[-0.00834567 -0.00803064 -0.00673407 -0.00554552 -0.00458878 -0.0038335\n",
-      " -0.00323332 -0.00274989 -0.0023548  -0.00202756 -0.00175331 -0.00152117\n",
-      " -0.001323   -0.0011526  -0.00100519 -0.00087697 -0.00076495 -0.00066668\n",
-      " -0.00058016]\n",
-      "Intercept from own implementation:\n",
-      "0.9637117593816477\n",
-      "Intercept from Scikit-Learn Ridge implementation\n",
-      "0.9637117593816477\n",
-      "MSE values for own Ridge implementation\n",
-      "0.0023813163025848865\n",
-      "MSE values for Scikit-Learn Ridge implementation\n",
-      "0.002381316302584886\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_122_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -3720,32 +3075,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
-      "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/4162706317.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
-      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 2000x1400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_154_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "im = plt.imshow(J, **cmap_args)\n",
@@ -4032,32 +3362,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:6: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
-      "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3777801602.py:7: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
-      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 2000x1400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_172_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "im = plt.imshow(J_sk, **cmap_args)\n",
@@ -4111,32 +3416,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:9: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
-      "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/438060758.py:10: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
-      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 2000x1400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_175_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "_lambda = 0.1\n",
     "clf_ridge = skl.Ridge(alpha=_lambda).fit(X_train, y_train)\n",
@@ -4198,32 +3478,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:8: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
-      "  cb = fig.colorbar(im)\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3544313922.py:9: UserWarning: FixedFormatter should only be used together with FixedLocator\n",
-      "  cb.ax.set_yticklabels(cb.ax.get_yticklabels(), fontsize=18)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 2000x1400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_179_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "clf_lasso = skl.Lasso(alpha=_lambda).fit(X_train, y_train)\n",
     "J_lasso_sk = clf_lasso.coef_.reshape(L, L)\n",
@@ -4260,127 +3515,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "\r",
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-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_coordinate_descent.py:647: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations, check the scale of the features or consider increasing regularisation. Duality gap: 3.924e+00, tolerance: 1.797e+00\n",
-      "  model = cd_fast.enet_coordinate_descent(\n",
-      "\r",
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-      "\r",
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wtuSOpfne++///u/0a1/72vSiRYvS73vf+9L33ntvoK/fs2dP+sYbb0wfd9xx6SOPPDJ94YUXpm+77bb0vHnz0i+99NK+du655570m9/85vQRRxyRPv7449OXX355+sUXXyx4uYeaI7jyg3SaHIEcAQAObtnj5C9/+cv0aaedlj7yyCPTK1asSF9yySXpJ598Mj1//vz0Pffck06n/b7jWzE+5xV8kQcMGGoeMBz5QjpNHgAABzJqAcNnLH7PL2TMLmT+AICxh1oA5wAKiSVHGF9i6XQ6PdoXtwGj7ayzztKtt9667zaYAAAgOm1tbVq9erVOOOEETZkyZd/7X/jCF3T//ffriSeeGMWly4/8AACA8Ys8AACAgxNjPAAAw4daAHBw4lGYGHPS6bT6+vrMuHg8rng8PuT5/f73v1d3dzcDBQAAw6SsrEw33HCDDj/8cH3gAx9QeXm5nn76aX3nO9/RRRdd5N3OSOYI5AcAAIwdnCcAAODgxBgPAMDBhVoAcHDijmUYc5544gm9//3vN+MuueQSXXrppUOe34svvqiJEyeqqqpqyG0BAIBwzz77rG699VatWbNGXV1dmj17ts4880ydddZZisViXm2MZI5AfgAAwNjBeQIAAA5OjPEAABx8qAUABx8uLMOY09HRoeeee86Mmz59umbMmDECSwQAAMYCcgQAAMYncgAAAA5OjPEAACAMOQIwtnBhGQAAAAAAAAAAAAAAAAAgYOgPpQcAAAAAAAAAAAAAAAAAHFS4sAwAAAAAAAAAAAAAAAAAEBD5hWWpVEq33367TjjhBB111FE677zz9Pzzz0c9GwAAMMaQAwAAMD6RAwAAMD6RAwAAMH6RBwDA+BFLp9PpKBu84447dO+99+rf//3fNWPGDH3pS1/SCy+8oAcffFAlJSUFt5dKST09A69jMamkJPNe/5J3dNjt1FT2OKeni+1l6+uz55NM2jETJtgxsZQ9s2S6yDk9EU/ZM8r9ULGYVFSUeX/vCu5JF5vNlMTtD56KJ8yYeNr9uXd3uj+zJE2caIYo3rvHjEmX2BsqtqfbOT1VUrr//4kN7Lv9r6OQ8tjcRb3u5ZXCl7lQ8ZjdrST77A9eZG9u5fZguetXkuIp9/6ZLrL3zVivuw+RpN6Y3Y8Up+x9Tz59pbXB4/Z1w7va3dtg0iSvZoB9os4B9juYQ+xstfuSqdXudlJpuw2fPtYnT5hQEk3aZfWhCXkkJGEd6DDlAH0xu58tirvXTWeXvZ18drNEuteMSRXZnzu+p8s5PVlctt97/at337J45Gopj9+B+OQSVs4i2TmAz/juI6ocwEesL4IcwGhD8tzHPfIwry8KRmfj85ms708TJ5IDoDCjkQNsfq7VjJnzqmrndJ+xxac/arUXRTNr7c+Ulr08vcYwVpLwSFrC5HyRernL7gQmTrD7x9603ScVx9392maPukRZmb2hZiZ22A3V1Ngxzc3OyW2ltYHX8Xjmu9Xu3QM5ZdXkaMbU3qS9zxR3vGTGNO2Z4pxeO8FuQ2X75z652rrt8w1VE+1cTQl7v1Jnp3u6z5jr0QG07LS3Qc1Ue3v7fCeJd7oH8A5VmG1s397mnH7IIZNUXBxRIoZxIfIcQMF6QFgtQKIekE/B9YCQ8wAS9QCXQusBYeeqqQfkV2g9IGz9StQD8nHVAyZNyszCJ80C+lEPsGPGbD1gmHMA6gH71wIk6gEu1ANcMxveesDEiX45QKQXlvX09Gj58uX6+Mc/rve85z2SpPb2dp1wwgm68cYbddpppxXcZne39Je/DLwuL5eOPFL6618HzhF997t2O7dfstG97PXzzDZaWuz5bNlixyxbZseUtG03Y5rT053TZ5S12zPK/VAlJVJdndTQsO8b/MbkHLOZeaVbzZj2qtlmTGXSfUb+vx90FwYk6V3vMkNUvuFpM6Zn0VIzpuSpR53TO5ccH3gdi2XOtXZ1DYzTUSXqPidUqje4l1eS2hcdb8ZYKkvtL11bm+zRvrbWDAmcvAlbv5JU3tbobCNVO8ucT3yTuw+RpM0Jux+Z02bve1qyxI6xOqSqKrOJr93t3gZnnSVNnmwvCiANTw6gdDrkStF44Fvdx66wk+xbbnL3SZ1Juz/yyQHa2uyYxQvs/tFHY4t7mWcl7XF5v7Pfg80BKtx9rCS1ltr9bHWFe9385mF7Oy1YYIZodnKzGdNeY3/uyjWrndMb554YeF1cLE2bJu3YMXBRwKwqo+ApqT1ZbsaUepwDLlnzpBnTuegY5/Ty0kFerJBja4N93PrkANliscw67u0NdhslLe79s6fG3jetNiTPfXyTvQ28vig0NDgn99TaOfc997in/+u/Zk4qAz5GKweIFX3Sbqbv353Tf/Nbuz/yuc7oqqvsmN/8yu5De5L28mza5J6+sN4eW/bLAeJxqaIi86Vy7zr+6cOVZjNvWWb3j5u77f5xTpX7PEBsqn1C741vdJ8fkaRfzjzPjNHdd9sxxkmHLxx7f+D1jBnSOedI3/rWwDVpn/i4x5jqcaXC5gY7P5rzPzeYMe/489XO6fcv+ZzZhk491Qz5wh/s8w2f+Fc7V1N9ffB1Tv8gSXrgAXcbPmNuXZ0Z8uHL7OP29lX2d4D2bntbVv7qB87p30//P7ONM8+8yTn9n/+8SHPmVJntANIw5QAK1gPCagES9YB8Cq4HhJwHkKgHuBRSD8h3rpp6QH6F1APyrV+JekA+rnrAWWdl/qYeAF8jci4gJM+nHhCu4HrAUHIA6gGhsusBYbUAiXqASyH1gHy1AIl6QD6uesC//mvmb6seEOnv0Dds2KCXX35Zy5cv3/deZWWlFi5cqD/96U9RzgoAAIwh5AAAAIxP5AAAAIxP5AAAAIxf5AEAML5EemFZU1OTJGnmzJmB96dPn65t27ZFOSsAADCGkAMAADA+kQMAADA+kQMAADB+kQcAwPgS6dOyu7oyz5bNfW7yhAkTtGvXrkG1GYtlbnndr//Wftm3+PO4M735fFKfZ9EW24/X1cSJdozPvHzuh5ywHmLq8Uz1/R4+3P8hsz7sBJ9n2nqsHJ/FsR6gW23f+dpv/ZaVmSFe7RgbPLeN/tfZ73vNx4PXs4c9dlCv7WTx+FA+x5PXM6JD1uV+/89nZhaPZxyX+GwDj33Pi/mgY3vlWY/1iep51hgfhiMH8PGKV3gEGcdDVDmA1+EdUadvLk/MY4FzO/xhzAG8+hNj3fg8ls+ru4/bt9D2GgsrKgpalv5uO9B9e+wPPsvitVuV27fQjionsUSVA3j9X2NmXvOJah/32AZeIvhMU6e6p0eSD2LcGK0c4Oij7VvOW3zGFp/xfe7cIS+KJL/j13zcgU8juQd5/+us970egePRP5b4PDXB6ESPPtpu4tBDPeZTYz8awMsc9yMyZswIvu4/j+FzPiPAY1vmntIJ5fE8CeMj+T2TwuN8Q+66CeX1oTxYj4OK4jyBPM9JRpTzWZ9pikcTRx/t3gglXic2gIzhygGy6wFhtQCJekBehdYDQs4DSNQDnAqoB+Q7V009YEjN7LdeQ/8P9YBQrnpAUZHU11fgMmFcox5wgNcDhjkHGO/1gNBagEQ9wGGwy1LoNQHUA/YX8tTh8Pmk07lPHh28X//61/rwhz+sv/zlLyrN+rb3kY98RD09PbrzzjsLbjOdHrmdGgAADM5w5AAkAQAAjH3kAAAAjE/DkgOINAAARsuuXZ4/MAHEuQAAOJjs3m1fzBnpHcv6b3e5fft2zZ498EvQ7du3a8GCBYNqs6dH2rhx4HVpqXTYYdI//iF1d2fe++Uv7XaufPfzzum9s15pttHWZs+nsdGOWbjQjine3WrG7Ey7f64zdUKHPaPcD1VcnPkJaXOz1NsrSXq+z/4J2CtL7NuadkyaacZU9LmvYn/wD3ZW+9rXmiEq2/KsGdM793Azpnj9X5zTu+YdFXgdi2X24e7uTH4kef0YzUtnpx0zeYt7eSWp49CjzBhLxYReM2Zbi321r3VHLUlKJgf+HbZ+JamsY4ezjdTUaeZ84i+4+xBJaiiy+5G63fa+p/nz7RirQ/K4lP8HP3Zvgze/2bwAH9hnOHIASftfJp9z6fzNX7Z/vnH5h919UlfS7o98coAOj2H3sHq7f/Sxo829zNOSHrcbz/0Z4mBzgHJ3HytJu0rsfnZyuXvdPPaUvZ3q680QzexrMGM6quzPXbHxaef0HYcsDbxOJKQpU6SXXhoYu6ZVdNnL0mf/9M3jR7Qq/vs6M6br0EXO6WUTfG47Y9vWbB+3PjlAruLifbvuwHtt7v2zt8reN602JM99/AV7G3h9UWhudk7urbFz7l/8wj391FP97rwASKOXAyxd9hWziaefutQ5/bEn7P7IuumRJH3FXhR97Q67D+3ts5fnhRfc0+fMtMeW/XKAeDzzK8rOzn3r+Pd/tr8InLTQ7h8b9tj9Y90k93mApafYt044/nj7diZ31Fxnxujaa+2YK690Tv7WolWB19XV0lveIv30p1Lr3lM957zfY0z1uGVEQ7OdH9X9+j/MmCuePd85fdW8b5ht6NhjzZBvPWOfbzjnVDtX06ycOxaG/bz24YfdbRxun/PxucXaF1fZx+2VH7W/A3TssbdlxaO/cU7/jV5vtnHVVf/lnP7Tn75LdXUetwYANHw5QHY9IKwWIFEPyKfgekDIeQCJeoBLIfWAfOeqqQfkV0g9IN/6lagH5OOqB7z5zfYiANlG5FxASJ5PPSBcwfWAoeQA1ANCZdcDwmoBEvUAl0LrAWG1AIl6QD6uesCpp9qLIEV8YdmCBQtUUVGhJ554Yt8g0t7ervXr1+vss88eVJvpdHiC3N098H6Dxzkn7dljzscStnPmevllO8brHnHZvUy+EKudYo+Dvacn/P3e3n3T9tiLIsXsleNzCz3rxGmr/f3ab/122R23VzvGBs/XRjo9MC2qewZ63abYYwf12k4Wjw/lczz5rJuwmOz16z0zi9GHSFKPT4/qse95sfoIj5XX0uK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-      "text/plain": [
-       "<Figure size 3200x5400 with 30 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_181_13.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "lambdas = np.logspace(-4, 5, 10)\n",
     "\n",
@@ -4448,22 +3583,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 2000x1400 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_183_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "fig = plt.figure(figsize=(20, 14))\n",
     "\n",
@@ -4587,32 +3707,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:9: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
-      "  ax = fig.gca(projection='3d')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7650/3980313467.py:37: MatplotlibDeprecationWarning: Auto-removal of grids by pcolor() and pcolormesh() is deprecated since 3.5 and will be removed two minor releases later; please call grid(False) first.\n",
-      "  fig.colorbar(surf, shrink=0.5, aspect=5)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter3_188_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from mpl_toolkits.mplot3d import Axes3D\n",
     "import matplotlib.pyplot as plt\n",
@@ -4978,19 +4073,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'scipy' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [31]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mscipy\u001b[49m\u001b[38;5;241m.\u001b[39mmisc\u001b[38;5;241m.\u001b[39mimread\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'scipy' is not defined"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "scipy.misc.imread"
    ]
@@ -5072,7 +4155,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
index 1c1376439..531d2afc9 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter4.ipynb
@@ -182,148 +182,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>ID</th>\n",
-       "      <th>Age</th>\n",
-       "      <th>Agegroup</th>\n",
-       "      <th>CHD</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>1</td>\n",
-       "      <td>21</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>2</td>\n",
-       "      <td>23</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>3</td>\n",
-       "      <td>25</td>\n",
-       "      <td>1</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>4</td>\n",
-       "      <td>29</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>5</td>\n",
-       "      <td>21</td>\n",
-       "      <td>1</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>...</th>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "      <td>...</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>95</th>\n",
-       "      <td>96</td>\n",
-       "      <td>61</td>\n",
-       "      <td>8</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>96</th>\n",
-       "      <td>97</td>\n",
-       "      <td>69</td>\n",
-       "      <td>8</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>97</th>\n",
-       "      <td>98</td>\n",
-       "      <td>65</td>\n",
-       "      <td>8</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>98</th>\n",
-       "      <td>99</td>\n",
-       "      <td>64</td>\n",
-       "      <td>8</td>\n",
-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>99</th>\n",
-       "      <td>100</td>\n",
-       "      <td>63</td>\n",
-       "      <td>8</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "<p>100 rows × 4 columns</p>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "     ID  Age  Agegroup  CHD\n",
-       "0     1   21         1    0\n",
-       "1     2   23         1    0\n",
-       "2     3   25         1    1\n",
-       "3     4   29         1    0\n",
-       "4     5   21         1    0\n",
-       "..  ...  ...       ...  ...\n",
-       "95   96   61         8    1\n",
-       "96   97   69         8    1\n",
-       "97   98   65         8    1\n",
-       "98   99   64         8    1\n",
-       "99  100   63         8    0\n",
-       "\n",
-       "[100 rows x 4 columns]"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_8_1.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Common imports\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mos\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -403,22 +275,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_10_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
     "group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
@@ -536,50 +393,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_18_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_18_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_18_2.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"The sigmoid function (or the logistic curve) is a\n",
     "function that takes any real number, z, and outputs a number (0,1).\n",
@@ -1090,32 +904,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(426, 30)\n",
-      "(143, 30)\n",
-      "Test set accuracy with Logistic Regression: 0.94\n",
-      "Test set accuracy Logistic Regression with scaled data: 0.96\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1163,36 +952,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x2000 with 30 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_57_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 1500x800 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_57_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1334,77 +1094,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(426, 30)\n",
-      "(143, 30)\n",
-      "Test set accuracy with Logistic Regression: 0.94\n",
-      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
-      "[1.         1.         1.         1.         1.         1.\n",
-      " 1.         1.         0.92857143 0.92857143]\n",
-      "Test set accuracy with Logistic Regression  and scaled data: 0.96\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_2.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_3.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter4_64_4.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1464,7 +1154,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter5.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter5.ipynb
index 12b1fb151..8c3154897 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter5.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter5.ipynb
@@ -54,27 +54,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "LinearSVC:                    [0.28475098] [[1.05364854 1.09903804]]\n",
-      "SVC:                          [0.31896852] [[1.1203284  1.02625193]]\n",
-      "SGDClassifier(alpha=0.00200): [0.117] [[0.77714169 0.72981762]]\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01msklearn\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m datasets\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01msklearn\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01msvm\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m SVC, LinearSVC\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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ErqaiPhhNyMLCwmAmMzg4GFB1Vg8dOvTK+8UG9gAdOnRg8+bNFC9enE6dOpEnTx4sLS15/PgxM2bMSLDvGCBPnjxJBq4AFStWpGLFivr3e/fupXv37uzZs4c5c+bwxRdf6I/lzZuXFi1asHHjRnbv3k3Dhg05ePAgly9fplGjRgaBK4CzszMAgYGBSY5BCPH28feHEiXgpdQGBqyt4fJlCWAzO1k2bCKXLsHUqSo3Uyw/P/jySyhQAM6eTcHN8uSBUaPUDTZvhubNVXD711/Qtq2qITtxIvy3hEoIIcTbK/YT6mHDhqFp2itf48aNA8DHx4fNmzfTtGlTLly4wIIFC/j+++8ZP378K5M1Aa8NXBNTv359vvvuOwB2796d4PjLiZsSS9QUq1atWgDs2rUrxeMQQmRtQUFJB66gjic1MysyBwleTcTREb76SsWbf/6pkgjHypsXXpMYMXHm5mqWdetWdeORI9Wah1u34JtvoGBB6NQJ9u2TcjtCCPGWqlq1KjqdjiNHjiTr/Njlxi1atEiw7/XAgQMmH19is+GxmjdvTr58+diwYQOBgYH88ccf5MqVi7Zt2yY4t0OHDuTMmZN169Zx6dKlJPtMbOZYCCFE5ifBq4mZm0Pr1vD333Dhgtr7Ony4ao+vd281eXr/fjJvXLgwTJmiAtdly+C99yAqCv74A+rXVwmgZs2CkBBTP5IQQogMzNnZmY8++ojDhw/zww8/kFgqi2PHjhEWFgaoZE1Agvqv58+fZ/LkySnu//r168yaNYsnT54kOPbs2TNmzJgBQO3atRMcNzc3p1evXjx//pxOnTrx9OlTunfvnmipG3t7e3744QciIiJo0aIFp06dSnBOdHQ0Xl5eDBgwIMXPIYQQIuPLOJt7sqBSpWDmzITtly+rRMIA330HH32kgtzq1ZNxUysr6NZNvU6fVgmeli1TkfLQoWq5cbduam9svH1HQggh3ryzZ88aJGKKr3LlykkmpUiJOXPmcPnyZb766iuWLl1KzZo1sbOzIyAggBMnTnDlyhXu3LmDra0t1apVo1q1avzxxx/cuXOHGjVq4O/vz6ZNm2jRogVr165NUd8hISEMHTqUESNGUKdOHcqUKYONjQ2BgYFs2bKF4OBgqlSpwtChQxO9vk+fPkyZMkW/X7dPnz6v7OuTTz4hNDSUUaNGUblyZerWrUulSpX0/e3atYvAwED69euXomcQQgiRSaRdtZ7UCQ0N1UaMGKE1btxYX69v3Lhxybq2Xr16+tp4ib3u3Lnz2nNfV5PvZcmtSRTfb79pmk4XV9419lW1qqZ5eWlaisu+PX6sabNmaVrp0oY3rFlT05YuTcUNhRAi9aSGZVyd16RerVu3TrLOa7169RK9t6urq+bq6pqgPSwsTJs2bZpWpUoV7Z133tFsbGy0woULa23atNF+//13LTIyUn/u/fv3tT59+mj58+fXrK2ttXLlymmzZ8/Wrl27pgFar169ktWnpmlaeHi4tm7dOu2TTz7RKlSooDk5OWnm5uZarly5tNq1a2s///zza/8u1K1bVwO0ypUrJ3lerMuXL2tDhgzRSpcurWXPnl2ztLTUChQooLVp00Zbu3atFhMTk6z7pBf5HhHCtE6cSPhzdWKvEyfSe6TiVZIbU2W4Ujk3btygYsWKVKhQgeLFi7Nw4ULGjRvH+PHjX3vthQsXCA0NNWgLCwujWbNmVKlSxWA/UP369QkICGD58uUG59vb21OyZMlkjze5aZ1fduOGmjRduBD+SxSp5+QEH3+sJk8LFkz2LdX35YEDMGcOrFunlhWD2pDbty/07w9FiqTghkIIkXJSBkSIpMn3iBCmdfIkVKny+vNOnIDKldN+PCLlMm2pHFdXVx49eoROpyMoKIiFCxcm+9rSiWRF8vLyIjIyMtElRDY2NtSoUcOo8aaWm5vKTjx+PKxapZYXx5bzCwqCyZPh6FFIJDnjq+l0ULeuet29C4sWwW+/QUAATJsGP/ygis8OHKgyGL+8EVcIIYQQQgghMqgMl7BJp9OlKh3/qyxatIjs2bPTqVMnk93TlGxsVPKmEyfg0CHo0iWuhOvgwYbnxsTA06fJvLGzM4wZA9euqfTHTZuqmdnt2+HDD1UR2smTU5AxSgghhBBCiIzHyUnVcU2KtbU6T2RuGS54NaUrV65w4MABOnfuTPbs2RMc9/Pzw8HBAQsLC4oWLcqYMWN4/vx5OoxUTZq+9x6sWKEKLU+dqrIWx+ftrWrGfv45/PtvMm9sYaFutGMHXLmiUh87OMDNm/D11+DiAl27quXGGWsFuRBCCCGEEK9VqJBKiHrixKtfly+r80TmluGWDZvSokWLgMSLndeuXZtOnTpRsmRJnj9/zvbt25k2bRoHDx5kz549mJklHtdHREQY1I97eY+tKeTLp2rGvmzWLAgNhRkz1KtZM5Wl+IMP4BXDNeTurpYOT5igSuzMnQvHjsHKlepVtiwMGgTdu0OOHCZ/LiGEEEIIIdJCoUISnL4NsuzMa1RUFF5eXpQpUybRfa0TJ05k4MCBNGjQgObNmzNz5kymTJnC/v372bhx4yvvO3nyZOzs7PSvginKqJR6MTEqqI2/JGLHDmjZEooVg59/hkePknkzGxvo1Uttqj1xAvr1U23nzqngNX9+9evZs2nyLEIIIYQQQgiRUlk2eN22bRt3795NUa237t27A3D06NFXnjN69GhCQkL0r4CAAKPHmhxmZir3UmCgmjx1c4s7du0aDBumlhR/8ol6n2yVK8OCBXD7NkyfDiVKqI21c+dC+fJQp46alY032yyEEEIIIYQQb1qWDV4XLVpEtmzZ6NGjR4qvfdWSYQArKyty5sxp8HqTHBzUttWrV2HTJmjSJO7Y8+cqDn38OBU3treHzz6Dixdh1y7o0EFlIz54UO2JLVhQ7ZG9edNETyKEEEIIIYQQyZclg9e7d++ybds22rRpg6OjY7Kv8/LyAki38jkpYW4OrVrBzp0q3hw6VG1Tfe+9hPWrTpxQlXOSRaeD99+HNWtU5qhvv1XLiB88UNmJCxdWHW/frtYyCyGEEEII8Rbz91e1Zl/18vdP7xFmHRkyYdP27dt59uwZT548AeDChQusXbsWgObNm2Nra0vfvn3x8vLCz88PV1dXg+u9vLyIiop65ZLhAwcO8P3339O2bVuKFClCeHg427dvZ/78+bz//vu0atUqbR/QxEqWhF9/he+/hzt3DI9pmtre+u+/8NFHKsFT9eoqRn2t/Plh7FgYPRo2b1ZLib29YcsW9SpcGAYMgD59JPe4EEIIIYR46/j7q1134eGvPsfaWrIdm4pO0zJefRQ3NzduvmJ56vXr13Fzc8PDwwMvLy/9+/hKlCjBixcvuHbtWqI1Y69evcpnn33G6dOnCQoKQqfTUaxYMTp37sywYcOwsrJK9lhDQ0Oxs7Njx44dNGrUCHNz8xQ9a1rbuxcaNDBsq1JFzdR26vT6mlgJXL4M8+aBp2fc+uRs2VRkPGgQ1KiRzMhYCJFVhYeHc/36dQoXLox1iv+RESLrk+8RIbKOkyfVz9avc+JEwtWRIk5sTBUSEpLktswMGbxmJrF/0ACurq5cvnw5RcFvWgsMVCV2FiyAhw8Njzk6wscfw8CBqfgkKCwMVq2COXPUd2OsChVUENu1KyRSW1cIkfXJD+ZCJE2+R4TIOiR4NY3kBq9Zcs9resiVKxcVK1Y0CFx37tzJw5cjxjesQAG1VTUgAJYsMfymefgQpkxRq387d1ZLjJPN1lYtF/b1hePHoXdvNY17+jT07686HjoULlww+TMJIYQQQggh3j4SvJrI5cuXmTt3rv59SEgIbdq0IV++fPj5+aXjyBQbG/DwULHm4cNqYtTSUh2LiQELCyNW+1atCosXq2nen34Cd3cIDVVTvmXKQP368Mcf8OKFiZ5GCCGEEEII8baR4NVErKysyJcvn/79rVu3KFWqFMWKFaNIkSL69h07dvDPP/+QXqu1dTqoWROWL49LJpwvn0rkFN/z5zBihNrimmwODvDll+qiv/6CNm1Ugdp9+9QG20KF4Jtv1DSwEEJkYWFhYUyaNInKlSuTPXt2rK2tcXFxoU6dOowePRo/Pz927tyJTqejWbNmr71f+/bt0el0rF+/3qA9KiqKJUuW0Lx5c5ydncmWLRt2dnZUrVqV//3vf6/MHyGEEEJkRrLn1UivW5/96NEjcuXKBUBMTAxFixblxo0b/Pnnn7Ru3fpNDzdRkZEJZ14XL4a+fdXvmzRRK4A/+ECV6EmRgAC14XbBgrh6PWZmqtzOoEHQqJF6L4TIMt72/XxPnjyhdu3anDlzBnd3dxo2bIi9vT0BAQGcP3+e06dPs2DBAvr06UPhwoW5desWN2/exMXFJdH7BQUFkT9/fuzt7QkMDMTyv2UzN2/epHXr1pw+fZq8efPSuHFjChYsyLNnzzh58iRHjhzBwsKCc+fO4e7u/ib/CMRrvO3fI0JkJbLn1TSSu+c1Q5bKyUpiA1dQX5Rq1aoRFhZG48aN9e179+7l/v37fPjhh+nyn1js8uH4Fi2K+/1ff6lX4cIq3uzTR02yJkvBgjBhgppx/fNPVW5nzx7YuFG93N1VuR0PD5VBSgghMrnp06dz5swZ+vbty4IFCxJkvb9+/ToRERGYmZnh4eHBhAkT8PLyYsyYMYneb+nSpURGRtKzZ0994PrkyROaNm3K5cuXGTFiBBMmTEjw/8fVq1f58ssvefr0ado8qBBCCPGGyZTXG2Rvb8/q1avx9/fH1tZW3z5p0iQ6derEjz/+mI6jM7R5M/z4owpYY12/rpYSu7ioLMWnT6fghpaW0LEj7N4N58+rqdycOeHqVRg+XN3Uw0Mlf5LFAEKITOzIkSMADBkyJNFybYULF6ZkyZIA9O7dG51Oh6en5yvvt2TJEgD69Omjb/vxxx+5fPky3bt3Z9q0aYl+8Onu7s6mTZsoXbq0MY8jhBAiCU5Ory89aW2tzhPGk+A1HcTPSKxpGjVq1KBQoUJ07dpV33769GkmTZqEv79/egwRBwcYNgyuXFGBbNOmcceeP4eFC6FiRfjtt1TcvHRp+PVXuH0b5s9XNwoPBy8vqF4d3n1XTf2GhZnoaYQQ4s1x+G9pytWrV197rpubGw0bNuTq1avs378/wXFfX1/Onj1LzZo1DYLQxYsXAzB27NjX9pEtW7bkDl0IIUQKFSqk0r2cOPHq1+XLqShLKRIlwWs60+l0TJgwgRs3bhgkdlqwYAFjxoxh9OjR6Tg6tce1ZUvYsUN94332mZowjT3WooURN3/nHTWFe/IkHDkCPXqAlZV636+fKrfz+ecpzBolhBDpq2PHjgD07duXUaNGsXv3bh49evTK8/v+l2AgdoY1vtggNfYcUHtdb926hYuLC8WKFTPl0IUQQqRCoUJqP+urXhK4mo4ErxnEy0vL6tWrR/369fHw8NC3PXjwgD59+rB37943O7j/FC8O06fDrVswZ46amX05v8h330G3bioWTfbqX50OatSA339XN582DYoUgcePYcYMKFkSGjaEdetUdikhRKb388/q34/XvT78MOG1H36YvGt//tnwuidPUnddSrVu3Zpp06YRExPD1KlTadiwIQ4ODri7uzNkyBCuXLlicH7btm3JlSsXa9asMdifGh4ezsqVK3nnnXfo1KmTvv3uf8nvXpXgSQghhMiqJGFTBtWxY0f9p/exVqxYwZIlSzh37hzHjx9Pp5FBjhwwcGDC9ogIVdr1/n1YsUJ90jR0qKqSY2OTzJs7OamNtcOGqSxRc+bA1q1qr+zu3aquzyefqBnbAgVM+lxCiDcnNFSVhn6dggUTtj14kLxrQ0MN32ta6q5LjREjRjBgwAB27NjB4cOH8fX15dixY8yePZtFixaxevVqPvwvMreysqJbt27MmjWLP/74Q7+3df369Tx+/JjevXuTPXt24wclhBBCZHIy85qJ1KlTh379+jEwXuQYFRVFmzZtWLBgAREREek4Orh0CWJi4t6fPAm9e6sfPkeNghSVGzQzg2bNYNMmuHYNvv4a8uSBO3dUcVpXV2jfHnbtkgRPQmRCOXOqz59e98qdO+G1uXMn79qXM+3rdKm7LrVy5MhBx44d+eWXXzhw4AAPHjxg0KBBhIeH07dvX168eKE/N7Glw4ktGQZwdnYGIDA5kbgQQgiRhUidVyMltyZRWtm2bRstWrTAycmJwMDAdE/MER4Oq1fDzJlqg3p8ZmZqud+QIfD++4Z1ZZPlxQtYv16V24mf2KRECVVup1cviFeaSAiRPqSG5atpmkbhwoW5efMmvr6+VIlXHLBKlSqcPHmSy5cvY21tjZubG8WLF+fSpUsJ7uPi4kJgYCD//vuv7HvNhOR7RGRk/v4QFPTq405OabeHMz37Tk9v63PHJ3Ve3xKVK1dm6tSpmJmZGQSuHTt2pHDhwnz55Zf6T+nfBGtrFUP27AnHjqllxH/8obaqxsSoUq/796utrcleShwrWzbo3Fm9zp1TQezSpSqh0xdfqNnZLl1UMdrkVIsWQog3TKfTGZRKi69v376cPHkST09PrKys0DQtwaxr/HMnTJjAxIkT8fLySrLPFy9epPsHm0KIzMHfX80JhIe/+hxr67TJnpuefaent/W5U0uWDWdyzs7OfPXVVwwfPlzfduXKFdauXctPP/1E/In1NznJHpuDadkyCAhQiZzy51fH+vVLGLjeu5fCDsqWhdmz1Qa2uXOhXDlVw2fxYlVqp3p18PRUbUII8Qb99ttv+Pj4JHps/fr1XLp0CXt7e8qWLWtwrGvXrlhbW/P777/j6emJhYUFPXv2TPQ+w4cPp0SJEvz+++98/fXXiW4buX79Om3atOHChQvGP5QQ4q0QFJR0EAXqeFKzhJmx7/T0tj53asnMaxZUqFAh1q9fz7lz58iXL5++fcCAATx48IBvvvmGSpUqvbHx5M0L//sfjBypZl6rVzc8fu+e+iSpXj21pLhFC1WGJ1ly5FBLhvv3h8OHVYKnNWvg+HH1+vJLtfF2wACQpXVCiDdg+/btDBgwAHd3d2rVqkX+/Pl5+vQpp06d4sCBA5iZmTFnzhyDmt8A9vb2tG/fnuXLlwPQpk0b8ubNm2gfOXLkYOfOnbRu3ZrJkyezZMkSmjRpgouLC2FhYfzzzz8cOnQICwsLfvzxxzR/ZiGEEOJNkD2vRkrvPa/JFRYWRp48eXj27BkHDx6kVq1agEr4ZG5unqBUz5s0cSJ8803cezc3tfK3Tx9wdEzFDe/fVzOw8+YZZolq0kSlSW7ZEizkcxsh0srbvp/v8uXLbNq0ib///purV69y584dAAoUKEDt2rUZOnSowV7X+Pbs2cP7778PwKZNm2jVqlWSfUVGRrJs2TL++OMP/vnnH4KDg7G2tqZYsWI0bdqUgQMHUjCxlM0iXb3t3yMi4zp5Mnk7r06cUFUlskrf6eltfe6XJTemkuDVSJkleAU4e/YsGzduZMyYMfpgddKkSaxcuZKxY8cmKM3zpixZogLYa9cM262tVc3YIUOgYsVU3Dg6GnbsULOx27fHZSV2cVHldvr1U6V3hBAmJT+YC5E0+R4RGZUEr2/e2/rcL0tuTCV7Xt8i5cqV43//+5/BLOvq1as5d+4cT58+1bdFRkYS/rrF9ybUuzdcuQJbtqjqOLHCw2HRIqhUCWrXhp07U3hjc3O1BnnrVvDzU+uWnZxUtqixY9Va5Y8+gr17pdyOEEIIIYQQGZwEr2+5vXv3Mm/ePDp06KBv27hxI87OzowbN+6NjcPMTMWZ27fDv//CZ58Z1lo8dAiuXzeig8KFYcoUFbguWwbvvQdRUWp/bIMGUKaMqu8TEmL0swghhBBCCCFMT4LXt1yuXLno378/OXLk0Ldt2bKFkJAQIiMjDc69ffv2GxlTsWIwfXpcIuEyZcDODrp3NzzvyhUV1KZo0tTKSq1FPnQITp1SiZ7eeQcuXoRPP1Upkfv3V8eEEEIIIYQQGYYEryKBxYsXs2vXLvr3769vO336NC4uLjRv3pyYmJg3Mo7s2VWS4LNn1X6A7NkNj0+erJYTV6mi8jOluCpOhQoqqdPt26ogbenSEBYG8+ertcrvvafqyL7BJdRCCCGEEOnFyUnlHEmKtbU6Lyv1nZ7e1udOLUnYZKTMlLDJGLNmzWLo0KG0b9+etWvX6tvPnz9PqVKlMDN7s5+DPHwIBQpA/NKGDg4qB9PAgSpjcYppGhw4oBI8rVunlhWDSnncp4+KpIsUMcXwhcjSJBmNEEmT7xGRkfn7J11T1MlJpQ3Jan2np7f1ueOTbMNvyNsSvALcvHmT8PBwSpQoAcCjR49wdnYmX758+Pj4kDt37jc2logIWL1abVP19TU8ptNBq1YwdCg0bKjep9jduypb1G+/QUBA3I2bNVPRcfPmKShGK8TbRX4wFyJp8j0ihBCGJNuwMDlXV1d94Apw5swZrK2tsbOzwyneWgZfX19C0jjxkZUV9OwJPj5w7JjaD5stmzqmabBpEzRurFYCBwamogNnZxgzRtXv2bgRmjZVN96+HT78EIoWhUmT4N49kz6XEEIIIYQQInESvIpUq1evHnfv3mXNmjX68jsxMTG0a9cOZ2dnjhw58kbGUa2a2prq76/qxRYoEHcsJsbIUq4WFipY3bFDZYgaPlytT755UwW3BQtC165qubEsYhBCCCGEECLNSPAqjGJjY0Px4sX172/fvk2OHDmwtramUqVK+nZfX1/Onz+fpmPJm1fFk9evqwo49erB4MGqDE98X32lJlOjo1PYgbs7/PCDKrfj5QXVq0NkJKxcCXXrQvnyar9saKjJnkkIIYQQQgihZLjg9cmTJ3z11Vc0adKE3Llzo9PpGD9+fLKu9fT0RKfTJfq6e/dugvO9vb2pWbMmtra2ODk54eHhwf379038RG8XFxcXzp07p19SHOurr76ibNmyzJ8/P83HYGkJHTrA3r1q32t8586p+LNNG7Xyd9o0lfwpRWxs1Jrlo0fhxAmVJcrGRt188GA19TtokEqTLIQQQgghhDAJi/QewMsePnzI/PnzqVChAm3atGHhwoUpvseSJUsoWbKkQZujo6PB+3379vHBBx/QokULNm7cyP379xk5ciQNGzbE19cXKysro57jbabT6ShYsKD+fVRUFPb29mTLlo1mzZrp28+fP8/Vq1dp3rw5lpaWaTQWw/crVsT9/uZNGDkSxo2DLl1UoBtvsjh5KleGBQtURPz772rm9fJlVaB27lxVy2fQIGjXTm3UFUIIIUSWl5mzx06Zoj6bf5UqVWDUqMSPGfvc6fnnduSISnXyKkWKQM2aadO3SAEtg4mJidFiYmI0TdO0Bw8eaIA2bty4ZF27ZMkSDdB8fHxee27VqlW10qVLa5GRkfq2Q4cOaYA2Z86cZI83JCREA7SQkJBkX/O2evz4scH7Tz75RAO0AQMGvLExREdr2tatmvbBB5qmNqkavt57T9NWrNC0iIhUdhATo2m7d2tahw6aZm4ed+PcuTVt9GhNu37dlI8jRIb0/Plz7cKFC9rz58/TeyhCZEjyPZK13bypadbWif+cEfuytlbnZTSTJyc97tjX5MkJrzX2udPzz+3w4eQ99+HDpu9bKMmNqTLcsuHYZb5pKTAwEB8fH3r06IGFRdzk83vvvUfx4sXZsGFDmvb/trKzszN47+LigrOzMx07dtS33b17lx9//JE7d+6kyRjMzFSVm23bVP6lL76A+MM6fFjlX+rZM5Ud6HTQoIHadOvvD99+C/nzw4MHMHmy+tiuVSs1gBRvuhVCCCFERhcUBOHhSZ8THp70DGN6SWrG9XXnGfvc6fnnltSMa2rOE2knwwWvptCyZUvMzc1xcHCgXbt2nDt3zuB47Pvy5csnuLZ8+fIJzhdp45tvviEgIID69evr25YvX86IESMMAtq04u4OP/+s8i/Nmwdly8Yd69bN8NzYz9xSJH9+GDtWrU9evx4aNVI32bIFWrSAYsXUptuM+L+XEEIk4saNG+h0Ojw8PNJ7KAbGjx+PTqdj7969CY798ssvlCpVChsbG3Q6HZ6enhn2OYQQQiQtSwWvzs7OjBkzhoULF7Jnzx6+++47fHx8qFGjBqdPn9af9/C/DD0ODg4J7uHg4KA/npiIiAhCQ0MNXiL1LCwsMIuXDrhIkSLUrFmTHj166NsiIyP5/PPPOXLkCFoalKPJnh3694czZ1SSpwED1OxsfFu3qu2tixZBWFgKO7CwgLZt4e+/1X7YL74Ae3uVFnnkSJXgqUcPNe0r5XaEyBLCwsKYNGkSlStXJnv27FhbW+Pi4kKdOnUYPXo0fn5+Ca55/PgxU6dOpW7duuTOnRtLS0vs7OyoUqUKn3/+OScSmerw8PAwSE5oYWFBrly5KF26NN26dWPt2rW8ePEiybE+evSIiRMnUrNmTRwdHbG0tCR37tw0atSImTNn8vTpU5P9ubxpK1as4Msvv8TW1pYvvviCcePGUbFixfQelhBCiFTKcAmbjNGsWTODhEB169alRYsWlCtXjrFjx7Jx40aD81+1PDmpZcuTJ0/m22+/Nc2ARQJt27albdu2BkHq9u3bmTFjBqtWreLWrVsGS71NSadT5XXq1Ut4bNYsOHVKJRYeMQL69lV5mAoXTmEnxYur6d6JE2H1apXgydcXli1TrwoVYOBANfWbPbspHksI8YY9efKE2rVrc+bMGdzd3enevTv29vYEBARw/vx5pkyZQtGiRSlatKj+mt27d9OpUyeCgoIoXrw4rVu3Jm/evDx9+pRz584xb948ZsyYwdy5cxkwYECCPvv27YuLiwuaphEaGsq///7L5s2bWbFiBaVKlWLVqlWJrjbatWsXH330EcHBwZQqVYqOHTvi6OjIw4cP2b9/P59++inTp09PNNjOSIYMGULnzp0p9FIml23btgGwdetWnJ2d9e2RkZFcvHgxwXYWIYQQGVuWCl4T4+bmRu3atTl69Ki+LTbzcGIzrMHBwYnOyMYaPXo0X375pf59aGioQWZdYRrxP0BwdXWlZ8+euLq6GgSuQ4YMoVq1anTs2BEbG5s0G0t4ODx+HPf+0SP48Uf46Sdo2RKGDFErgl+uJ5skW1vo3Vu9fHxUZuKVK+H0aTX1O2IE9OqlAtnSpU39SEKINDR9+nTOnDlD3759WbBgQYIPRK9fv05ERIT+/alTp2jZsiVmZmasWLGCLl26JLhnUFAQP//88ytX+/Tr148aNWoYtD158oSxY8cyffp0mjRpwsmTJ8mfP7/++OnTp2nVqhUAy5Yto9vL+yWAvXv3Mnr06OQ/fDpxcnLCyckpQfvt27cBDAJXAEtLywRVCYQQQmR8WWrZ8KtommawNLXsf5sbzyZSh/Ps2bP644mxsrIiZ86cBi+RtipUqICXlxcTJkzQt128eJHZs2fTt29fnjx5kqb9W1urkq7HjqlETtmyqXZNg82boWlTFV/OnAmpWkVetSosXgyBgSoiLlYMnjxR071lykD9+vDHH/CapX9CiIzhyJEjgPqALbGVPIULFzYInD799FOeP3/O3LlzEw1cQQVnkyZNMvjw9HVy5MjBL7/8Qu/evbl37x4TJ040OB7b78yZMxMNXAHq16+f6D7Sl504cYIhQ4ZQtmxZ7OzssLGxoVy5ckyZMoXIyMgE51+5coXevXtTuHBhrK2tcXJyonLlygwbNszgvDt37vDZZ59RrFgxbGxscHBwoFy5cgwaNMggkH95z2ts3fc9e/YAcckg3dzcgKT37j558oRx48ZRpkwZbGxssLe3p1mzZhw8eDDRPx+dTkdERARjx47F3d0dS0vLZNenF0IIkTJZPni9fv06hw4dMvhEukCBAlSrVo1ly5YRHS/j69GjR7l8+TLt2rVLj6GKFHB0dOS7775jwIAB5MmTR98+cuRIvvnmGwIDA03eZ7Vq4OWlEjxNmgTxJ9wvX4ZPP1W5mVLNwQG+/BIuXYK//lL7ZM3MYN8+6NRJFTb75hsICDD6WYQQaSd29c7Vq1dfe+6VK1c4cOAArq6urwwg40vNtolvvvkGgD/++EO/JePq1avs378fFxcXevfuneT1yal7vmDBAjZs2EC5cuXo378/ffv2RdM0Ro8eTefOnQ3OvX37NtWqVWP58uVUrFiRzz//nM6dO5M7d25mzpypPy8sLIxatWoxc+ZMihYtytChQ+nZsyeFCxfG09OT4ODgV46nYsWKjBs3DldXVwDGjRvHuHHj+Pzzz5N8juDgYGrWrMmECRNwdHRk4MCBtG/fHl9fXxo0aMCff/6Z6HXt2rVj8eLF1KtXj88//5wiRYq89s9MCCFEKqR50Z5U2LZtm7ZmzRpt8eLFGqB17NhRW7NmjbZmzRrt2bNnmqZpWp8+fTRzc3Ptxo0b+usaNmyoffvtt9qGDRu0Xbt2adOnT9fy58+v5ciRQzt79qxBH3v27NEsLCy0tm3ban///be2fPlyrWDBglrZsmW18PDwZI9V6rxmHCEhIZqNjY0GaEePHk3z/iIjNW3dOk1r0EDlIq5fP+E5166p81ItIEDTxo7VNGfnuCJjZmaa1rq1pu3cqQrXCpHBJFnDMiZG054+zfiv/+qNp8aff/6pAVrOnDm1kSNHart27dKCg4MTPdfLy0sDtJ49e6aqr169emmAduTIkSTPK1iwoAZofn5+mqZpmqenpwZo3bt3T1F/169f1wCtV69eBu03btzQoqKiDNpiYmK0Pn36aIB28OBBffuvv/6qAdqMGTMS3P/Bgwf632/atEkDtC+++CLBeaGhoVpEvILc48aN0wBtz549BufVq1dPS+xHnVc9R9euXTVAW7x4sUH73bt3tYIFC2q5c+c2+Hsde/+KFStqDx8+TNDPq0id16xN6rxKnVeRcsmNqTLknteBAwdyM94U1po1a1izZg2gZlLd3NyIjo4mOjraILFPuXLlWL16NT/++CPPnz8nT548vP/++3zzzTcUL17coI/69euzbds2xo4dS6tWrbC1taVly5b88MMPyfqUWWQ8VlZWLF68mF27dlGtWjV9+7Rp0zh58iRffPEF1atXN1l/FhbQrp16nT+fsDZZTAw0a6baBw5UyZ4S2ZKVNBcXVSv2f/+DP/9Ue2P37IGNG9WraFF1cw8P+G8vtxAZWlhY5khG9vQpvPNOqi5t3bo106ZNY8KECUydOpWpU6cCULRoUZo1a6ZfBguqtjVgsBc1VnBwML/++qtBm5OTE0OGDEnxmPLnz09AQABBQUEUKVJE36+Li0uK75WY2BnO+HQ6HYMHD2bx4sV4e3tTq1Ytg+OJ5SpIbN9qYuflyJHDiNEmLigoiNWrV9OwYcMEs9F58+ZlxIgRfPrpp3h7e9OyZUuD499++22S+TLE26VQIbUiK6lKeE5O6ryMZtQo9WtS9V6rVIk7Lz5jnzs9/9xq1lRFH5Kq41qkiDpPpK8MGbzeuHHjted4enri6elp0PbLL7+kqJ/GjRvTuHHjFF0jMi4rKys6d+5ssERN0zR+++03rl27RsuWLfXBq6ZpSWaVTqkyZRK2eXvDv/+q348eDePHQ5cuKsFTlSop7MDSEjp2VK+LF1VhWk9P8POD4cNhzBjo3FmlQK5aVaVOFkKkmxEjRjBgwAB27NjB4cOH8fX15dixY8yePZtFixaxevVqPvzwwyTLfwUHByfIbl+iRIlUBa9J9WMKL168YNasWaxatYpLly7x9OlTgz5jEyeBqsU+atQoBg8ezN9//02zZs2oXbt2gg+Z69ati7OzM5MnT+bUqVO0aNGC2rVrU65cOZP++x3Lx8eH6OhowsPDE92zeuXKFQAuXbqUIHiN/4GpEKACrIwYnCZHYoFpchn73On551azpgSnmUGGDF6FMKU//viDZcuW0bZtW33bqlWr+Omnn/jiiy+Stc8sNXLlghYtYNs2tdgkIkLFm56eUKOGCmI7doxLAJVspUrBjBlq4+2KFarczqlTakOul5cqSDtokIqUbW1N/2BCGMPWVs1qZnQm+N7JkSMHHTt2pGPHjgCEhITw9ddfM2fOHPr27UtgYCB58+YFSHSfvru7u0EAaEzAdufOHQBy584NxGXfNVV+gA4dOrB582aKFy9Op06dyJMnD5aWljx+/JgZM2YYZFcuXLgwR44c4dtvv2X79u36lVUlSpTgu+++0/952dnZceTIEcaNG8fmzZv1ZW9cXFwYPXo0gwYNMsnYY8XuoT106BCHDh165XnPnj1L0Bb7dRRCCJG2JHgVWZpOp6NKlSpUeWmqc9myZZw4cYLLly/r2zRNIyoqCktLS5P0XbUqbNkCV6+q1b6LF8eV3Dl6VL2GDVOJnr7+OhUdvPMOfPyxWo987JjqZPVqOHlStQ0bppYTDxgAUhJCZBQ6XaqX42Z2dnZ2zJo1i61bt3Lz5k3Onj3Le++9B8C+ffuIiYkxyIxvKteuXSMgIAAnJyd9tt3YJbx79+41ul8fHx82b95M06ZN2bp1K+bm5vpjR48eZcaMGQmuKV++POvWrSMyMpITJ06wfft2fv31Vzp16kT+/Pn143Nzc8PLy4vo6GjOnj3LX3/9xa+//srgwYPJlSvXK7Mzp0Zs9YBhw4bx448/pujatJgJFkIIkVCWzzYsRGI8PT2ZMWOGwb6m2BqII0eONGlf7u6qAs6tWzB/PpQrF3fs3j0V3BpFp1NTubGpkKdNUxszQkLUDG2pUtCwIaxbB4mUrBBCvDk6nQ7beLO6xYsXp1atWvj7+7Ns2bI06fO7774DoHPnzvogy93dnbp16xIQEICXl1eS18efNU2Mn58fAC1atDAIXAEOHDiQ5LWWlpbUqFGDb7/9ll9//RVN09iyZUuC88zNzalYsSJfffUVK1euBGDTpk1J3julqlatik6n05c6EkIIkfHIzKt4K+XOnZtPP/3UoO2PP/4gKCgIf39/g/aQkBDs7OyM7jP+ROnBg6ou7Pr1avlwfE+fqgnUVK36dXKCESPUrOtff6nZ2C1bYPdu9cqXDz75RA2kQAGjn0kIkdBvv/1G5cqVqVq1aoJj69ev59KlS9jb2+tris+YMYPatWszaNAgsmXLlqC0DKh/h1Iqtl6pp6cn+fLl4+uXlnj8+uuv1KxZkyFDhmBra0unTp0S3OPAgQOMGjUqyWW0scmaDh48yNChQ/Xt58+fZ/LkyQnO9/HxwdXV1aDMGcC9e/eAuARN586dI0eOHAmSQb18nqk4Ozvz0UcfsXr1an744QeGDx+eYEb12LFjlCtXzuADCJG2/P0zZ+Kj9HTkSPolHjL262XM2OXvyttBglch/vP9999Tv359g71LQUFBFCxYkPr167Nu3TqT/MCi00GdOup1/z689PMby5erlb7Dh0Pfvmr7aopLBpqZqVTHzZqpf83nz4cFC+DOHZW9eOJEaN1a3fz99yXBkxAmtH37dgYMGIC7uzu1atUif/78PH36lFOnTnHgwAHMzMyYM2eOPrN9lSpV2LRpE507d6ZLly6MGzeOunXrkidPHp48ecLNmzf566+/AKhdu3aifS5cuJAdO3agaRpPnjzh33//Zf/+/Tx58oQyZcqwatUq8uXLZ3BNhQoV2Lx5Mx999BGdO3dmwoQJ1K1bFwcHB4KDgzl06BBnz57F3d09yeetVq0a1apV448//uDOnTvUqFEDf39/Nm3aRIsWLVi7dq3B+cuXL2fOnDnUr18fd3d3cubMyYULF9i2bRtOTk706dMHAG9vb4YNG0atWrUoWbIkjo6OXLt2jU2bNmFjY5OqxFWvM2fOHC5fvsxXX33F0qVLqVmzJnZ2dgQEBHDixAmuXLnCnTt3JHh9Q/z9oUSJhNn847O2VhlqJShRjhyB/3YjJOnwYdMHsMZ+vYwZu/xdeYukacGet4DUec3aVq1apQFa5cqVDdr9/f21GCPqQL5KTIymlS1rWFNMp9O0li01bccOI8u6RkRo2sqVmla3rmEHxYtr2i+/aNor6lAKkVJvew3LS5cuadOmTdMaN26sFS5cWLO2ttasra21okWLar169dJ8fX0TvS44OFj7/vvvtVq1amkODg6ahYWFljNnTq1SpUra0KFDE70uts5r7Mvc3Fyzt7fXSpcurXXr1k1bs2aN9uLFiyTH+/DhQ+27777TatSooeXKlUuzsLDQHB0dtfr162szZszQnj59qj/3VfVR79+/r/Xp00fLnz+/Zm1trZUrV06bPXu2du3atQTnHz16VOvfv79WtmxZzd7eXrOxsdGKFSumffrpp5q/v7/+vAsXLmifffaZVqlSJc3R0VGzsrLSihQponl4eGgXLlww6N9UdV41TdPCwsK0adOmaVWqVNHeeecdzcbGRitcuLDWpk0b7ffff9ci4xXvftX9X+dt/x5JrhMnkld788SJ9B5pxrFsWfL+zJYtM33fxn69jBm7/F3J/JIbU+k0LY3z52dxoaGh2NnZERISok/2ILKWK1euEBQURM3/PuaLjo6mUKFCvPPOO2zZsiVBeQdj+fjA7NmwapXKUBxfsWIweLDKw2TUSuZz59SS4qVL4ckT1WZjo9YqDxqUilo+QsQJDw/n+vXrFC5cGGtr6/QejhAZjnyPJM/Jk8n77+jECZVoX6jVW927v/68ZcvA1MUWjP16GTN2+buS+SU3ppKETUK8RrFixfSBK8DFixcJCQnh4cOHBnuxrl69ylMTlACpWlWV0wkIgMmToWDBuGNXrsDnn6vtqv9VjUidsmVVhBwYqILYcuXg+XOVEvndd6FaNTWI58+NexghhBBCCCFMRIJXIVKobNmy3L17l23btun3rAH07t0bZ2fnRDNlpkbu3KpQ+LVrKrHT++/HHXvxwkSTozlyqA22p0+rLFJdu6rCsz4+0Lu3ipKHDVNRsxBCCCGEEOlIglchUiF79uxUr15d//7p06fcu3eP58+fU6lSJX27n58fV4wM/CwsoG1b2LULzp9Xq3r79IF4eaUAVY5n8mR48CAVneh0UKuWWrMTO+Xr5gaPHsHPP0Px4tCkCfz5J0RFGfU8QgghhBBCpIYEr0KYQPbs2bl8+TJnzpyhQLwSNN9//z3Fixdn0qRJJumndGm12nfePMP2589h0iT4+mu1zNjDA3x9U9lJnjxqyvfqVVVmp3lzFdz+/beKogsXhu++U5mLhRBCCCGEeEMkeBXCRHQ6HWXKlDFoCwsLw8zMjDp16ujb7t69y/bt24ky4QzmgQNqkhRUkicvL7V3tkYNldjg5cRPyWJuDi1awNat4OcHI0eqImm3bsHYsSrX/Ecfwd69KomfEEIIIYQQaUiCVyHS0KpVq7h16xa1atXSt3l6etK8eXM6duxosn6aNFETpcOHQ65cce3HjkGPHmo29n//U3FnqhQuDFOmqBssW6aWGEdFwZo10KABlCkDM2dCSIhJnkcIIYRwclK1OZNiba3OE0py68KnuH58Mhj79TJm7PJ35e0hpXKMJKVyREr9+OOPTJ06lSlTptC3b18AIiIiWLhwIZ06dcLJyH9Zw8JgxQqYNUvlYYovf35VyNvc3KgulNOnVabiZcvg2TPVZmur8tcPGgQVK5qgE5EZSRkQIZIm3yPJ5+8PQUGvPu7kpBYCiThHjqhkj69SpAjEK6JgUsZ+vYwZu/xdydySG1NJ8GokCV5Farx48QJN0/TZitevX0/79u1xc3Pj2rVr6HQ6o/vQNDh0SAWx69apidL//U9tV40vMhIsLY3oKDRU1YudO1dllIpVo4YKYjt2fP3HoSJLif3B3M3NDRsbm/QejhAZzvPnz7lx44YEr0II8R+p8ypEBpYtWzaDMjvW1tZUqVKFTp06GQSukydP5sSJE6TmMyadDmrXhlWr4OZNtU21f3/DcwID1Wzsl1+qZcepkjMnDB4MZ8/Cvn3QqZNKkXz0KPTsCS4u8NVXSX+UKrIUS0tLdDodz2Jn5IUQBsLCwgD1vSKEECL5ZObVSDLzKkwpKioKCwsLAM6ePUv58uWxtLTk7t27ODg4mLy/sWPjZmJ1OvjgAxgyBJo2BTNjPtq6excWLYLfflOld2I7aNpUzcY2b26itcsio7pz5w6PHz8mZ86c5MyZEwsLC5OsKBAiM9M0jbCwMO7fv4+9vT358uVL7yEJIUSGkNyYyuINjkkI8RqxgSuAubk5nTt3xszMzCBwnTp1Kq6urrRu3droJZnh4WBlpbIRaxps26Ze7u4qxuzdG+ztU3FjZ2cYM0ZlKN62DebMgZ07YccO9SpUSE0D9+2bsGCtyBKcnZ2xsbHh/v37hIaGpvdwhMhQ7O3tcXZ2Tu9hCCFEpiMzr0aSmVeR1jRN089YPXr0iHz58hEREcGJEyeoXLmy0fcPClKTpHPmqGQH8dnaqmzFn38OJUsa2dHVq2omdvFiCA5WbZaW0L69ipRr11azsyJL0TSN6Ohok5aGEiIzs7S0xFxWngghhIE0T9jk7e3Nzz//jI+PD48fPyYmJibhzXW6LP8DiwSv4k0KDg5m+vTpnDhxgi1btuiD2tmzZxMcHEzv3r1xcXFJ1b2jo2HLFlXxZtcuw2OLFkGfPsaO/j/Pn6sSO3PmqFo+scqWhYEDoXt3tY9WCCGESbytWVg3bDDMI/iyMmWgbdtXHzcm862xGX/TM+uuMde/rX/XhPHSNHhdt24dnTp1IiYmBldXV1xcXAyWO8a3Z8+elN4+U5HgVaS3mJgYChcujL+/PytXrqRz585G3/PiRZg9G7y8IFs2Vd41/grlmzfV+zx5jOzo5EmVpXjFClXjByB7dhXADhoE5coZ2YEQQrzd/P2hRAm1TeRVrK3h8uWsFVRs2ADt2r3+vPXrEw9gjxyB9957/fWHDycMIo251tjrjf16G3P92/p3TZhGmmYbnjBhAjY2Nnh7e3P9+nUOHDjAnj17En0JIdJWTEwM3333HS1btqR169b69jVr1tCrVy+OHDmS4nuWKqVK7AQGwubNhoErqO2sBQuqZMLHjxsx+MqVYcEC1dGMGep/vadPYd48KF8e6tRRgW1EhBGdCCHE2ysoKOlgAtTxpGbLMqOkZlyTc15yE+Qndp4x1xp7vbFfb2Ouf1v/rok3K1XB6+XLl+ncuTPvv/++qccjhEghCwsLevbsyebNmw0SOP3222/8/vvveHt7p/reOXMm/PT33j344w948UKVd61eHapVU79PdYxpbw+ffqqmfHfvhg4dVLmdgwehWzcVKY8eDTdupPpZhBBCCCFE5paq4NXJyQlbW1tTj0UIYUITJ06kf//+9OjRQ9927Ngx3nvvPby8vFJ9XzMzlcApV664Nh8fNQtbsKCalY2tjpNiOh00aKD2xN68Cd9+qwrRPngAU6aoTT6tWqkMxtHRqX4GIYQQQgiR+aQqeP3oo4/w9vbO8smYhMjMatSowbx583Bzc9O3eXp6cuTIkQSzsSnZ+p47N0ybpvbBLloEFSvGHXvwACZNgsKF1eSpURVS8udXhWhv3lSbkho1UvV8tmyBFi2gWDGYOlV1KoQQQgghsrxUBa8TJ04kV65cdOrUCf+Xa2sIITKssWPH8sMPPzB48GB9271793B1dWX48OEp+kDK1lZlID55Uq3u7dxZrfQFNSl66RLkyGGCQVtYqGwaf/+tsjx88YVaZnz9OowaBS4uKsHT4cMquBVCCCGEEFlSsoLXIkWKGLzKli3LzZs3+fPPPylcuDCOjo4JzilSpAhFixZN8YCePHnCV199RZMmTcidOzc6nY7x48cn69r169fTpUsX3N3dsbGxwc3NjW7dunHlypUE59avXx+dTpfg1axZsxSPWYjMIl++fAwfPpwaNWro21avXk1AQAAHDx40yBoekcwNrDod1KoFK1eqSdJx48DZGYYMSVi29ZdfIJFvx+QrXhx+/lkleFq8GN59V22+Xb5cDaJSJVVL9ulTIzoRQgghhBAZUbKC15iYGDRNM3hZWFhQqFAhChUqRM6cORMc1zQt0dqvr/Pw4UPmz59PREQEbdq0SdG1U6dOJSwsjDFjxrBjxw4mTpzIP//8Q+XKlTmfSDq5IkWKcOTIEYPX9OnTUzxmITKzAQMG8Oeff/Ltt9/q2yIjI3F3d6dNmzbcu3cv2ffKnx/Gj1dBbO/ehsdOnoQvv1Tx5wcfqG2rqfgnQrG1VR34+Kh0x717q/z7p0/DgAFqIEOHwoULqexACCGEEEJkNIkXZ33JjTeY4dPV1ZVHjx6h0+kICgpi4cKFyb528+bN5Hmp8OT777+Pm5sbv/zyS4J72djYGMxACfE2ypYtm0GJHYBDhw5x69YtIiIicHBw0Lc/evQIe3t7dC9PqSa4Z8K2uXPjfr9jh3oVLarKufbubZgAKkWqVlWvH39UhWnnzlXTu7NmqVe9ejBwoFp6nNjAhBAiC3NyUp/tva72ppPTmxvTm1CmjHHnFSmSvOsTO8+Ya4293tivtzHXv61/18SbpdNSkqnlDQsKCiJ37tyMGzcu2UuHE1OkSBGKFSvGzp079W3169cnKCiIc+fOGTXG5BbUFSKzOX/+PNeuXaNVq1b6tpo1axIaGoqnpydVq1ZN0f0ePlQrfefMSVjxxtZWbVsdPFiVdzVKTIwqtzNnDmzcGDe9mzcvfPwxfPKJSosshBBvCX//pGtrOjlBoUJvbjxvyoYNSdd7LVNGfa75KkeOJF1ztUgRqFnT9Ncae72xX29jrn9b/64J4yU3pkpV8FqkSBE+//xzPv3001eeM2/ePKZNm8a15FZaToQpgtdr165RrFgxPvvsM37++Wd9e/369Tl27Bg2NjaEhobi6upK586d+d///mdQK/NlERERBnsBQ0NDKViwoASvIsu7d+8ebm5uREZGcuvWLZydnfXtOXPmTPL7Jr7oaNi6VU2K/v13wuOjRsHkySYa9K1bsGABzJ8Pd++qNjMzVW5n4EBo3Fi9F0IIIYQQ6Sa5wWuqfmq7ceMGjx8/TvKckJAQbt68mZrbm0xUVBR9+/Yle/bsfPHFFwbHateuzc8//8y6devYtGkTzZs3Z9q0aTRr1izJvbqTJ0/Gzs5O/yooMzjiLZE3b17u3LnD5s2b9YErwFdffYWzszPLli1L1n3MzeHDD+Gvv+DiRZXYKXv2uOP165tw0C4uqlasv7+qHduggZqJ3bgRmjVTG3B/+klNCwshhBBCiAwtzaYcQkJCsLKySqvbv5amafTt25cDBw7w+++/JwgyJ06cyMCBA2nQoAHNmzdn5syZTJkyhf3797Nx48ZX3nf06NGEhIToXwEBAWn9KEJkGPb29nzwwQf69zExMZw4cYLQ0FCD7OJBQUHJ2itfsiTMnKmSB8+aBS1bqsnQ+DZuhB494NgxIyrhWFqqwrO7d6skTp9+Cjlzgp8fDB8OBQqAh4eRnQghhBBCiLSU7OB1//79+heo2df4bbGvPXv2sHTpUpYuXUrx4sXTbOBJ0TSNfv36sWzZMjw9PRMko3mV7t27A3D06NFXnmNlZUXOnDkNXkK8rczMzDhz5gwHDx40SH42b948ChcuzIgRI5J1n5w51X7XzZsTruKdPh2WLYMaNaBaNZWTKalkEK9VqhTMmAG3b6slxZUqQUSEunGNGqr8zsKF8OyZEZ0IIYQQQghTS1a2YYiriwqg0+nw8vLCy8sr0XM1TUOn0zFp0iTTjDIFYgPXJUuWsGjRIn1AmhJmsgdOiGQzMzOjVq1aBm03btxAp9NRrlw5fVt4eDiHDx+mfv36yf4ee/gQzp6Ne+/rqyZIhw9XuZcGDDAi8cM770C/ftC3ryq3M2cOrF6tavp8/LHqxMNDdVKyZCo7EUIIYYzMmjzobe3bWJl57OLNSHbwOnbsWHQ6HZqmMWHCBOrVq0f9RDanmZub4+DgQIMGDShVqpQpx/pamqbx8ccfs2TJEn777Td6v1xo8jVig3EpnyOEcRYuXMjYsWNxipcPf+PGjXTu3JnatWtz4MCBZN3H0RECAmDVKrW8+J9/VHtQkErqNHUqtGmj9s3Wrw+vqeCTOJ0OqldXr59+Ak9PVW7n2jU1QztjBrz/vkrw1Lq1WoIshBAizfn7Q4kSry+9cvlywoDGmGuN9bb2bazMPHbx5iQ7eI2f7Xffvn307t2bnj17psWY2L59O8+ePePJkycAXLhwgbVr1wLQvHlzbG1t6du3L15eXvj5+eHq6grAp59+yqJFi+jTpw/lypUzWP5rZWVFpUqVADhw4ADff/89bdu2pUiRIoSHh7N9+3bmz5/P+++/b1AaRAiROoVe+p/l4cOH2NvbU69ePX2bpmmsWrWKDz74AHt7+0TvY2Oj6sB6eMDRoyqIXbMGoqJU7qX169XryhVwdzdy0E5Oasb1yy9VKuQ5c2DLFrVXdvduyJdPldr5+GO1T1YIIUSaCQp6/TaR8HB13svBjDHXGutt7dtYmXns4s3JkHVe3dzcXpmp+Pr167i5ueHh4YGXl5f+/euuc3V11SeQuXr1Kp999hmnT58mKCgInU5HsWLF6Ny5M8OGDUtRoimp8ypE8oWHhxMREYGdnR0A//zzD5UrV8bOzo67d+9ibW2drPvcuaO2q86bp37fpAnEK+MMwNOnhlmMU83fX5XaWbAA7t9XbebmahZ24EBo2DCVU75CCCGScvIkVKny+vNOnIDKlU13rbHe1r6NlZnHLoyXpqVy0tqNGzfQNC3RV2yg6unpafD+ddfFz3zq7u7O1q1buXXrFuHh4Tx//pwzZ87w9ddfp2uGZCGyOmtra33gCvD48WPKlStH06ZNDQJXLy8vzsbf7PqSfPlg7Fi4eVMtKf7mG8Pj0dFQoYKqhrNli3qfaoUKwcSJav3yypVQt6664fr1KjVyyZIqq9SjR0Z0IoQQQgghXidZwauZmRnm5uYpfllYJHtVshDiLdSgQQNOnz7NkiVL9G3BwcF8/PHHlC9fnsuXLyd5vaUldOoEtWsbtm/frras7twJrVrFlXM1Kr7Mlg06d4Z9+1QWqcGDIUcO+Pdf+OILtYy4b1/1kbAQQgghhDC5ZAWvdevWTfAqV64cmqZhZmaGq6sr1apVw9XVFTMzMzRNo1y5ctSpUyetxy+EyOR0Oh22trb6948fP6ZVq1ZUr16dEiVK6NuXL1/Ohg0bePHixWvv+eIFxFuUwbVrceVcP/kEzpwxctBly6rCtIGBKrlT+fLw/DksXqxK7VSrphI/PX9uZEdCCCGEECJWsoLXvXv3smfPHv1r6dKlPHr0iK5du+Ln58e1a9c4cuQI165dw8/Pjy5duvD48WOWLl2a1uMXQmQxRYoUYd26dRw6dEjfFh0dzciRI2nXrh2bN29+7T3atYOrV2HTJrUfNtbz52rraoUKavXvn38aOdgcOVQpnVOn4OBB6NZNzdD6+KgsUwUKwLBhKpuUEEIIIYQwSqr2vA4fPpx8+fKxbNmyBBlFCxUqxPLly3F2dmbEiBEmGaQQ4u1jbm6u//3z58/p1q0bZcuWpWXLlvr2TZs2MW3aNG7fvp3I9WrJ8M6dcOkSDB2qYs1YBw7Ajh0mGqxOB7VqwbJlcOsWTJmipn4fPYKff1brlps0UdFyVJSJOhVCCCGEeLukKnj19vamYcOGSZ7z/vvv4+3tnapBCSFEfNmzZ2fq1KmcOXPGIKnaTz/9xMiRI/U1ml+lRAn49Ve1ynf2bIgtQT14sOF5oaFw5AgYlYM9d24YOVJN/W7ZAi1aqOD277+hbVsoXBi++06lSRZCCPFKTk6qrmdSrK3Veaa81lhva9/GysxjF29OqjIqhYeHc+c1P3jdvn2b57LfSwhhQrp4JWk0TaNHjx7ExMTQvXt3ffvRo0dZtGgRffv2pUaNGgbX58gBgwapCje+vlCunOH9PT3hs89Uqv4hQ1R+pmRW70nI3FwFri1awPXrqtzOwoVqZnbsWJgwQQWzgwZBvXpSbkcIIV5SqBBcvqzqer6Kk1PiNT+NudZYb2vfxsrMYxdvTqrqvNarVw8fHx927dpFzZo1Exw/fPgwDRs2pEaNGuzZs8ckA82opM6rEBnLxx9/zMKFC/Hw8DDIYvw6MTFqRvbff+PaHB3h44/VtlZXVxMMLiIC1q2DOXMg3p5eSpVSEXXPnhCvlJAQQgghxNsguTFVqoLXgwcP0rBhQ6Kjo2nVqhW1a9cmT5483L9/nwMHDrBlyxYsLCzYtWsXtWrVMupBMjoJXoXIWA4ePKifea39Xw2d27dv0717d3r27EmvXr0MZnBjRUWpLaszZ6pC6fGZmcGHH6p9sw0amGiS9MwZlal46VJ49ky12dqqpE8DB0KlSiboRAghhBAi40vT4BVg165dfPLJJ1y/fl3dSKcj9laFCxdm/vz5r90XmxVI8CpExjdt2jRGjhxJrVq1OHjwYJLnahocO6aC2DVrIDLS8HipUrB8uQljy9BQFcDOnQvnz8e116ihlhR37GjE2mUhhBBCiIwvzYNXUHvODh48yOnTpwkJCcHOzo4KFSpQu3btRGc2siIJXoXI+AICAli6dCklSpSgffv2ALx48YKaNWvSrFkzRo8eTfbs2RNcd/euKq0zbx7EJjS2tlbbVh0dTTxITVMpkOfMgfXr46JmR0fo0wf694eiRU3cqRBCCCFE+nsjwauQ4FWIzOrPP/+kbdu2ODs7ExAQgIWFyl8XExODmZlhIvbISNiwAWbNAnd3WLzY8F4LFoCzMzRvrvI0Ge3uXVi0CH77DQICVJtOB02bqtlYk3UkxJvn7y8JWd4mxn695e+LEG8HCV7fEAlehcicwsPD2bRpE2FhYXh4eOjb69SpQ758+ZgyZQpFihRJcN2LF5AtW9z7p0/BxQVCQlQVnEGD1ESpg4MJBhkdDVu3qiXF8YvSFiqkZmL79oW8eU3QkRBvhr+/Kl0VHv7qc6ytVcZRCUgyP2O/3vL3RYi3h0mD1wkTJqDT6Rg8eDAODg5MmDAhWYPQ6XR88803yR91JiTBqxBZx7///kuJEiWwsLDg9u3b5M6dG1CBrvUr9p16ekLv3oZt1tYq79LQoVChgokGd/WqmoldvBiCg1WbpSW0b68i5tq1pdyOyPBOnlSlqF7nxAmoXDntxyPSlrFfb/n7IsTbw6TBq5mZGTqdjosXL1K8ePEES+peeXOdjujo6OSPOhOS4FWIrEPTNE6dOsWJEyfo16+fvr1r165cunSJn3/+mfr16xtcEx0N27erJcU7dya8Z+3aqmZsu3Yq1jTa8+cqk9TcuXD0aFx7mTIqiO3eHeTfIpFBSTDydpHgVQiRXMmNqSySc7PYWq2F/luTkdVrtwoh3k46nY5KlSpRKV4q4YiICLZt20ZISAjvvPOOvv3Jkydky5YNKysrWraEli1Vjdg5c2DJEpVEGODgQfV6913w8THBIG1sVD3Ynj3hn39UELt8ucpUPHgwjBypAtiBA6F8eRN0KIQQQgiRMSQreK1Xr16S74UQIquysrLCz8+PLVu28O677+rbf/rpJ2bOnMnEiRMZOHAgAMWLw/Tp8N13qmbsrFlw4YI6/8MP02BwlSrB/PkwbRr8/rsKZC9dUumR582DWrXUbGz79mBllQYDEEIIIYR4c5K3/vclMTExph6HEEJkWI6OjvTq1cugBJi3tzfBwcHY2dnp254/f05gYCA5cqiJz3PnYPduFTt+/LHhPW/ehGrV1Czt8+dGDtDeHj79VEXKu3dDhw5gYQGHDqnNtwULwujRcOOGkR0JIYQQQqSfVAWvuXLlolWrVvz000+cOHECSVgshHjb7Nu3jx07dtCmTRt92/r16ylUqBAf/xep6nTQoAGsXatK6cQ3d65aRtynj4otR41SAa1RYjtcs0bd7NtvoUABePAApkyBIkXU+uZt29RmXSGEEEKITCRVwWvJkiXZuXMnI0aMoFq1ajg4ONCmTRumT5/OqVOnTDxEIYTIeMzNzWnatCm2trb6tn/++YeYmBgKFCigb9M0jWPHjiX4kO/06bjfP3wIU6eq2LJNG/D2BqM/E8yfH8aOVbOt69dD48bqplu3QosWqmDt1KkqsBVCCCGEyARSXef16dOnHDhwgN27d7N37179D206nQ57e3vq1atHgwYNGDp0qKnHnKFItmEhRHx+fn5kz56dvP/VXz1+/DjVq1enXLlynDp1Sp+tXdPg+HG1L3b1aoiMNLxPyZIqS3HPnpAjh4kG9++/ai/skiXw+LFqy5YNOnZUe2Nr1pRyOyJNSd3Ot4vUeRVCJJdJS+Ukt8P9+/ezZ88eli1bRlBQEICUyhFCvNWWLVvGwIED+fDDD1m+fLm+/e+//6ZGjRrkyJGDe/dgwQK1lPj2bcPrly5VyYNNKixMRcxz5oCvb1x7+fIqiO3WDbJnN3GnQij+/vDfjwiJcnKSQCQrMfbrLX9fhHg7vNHg9ebNm+zZs0f/unXrFgCurq5cv37d2NtnaBK8CiFe59mzZ4SEhJA/f34AHjx4QP78+cmWLRt+fn44/7chNjISNm6EmTNh/37Ik0f94BY/UXBwMNjZgbm5iQbn46Oi5pUr46Y3cuRQU74DB6r6sUIIIYQQaShNg9fbt2/rA9Xdu3dz8+ZNNE0jf/78NGjQQP8qXLiwUQ+RGUjwKoRIKV9fX7p3706OHDnwiVf8dfv27RQpUoQSJUpw5gxcvw6tWxte+9FHKt4cNEgle3J0NNGggoPBy0sFsleuxLXXq6eC2LZt1RJjIYQQQggTS9Pg1fy/j/zz5Mmj39vaoEEDihcvnvoRZ1ISvAohUkPTNB4+fIiTkxMAUVFRuLi4cO/ePXbv3k2DBg0SXBMYCK6ucYmCra2ha1e1N7ZSJRMNLCZGlduZMwc2bYrrLG9e6NcPPvlE1ugJIYQQwqSSG1OlKtuwpmlomkbevHnJnz8/+fPn1ycnEUII8Xo6nU4fuAI8fPiQd999F2dnZ2rVqqVv9/b2ZuvWrURFRfHkCTRpEneP8HBYvBgqV4batWHVKnjxwsiBmZlBo0YqQ/GNGypjsbMz3LsH338PhQur6eCdO1WgK4QQQgjxhqQqeD1+/DjTpk2jQIECLFq0iNatW+Pk5ETVqlUZOXIkO3bs4NmzZ6ka0JMnT/jqq69o0qQJuXPnRqfTMX78+GRff//+fTw8PHBycsLW1paaNWuya9euRM/19vamZs2a2Nra4uTkhIeHB/fv30/VuIUQwhh58+Zly5YtXLt2jWzxlueOGzeOli1bMmvWLEqWVCVa//0XPv8c4n8weegQdOkCbm6qvOvL2YtTxcVF3czfX9WObdBABaybNkGzZlC8OPz4o6r1I4QQQgiRxoxO2BQdHY2Pjw979uxh3759HDp0iLCwMMzNzalatSqHDh1K0f1u3LhBxYoVqVChAsWLF2fhwoWMGzcuWQFsREQE7777Lo8fP2bKlCnkyZOH2bNns3XrVry9valXr57+3H379tGoUSNatGjB4MGDuX//PiNHjiRXrlz4+vpiFT9DShJk2bAQIq1ER0czYsQIVq1axYkTJ8iXLx8APj4+HDp0iNatu7FzZ25mzYLz5+Ouq1QJTpxIo6o3Fy+qcjteXhASotqsrKBTJ7URt1o1KbcjsqwjR+DatVcfL1JEVZzKan1n1oy/kulYiMwj2TGVZiLR0dHa8ePHtQkTJmh58uTRdDqdZmZmluL7xMTEaDExMZqmadqDBw80QBs3blyyrp09e7YGaIcPH9a3RUZGaqVLl9aqVatmcG7VqlW10qVLa5GRkfq2Q4cOaYA2Z86cZI83JCREA7SQkJBkXyOEECkRHR1t8N7Dw0MDtI8//ljTNE2LidG0PXs0rV07TTMz07RFiwyvj4nRtLVrNS0szISDevpU0xYs0LRKlTRNla1Vr8qVVfvTpybsTIj0d/iw4V/1V73i/QiSJfq+eVPTrK2T7tfaWp2XkRg77sz63EJkVsmNqVK1bDjWqVOn+Pnnn2nVqhUODg7UqFGD8ePHExwcTLVq1fjqq69SfE+dToculZ/ab9iwgRIlSlAz3kePFhYWdO/enePHjxMYGAhAYGAgPj4+9OjRAwsLC/257733HsWLF2fDhg2p6l8IIdKCmZnhP9V169alatWq9OrVC1ATnUWLBuDsPJg//zxNly6G1x8/Dh06qFXAI0eqraxGe+cdlcDpxAk4elSV1rGygpMn4eOPoUAB+OwzuHTJBJ0Jkf6SmvVMzXmZpe+goLgqWq8SHp70DGV6MHbcmfW5hcjqUhW8tmvXDkdHR6pUqcLw4cPZvn07xYoVY9iwYWzevJng4GCOHj3K5MmTTT3eJJ07d47y5csnaI9tO//furpz584ZtL98buxxIYTIiHr37s3x48cNEjstXbqUOXPm8NNPn2FjY3j+zJnq1+BgmDZNLS9s3Rr+/lvNHxhFp4Pq1dUy4sBA+OEH1UFICPz6K5QqBQ0bwtq1JtqIK4QQQoi3VaqC102bNuHq6srnn3/Oxo0befjwIT4+PkybNo3mzZuTI0cOU48zWR4+fIiDg0OC9ti2h/8lFYn99VXnPkwi+UhERAShoaEGLyGESG/16tWja9eufPLJJ/q28PBw2rVrR4kSO+jWLUZfplXTVM6lJk1UbDlrFpjknzJHRxg+XNWJ3bEDPvxQZS/evRs6dlR1fsaNg1u3TNCZEEIIId42qQpeHzx4wMmTJ/npp59o1aoVdnZ2ph5XqiW15PjlY686N6l7TJ48GTs7O/2rYMGCqRuoEEKYUK1atVi+fDldu3bVt23evJkNGzYwf/7HeHlpBATAxIlqRW+sy5dh6FDVtnixiQZjZgZNm8LGjXD9OowZA3nywJ07MGGCSoncvj14e0u5HSGEEEIkW6qC11y5cpl6HCbh6OiY6KxpcHAwEDfT6ujoCPDKcxObkY01evRoQkJC9K+AgABTDF0IIUyuevXqjBs3juHDh2Nubk6ePCqOrFKlPR999Ae1a8ct4336VK32NblChVTEHBCgCtHWrQvR0aqObOPGaur3l1/g0aM06FwIIYQQWYlRCZsymnLlynH27NkE7bFtZcuWNfj1VefGHk+MlZUVOXPmNHgJIURGVKhQIcaPH89nn32mbzt16hSbNq3nzz97sHHjE86ehf791bbVeNXEANi6FaZONVEZ12zZVDmdffvg7FkYPBhy5FBFa7/8Uk399u0Lvr4m6EwIIYQQWVGWCl7btm3LpUuXOHbsmL4tKiqKZcuWUb16dfLnzw9AgQIFqFatGsuWLSM6Olp/7tGjR7l8+TLt2rV742MXQog3oXjx4ixdupSxY8fi4OBA2bKqbGuJEr3p0aM7Fy9e1J87aRKMGqWyFPfpoxIJm0TZsmqjbWCg6rx8eXj+XK1brlpV1YpdsgTCwkzUoRBCCCGyggwZvG7fvp21a9eyefNmAC5cuMDatWtZu3YtYf/9MNO3b18sLCy4efOm/ro+ffpQpkwZOnbsyIoVK/D29uajjz7i8uXLTJ061aCPqVOncunSJTp27Ii3tzcrVqzgo48+omzZsvTu3fvNPawQQrxBtra2dO/enTFjxujbHj16xKpVK1i+fDkREREAXL0Khw+r4+HhKpasUgXeew9WrIAXL0wwmBw51LTvqVNw6BB066ZmaH18VLTs4gLDhqkEUEKks+Quq0+L5ffp2beTE1hbJ32OtbU6LyMxdtyZ9bmFyOp0mmZ0oQSTc3NzMwhK47t+/Tpubm54eHjg5eWlfx/r3r17fPXVV2zZsoWwsDAqVqzId999R6NGjRLc6++//2bs2LGcOnUKW1tbWrZsyQ8//ECePHmSPdbQ0FDs7OwICQmRJcRCiExJ0zSOHz/Ozp07GTt2rL594MCf2LAhH0+fduTZM0uDa/LmVXFn//7w36IW03jwQM3AzptnWJC2cWMYOBBatYJ49bmFeJOOHEm6lmqRIhCv1HyW6dvfP+l6pk5Oant7RmPsuDPrcwuRGSU3psqQwWtmIsGrECIr0jQNd3d3rl27hpfXWsLD2zNzJrxcBjtbNlX5JnduEw8gOhp27oQ5c2DbtriCtAUKqIi5Xz/Il8/EnQohhBAiPSQ3psqQy4aFEEKkL51Ox+HDh5k+fToffdSCTz6BM2dg1KgdWFltwsxMlbhp0iRh4GqSj0TNzaF5c9iyBfz81OZbJye1T3bsWDXd8dFHsGePiToUQgghREYnM69GkplXIcTbpF27dmzYsIERI2ZgZfUpDRtCvXoaQUFB5M6dm6goePfduFW+Jt2DFxEB69ap2dhDh+LaS5WCAQOgZ0+wtzdhh0IIIYR4E0y6bNjMzAydTpfiQeh0OqKiolJ8XWYiwasQ4m0SGRnJjh07qFKlij6D+5EjR6hbty4dO3akffvldOig/r/Q6aBFCxg6FBo1AjNTrvU5cwbmzoWlS+HZM9Vma6uSPg0cCJUqmbAzIYQQQqSl5MZUycp6Ubdu3VQFr0IIIbIWS0tLWrVqZdC2e/duoqKisLS05No1HdmyqWzEmqZW/W7ZAsWLq9KuvXqBnZ0JBlK+vApep05VAezcuXD+PCxYoF41asCgQdCx4+tThgohhBAiU5Blw0aSmVchhICLFy9ibm5O8eLFefAAfvnlCZMnPwIMU3G+845a3TtkCJQubcIBaBocOKCC2HXrIDJStTs6qrI7/ftD0aIm7FAIIYQQpiIJm4QQQrwxpUqVonjx4oBK4FSr1n6srctQvPhoGjSIO+/ZMxVfzptn4gHodFC3LqxcCQEB8P33ULAgPHwIP/wA7u7wwQewebPKZCyEEEKITEeCVyGEECbXokUL7t0LZOPGXuzerUrs9O8fDaj9qY0aXTY4/8kTVeLVJPLmha+/huvXYeNGaNZMte/YAR9+qLJITZoE9+6ZqEMhhBBCvAlGLRs+cuQI3t7e3L59m4iIiIQ31+lYtGiRUQPM6GTZsBBCJM+VK1do3LgDjx+/S1DQb1hYqLQLPj4+bNhQhJ9/dqRzZ7Wk+N13Tdy5nx/89hssWgTBwarN0hLat1d7Y2vXVrO3QgghhHjjTJpt+GVRUVF06dKF9evXo2kaOp2O+LeJfa/T6YjO4suzJHgVQojki4mJwd/fHzc3N31btWo18fFZDsTV1aleXWUp7tABrKxMOIDwcFizRpXbOXo0rr1MGRXEdu8O8m+5EEII8Ual6Z7Xn376iXXr1tG7d298fX3RNI3PP/+cI0eOMHXqVOzt7enYsSN+fn6pfgAhhBBZj5mZmUHg+vz5c3LkyI2Z2Ubs7GL07ceOqTiyUCGNb76BwEATDcDaGnr0gCNH4ORJ+PhjVWLn/HmVDrlAAVVq58wZE3UohBBCCFNJ1cxr+fLlATjz33/uZmZmjB8/nrFjxwJw/vx5qlWrxs8//0z//v1NONyMR2ZehRDCeMHBwVhbO7BiBcycmTB2NDeHdu3gxx+hUKHE75Fqjx+rcjtz5sClS3HttWqp2dj27U08/SuEEEKI+NJ05vXq1avUr19f/16n0xEZW5YAKFOmDK1atWLu3Lmpub0QQoi3jIODA7a20K8fnDoFnTrNxtJyA+bm6vPV6GjYsiWGNWsWERy7Z9VU7O3VGuULF2D3blUb1sICDh2Cbt1U1uLRo+HGDdP2K4QQQogUSVXwmi1bNmxtbfXvs2fPzv379w3OcXV15cqVK8aNTgghxFtHp4NVqwbz5ElzbtyAb76BPHmgTJmTDB/ej27duunPXb9e5WIyWccNGsAff4C/P0yYoJYRP3gAU6aoLMUtW8LWrVJuRwghhEgHqQpeCxYsSEBAgP59yZIl2b9/v0HSpqNHj+Lg4GD8CIUQQryVrKyscHHRMWGCiiX79PGjQoUK+uA1JAR69tRwd4+hbt1QduyAmJjX3DS58uVTUfONGypCbtwYNE0Fri1bqrqxU6easL6PEEIIIV4nVcFrvXr1DILVTp06cfnyZVq2bMns2bPp0qULBw8epFlsbT0hhBDCCFZWMHBgJ06dOkXXrl0B8PKCZ890gBkHDuTkgw+gRAmYPl1tYzUJCwto2xb++gsuX4YvvoBcuVRQO2oUuLiozFKHD6vgVgghhBBpJlUJm06ePMmCBQv4+uuvKViwIJGRkbRv354tW7boz6lWrRpbt27F0dHRpAPOaCRhkxBCpI+gIBg79iZeXraEheU2OGZhEUGDBreYOrUQlSpZmrbjsDBYvRrmzgUfn7j28uVVgqdu3SB7dtP2KYQQQmRhaVrn9VV8fX3x8/PD1dWVatWqYWaWqondTEWCVyGESF9RUbBlC8yaBbt2JTzeowf8/nsade7rq4LYFStUDVmAHDmgZ09VcqdMmTTqWAghhMg60iV4fRtJ8CqEEBnHhQswdeoTVq7MRmSkKm8zZQqMHAnDhg3DycmJfv36kTt37tfcKYWCg9U65rlzIX6ywrp11Wxs27aQLZtp+xRCCCGyiDQtlWNubs53332X5DlTp07FwsIiNbcXQgghUqV0afDyysGDB1b8+itUqAB9+0JQUBAzZ87k66+/5vjxR/TqZbji12gODmo/7KVL8PffqiituTns3w+dO6vitP/7n8o8JYQQQohUSVXwqmkayZmwlUldIYQQ6cHOTpVuPXUKnJzA1taWefPm8cknn+DtXZzff4dq1aBgwUDq1VuAr+9Z03RsZgaNGsG6dSqp09ixKnPxvXvw/fdQuDC0bg07d5owNbIQQgjxdkizTakPHjzAxsYmrW4vhBBCJJutrS19+vRh7tzf2Lgxrv3WrQLs3/8xDRsW53//g1u3TPjBq4sLfPst3LwJa9bA+++rgHXTJmjWDIoXhx9/hIcPTdOfEEIIkcUle8/r7/GyXXh4eNCmTRvatGmT4Lzo6Ghu3brF9OnTKVasGEePHjXZYDMi2fMqhBCZS1gYrFwJM2dqnD6tMzhmbg4VK17nxYufmTChEW3atDZt5xcvwrx5an9sSIhqs7KCTp3U3thq1UCnS/oeQgghRBZj8oRNZmZm6JLxH2rs7WxsbFi3bl2Wr/UqwasQQmROmgaHDqksxevWqazF8fXqtRZPzw7/nasRExODubm5aTp/9kxF0HPmwD//xLVXqqSC2C5d4J13TNOXEEIIkcGZPHj18vIC1H/gffr0oU2bNrRunfATaXNzcxwcHKhZsya5cuVK5fAzDwlehRAi87t9G+bPh99+g7t3IWfOJ5w+HYqbWwEA9u/fT5cuPRg06BPGjBljuo41DY4fV0Hs6tUQEaHa7eygVy9VbqdkSdP1J4QQQmRAaVoqp3fv3rRt25YPP/zQqEFmBRK8CiFE1vHihZqFjYxUpVpjDRo0iLlzG+Hi4s78+eVp2lTlZnr69CnZs2c3TecPH8KSJWpZsZ9fXHuDBmo2tnVrsLQ0TV9CCCFEBpKmpXKWLFmSpoHr06dP+fzzz8mfPz/W1tZUrFiRVatWvfa6+vXro9PpXvm6e/fua8/N6suchRBCvFq2bGrFbvzAFeCzz35Bp2vLrVvlad5c5VoaP/4xuXMXo2PHjkRGRhrfuaMjDB8O//4LO3bAhx+qCHnPHujYEVxdYdw4lVVKCCGEeAulauY11oYNG1i5ciWXLl0iLCyMq1evAnDp0iU2bdpEt27dKFCgQIrv26RJE3x8fJgyZQrFixdnxYoVLFy4kOXLl9O1a9dXXnfhwgVCQ0MN2sLCwmjWrBlVqlThyJEj+vb69esTEBDA8uXLDc63t7enZAqWaMnMqxBCZH379qlVvDdvvnzkGc7O3vz1V2vKlVMtd+/exdnZ2TQd+/ur9cwLF6pyO6CySn34oZqNff99FeAKIYQQmViaLhuOiYmhS5curF27FlDJmZ4/f050dDQA9+7dw8XFhQkTJjB69OgU3Xvbtm20aNGCFStW0KVLF317kyZNOH/+PP7+/ilKmOHl5YWHhwcLFy6kb9+++vb69esTFBTEuXPnUjS+l0nwKoQQb4foaNiyRSV48vZOeLxePRgwIJJBg5wpWNCFLVu2ULBgQdN0/uIFbNig9sbu3x/XXrw4DBgAHh7wFuSZEEIIkTWl6bLhX375hTVr1tC/f38ePXrE8OHDDY7nzZuXOnXqsHXr1hTfe8OGDWTPnp2OHTsatPfu3Zvbt29z7NixFN1v0aJFZM+enU6dOqV4LEIIIUQsc3O17fTvv+HCBRg8GOJvd923DyZODOfZs6cEBQWRP39+/TE/Pz8iYpMxpUa2bKqczr59cO6c6jxHDrXE+MsvoUAB6NMHfH2NeEIhhBAiY0tV8Orp6cm7777LnDlzyJkzZ6IldNzd3bl+/XqK733u3DlKlSqFhYWFQXv58uX1x5PrypUrHDhwgM6dOyeaUMPPzw8HBwcsLCwoWrQoY8aM4fnz5ykesxBCiLdLqVJqBjYwEGbOhBIlVPuoUTm4c+cO69atw9zcHE2DU6egY8eO5MuXj3379hnfeZkyqvPbt1Vyp/Ll4flzleypalX1WrJEFbQVQgghspBUBa9Xr16lbt26SZ7j6OjIw4cPU3zvhw8f4uDgkKA9ti0l91y0aBGAwXLhWLVr1+bnn39m3bp1bNq0iebNmzNt2jSaNWtGTEzMK+8ZERFBaGiowUsIIcTbKWdOGDIELl5UM7IdO6r/r2rUqAHAgQOqdOu5c4sJDW2Du3tZ/bVXrlzhljHJl7Jnh/79VXR86BB066ZmaH191Sysi4ualf33XyOfUgghhMgYUhW82tjYvDZou3nzJvb29qm5faIzuck5Fl9UVBReXl6UKVNG/0NEfBMnTmTgwIE0aNCA5s2bM3PmTKZMmcL+/fvZuHHjK+87efJk7Ozs9C+T7WcSQgiRael00KgRWFkZts+apX6NjKxIdPRiKlVyZMwYCAiAb775hkKFCjF79mzjO3/vPVi2TGUinjIF3Nzg0SP45Rc1Ldy4sdozGxVlXF9CCCFEOkpV8FqpUiV27tz5yv07wcHB7NixI9Gg8XVeNWMbHBwMkOisbGK2bdvG3bt36devX7L77t69OwBHjx595TmjR48mJCRE/woICEj2/YUQQrxdWraEihXj3j94AJMmQeHCGnv3DkbT6lKjRk398Vu3brF///4kVwAlKXduGDkSrl6FrVuhRQsV3Hp7Q7t2KqidMAHu3DHquYQQQoj0kKrg9dNPPyUgIIAOHToQGBhocMzPz4+2bdsSEhLCp59+muJ7lytXjosXLxL10qfDZ8+eBaBs2bKJXZbAokWLyJYtGz169EjxGMySKDtgZWVFzpw5DV5CCCFEYnr2hJMn1arezp0hNp1DdLSOe/fqAHvp1auSPnvxb7/9Rr169RLd7pIi5ubQvLlKj+znB6NGqcA2MFDVii1USK1x3rMHUl8xTwghhHijUhW8tm7dmlGjRrF161YKFSrETz/9BECePHkoXrw4Bw4c4H//+x/vv/9+iu/dtm1bnj59yrp16wzavby8yJ8/P9WrV3/tPe7evcu2bdto06YNjo6Oye7by8sLIFUzxkIIIURiYlf1rlypyraOHw/xy8CeP6/D1jbufY4cOWjatKn+/bNnz1i0aFHqcywULgyTJ6u1ysuXQ61aavnw2rWqTmzp0vDrr/D4ceruL4QQQrwhqarzGuvvv/9m1qxZHDt2jODgYHLmzEn16tX59NNPDf7jTakmTZrg6+vL1KlTcXd3Z+XKlSxYsIBly5bRrVs3QCVh8vLyws/PD1dXV4Prp06dyqhRo/jrr79o3LhxgvsfOHCA77//nrZt21KkSBHCw8PZvn078+fPp169evz9999Jzr7GJ3VehRBCpNSLF7B+vdoTGxYGJ06oIBcgLCyMffssiYmx5IMPYPnypfTs2ZNy5cpx5swZ0wzgzBmYOxeWLoVnz1Sbra1K+jRwoMoyJYQQQrwhyY2pjApe08rTp08ZM2YMf/zxB8HBwZQsWZLRo0fTuXNn/TkeHh54eXlx/fp13NzcDK4vUaIEL1684Nq1a4kmeLp69SqfffYZp0+fJigoCJ1OR7FixejcuTPDhg3D6uWMG0mQ4FUIIYQxQkNV1uJYmqaq3Zw4AUWKQK1apzh2bADdujVn7Nix/52jMW3aND788ENKlSplXOfLlsGcOXD+fFx7jRoqiP3oI7C2Tv39hRBCiGRIk+D16NGjjBkzBh8fHwCqVavGpEmTqFatmvEjzqQkeBVCCGFKx4/DyztkbG01unSJ4dNPzSlfXv1/XLNmTWxtbbl//z7vvPOOcZ1qGhw8qILYdesgMlK1OzpC794wYAAULWpcH0IIIcQrmDx4PXv2LNWrVyc8PNyg3cbGhuPHj1OmTBnjRpxJSfAqhBDClKKjVaLgWbNU7diX1a0LzZtf48CBYeTJk4vFixfrj02ZMoUyZcrQrFkzLC0tUzeAe/dg0SL47Te1STdWs2ZqNrZFC5UQSgghhDARkwev3bp1Y+XKlYwZM4ahQ4ei0+mYMWMGkyZNonv37vz+++8mG3xmIsGrEEKItHLpkpoM9fSEJ08Mj7m6woULGra2anvMvXv3KFCgANHR0Vy8eJGSJUsa13l0NGzbpgawc2dcVuJCheCTT6BfP8ib17g+hBBCCNIgeC1UqBBubm7s37/foL1OnTr4+/tz8+ZN40acSUnwKoQQIq2FhqrcSrNmqYAWVNnW+In57969yw8//MDVq1fZuHGjvn3GjBlER0fTvXt38uTJk7oB+PmpmdhFi+C/uutYWkL79mo2tk6duIxTQgghRAolN6ZKdqmce/fuJVpCpkaNGty7dy91oxRCCCHEa+XMCYMHw4UL4O0NbdrA0KGG5zg4OHPp0k+0a7eR2B0+kZGRTJo0iWHDhnHs2LHUD6BoUZg2TdWJ/f13ldApMhJWrYJ69aBcOZg9W0XZQgghRBpJdvAaGRlJ9uzZE7Rnz56dyNjEDkIIIYRIMzodNGwIGzZA/fqGx9avV6t8PTygYEH4+mu4cSOGb7/9lg8++IBmzZrpz126dCkDBw7k1KlTKRuAtTX06AFHjsDJk/Dxx6rEzvnzMGQI5M+vZmJNVdJHCCGEiCfZwasQQgghMq5du+J+HxQEkydDyZJW/PXXAIYP34aFRVwCpzlz5jBv3jx2xb8opSpVgvnz1Wzsr79CyZKqZuy8eVChAtSuDcuXQ0SEEU8lhBBCxEn2nlczMzPc3d1xd3c3aL969Sp+fn40bdo04c11OrZu3WqakWZQsudVCCFERqBpcPQozJwJa9ZAVJTh8dKl1eRojx5w9Kg3Xl5e/PDDDzg7OwOwZ88evv/+ewYOHEj79u1TN4B9+1SCpw0b4gaQOzf06QP9+0PhwkY+pRBCiKzI5AmbzMxSPkmr0+mIjo5O8XWZiQSvQgghMpo7d2DBAjUJeueO4bGvvoKpUxNe07NnT5YuXUr//v2ZN2+evl3TNHQpTcZ05w4sXKiSPAUGqjadDpo3V8uKmzWTcjtCCCH0TB68pjabsKura6quyywkeBVCCJFRRUaqvbCzZsHBgyp+vHoVihSJOyc8XCUO9ve/ztKlS2nZsiWVK1cG1P/977//Pj179mTs2LEpD2KjomDzZpg717BorZsbDBigZmRz5zb+QYUQQmRqJg9eReIkeBVCCJEZnDoF+/fDp58atk+apCrgDBoEvXuDg0P8Y5MYM2YMDRo0YPfu3fr2yMhILC0tSZErV9RU8JIl8OiRasuWDTp2VLOx770n5XaEEOItJcHrGyLBqxBCiMwqKkptQ711S723sYFu3dTe2AoVICwsjD///JM8efLQqFEjAJ4/f07RokWpX78+s2fPJleuXCnr9PlzWL1a7Y318YlrL19eRdDdukEi1Q2EEEJkXRK8viESvAqRNWlaNI8fH+DFiztky5YPe/s66HSyR09kLXfvQq9e8NdfCY/VqaOC2LZt1bLiWJs2baJ169YUKlSI69ev63NihIaGpvz/QV9ftaR4xQr0xWlz5ICePdVsbJkyqXwyIYQQmYkEr2+IBK9CZD0PHqzn6tXPiIi4pW+zsnLB3X0GuXO3S8eRCZE2Ll9WE6FLlsCTJ4bH8udX21M/+wxy5lQJnHx9fbl37x4tW7YEVFuFChWwsrJiyZIllC1bNmUDePQIvLzUIK5ciWuvW1fNxrZtq5YYCyGEyJIkeH1DJHgVImt58GA95893AF7+p1HtxStTZq0EsCLLevIEli5VCZ4uXoxrz5FDJQ3OkSPx665fv07x4sUxNzfnzp07+qXE9+7dw8HBIfn7Y2NiYPduNRu7cSPEVizImxf69YNPPoFChYx4QiGEEBlRcmOqlNe/EUKILErTorl69TMSBq7o265e/RxNy9olwMTbK0cONdF5/jx4e0ObNmBmBh4eCQPXQ4fU9lWAwoULExgYyLp16wz2wA4ePJgCBQrw559/Jm8AZmbQqBGsWwc3b8K4cZAvH9y7B99/rzbotm4NO3aoQFcIIcRbRWZejSQzr0JkHY8e7eX06QavPa9ChT3kylU/zccjREZw8yZYWECBAnFtwcHg4gK2tmpCdOBAeLky3osXLyhWrBj+/v6cPn2a8uXLA2o2VtM0nJ2dkzeAyEjYtEktKY6X8ZiiRdV65t69wdHRyKcUQgiRnmTmVQghUujFizsmPU+IrMDV1TBwBVi8WM26PnwIU6equrFt28KuXRD7kXi2bNnw8/Nj9+7d+sAVYPr06bi4uPDdd98lbwCWltC+vbr5xYtq862dHfj5wYgRanC9esHRo3GdCyGEyJIkeBVCiP9ky5bPpOcJkVU1aKAq2sRuZY2JgT//VCt+y5RRk6RPnoCFhQUNGhiuZrhy5QrR0dGULl1a3/bkyROOHj3KaxeDlSwJ06erDbgLF0KlShARAb//DjVrQpUqqv3ZM9M+sBBCiAxBlg0bSZYNC5F1aFo0R4+6ERERSOL7XnVYWblQo8Z1KZsjBKrUzoIFMG8e3L5teCxnTvj6axg5MuF1ly9fxs3NDSsrKwAWL15M3759admyJZs3b07+ADQNjh9XCZ5WrVKBLKiZ2V691HrmkiVT+XRCCCHeFFk2LIQQKaTTmePuPiP23ctHAXB3ny6BqxD/cXaGb76BGzdg9WpVGzZWaCj8F5smUKJECX3gCvDgwQNsbW1577339G2aprFmzRqeJTWLqtNB9erg6almY3/4Qe2FDQmBX3+FUqXg/fdh7Vq1d1YIIUSmJjOvRpKZVyGynsTrvBbE3X26lMkR4jVOn1aldv78U5VstbePO3bpEmzZAn36gIOD4XVPnjwhJiYGOzs7AA4ePEidOnXIly8f/v7+WFhYJG8AMTHw999qNnbz5risxPnywccfq5eLi9HPKYQQwnSkzusbIsGrEFmTpkXz+PEBXry4Q7Zs+bC3ryMzrkKkQEREwpnXwYPVflhra7VndsgQqFgx8eu3bNnCZ599Rt26dVmyZIm+/ffff6dWrVoULVr09YPw94f589U+2Hv3VJu5OXz4oaoJ9P77qjyPEEKIdCXB6xsiwasQQgjxes+fQ968KpFTfLVrqyC2Xbu4BFCxNE3j6dOn5PivyOzt27cpWLAgMTExBAQE4JLcGdQXL2DDBjUbu29fXHuxYmpfrIcHxKtPK4QQ4s2SPa9CCCGEyDBsbMDXV1W6if9zycGD0LmzKskzYYJKAhVLp9PpA1eAx48f07hxY+rWrWsQuC5dupSdO3cSHR2deOfZskGnTrB3L5w7p6LlHDnUuuYvv4T8+dVaZl9fEz+1EEIIU5KZVyPJzKsQQgiRMk+fwtKlam/shQuGxywt4dAhqFr11ddHRkZi+d807YsXL8ifPz8PHz5k586dNGnSJPmDWL5crWM+cyau/d131ZLiTp3A1jaFTyaEECI1ZOZVCCGEEBlS9uxqte65c7B7N7RtG7f1NF8+Vb41KZbx1hc/e/aMzp07U65cORo2bKhvX7duHbNmzeLhw4evHkT//nDqlIqWu3dXM7S+vmoWtkABNSv7779GPq0QQghTyZDB69OnT/n888/Jnz8/1tbWVKxYkVWrVr32Ok9PT3Q6XaKvu/HXIf3H29ubmjVrYmtri5OTEx4eHty/fz8tHkkIIYQQL9HpoEEDWL8erl+H0aNh1Ch4ObFwjx6qXuyNGwnvkStXLmbNmsXp06cxN49LqjZ58mSGDh3K8uXLXz+I995TU8G3bsGUKeDmBo8fwy+/QIkS0Lix2jMbFWXsIwshhDBCMvPOv1nt2rXDx8eHKVOmULx4cVasWEGXLl2IiYmha9eur71+yZIllHypKLmjo6PB+3379vHBBx/QokULNm7cyP379xk5ciQNGzbE19fXoP6cEEKklGQrFiJlChWCSZMStl+9CsuWqd//8AO0agVDh0LDhirujKWL9yYmJoYePXpgbm5Oly5d9O379u1jw4YN9O7dmwoVKiTsLHduFSUPHw47d6oET1u3gre3ehUoAJ98Av36qX2yQggh3qgMt+d127ZttGjRQh+wxmrSpAnnz5/H39/f4JPV+Dw9Penduzc+Pj68++67SfZTrVo1nj17xunTp/W14w4fPkytWrWYM2cOAwcOTNZ4Zc+rEOJlideJdcHdfYbUiRUihZYvh969ITLSsL1kSVV6p2dPwwRQSenatSsrV65kyJAhzJw5M3kX3bgBv/0GixbBgweqzcIC2rRRe2Pr1zeMooUQQqRYpt3zumHDBrJnz07Hjh0N2nv37s3t27c5duyY0X0EBgbi4+NDjx49DIqev/feexQvXpwNGzYY3YcQ4u304MF6zp/vYBC4AkREBHL+fAcePFifTiMTInPq1g0CAmDiRDXxGevSJTUDW6CASh586dLr7+Xh4cFHH32Eh4eHvs3Pz48WLVqwbt26xC9yc4PJk9Ugli+HWrXU8uG1a1Wd2NKl4ddf1TJjIYQQaSrDBa/nzp2jVKlSBkElQPny5fXHX6dly5aYm5vj4OBAu3btElwT+z72ni/3k5w+hBDiZZoWzdWrnwGJLWhRbVevfo6mvaKchxAiUXnzwpgxal/smjVQr17csadPYfZstZr3dZo0acLq1aupUqWKvu33339n27ZtzJ8/P+mLrayga1dV2+f0aRgwQCV9unRJ1f8pUAA+/hhOnkzlUwohhHidDBe8Pnz4EAcHhwTtsW2vzBoIODs7M2bMGBYuXMiePXv47rvv8PHxoUaNGpw+fdqgj/j3fLmfpPqIiIggNDTU4CWEEACPHx9IMONqSCMiIoDHjw+8sTEJkZVYWkKHDqpc65kzKllwbDWboUMNz9U0CA5+/T27d+/O119/zZAhQ/RtYWFhVK1ale+//57w8PCEF5Uvr/bDBgaqyLlMGQgLg4ULoUoVqFEDfv8dErtWCCFEqmW44BUMky6k5FizZs2YOHEiLVu2pG7dugwePJgDBw6g0+kYO3Zssu+VVB+TJ0/Gzs5O/ypYsGASTyKEeJu8eHHHpOcJIV6tXDmYN08lCJ41S21BjW/3bjUZ2rcv/PPPq+9TrFgxvv/+e1q1aqVv27BhA76+vixatIhs2bLp2xOkCcmZU+17PXsW9u+Hzp1VhH3sGPTqBS4uMGIE+PmZ4ImFEEJkuODV0dEx0ZnP4P8+Pk1stjQpbm5u1K5dm6NHjxr0AYnP4gYHByfZx+jRowkJCdG/AgICUjQeIUTWlS1bPpOeJ4R4vVy5VOKmeKVfAZg5U018Ll4MlSurraqrVsGLF6+/54cffsiSJUv49ttvMfuvAK2madSoUQMPDw8CAwMNL9DpoE4dWLlS7Y39/nuVPvnhQ/jxR3B3h2bNYNMmiJZtA0IIkVoZLngtV64cFy9eJOqlWmpnz54FoGzZsim+p6Zp+v984t8j9p4v95NUH1ZWVuTMmdPgJYQQAPb2dbCycgFetXpDh5VVQezt67zJYQnx1tE0FS/a2cW1HT4MXbqAqyuMHw+3b7/6+hw5cuDh4UGPHj30bf/88w/Hjx/njz/+IEeOHPr2Fy9Hw3nzwtdfw7VrKlht1kwFtzt3QuvWULiwCm7v3TPR0wohxNsjwwWvbdu25enTpwmy/nl5eZE/f36qV6+eovtdv36dQ4cOUaNGDX1bgQIFqFatGsuWLSM63iegR48e5fLly7RrJ6UshBApp9OZ4+4+I/bdy0cBcHefLvVehUhjOp2a8Lx1Sy0tjv+Z9N278O23Kojt3BkuXEjePStVqsTBgweZOXOmwQfXH330EbVr105YDcHcXBWl3b4drlxRy4cdHdXM7P/+BwULqgHs36+ibSGEEK+V4eq8gsoG6Ovry9SpU3F3d2flypUsWLCAZcuW0a1bNwD69u2Ll5cXfn5+uLq6AtCoUSPq1q1L+fLlyZkzJ2fPnmXatGk8efKEw4cPG8yo7t27l8aNG9OqVSsGDRrE/fv3GTVqFHZ2dvj6+mJlZZWssUqdVyHEyxKv81oQd/fpUudViHSgaSpGnDkT/vzTcOWujw+8pjT8K4WGhpInTx4iIiI4f/48pUuXBuDJkyfY2tomrEsfHq7SJc+ZA/G2M1GmDAwcCD16JL9orRBCZCHJjakyZPD69OlTxowZwx//b+++46ou3z+Ovw4bJME9URRc4cDcOUL95qyvIy1xlCMrV5rftMhKm2pmP1eaaTly58jMlXummZaZiinOcKOoKEPg/P74BHpkyDwH8P18PHgU9+e+z30doOTyHteSJVy7do3KlSsTFBREly5dEvv07NmTOXPmcOrUKby9vQF44403+Pnnnzl37hyRkZEULVqUZs2a8d5771GxYsUk82zYsIH333+fP/74Azc3N5555hnGjRtH0aJF0xyrklcRSY7ZHEd4+A5iYi7g5FQCT8/GWnEVyQHOnYPp0+Hrr6F8ecscEoy7looWNXb3psX58+dZv349vXr1SmwbNmwYCxYsYOzYsXTv3j35gb//btxYPH++cVMxQL580L27kcjWqJGBdycikjvl6uQ1N1HyKiIikvtERxvnXu9PUs1m8Pc3Lg9+5hmj/E7z5mCXjkNWZrM5sWb8Dz/8QLt27QC4ffs2UVFRiZdGJrpxwyirM3WqUTM2wZNPGjcZd+pk1JgVEcnD0ppT5bgzryIiIiLZzdk56erqjh1G/VizGVatghYt4PHHje3GaS3rbjKZ2L9/PytWrKB169aJ7fPnz6dEiRIMGzbMcoCHh5ElHzkCW7ZA587g4GDcMNW9u1Fu5+234dSpTL5jEZHcT8mriIiICEai+sknRr6Y4NgxeP11o2bsgAFpu+DJycmJ9u3bW9SI/fXXX7l7967F0aT4+HgOHjxo1I81mSAgAJYsgbNn4cMPjUmvXoWxY8HHx1gOXr1a5XZE5JGlbcOZpG3DIiIieUtsrFHlZsoUYzH0QS1bwpo16dtODEY5vhIlSlC4cGEAtmzZQrNmzWjcuDHbtm3DZHrglvLYWPjpJ2NL8YYN99q9veHVV6F3b+OArohILqdtwyKSI5jNcVy/vpVLlxZy/fpWzGbrrRjExUXy998D+eOPlvz990Di4iLTPDazcdvyfdtybpG8wMEBOnaEzZuN86+vvQZubveeFyiQ/sQVjFr2CYkrQHBwMM7OzlSuXNkicd2yZQtRUVFGIO3bw88/w99/w9ChxuSnT0NQkFFup1s32LVL5XZE5JGglddM0sqrSMqSLxlTGl/fidleMubQofaEha1M0l6oUDuqVfsh1bGZjduW79uWc4vkZeHhMGeOsRo7ezY0bHjvWVSUkVf26QO1aqXvda9fv05kZCQlS5YE4Ny5c5QtWxZPT09OnTqFh4eH5YDISFi82FiN3bfvXnv16sYtxd26wWOPZeg9iojYim4bthIlryLJu3JlOYcPdwIe/F+Msbrg57c025KplBLXBKklsJmN25bv25Zzizwq4uON46n37/CdMwd69jT+vX594/6lTp3gviOvabZt2zZ69OhB+fLl2bp1a2L72rVr8fPzo0yZMvc6//abUW5nwQIjgwYjcX3xRSOR9fNLfwAiIjag5NVKlLyKJGU2x7Fnj7fF6p8lE87Opalf/1SW1z6Ni4tkxw63h/Zr3PgO9vauFm2ZjduW79uWc4s86v7zH9i0ybKtWDF45RVjy/G/i6ppFh8fz5UrVyhWrBgA0dHRFC9enBs3bvDrr79Su3ZtywHXrxsZ9LRpxvbiBE2aGElsx44Zy6RFRKxEZ15FxGbCw3ekkkQBmImOPkd4+I4snzskZNjDO6XQL7Nx2/J923JukUfdypXw9ddQrdq9tkuX4KOPoGxZeOEFowxPWpcL7OzsEhNX47Uu4e/vT+nSpalZs2Zi+88//8yWLVuI9/CAIUOMOrEbNxrJqr09bN8OgYHG2dgRI4xbjEVEcjElryKS5WJiLmRpv/S4c+d4hvtlNm5bvm9bzi3yqMuXD/r2hYMHjXyxc2cjdwTjwuAlS4xF0AkTMvb6ZcqUYcuWLRw5cgR7+3s7J4YPH06zZs2YPXu20WAyQfPmsGwZnDkDI0dCiRJw+TJ8+qlR2LZdO1i3ztj/LCKSyyh5FZEs5+RUIkv7pYebW4UM98ts3LZ837acW0QMJhM0bmwkq2fOwHvv3atkY2dnnIO9X3oPbrm7uyf+e3R0NHXr1qVo0aK0b98+sX3Xrl3MmDGDG+7uMGqUEcjSpdCsmZGw/vgjtG4NFSvCuHFGHVkRkVxCZ14zSWdeRZK6d/4ylKSXB0HOP/Oasbht+b5tObeIpCw62sgdg4ONbcT3+/BD+PVX44Knp5/OWPmd2NhYHBwcEj/v3LkzS5cu5Y033uCLL76w7BwcDF99ZVyXfOOG0ebsDM8/D/37Q716ljdRiYhYic68iojNmEz2+PpOTPjswacA+PpOyJYkyt7elUKF2qXap1ChdkkSV8h83LZ837acW0RS5uxsVK95MHGNiTHuV1q9Glq1gsqVYeLEezllWt2fuAI0atSIxx9/nBdffDGx7fjx4wwfPpzDcXHG3uXQUJg5E2rWNLLr776DBg2MOj8zZsDt2xl8tyIi2Usrr5mklVeRlCVfc9QLX98JubDOa9rjtuX7tuXcIpJ2wcHQogWcO2fZni+fUelmwICMV7oxm82Y7ltBHTFiBJ9++ilt2rRh9erV93c0ln6nTYNFi4xEFsDDA156ybgquUqVjAUhIpIOKpVjJUpeRVJnNscRHr6DmJgLODmVwNOzsdVW/+LiIgkJGcadO8dxc6uAj8+4ZFdck5PZuG35vm05t4ikXWwsrFoFU6bA5s1JnzdtCgMHwn//Cw8ssKbLhg0b+PLLL3nxxRfp2NH4S6yIiAj69OlDYGAg//3vf7G7ft3YTjxtGoSEWAbRv79x0ZOjY8aDEBFJhZJXK1HyKiIiIpl1+DB8+SXMnWu5a9fT09jl6/bwo/zpMnv2bHr16kWFChU4duzYvZXa+HjYsMFIYletuncrcYkSxpXKfftC6dJZG4yIPPJ05lVEREQkl/Dzg6lTjUR14kSo8O+F6H36JE1cz5zJ/HxPPvkkb775JkOGDElMXM1mM+06dODzQ4e49d13cOoUvPsuFCsGFy4YN0x5ext1ZDdsULkdEbE6rbxmklZeRUREJKslLIBWqQJlytxrv3LFWPisWdPYUty5s3EpVFbYvXs3DRs2JF++fFy8ePFeaZ6YGPjhByO73rbt3oAKFaBfP+jZEwoUyJogROSRpJVXERERkVzKzg5atrRMXMG4DDgmBvbuhR49jOfvvQf//JP866SHn58f06dPZ8SIERY1Zbv16sWrmzZxatYs+OsvI2t+7DE4fhyGDoWSJaF3b9i3L/NBiIikQiuvmaSVVxEREbGW77+Hjz+GP/+0bLe3N3bzDhwIjRtnXbnWixcvUrp0aeLi4jh27BgVK1YEIP7mTewWLTJWYw8evDegdm1jNbZLl6w/qCsieZYubLISJa8iqYuPjyE0dCqRkSG4uvpQqlR/7Oyc0jQ2M7cFg278FZG8yWyGnTuNW4qXLYO4OMvn1arBqFFGMptZ8fHxbN26lZ07d/L+++8ntg8dOpQ//viDke+/z1POzkYSu2SJsSwMxk1TvXoZ5Xb+TXhFRFKi5NVKlLyKpCwkZDjnzn0B3P+blT1eXkPx8fks1bGZqdMKKdU7LY2v70Qb1Vq1ztwi8mgJDYXp042Py5fvtX/5pVHhJjvExcVRqlQpLl26xE8//UTbtm0BiAkNxWHePOymTzcue0rwn/8Yq7GZrfkjInmWzryKiE0Zies4LBNXgDjOnRtHSMjwFMemlLgChIWt5NCh9qnOfeXKcg4f7mSRPAJER4dy+HAnrlxZnoZ3kDG2nFtEHj2lShmXAJ89C/PnQ/36xnHUHj0s+x07BmvXZs0Fwfb29uzdu5exY8fSsmXLxPaZK1dSbupUZgwfDqtXwzPPGPuXN26E554zbir+8EM4fz7zQYjII0nJq4hkufj4mH9XXFN27twXxMfHJGmPi4tMMXFNEBa2kri4yGSfmc1xnDgxGEhuU4nRduLEEMzmB5PqzLPl3CLyaHN2hq5d4Zdf4OhRI4G93+efQ5s2UKkSTJgA4eGZm69s2bIMHz4ch/tWUpcvX87Zs2eJiIw0Jlu1irjjx4kaMgSKFDGWiUeOhLJljWuSt2wx9kCLiKSRklcRyXKhoVNJuuL6oLh/+1kKCRmWpjlS6hceviPJqqclM9HR5wgP35GmedLDlnOLiCQoVcry82vXjFVZgBMn4I03jHI7/foZlwdnlVWrVrFw4UK6deuW2Lb55Ek8p01jUPv2RhCNGkFsLCxdCs2aweOPw6RJmc+mReSRoORVRLJcZGRIhvvduXM8TWNT6hcTcyFN49PaLz1sObeISEo8PGDBAmje/F7b7dvw1VfG5U5NmxoXP8XGZm4eV1dXunTpQtGiRRPbNmzYQHR0NHEODsbS8I4d8Oef3OzWDdzdITgYBg82Mu6+feHAgcwFISJ5mpJXEclyrq4+Ge7n5lYhTWNT6ufkVCJN49PaLz1sObeISErs7aF9e+Po6eHDxkVO+fLde751K3TqBOXKWd6zlBXGjh3Lb7/9xtChQxPbTrm74zF/Ps0qVeLuxIlQtSrcuQMzZ0KtWsbB3blzISoqa4MRkVwvRyavERERDBkyhJIlS+Li4oK/vz+LFi166Ljly5cTGBiIr68vrq6ueHt7061bN44fT7pCExAQgMlkSvLRqlWr7HhLIo+UUqX6Aw8rC2P/bz9LPj7j0jRHSv08PRvj7FwaSKnIoQlnZy88PRunaZ70sOXcIiJp8fjjxk3EoaHGbt37q9g4OxvHUbOSyWSiVq1a+Pr6Jrbt3bsXBwcH7AsUwPH1142itdu3c71VK8yOjrB3L7z0krEaO2wYhKRtN4+I5H05Mnnt2LEjc+bMYeTIkaxdu5Y6deoQGBjIggULUh03duxY7ty5w4gRI1i3bh0ff/wxv//+O0888QSHDx9O0r98+fL88ssvFh8TJkzIpncl8uiws3PCy2toqn28vIYmW+/V3t6VQoXapTq2UKF2KdZ7NZns8fWdmPDZg08B8PWdkC01V205t4hIenh4wKBBxuVOP/8Mzz5rfG73wG+GQ4bAd99BdHTWzd2lSxcuXLjA5MmTjQaTicjatfHevRu/xx4j7H//gzJljMO6n38Ovr7QqhX8+GPSorYi8kjJcXVe16xZQ9u2bVmwYAGBgYGJ7S1atODw4cOcPXsWe/vkf/G7fPmyxTkLgPPnz+Pt7c2LL77IzJkzE9sDAgK4evUqf2XypgLVeRVJWc6r8+qFr+8EG9V5tc7cIiIZZTYblW0SHD1qrNSCcVnwK6/Aa68Zlz1ltYMHD9K6dWucnJw4efIkdmYzrFlD+OjReOzZgynh11UvL3j1VejTB4oXz/pARMQm0ppT5bjktW/fvixatIjr169bXL++cOFCunbtyq5du3jyySfT9Zrly5enQoUKrF+/PrFNyauIdcTHxxAaOpXIyBBcXX0oVap/siuuyYmLiyQkZBh37hzHza0CPj7jUlxxTY7ZHEd4+A5iYi7g5FQCT8/GVlv1tOXcIiJZ4ZNP4N13LdsSzs8OHAhPPWWZ7GZWbGwsZ86cwcfHuA/BbDZTtWpVYo4eZV3Hjvhs3QphYUZnBwejdmz//tC4cdYGIiJWl9acKsdtG/7rr7+oUqWKReIKUL169cTn6XHy5EnOnDmDn59fkmchISEULFgQBwcHfHx8GDFiBJGRydeOTBAdHc3NmzctPkQkZcYW4iFUrDgZL68haU5cwdhCXLHiFPz911Ox4pR0Ja5gbOMtUCCAYsUCKVAgwKrJoy3nFhHJCu+8Azt3wgsvGLkiGLt2ly0zbiiuXh2mTzduLs4KCb+PJbhx4waenp784+xM4W++gX/+gblziahe3bgaefFiI4OuVs04yKvfyUTyvByXvIaFhVGwYMEk7QltYQl/45YGsbGx9OnTB3d3d9544w2LZ40aNeKLL75g2bJl/Pjjj7Rp04bPPvuMVq1aER8fn+Jrjh49Gg8Pj8QPLy+vNMcjIiIikluYTNCwISxaBGfOwMiRljt1//rL2EbctWv2zO/p6cmuXbs4c+YMHh4e4OICPXrQo3x5/IEDtWuDm5txhfLAgVCypBHQwYPZE5CI2FyOS17BuJkuI8/uZzab6dOnDzt27GDu3LlJksyPP/6Yfv360bRpU9q0acPkyZMZM2YM27dvZ+XKpOfsEgQFBXHjxo3Ej3PnzqXtTYmIiIjkUiVLwqhRRhK7YAHcf4KrVy/LvvHxxkdWuf8+E7PZTJEiRTiRLx9Os2bB+fMwaRLRPj7GEvD06eDvb2Td8+dn7U1TImJzOS55LVSoULKrq9euXQNIdlX2QWazmZdffpl58+Yxe/Zs2rVL/ebSBN27dwdgz549KfZxdnYmf/78Fh8iIiIijwInJwgMhF27YP9+eOMN46bi+61fb5Tg+b//g/DwrJ3fZDLx9ddfc/nyZapWrZp4bfJ7HToQAPxSurSxx3n3buje3bhd6u23s76ArYjYRI5LXqtVq8bRo0eJjY21aD906BCA8T+qVCQkrrNmzWLmzJmJCWl62D14T7yIjZnNcVy/vpVLlxZy/fpWzGbrlQqIj4/h3LkJ/P33IM6dm0B8fEy6xsfGRnDoUAd+/bU6hw51IDY2Is1jo6IusmtXcbZudWHXruJERV1M19zR0Vf45ZdybNvmzi+/lCM6+kqax969e4MDBxqxe3cZDhxoxN27N9I1ty2/Z7acW0QeHU88AV98YVzidL/Jk43SrEOHGqVaX30V/v01Lsu4ublZfO5drhyhvr5cnDQJzp6FDz8kvlQpuHoVxo4FHx9o2xZWr1a5HZFcLMfdNrx27VratGnDokWLeOGFFxLbW7duzZ9//plqqRyz2Uzfvn359ttvmT59On379k3X3J999hlvvfUWP/zwQ5pXa3XbsGS35MuulMbXd2K2l13JTKkbgN9+q0tExL4k7e7udahd+9dUx27fno/4+DtJ2u3s3GjS5OG3g+zY4UlcXNKE097eg8aNw1Mdu2ePL1FRIUnaXVx8qF//xEPntuX3zJZzi4jcvQvPPGPUjn3QU08ZR1Pbt793AVRWMpvNmM3mxEWIb6ZPZ9VrrzEsXz4a3n+rVNmyxtnY3r3hgRKLImIbubZUDhg1XX/77TfGjh2Lr68vCxcuZMaMGcybN49u3boB0KdPH+bMmUNISAhly5YFYNCgQUyZMoXevXsnSVydnZ2pWbMmADt27OCTTz6hQ4cOlC9fnqioKNauXcvXX3/NU089xYYNG9K8+qrkVbLTlSvLOXy4E/Dgf6bG2W8/v6XZlpAYieu4FJ97eQ1LNYFNKXFNkFoCm1LimuBhCWxKiWuC1BLYlBLXBA9LYG35PbPl3CIi9zt6FKZOhdmzIeKBDTelSxu546uvQuHC2RfD5s2b+fzzz2nevDn/++9/4auvMM+ahen6dQDMTk6YOnUyyu08+aTK7YjYUK5OXiMiIhgxYgRLlizh2rVrVK5cmaCgILp06ZLYp2fPnsyZM4dTp07h7e0NgLe3N2fOnEn2NcuWLcvp06cBOHHiBIMHD+bgwYNcvXoVk8lEhQoV6NKlC//73/9wdnZOc6xKXiW7mM1x7NnjbbGCZsmEs3Np6tc/leVlWOLjY9i+3Q3LFdcH2dOkyZ1kS9/Exkawc+djD52nUaNbODi4W7RFRV1kz54SDx1bv/4FXFySFqg3tgo//G/SGzS4jLNzEYu2u3dvsGuX50PHNmwYjqOjR5J2W37PbDm3iEhKbt6EuXNhyhQ4dszy2R9/QI0a1o1n54YNzGzRgkF2dtS6/1apatWMJLZbN3js4X9+iUjWytXJa26i5FWyy/XrWzl4sOlD+9WosYUCBQKydO5z5yYQEvLGQ/v5+PwfXl5DkrQfOtSBsLAfHjq+UKH2VKu2wqJt167i3L176aFjHR2L0bBh0jOwxtnW0w8d7+zsTYMGlhd4HDjQiJs3dz10bP78DXniiZ1J2m35PbPl3CIiD2M2w8aNRhK7ahU0agTbt1v2OXbM2NHr4pJ9cYSEhDBp0iScnZ357PnnYdo0WLgQIiONOB97DFOPHtCvHzzknhURyTppzal0M5FIDhUTcyFL+6VHZGTK22bT0i8z4+/eDU/T2JT6xcSk7VKm5PpFRZ1N09iU+tnye2bLuUVEHsZkgqefhpUrjcucJk2yfG42G2dhvbzgnXcguyoR+vj4MHHiRD777DOoXRu++YbQX3/lDeAYYLp1y9jvXK0aNGliFLmNSd9FhSKSfZS8iuRQTk4P3zqbnn7p4erqk6l+mRnv6OiZprEp9XNyKpJse1r6ubiUSdPYlPrZ8ntmy7lFRNKjXDmjFOv9Nm2C4GDjcuDRo8HbG557DrZsMRLb7OTu5UX5SZOY8OqrxvJwx47GFco7dkBgILElS8KIEcYtxiJiU9o2nEnaNizZ5d4ZxlCSXsADOvOak8+8Wv97Zsu5RUQy66+/4NNP4fvv4YFqifj5GbcUd+8O7u7Jj89q0SdPMsHPj+5RUZRKaLSzM8rt9O8PLVoYn4tIltC2YZFczmSyx9d3YsJnDz4FwNd3QrYkInZ2Tnh5DU21j5fX0GQTVwAHB3fc3eukOt7dvU6SxBXAxaU4dnZuyYy4Pz63ZBNXAGfnItjbJ00s72dv75EkcQVwdPTAxSX1VWMXF59kE1ew7ffMlnOLiGRW1aqwYIGxuDlqFBS/73/xhw8bR1BLl4agIOvE41C2LDVWrOCTl18mbskSaNYM4uONA7utW3OndGkYN85YKhYRq9HKayZp5VWyW/J1O73w9Z2gOq+pyHl1Xq3zPbPl3CIiWSUmBpYvNy542nXfPXovvWSU37GJ4GAWNGlCmytX8Exoc3bG3Lkz9O+PqX59ldsRySDdNmwlSl7FGszmOMLDdxATcwEnpxJ4eja22gpafHwMoaFTiYwMwdXVh1Kl+qe44pqc2NgIjh7tkTi+SpXvkl1xTU5U1EX27/fn7t1wHB09qVXrjxRXXJMTHX2FAwfqEhNzBSenIjzxxK/Jrrgm5+7dGxw61JaoqLO4uJShWrXVKa64JseW3zNbzi0iktV+/91IYhcsMI6h1q5979nt2zBjhpHUFiiQ/bEcP36chTNnMrRkSdznzoUDBxKfXS5dmqLvvw9du0K+fNkfjEgeouTVSpS8ioiIiGS/8HDw9LRsmzEDXnkFXF2NM7EDB0L16lYKyGyGffvYERhInZMnSazwkz8/vPQSUb164VKzppWCEcndlLxaiZJXEREREdvw94eDBy3bmjQxktj27cHRMftjiIiIYPXcuQScPk2x5cuNWkD/Olq8OJUmTMCuY0frBCOSSyl5tRIlryIiIiK2ERxslGWdPRtu3bJ8VqoUvPYa9O0LxYpZKaD4eNi4keNDh1L+8GESD2yUKAEvv8y1Tp0oaLWlYZHcQ8mrlSh5FREREbGtW7dg7lzjbGxwsOUzR0dYuNCoG2stZrOZAytXUvzHHym1Zg1cugRALLCzYEH8v/oKz+eeU7kdkX8pebUSJa+SG+TWC3wye1lUZseLiEjuYjbD5s1GEvvjj8ZCqIMDnDkDJUvaKKiYGPjhB65/8gkF/vzzXnuFCvDaa5xp2pRS1arh4OBgowBFbE/Jq5UoeZWcLvnSKaXx9Z2Yo0unZLZMT2bHi4hI7nb6NHz1lbEq++WXls/GjYNr14z6sWXKWC+mK1u3EvfllxT/+We4eROAKJOJH1xcqD5tGo+/9JL1ghHJQZS8WomSV8nJrlxZzuHDnYAH/zM36tD5+S3NkQmskXiOS/G5l9ewVBPQzI4XEZG8KyoKvLzg6lVj1267dsYFT02bWrFMa0QELFhAzMSJOB05cq+9dm3o148TtWvjUaIERYqkrbybSG6n5NVKlLxKTmU2x7Fnj7fFiqslE87Opalf/1SO2kIcHx/D9u1uWK6YPsieJk3uJLsFOLPjRUQkb9u+Hf7zH7h717L98ceNJLZHD3BPWznyzDObubtjBzfHjqXQxo3GFmMgwtGRb2JjKTNmDB2GD7dSMCK2k9acSqfERfKo8PAdqSSuAGaio88RHr7DajGlRWjoVFJPPAHi/u2X9eNFRCRva9IEzp6FDz4wLgFOcOQI9O9v3FI8eDD8/bcVgjGZcGzShEKrV8M//8DYsZjLlcP97l0Gm810eOstePppWL6c0ydO8Ntvv6F1J3mUKXkVyaNiYi5kaT9riYwMeXinVPpldryIiOR9xYvD++8bFzktXgyNGt17dvMmTJpktD24OputihSB4cMxHT8Oq1dzO2Ef88aN8NxzeNasyY916jCyb18rBiWSsyh5FcmjnJxKPLxTOvpZi6urT6b6ZXa8iIg8Ohwd4fnnYccO+P13ePllcHU1nr38svH8fpGRVgjK3h7atCHf5s1w8iQEBUGRInhGRPAhMGrWLOjcGTZv5vq1ayxatIhIqwQmYns685pJOvMqOdW9M6+hJL2wCXTmVWdeRUQkqWvX4NtvjaT2/puIL1yAypWN9oEDoUYNKwYVHQ3LlxM7eTIOv/yS2Hy9eHFGXrzI8fr1WXtfu0huozOvIo84k8keX9+JCZ89+BQAX98JOSpxBbCzc8LLa2iqfby8hqaYeGZ2vIiIPNoKFoQ330xaQmf6dGNL8cyZ4O9vnJ1dssRKW4udnSEwEIfdu+HPP40aP+7uFLh4kUnAjwcOQN++cOAA8fHxjB8/njNnzlghMBHrUvIqkocVKdIRP7+lODuXsmh3di6dY8vkAPj4fIaX1zDgwcTaPk1lbjI7XkRE5EH29vDYY/c+37EDXngBvL3ho4/g4kUrBVKtGkydCufPw9SpmKtWxTEmxsiqa9Xilp8ff775Jg38/blr1UO7ItlP24YzSduGJTcwm+MID99BTMwFnJxK4OnZOMetuCYnPj6G0NCpREaG4OrqQ6lS/dO1YprZ8SIiIve7dQvmzYMpU4zbie/n6GgcRX3zTahZ04pBmc2wa5eR0C5dmrgUHOHsjPugQfDaa+Djw+jRo6lXrx4BAQHY2Wn9SnIW1Xm1EiWvIiIiIo8Wsxm2boXJk2HlSoiPv/dsxgzjsiebuHTJOLD71VdGPaB/RTZpQpft21kNnDxzhjIP7okWsTElr1ai5FVERETk0XX2rJErzpgBsbEQGgpubveenzoFdnZQtqwVg4qLg7VrjdXYdeuMbBu44upKkREjoE8fKF6c8ePH4+7uzgsvvICnp6cVAxSxpOTVSpS8ioiIiEhUFPz1F9Subdn+0kvGVuP//te4pbhZM6N8q9WcPGncNvXNNxAWZrQ5OBDbvj3t1q5lze3bbNq0iWbNmlkxKBFLSl6tRMmriIiIiCTnyhUoXRpiYu61Va5sJLEvvmh5AVS2i4oyzsROnQr3ldU54+6O16efYvfii+DhwTfffMPRo0fp27cvlSpVsmKA8ijL1aVyIiIiGDJkCCVLlsTFxQV/f38WLVqUprGXL1+mZ8+eFC5cGDc3Nxo0aMCmTZuS7btx40YaNGiAm5sbhQsXpmfPnly+fDkr34qIiIiIPKIcHeHdd6FkyXttwcFG8lqqFAwaZHxuFS4u0L077N4Nv/8Or7wCbm6UjYjA7vXXoVQpzK++ytoxYxg/fjxbtmyxUmAiaZcjk9eOHTsyZ84cRo4cydq1a6lTpw6BgYEsWLAg1XHR0dE0b96cTZs2MXHiRFauXEmxYsVo1aoV27Zts+i7bds2WrduTbFixVi5ciUTJ05k48aNNG/enOjo6Ox8eyIiIiLyCPD0hPfeg9OnjZqwTZrce3brlnFrcZUq0KIFXLtmxcD8/Y2txOfPw6RJRhC3b2P6+muWnjjB0UKF6GFnB//+TrxmzRratWvHunXrrBikSFI5btvwmjVraNu2LQsWLCAwMDCxvUWLFhw+fJizZ89ib598iY+pU6cyYMAAdu/eTYMGDQCIjY2lRo0auLu7s3fv3sS+devW5fbt2xw8eBAHBwcAdu/eTcOGDZk6dSr9+vVLU7zaNiwiIiIiafXnn/Dll/DddxAZabRVrmyU3rHqWdj7mc2wbRtMmwbLlxs3TwEULgx9+tDvjz/4av16hg4dyvjx4+8bZsZks6AlL8m124ZXrFiBu7s7nTt3tmjv1asX58+ft0hAkxtbqVKlxMQVwMHBge7du/Prr78SGhoKQGhoKPv27aNHjx6JiSvAk08+ScWKFVmxYkUWvysREREREahe3Vj0DA2F8eOhfHljG/GDOeCYMfDHH1YKymSCgABYvNi4Pvmjj4zDulevwtixTP35Z46UL8/rPj7GTcZAcHAwVatW5f/+7/+sFKRIDkxe//rrL6pUqWKRVAJUr1498XlqYxP6JTf28OHDFq+RUt/U5hARERERyawCBWDoUDh+HPr2tXx28CAEBUHNmtCoESxaZHnpU7YqUcI4qHvqFKxYAS1aYDKbqXLyJGUHDAAfHxgzhmXTpnHkyBE2b95sMTzu3+RWJDs4PLyLdYWFhVG+fPkk7QULFkx8ntrYhH6pjU34Z0p9U5sjOjra4kzsjRs3AGOpW0REREQkI6Ki7v37lCn3/n3XLuOjWDHo1cv4KF7cSkE1a2Z8hITAt98aNX/OnIGgIAY6ONCmVi0iGjfm5o0bYDJx69YtatWqRcuWLRkzZgz58uWzUqCS2yXkUg870Zrjklcg1b3zD9tXn56xKfVN7TVGjx7NBx98kKTdy8sr1bhERERERDLq0iVjK/GYMbaO5F+xsbB/v/Hx1lsWj+bOncvcuXNtFJjkZrdu3cLDwyPF5zkueS1UqFCyK5/X/r2CLbnV0vSOLVSoEJD8Ku61a9dSnSMoKIihQ4cmfh4eHk7ZsmU5e/Zsql9okcy6efMmXl5enDt3TpeDSbbSz5pYi37WxFr0sybWop+1jDGbzdy6dYuS99eVSkaOS16rVavGwoULiY2NtTj3eujQIQCqVq2a6tiEfvd7cGzCPw8dOkSbNm2S9E1tDmdnZ5ydnZO0e3h46AdUrCJ//vz6WROr0M+aWIt+1sRa9LMm1qKftfRLy0JgjruwqUOHDkRERLBs2TKL9jlz5lCyZEnq1auX6tjg4GCLG4ljY2OZN28e9erVS8zkS5UqRd26dZk3b57FofI9e/Zw7NgxOnbsmMXvSkRERERERDIjxyWvrVu35umnn6Zfv37MmDGDLVu28Morr7Bu3To+++yzxBqvffr0wcHBgTNnziSO7d27N35+fnTu3JkFCxawceNGnn/+eY4dO8bYsWMt5hk7dizBwcF07tyZjRs3smDBAp5//nmqVq1Kr169rPqeRUREREREJHU5LnkFWL58OT169OD999+nVatW7N27l4ULF9KtW7fEPnFxccTFxVncSOXs7MymTZto2rQpgwYN4tlnn+XChQusXbuWp556ymKOgIAA1qxZw4ULF3j22WcZNGgQTZs2ZdOmTcluC06Js7MzI0eOTNcYkYzQz5pYi37WxFr0sybWop81sRb9rGUvk/lh9xGLiIiIiIiI2FiOXHkVERERERERuZ+SVxEREREREcnxlLyKiIiIiIhIjqfkNYMiIiIYMmQIJUuWxMXFBX9/fxYtWmTrsCQPunXrFsOHD6dFixYUKVIEk8nEqFGjbB2W5DGbN2+md+/eVK5cmXz58lGqVCnatWvH/v37bR2a5DF//PEHbdu2pUyZMri6ulKwYEEaNGjAvHnzbB2aPAJmzpyJyWTC3d3d1qFIHrJ161ZMJlOyH3v27LF1eHmKg60DyK06duzIvn37GDNmDBUrVmTBggUEBgYSHx9P165dbR2e5CFhYWF8/fXX1KhRg/bt2zNz5kxbhyR50LRp0wgLC2Pw4ME8/vjjXLlyhfHjx1O/fn3Wr19Ps2bNbB2i5BHh4eF4eXkRGBhIqVKluH37NvPnz6dHjx6cPn2ad99919YhSh4VGhrKm2++ScmSJblx44atw5E86NNPP6Vp06YWbVWrVrVRNHmTbhvOgDVr1tC2bdvEhDVBixYtOHz4MGfPnk2sRyuSWQn/iZpMJq5evUqRIkUYOXKkVl8lS12+fJmiRYtatEVERODr60vVqlXZuHGjjSKTR0X9+vU5f/48Z8+etXUokkc9++yzmEwmChYsyNKlS4mIiLB1SJJHbN26laZNm/L999/TqVMnW4eTp2nbcAasWLECd3d3OnfubNHeq1cvzp8/z969e20UmeRFCdtORLLTg4krgLu7O48//jjnzp2zQUTyqClcuDAODtoQJtlj3rx5bNu2jalTp9o6FBHJBCWvGfDXX39RpUqVJH/IVq9ePfG5iEhud+PGDQ4cOICfn5+tQ5E8KD4+ntjYWK5cucLUqVNZv349b731lq3Dkjzo8uXLDBkyhDFjxlC6dGlbhyN52IABA3BwcCB//vy0bNmSnTt32jqkPEd/xZkBYWFhlC9fPkl7wYIFE5+LiOR2AwYM4Pbt24wYMcLWoUge1L9/f6ZPnw6Ak5MTkyZN4tVXX7VxVJIX9e/fn0qVKtGvXz9bhyJ5lIeHB4MHDyYgIIBChQpx4sQJxo0bR0BAAKtXr6Zly5a2DjHPUPKaQalt49QWTxHJ7d577z3mz5/P5MmTqVWrlq3DkTzonXfe4eWXX+by5cusWrWKgQMHcvv2bd58801bhyZ5yLJly1i1ahW///67fj+TbFOzZk1q1qyZ+Hnjxo3p0KED1apVY/jw4Upes5CS1wwoVKhQsqur165dA+6twIqI5EYffPABH3/8MZ988gkDBw60dTiSR5UpU4YyZcoA0KZNGwCCgoJ46aWXKFKkiC1DkzwiIiKCAQMGMGjQIEqWLEl4eDgAMTExgHHztaOjI/ny5bNhlJJXeXp68swzz/DVV18RGRmJq6urrUPKE3TmNQOqVavG0aNHiY2NtWg/dOgQoCuxRST3+uCDDxg1ahSjRo3inXfesXU48gipW7cusbGxnDx50tahSB5x9epVLl26xPjx4ylQoEDix8KFC7l9+zYFChSgW7dutg5T8rD7K0ZI1tDKawZ06NCBGTNmsGzZMl544YXE9jlz5lCyZEnq1atnw+hERDLmo48+YtSoUbz77ruMHDnS1uHII2bLli3Y2dkle6eESEYUL16cLVu2JGkfM2YM27ZtY+3atRQuXNgGkcmj4Pr16/z000/4+/vj4uJi63DyDCWvGdC6dWuefvpp+vXrx82bN/H19WXhwoWsW7eOefPmqcarZLm1a9dy+/Ztbt26BcCRI0dYunQpYGy3c3Nzs2V4kgeMHz+e999/n1atWtG2bVv27Nlj8bx+/fo2ikzymldeeYX8+fNTt25dihUrxtWrV/n+++9ZvHgxw4YN05ZhyTIuLi4EBAQkaZ89ezb29vbJPhPJiK5du1KmTBlq165N4cKFOX78OOPHj+fSpUvMnj3b1uHlKSZzwnq2pEtERAQjRoxgyZIlXLt2jcqVKxMUFESXLl1sHZrkQd7e3pw5cybZZ6dOncLb29u6AUmeExAQwLZt21J8rj8qJKvMmjWLWbNmcfToUcLDw3F3d6dGjRq8/PLLdO/e3dbhySOgZ8+eLF26lIiICFuHInnEmDFjWLx4MadOnSIiIoKCBQvSqFEjgoKCqFOnjq3Dy1OUvIqIiIiIiEiOpwubREREREREJMdT8ioiIiIiIiI5npJXERERERERyfGUvIqIiIiIiEiOp+RVREREREREcjwlryIiIiIiIpLjKXkVERERERGRHE/Jq4iISC4SEBCAyWRKU9/Tp09jMpno2bNn9gaVzUaNGoXJZGLr1q22DkVERGxIyauIiDzyEpK8+z+cnJzw8vKia9eu/Pnnnxl+7dmzZ2MymZg9e3bWBZzH5JUkW0REspeDrQMQERHJKXx8fOjevTsAERER7Nmzh4ULF7J8+XI2b97Mk08+aeMIRUREHl1KXkVERP7l6+vLqFGjLNreffddPvnkE0aMGMGWLVtsE5iIiIho27CIiEhqBg0aBMC+ffss2leuXEnz5s0pUKAALi4uVK1alc8//5y4uLjEPj179qRXr14A9OrVy2JbcoL9+/czcOBAqlatioeHB66urlSrVo0xY8Zw9+7dbHtft27dYuTIkfj5+eHq6oqnpyetWrVi586dSfomnLONjY3lo48+oly5cjg7O1OxYkWmTp2a7OtfvXqVV155haJFi+Lm5kadOnVYsWJFkm3Us2fPply5cgDMmTPH4muU3BnXJUuW8MQTT+Dq6kqJEiV4/fXXiYyMzLKvi4iI5FxaeRUREUlFcpcjvfPOO4wePZrSpUvz3HPPkT9/frZv386wYcPYu3cv33//PQDt27cnPDyclStX0q5dO/z9/ZO81owZM1i1ahVNmjShTZs23Llzh61btxIUFMS+fftYtmxZlr+na9eu0aRJEw4fPkzjxo1p2bIlN27cYOXKlTRt2pTvv/+e9u3bJxkXGBjI3r17ad26Nfb29ixZsoQBAwbg6OhI3759E/tFRETw1FNPceTIERo1akSjRo0IDQ0lMDCQFi1aWLymv78/gwcPZuLEidSoUcNiXm9vb4u+X375JWvXrqVdu3YEBASwbt06Jk+eTFhYGPPnz8/KL5GIiOREZhERkUfcqVOnzIC5ZcuWSZ6NGDHCDJgDAgLMZrPZ/PPPP5sBc+vWrc23b99O7BcfH29+7bXXzIB56dKlie2zZs0yA+ZZs2YlO/fp06fNsbGxFm3x8fHm3r17mwHzzp07LZ499dRT5rT+8Z3wvl566SWL9q5du5oB87fffmvRfvHiRbOXl5e5SJEi5sjIyCRz1qtXz3zjxo3E9uDgYLODg4O5UqVKFq/z7rvvmgHzgAEDLNq3bNliBpJ8PVKKM8HIkSPNgNnDw8McHByc2H7nzh1zxYoVzSaTyRwaGpqWL4mIiORi2jYsIiLyrxMnTjBq1ChGjRrFm2++SaNGjfjkk09wcXHh008/BWDKlCkATJ8+HTc3t8SxJpOJMWPGYDKZWLhwYZrnLFu2LPb29hZtJpOJAQMGALBx48bMvi0LV69eZfHixTRv3jxxS3OCYsWKMWzYMK5cuZLsvKNHjyZ//vyJn1eqVImGDRty7Ngxbt26ldg+b948nJ2dGTlypMX4gIAAWrZsmeHYBw8eTKVKlRI/d3V1JTAwELPZzP79+zP8uiIikjto27CIiMi/QkJC+OCDDwBwdHSkWLFidO3albfffptq1aoBsGfPHvLly8c333yT7Gu4uroSHByc5jljYmKYMmUKixYtIjg4mIiICMxmc+Lz8+fPZ+IdJbVv3z7i4uKIiopKcjkVwPHjxwEIDg7mmWeesXj2xBNPJOlfunRpAMLDw3nssce4efMmp0+fxs/PjyJFiiTp/+STT7J+/foMxf6w+UVEJG9T8ioiIvKvli1bsm7dulT7XLt2jdjY2MQkNzm3b99O85ydOnVi1apVVKxYkRdeeIGiRYvi6OhIeHg4EydOJDo6Os2vlRbXrl0DYNeuXezatSvFfsm9Bw8PjyRtDg7GrxIJF1XdvHkTINnEFYzV3YxKy/wiIpJ3KXkVERFJh/z582Mymbh69WqmX2vfvn2sWrWKli1bsnr1aovtw3v27GHixImZnuNBCdt+//e///H5559n2+tfuXIl2eeXLl3K8jlFROTRoDOvIiIi6VCvXj3CwsISt9c+TEJCmtzKYEhICABt27ZNcu51x44dmYw0eXXq1MFkMvHLL79ky+vnz58fb29vTpw4kWwCu3v37iRtqX2NREREEih5FRERSYfXX38dgN69exMWFpbk+cWLFzl69Gji5wULFgTgn3/+SdK3bNmyAElqqx4+fJjRo0dnWcz3K168OM8//zy7d+9m3LhxFudrE+zdu5c7d+5keI5u3boRHR2dZGv11q1bkz3vWqBAAUwmU7JfIxERkQTaNiwiIpIOrVq14r333uOjjz7C19eXVq1aUbZsWcLCwjhx4gQ7duzg448/pkqVKgA0aNAAV1dXJkyYwM2bNxPPgr799tvUrVuXunXrsmTJEi5cuED9+vU5e/YsP/74I23btmXp0qXZ8h6mTp3KsWPHGD58ON999x0NGjTAw8ODc+fOsX//fo4fP86FCxcsblNOj7feeotly5bx5Zdf8ueff9KoUSP++ecflixZwrPPPsuqVauws7v39+fu7u7UqVOH7du306tXLypUqICdnR1du3alTJkyWfW2RUQkl1PyKiIikk4ffvghTZo0YdKkSWzatInw8HAKFSpEuXLlGDVqFN26dUvsW7BgQZYuXcqoUaOYNm0akZGRgJG82tvb89NPP/H222+zbt069u3bR4UKFfj8889p3bp1tiWvBQsWZPfu3UyZMoXFixczf/584uPjKV68ODVq1OC9996jcOHCGX79xx57jO3btxMUFMTKlSvZt28ffn5+LFy4kJMnT7Jq1SqLkjsA3333HW+88QY//PADN27cwGw2U79+fSWvIiKSyGRObr+QiIiISDbo3r078+fP58iRI4mr0yIiImmhM68iIiKS5S5cuJCkbdu2bSxatIhKlSopcRURkXTTtmERERHJcm3atMHV1RV/f3/y5cvHkSNHWLduHfb29kyePNnW4YmISC6kbcMiIiKS5SZMmMD8+fMJCQnh1q1beHp60rBhQ4KCgqhXr56twxMRkVxIyauIiIiIiIjkeDrzKiIiIiIiIjmeklcRERERERHJ8ZS8ioiIiIiISI6n5FVERERERERyPCWvIiIiIiIikuMpeRUREREREZEcT8mriIiIiIiI5HhKXkVERERERCTHU/IqIiIiIiIiOd7/A0NK6bq0KKGFAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 1100x400 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_1_1.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -1185,27 +1178,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1100x400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_109_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import os\n",
@@ -1466,99 +1444,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/svm/_base.py:1206: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
-      "  warnings.warn(\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_2.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
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\n",
-      "text/plain": [
-       "<Figure size 1100x400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_3.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
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\n",
-      "text/plain": [
-       "<Figure size 1100x400 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_4.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Phi(-1.0, -2) = [0.74081822]\n",
-      "Phi(-1.0, 1) = [0.30119421]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1100x700 with 4 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter5_129_6.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from __future__ import division, print_function, unicode_literals\n",
     "\n",
@@ -1800,7 +1691,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1932,21 +1823,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid character '’' (U+2019) (3974140161.py, line 5)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  Input \u001b[0;32mIn [5]\u001b[0;36m\u001b[0m\n\u001b[0;31m    P = matrix(numpy.diag([1,0]), tc=’d’)\u001b[0m\n\u001b[0m                                     ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid character '’' (U+2019)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Import the necessary packages\n",
     "import numpy\n",
@@ -2007,7 +1889,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
index 12c0a8057..83fb0823c 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb
@@ -82,42 +82,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "2nd degree coefficients:\n",
-      "zero power:  4.0618352118150005\n",
-      "first power:  0.004339135748752641\n",
-      "second power:  1.9543538503067644e-05\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -530,122 +508,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
-      "0          17.99         10.38          122.80     1001.0          0.11840   \n",
-      "1          20.57         17.77          132.90     1326.0          0.08474   \n",
-      "2          19.69         21.25          130.00     1203.0          0.10960   \n",
-      "3          11.42         20.38           77.58      386.1          0.14250   \n",
-      "4          20.29         14.34          135.10     1297.0          0.10030   \n",
-      "..           ...           ...             ...        ...              ...   \n",
-      "564        21.56         22.39          142.00     1479.0          0.11100   \n",
-      "565        20.13         28.25          131.20     1261.0          0.09780   \n",
-      "566        16.60         28.08          108.30      858.1          0.08455   \n",
-      "567        20.60         29.33          140.10     1265.0          0.11780   \n",
-      "568         7.76         24.54           47.92      181.0          0.05263   \n",
-      "\n",
-      "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
-      "0             0.27760         0.30010              0.14710         0.2419   \n",
-      "1             0.07864         0.08690              0.07017         0.1812   \n",
-      "2             0.15990         0.19740              0.12790         0.2069   \n",
-      "3             0.28390         0.24140              0.10520         0.2597   \n",
-      "4             0.13280         0.19800              0.10430         0.1809   \n",
-      "..                ...             ...                  ...            ...   \n",
-      "564           0.11590         0.24390              0.13890         0.1726   \n",
-      "565           0.10340         0.14400              0.09791         0.1752   \n",
-      "566           0.10230         0.09251              0.05302         0.1590   \n",
-      "567           0.27700         0.35140              0.15200         0.2397   \n",
-      "568           0.04362         0.00000              0.00000         0.1587   \n",
-      "\n",
-      "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
-      "0                   0.07871  ...        25.380          17.33   \n",
-      "1                   0.05667  ...        24.990          23.41   \n",
-      "2                   0.05999  ...        23.570          25.53   \n",
-      "3                   0.09744  ...        14.910          26.50   \n",
-      "4                   0.05883  ...        22.540          16.67   \n",
-      "..                      ...  ...           ...            ...   \n",
-      "564                 0.05623  ...        25.450          26.40   \n",
-      "565                 0.05533  ...        23.690          38.25   \n",
-      "566                 0.05648  ...        18.980          34.12   \n",
-      "567                 0.07016  ...        25.740          39.42   \n",
-      "568                 0.05884  ...         9.456          30.37   \n",
-      "\n",
-      "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
-      "0             184.60      2019.0           0.16220            0.66560   \n",
-      "1             158.80      1956.0           0.12380            0.18660   \n",
-      "2             152.50      1709.0           0.14440            0.42450   \n",
-      "3              98.87       567.7           0.20980            0.86630   \n",
-      "4             152.20      1575.0           0.13740            0.20500   \n",
-      "..               ...         ...               ...                ...   \n",
-      "564           166.10      2027.0           0.14100            0.21130   \n",
-      "565           155.00      1731.0           0.11660            0.19220   \n",
-      "566           126.70      1124.0           0.11390            0.30940   \n",
-      "567           184.60      1821.0           0.16500            0.86810   \n",
-      "568            59.16       268.6           0.08996            0.06444   \n",
-      "\n",
-      "     worst concavity  worst concave points  worst symmetry  \\\n",
-      "0             0.7119                0.2654          0.4601   \n",
-      "1             0.2416                0.1860          0.2750   \n",
-      "2             0.4504                0.2430          0.3613   \n",
-      "3             0.6869                0.2575          0.6638   \n",
-      "4             0.4000                0.1625          0.2364   \n",
-      "..               ...                   ...             ...   \n",
-      "564           0.4107                0.2216          0.2060   \n",
-      "565           0.3215                0.1628          0.2572   \n",
-      "566           0.3403                0.1418          0.2218   \n",
-      "567           0.9387                0.2650          0.4087   \n",
-      "568           0.0000                0.0000          0.2871   \n",
-      "\n",
-      "     worst fractal dimension  \n",
-      "0                    0.11890  \n",
-      "1                    0.08902  \n",
-      "2                    0.08758  \n",
-      "3                    0.17300  \n",
-      "4                    0.07678  \n",
-      "..                       ...  \n",
-      "564                  0.07115  \n",
-      "565                  0.06637  \n",
-      "566                  0.07820  \n",
-      "567                  0.12400  \n",
-      "568                  0.07039  \n",
-      "\n",
-      "[569 rows x 30 columns]\n",
-      "     malignant  benign\n",
-      "0            1       0\n",
-      "1            1       0\n",
-      "2            1       0\n",
-      "3            1       0\n",
-      "4            1       0\n",
-      "..         ...     ...\n",
-      "564          1       0\n",
-      "565          1       0\n",
-      "566          1       0\n",
-      "567          1       0\n",
-      "568          0       1\n",
-      "\n",
-      "[569 rows x 2 columns]\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 2,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import os\n",
     "from sklearn.datasets import load_breast_cancer\n",
@@ -684,23 +552,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -739,53 +596,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[Text(0.5, 0.9166666666666666, 'X[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
-       " Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
-       " Text(0.5769230769230769, 0.75, 'X[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
-       " Text(0.3076923076923077, 0.5833333333333334, 'X[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
-       " Text(0.15384615384615385, 0.4166666666666667, 'X[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
-       " Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
-       " Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
-       " Text(0.46153846153846156, 0.4166666666666667, 'X[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
-       " Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
-       " Text(0.5384615384615384, 0.25, 'X[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
-       " Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
-       " Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
-       " Text(0.8461538461538461, 0.5833333333333334, 'X[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
-       " Text(0.7692307692307693, 0.4166666666666667, 'X[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
-       " Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
-       " Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
-       " Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
-      ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.datasets import load_iris\n",
     "from sklearn import tree\n",
@@ -806,27 +622,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "|--- petal width (cm) <= 0.80\n",
-      "|   |--- class: 0\n",
-      "|--- petal width (cm) >  0.80\n",
-      "|   |--- petal width (cm) <= 1.75\n",
-      "|   |   |--- class: 1\n",
-      "|   |--- petal width (cm) >  1.75\n",
-      "|   |   |--- class: 2\n",
-      "\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.datasets import load_iris\n",
     "from sklearn.tree import DecisionTreeClassifier\n",
@@ -986,24 +787,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "FileNotFoundError",
-     "evalue": "[Errno 2] No such file or directory: 'DataFiles/rideclass.csv'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mFileNotFoundError\u001b[0m                         Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [6]\u001b[0m, in \u001b[0;36m<cell line: 37>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     34\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21msave_fig\u001b[39m(fig_id):\n\u001b[1;32m     35\u001b[0m     plt\u001b[38;5;241m.\u001b[39msavefig(image_path(fig_id) \u001b[38;5;241m+\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m.png\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;28mformat\u001b[39m\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mpng\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m---> 37\u001b[0m infile \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mopen\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mdata_path\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mrideclass.csv\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mr\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;66;03m# Read the experimental data with Pandas\u001b[39;00m\n\u001b[1;32m     40\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mdisplay\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m display\n",
-      "\u001b[0;31mFileNotFoundError\u001b[0m: [Errno 2] No such file or directory: 'DataFiles/rideclass.csv'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -1534,7 +1323,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter7.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter7.ipynb
index 23bdfcee5..09663bf62 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter7.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter7.ipynb
@@ -86,7 +86,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m heads_proba \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.51\u001b[39m\n\u001b[0;32m----> 2\u001b[0m coin_tosses \u001b[38;5;241m=\u001b[39m (\u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[38;5;241m10000\u001b[39m, \u001b[38;5;241m10\u001b[39m) \u001b[38;5;241m<\u001b[39m heads_proba)\u001b[38;5;241m.\u001b[39mastype(np\u001b[38;5;241m.\u001b[39mint32)\n\u001b[1;32m      3\u001b[0m cumulative_heads_ratio \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mcumsum(coin_tosses, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m) \u001b[38;5;241m/\u001b[39m np\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m10001\u001b[39m)\u001b[38;5;241m.\u001b[39mreshape(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      4\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m8\u001b[39m,\u001b[38;5;241m3.5\u001b[39m))\n",
+      "Cell \u001b[0;32mIn[1], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m heads_proba \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0.51\u001b[39m\n\u001b[0;32m----> 2\u001b[0m coin_tosses \u001b[38;5;241m=\u001b[39m (\u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[38;5;241m10000\u001b[39m, \u001b[38;5;241m10\u001b[39m) \u001b[38;5;241m<\u001b[39m heads_proba)\u001b[38;5;241m.\u001b[39mastype(np\u001b[38;5;241m.\u001b[39mint32)\n\u001b[1;32m      3\u001b[0m cumulative_heads_ratio \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mcumsum(coin_tosses, axis\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m) \u001b[38;5;241m/\u001b[39m np\u001b[38;5;241m.\u001b[39marange(\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m10001\u001b[39m)\u001b[38;5;241m.\u001b[39mreshape(\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      4\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(\u001b[38;5;241m8\u001b[39m,\u001b[38;5;241m3.5\u001b[39m))\n",
       "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
      ]
     }
@@ -1597,7 +1597,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
index e3b7593db..fa0a99fe6 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter8.ipynb
@@ -295,10 +295,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.03822007730337899\n",
-      "3.989393825676568\n",
-      "[[0.90044211 2.80659468]\n",
-      " [2.80659468 9.73667253]]\n"
+      "-0.08860271693417623\n",
+      "3.7557911271214808\n",
+      "[[ 1.08361608  3.3060763 ]\n",
+      " [ 3.3060763  10.96612219]]\n"
      ]
     }
    ],
@@ -340,10 +340,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.07864140367329474\n",
-      "2.0511284278960114\n",
-      "[[1.         0.68282072]\n",
-      " [0.68282072 1.        ]]\n"
+      "0.07620892676178488\n",
+      "1.732950730376058\n",
+      "[[1.         0.64673189]\n",
+      " [0.64673189 1.        ]]\n"
      ]
     }
    ],
@@ -394,33 +394,14 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 0.21424133 -1.00310568]\n",
-      " [ 1.84955363  5.92472578]\n",
-      " [ 0.43773101  1.60738434]\n",
-      " [ 0.94910711  2.53617977]\n",
-      " [-1.00106025 -3.87889126]\n",
-      " [-0.2544356  -0.48005485]\n",
-      " [-0.72117282 -1.4229538 ]\n",
-      " [-0.48783291  0.5970842 ]\n",
-      " [-0.17565241 -0.84643086]\n",
-      " [-0.8104791  -3.03393764]]\n",
-      "          0         1\n",
-      "0  0.214241 -1.003106\n",
-      "1  1.849554  5.924726\n",
-      "2  0.437731  1.607384\n",
-      "3  0.949107  2.536180\n",
-      "4 -1.001060 -3.878891\n",
-      "5 -0.254436 -0.480055\n",
-      "6 -0.721173 -1.422954\n",
-      "7 -0.487833  0.597084\n",
-      "8 -0.175652 -0.846431\n",
-      "9 -0.810479 -3.033938\n",
-      "         0        1\n",
-      "0  1.00000  0.93503\n",
-      "1  0.93503  1.00000\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'pandas'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[3], line 2\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpandas\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpd\u001b[39;00m\n\u001b[1;32m      3\u001b[0m n \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m10\u001b[39m\n\u001b[1;32m      4\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mnormal(size\u001b[38;5;241m=\u001b[39mn)\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pandas'"
      ]
     }
    ],
@@ -449,52 +430,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0         1         2         3         4         5         6         7   \\\n",
-      "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.082232  0.082339  0.080863  0.080028  0.078987  0.072334  0.071321   \n",
-      "2   0.0  0.082339  0.085298  0.084636  0.085154  0.085104  0.077849  0.077521   \n",
-      "3   0.0  0.080863  0.084636  0.085290  0.086290  0.086690  0.079860  0.079858   \n",
-      "4   0.0  0.080028  0.085154  0.086290  0.088026  0.088995  0.081970  0.082385   \n",
-      "5   0.0  0.078987  0.085104  0.086690  0.088995  0.090424  0.083319  0.084079   \n",
-      "6   0.0  0.072334  0.077849  0.079860  0.081970  0.083319  0.077182  0.077910   \n",
-      "7   0.0  0.071321  0.077521  0.079858  0.082385  0.084079  0.077910  0.078901   \n",
-      "8   0.0  0.070302  0.077012  0.079649  0.082509  0.084487  0.078333  0.079546   \n",
-      "9   0.0  0.069312  0.076408  0.079319  0.082449  0.084666  0.078555  0.079958   \n",
-      "10  0.0  0.063977  0.070119  0.072959  0.075620  0.077491  0.072176  0.073337   \n",
-      "11  0.0  0.063115  0.069617  0.072682  0.075590  0.077676  0.072384  0.073717   \n",
-      "12  0.0  0.062295  0.069072  0.072344  0.075455  0.077724  0.072474  0.073955   \n",
-      "13  0.0  0.061529  0.068521  0.071982  0.075263  0.077690  0.072492  0.074102   \n",
-      "14  0.0  0.060822  0.067984  0.071619  0.075045  0.077611  0.072468  0.074193   \n",
-      "\n",
-      "          8         9         10        11        12        13        14  \n",
-      "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.070302  0.069312  0.063977  0.063115  0.062295  0.061529  0.060822  \n",
-      "2   0.077012  0.076408  0.070119  0.069617  0.069072  0.068521  0.067984  \n",
-      "3   0.079649  0.079319  0.072959  0.072682  0.072344  0.071982  0.071619  \n",
-      "4   0.082509  0.082449  0.075620  0.075590  0.075455  0.075263  0.075045  \n",
-      "5   0.084487  0.084666  0.077491  0.077676  0.077724  0.077690  0.077611  \n",
-      "6   0.078333  0.078555  0.072176  0.072384  0.072474  0.072492  0.072468  \n",
-      "7   0.079546  0.079958  0.073337  0.073717  0.073955  0.074102  0.074193  \n",
-      "8   0.080384  0.080965  0.074161  0.074692  0.075064  0.075330  0.075529  \n",
-      "9   0.080965  0.081699  0.074752  0.075418  0.075911  0.076288  0.076588  \n",
-      "10  0.074161  0.074752  0.068701  0.069233  0.069621  0.069911  0.070139  \n",
-      "11  0.074692  0.075418  0.069233  0.069886  0.070381  0.070769  0.071086  \n",
-      "12  0.075064  0.075911  0.069621  0.070381  0.070975  0.071453  0.071853  \n",
-      "13  0.075330  0.076288  0.069911  0.070769  0.071453  0.072016  0.072493  \n",
-      "14  0.075529  0.076588  0.070139  0.071086  0.071853  0.072493  0.073045  \n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -788,7 +729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -854,7 +795,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -905,24 +846,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "          0         1\n",
-      "0  3.965838  1.971865\n",
-      "1  1.971865  1.997830\n",
-      "[[3.96583833 1.97186457]\n",
-      " [1.97186457 1.99783004]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "print(df.cov())\n",
     "print(np.cov(X_centered.T))"
@@ -938,36 +867,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Centered covariance using own code\n",
-      "[[3.96583833 1.97186457]\n",
-      " [1.97186457 1.99783004]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter8_65_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# extract the relevant columns from the centered design matrix of dim n x 2\n",
     "x = X_centered[:,0]\n",
@@ -1033,34 +938,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Eigenvalues of Covariance matrix\n",
-      "5.185584177293881\n",
-      "0.7780841853755783\n",
-      "First eigenvector\n",
-      "[0.85044503 0.52606392]\n",
-      "Second eigenvector\n",
-      "[-0.52606392  0.85044503]\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Eigenvector of largest eigenvalue\n",
-      "[0.85044503 0.52606392]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# diagonalize and obtain eigenvalues, not necessarily sorted\n",
     "EigValues, EigVectors = np.linalg.eig(Cov)\n",
@@ -1225,170 +1108,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
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-       "      <td>0.401842</td>\n",
-       "      <td>-1.213743</td>\n",
-       "      <td>1.138775</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "          0         1         2         3         4\n",
-       "0 -1.574465  0.259153  1.197370  0.147400  0.649382\n",
-       "1  0.689519  0.137652 -1.025709  0.210340 -0.076938\n",
-       "2 -0.282727  0.351636 -0.539261  1.216683  0.340782\n",
-       "3  0.070889 -0.614808  1.074067 -0.038300 -1.450257\n",
-       "4  1.794282  1.458078 -0.207545 -0.442600 -0.147420\n",
-       "5  1.112383  0.647473  1.405890  0.073598 -0.276263\n",
-       "6  0.397700 -1.526744 -0.712018  1.216290  0.418506\n",
-       "7 -0.280647  1.106095 -1.646283 -0.956563 -1.564374\n",
-       "8 -0.369139 -0.751699  0.051649 -0.213103  0.967809\n",
-       "9 -1.557795 -1.066837  0.401842 -1.213743  1.138775"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0    1    2    3    4\n",
-      "0  0.0  0.0  0.0  0.0  0.0\n",
-      "1  0.0  0.0  0.0  0.0  0.0\n",
-      "2  0.0  0.0  0.0  0.0  0.0\n",
-      "3  0.0  0.0  0.0  0.0  0.0\n",
-      "4  0.0  0.0  0.0  0.0  0.0\n",
-      "5  0.0  0.0  0.0  0.0  0.0\n",
-      "6  0.0  0.0  0.0  0.0  0.0\n",
-      "7  0.0  0.0  0.0  0.0  0.0\n",
-      "8  0.0  0.0  0.0  0.0  0.0\n",
-      "9  0.0  0.0  0.0  0.0  0.0\n",
-      "[[-1.5378811   0.94639099]\n",
-      " [ 0.86145244 -0.89288636]\n",
-      " [-0.00445655 -0.81633628]\n",
-      " [ 0.07145103  1.00433417]\n",
-      " [ 2.03707133  0.48476997]\n",
-      " [ 0.72174172  1.4557763 ]\n",
-      " [-0.55854694 -1.60673226]\n",
-      " [ 1.6999536  -0.43766686]\n",
-      " [-1.10405456 -0.31718909]\n",
-      " [-2.18673098  0.17953942]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -1431,7 +1156,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1455,29 +1180,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 1.5378811  -0.94639099]\n",
-      " [-0.86145244  0.89288636]\n",
-      " [ 0.00445655  0.81633628]\n",
-      " [-0.07145103 -1.00433417]\n",
-      " [-2.03707133 -0.48476997]\n",
-      " [-0.72174172 -1.4557763 ]\n",
-      " [ 0.55854694  1.60673226]\n",
-      " [-1.6999536   0.43766686]\n",
-      " [ 1.10405456  0.31718909]\n",
-      " [ 2.18673098 -0.17953942]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "#thereafter we do a PCA with Scikit-learn\n",
     "from sklearn.decomposition import PCA\n",
@@ -1497,23 +1205,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([-0.62373464, -0.5303329 ,  0.317367  ,  0.01873344,  0.47815203])"
-      ]
-     },
-     "execution_count": 13,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "pca.components_.T[:, 0]"
    ]
@@ -1533,36 +1230,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Train set accuracy from Logistic Regression: 0.95\n",
-      "Train set accuracy scaled data: 0.99\n",
-      "Train set accuracy scaled and PCA data: 0.96\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1611,7 +1284,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1635,7 +1308,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1682,7 +1355,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -1725,7 +1398,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter9.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter9.ipynb
index 099f10d42..3ae8e8703 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapter9.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapter9.ipynb
@@ -577,60 +577,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter9_29_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter9_29_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
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-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter9_29_2.png"
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-     "output_type": "display_data"
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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter9_29_3.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"The sigmoid function (or the logistic curve) is a \u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03mfunction that takes any real number, z, and outputs a number (0,1).\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mIt is useful in neural networks for assigning weights on a relative scale.\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;124;03mThe value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -1345,7 +1305,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
index a53571646..0ff5de13f 100644
--- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb
@@ -921,36 +921,20 @@
    },
    "outputs": [
     {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7714/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
-      "  ax = fig.gca(projection=\"3d\")\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlinalg\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mla\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "<mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x11e77b070>"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_61_2.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -996,22 +980,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "pt.axis(\"equal\")\n",
     "pt.contour(xmesh, ymesh, fmesh)\n",
@@ -1060,15 +1029,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 1.33333333 -0.26666667]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "def f1d(alpha):\n",
     "    return f(x + alpha*s)\n",
@@ -1097,32 +1058,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "[<matplotlib.lines.Line2D at 0x11ecf9850>]"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_69_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "pt.axis(\"equal\")\n",
     "pt.contour(xmesh, ymesh, fmesh, 50)\n",
@@ -1797,33 +1733,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.33196524 4.36593124]\n",
-      "[[4.09963157]\n",
-      " [2.99760425]]\n",
-      "[[4.09963157]\n",
-      " [2.99760425]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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vYuXKlejevTueeeYZJCUl4caNGzh8+DCWLVuG2bNnIzo6GitXrkROTg5efvll/dIMOTk5eO6559CnTx888MADALTB1bx585CcnIzWrVtj8+bNePvtt00GJrUVHh6Ovn374uWXX0bdunUxa9Ys7N271+z0+jlz5mDQoEEYOHAgRo8ejaioKFy4cAF79uzBli1bMH/+fIeUl8gmLh7ATSRJ27ZtE2PGjBHx8fHC399fBAQEiGbNmolHHnlE/PzzzwbHZmVlibp16xo9z+7du0X//v1FUFCQaNCggRg6dKg4evSoACBeeeUVg2OXLFkiWrduLfz8/ETTpk3Fm2++KV555RWzs8mEEOLKlSvi3//+t0hKShJ+fn4iJCREtGrVSkyaNMlgJhAAMX78+GrlNHbOKVOmiMjISOHl5VVtppAxn332mUhMTBR+fn6iefPm4osvvhBZWVkGs8mE0E6Jf+edd0SbNm1EQECAqFevnkhOThZjx44VBw4cEEJoZ4E98MADIjY2Vvj7+4uwsDDRu3dvsWTJEoNzXb9+Xfzf//2f/nnDwsJE3759xfr16w2O++KLL0SXLl1E3bp1RWBgoEhISBCPPPKI2LRpk/6Y3r17i9TU1Gr1MlaHvLw8kZycLHx9fY2+l1WdPXtWPPPMMyI+Pl74+vqK0NBQ0aFDB/HSSy+JK1euiBMnTohGjRqJvn37Gsyy0mg0IiMjQ9SvX18/s+/ixYvi0UcfFY0aNRJ16tQRPXv2FOvWrRO9e/cWvXv31j9WN8Or8hR4Ie4sg1B19qHus3b27Fn9Nt3nZdasWSIhIUH4+vqK5ORk8c033xg81thsMiGE+PPPP8WwYcNEo0aNhK+vr2jcuLHo27evmD17do2vF5GzKYQQwlWBGBERSZdCocD48ePx0UcfubooRA7F2WREREQkawyGiIiISNY4gJqIiIziKAqSC7YMERERkawxGCIiIiJZYzBEREREsiaLMUMajQYnTpxAUFCQ0bQJREREJD1CCFy+fNlsHsLakkUwdOLECcTExLi6GERERGSDkpISh62yDsgkGNKlECgpKbEojQIRERG5XllZGWJiYoymArInWQRDuq6x4OBgBkNERERuxtFDXDiAmoiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGTN5cHQ2rVrkZGRgcjISCgUCvzwww8mjx07diwUCgVmzJjhtPIRERGRZ3N5MHT16lW0adMGH330UY3H/fDDD9iwYQMiIyOdVDIiIiKSAx9XF2DQoEEYNGhQjcccP34cTz/9NH766Sekp6c7qWREREQkBy5vGTJHo9Fg1KhReP7555Gamurq4hAREZGHcXnLkDlvvfUWfHx88Mwzz1j8mPLycpSXl+vvl5WVOaJoRERE5AEk3TK0efNmzJw5E/PmzYNCobD4cTk5OQgJCdHfYmJiHFhKIiIicmeSDobWrVuHM2fOoGnTpvDx8YGPjw+OHDmCZ599FnFxcSYfN2XKFJSWlupvJSUlzis0ERERuRVJd5ONGjUK/fr1M9g2cOBAjBo1CmPGjDH5OH9/f/j7+zu6eEREROQBXB4MXblyBQcPHtTfLy4uxrZt2xAaGoqmTZsiLCzM4HhfX180btwYSUlJzi4qEREReSCXB0ObNm1CWlqa/v7kyZMBAFlZWZg3b56LSkVERERy4fJgqE+fPhBCWHz84cOHHVcYIiIikh1JD6AmIiIicjQGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGTN5cHQ2rVrkZGRgcjISCgUCvzwww/6fbdu3cI///lPtGrVCnXr1kVkZCQeeeQRnDhxwnUFJiIiIo/i8mDo6tWraNOmDT766KNq+65du4YtW7bg5ZdfxpYtW5Cfn4/9+/fjb3/7mwtKSkRERJ5IIYQQri6EjkKhwKJFi3D//febPGbjxo3o3Lkzjhw5gqZNm1p03rKyMoSEhKC0tBTBwcF2Ki0RERE5krOu3z4OO7ODlJaWQqFQoH79+iaPKS8vR3l5uf5+WVmZE0pGRERE7sjl3WTWuHHjBl588UWMGDGixggxJycHISEh+ltMTIwTS0lERETuxG2CoVu3bmH48OHQaDSYNWtWjcdOmTIFpaWl+ltJSYmTSklERES1plYDRUXA/PlOeTq36Ca7desWhg0bhuLiYqxevdpsv6G/vz/8/f2dVDoiIiKym/x8YOJE4Ngxpz2l5IMhXSB04MABFBYWIiwszNVFIiIiIkfIzweGDAGcPLfL5cHQlStXcPDgQf394uJibNu2DaGhoYiMjMSQIUOwZcsWqFQqqNVqnDp1CgAQGhoKPz8/VxWbiIiI7Emt1rYIuWCSu8un1hcVFSEtLa3a9qysLEydOhXx8fFGH1dYWIg+ffpY9BycWk9ERCRxRUVAlXigDEAI4PlT6/v06YOa4jEJLYNEREREjnLypMue2m1mkxEREZEHa9LEZU/NYIiIiIhcr1cvIDoaUCic/tQMhoiIiMj1vL2BmTO1/3dyQMRgiIiIiKQhMxNYsACIinLq0zIYIiIiIunIzAQOHwYKC4HPPnPKUzIYIiIiImnx9gb69AGGDnXK0zEYIiIiIlljMERERESyxmCIiIiIZI3BEBEREckagyEiIiKSNQZDREREJGsuT9RKREREEqdWA+vWaZOpNmmiTZ3h7e3qUtkNgyEiIiIyLT8fmDgROHbszrboaG3qjMxM15XLjthNRkRERMbl5wNDhhgGQgBw/Lh2e36+a8plZwyGiIiIqDq1WtsiJET1fbpt2dna49wcgyEiIiKqbt266i1ClQkBlJRoj3NzDIaIiIioupMn7XuchHEANREREVXXpIl9j7OGbvbaoUP2P7cRDIaIiIioul69tLPGjh83Pm5IodDu79XLvs9rbPaag7GbjIiIiKrz9tZOnwe0gU9luvszZth3vSFTs9ccjMEQERERGZeZCSxYAERFGW6PjtZut+c6QzXNXnMwdpMRERGRaZmZwODBjl+B2tzsNQdiMEREREQ18/YG+vRx7HO4cFYau8mIiIjI9RwxK81CbBkiIiKimjkjUau52WsOxJYhIiIiMi0/H4iLA9LSgBEjtP/Gxdk/L1lNs9ccjMEQERERGefsRK2mZq85mEIIF8xhc7KysjKEhISgtLQUwcHBri4OERFJnTO6haROrda2AJma4aVbdLG42P6vze3Xv+zQIYQ89pjDr99sGSIiIqrMWd1CUlebRK1qNVBUBOTlaf+1NrO9bvba0KHWPc5GDIaIiIh0nN0tJGW2Jmp1w2CSwRARERFQ8wrIum3Z2da3crgrWxK1umkwyWCIiIgIqF23kCfSTXU3NbNLoQBiYu4kanXjYJLBEBEREWB7t5CnsjZRqxsHkwyGiIiIANu6hTxR5cHPoaHA999blqjVjYNJrkBNREQEmF8BWTeVXNct5Iny87VdXZVbeKKjgffeAxo2rHmpATcOJtkyREREBFjfLeRpahr8/OCDwIULwEMPaae8G3sNrB1jJCEMhoiIiHRMrYBsrFvIk9hj8LMbB5MuD4bWrl2LjIwMREZGQqFQ4IcffjDYL4TA1KlTERkZicDAQPTp0we7du1yTWGJiMjzZWYChw8DhYVAbq723+Jizw2EAPsNfrZzMFlxo8Kq423l8jFDV69eRZs2bTBmzBj8/e9/r7b/P//5D9577z3MmzcPzZs3x+uvv47+/ftj3759CAoKckGJiYgqYdoGz6RbAVku7Dn4OTMTGDzY5u/FhUMXsfy93VAtBZYdibGsXLXk8mBo0KBBGDRokNF9QgjMmDEDL730EjJvR5NfffUVIiIikJubi7FjxzqzqEREhkwNNp0507NbEcjz2HvwsxXBpNAI7F32F1SflKDglwb4tawlNOhxe2+ZZc9XSy4PhmpSXFyMU6dOYcCAAfpt/v7+6N27N9avX28yGCovL0d5ebn+flmZc15MIpIR3WDTqmMsdCvtevL4EvI8Tp5Jd/PKTaydtRMFuZeh2hWHvyoSACTo97f0PwBlu+NIG+qHgc/a5SlrJOlg6NSpUwCAiIgIg+0RERE4cuSIycfl5ORg2rRpDi0bEcmYucGmCoV2sOngwewyI/egG/w8ZIj281v5s22nwc9ndp3Fsvf3QbXcGyuOp+Iy2uv3+aEcaWE7oEy7CuXEBMT1TASQqG3MkHswpKOoMipdCFFtW2VTpkzB5MmT9ffLysoQE+OcfkcikgFrBpvKadwJuTfd4GdjXb8zZljd0ik0AtsX7Ifq05NQ/R6GDVdSIdBTvz/C6wyUzfZBmemHfhNTUa9xRztVxHqSDoYaN24MQNtC1KRSP+WZM2eqtRZV5u/vD39/f4eXj4hkyo1X2iWqUS0HP1+/cB2FH+6Eav51qPYmoESdBCBJv79d4B5kdDoN5T8aocPIZHj5NHJQRawj6WAoPj4ejRs3xsqVK9GuXTsAwM2bN7FmzRq89dZbLi4dEcmWG6+0S2RW5cHPFsyWPLHlFJbO2A/VSn+sOtUS19BJvy8Q19AvYgeU/cqRnp2IqI4tALRwXl0s5PJg6MqVKzh48KD+fnFxMbZt24bQ0FA0bdoU2dnZmD59OhITE5GYmIjp06ejTp06GDFihAtLTUSyxrQNJAfGZks2bAjNhx9hS3lLFHx+BqqNEdhyvQWAxvpDor1PQJl0EMqhgej7TEsEhnZxftmt5PJgaNOmTUhLS9Pf1431ycrKwrx58/DCCy/g+vXrGDduHC5evIguXbpgxYoVXGOIiFzHCYNNiVzK1GzJs2ehGP4gfsbzeBX/AQAooEHnuruh7HoOyseboM3Q5lB4Rbqg0LZTCGHsZ41nKSsrQ0hICEpLSxEcHOzq4hCRpzD2yzkmxqbBpkSSoVYDcXEQx47B2FQlXdDwTv030PDvd2NQdhIiWja07XmqdsEBBtvK2rRBSGiow6/fDIaIiGqDK1CTh1DfVGPDl7ux64Of8fjuSeYfoMtib8vn3dgPibAw7b/nz+s3lUVGIuTECYdfv13eTUZE5NbklLaBgZ/HKT1aihUzdkO1WI1lxck4J1phOHbicUsefPasbctHmOqCqxQE6Z04Yd25bcRgiIiIzHOH1CMM1ixy8OcjUH10GAVrgrD2YitUoJt+XwhK0aLReeCMhSezdvmImhYsdSEGQ0REVDN3SD3iDsGai9y6dgvrP92Fgv9dgmpHU+y7eReAWP3+JL+/oGx1FMqH66PHE6nw9X8KaPKqtuXHHGuXjzC3YKmLcMwQERGZdnswrckLmG4ZgeJi17XCmArWdDP7FiwwXEiw0e2F/s6c8dgWpAuHLuLHd3dDtVSB5SUpuCTq6/f54BbubrADGb0vI31cLBL7x1U/wYIFwNChNT9JTIz173teHmDF0jhlAEIADqC2BwZDREQ2KioCKi1/YlJhoWvGTlkSrIWGAoGBpo/xgBYkoRHYozoE1exjUP2qy/x+J0gJU5xHevweKAd7Y0B2CkKahpg/6QsvAG+/bXyfQmFbi6Cln6fbnBUMsZuMiIhMk3rqEUvyxBkbmFuZlLr7rFBeVo61s3ZC9e2V25nfmwFopt/fKmA/lO1OQJkVhi5jUuDt19P0yYz5z3+ATp2AceOAc+fubK/N8hHmFix1EQZDRERkmtRTj9gjCBNC29KRna3tTpNwl5ku83vBjz5YcSIVV9BBv88P5egbvh3KtGtIfyYBcT2bA2heuyccOlQb9NhrYHpNC5a6ELvJiIjINF03lLnUI64aM2Rlt4tZruruM0GX+b1g7kmofg/HH1dTIOCl39/Y6zTSm+2vlPm9ngtLawVL1xmKikLI8ePsJiMiIheSeuoRe3e7uKq7r5LrF65j9Qe3M7/va4ZjVTK/tw/cA2Wn08h4tBHaj0iGl0+E6wprq8xMw0HtJlagRps22jFfDsaWISIiqZPC+jlSTj2im00G1D4gclHL0PFNJ7F0xgGoVvlj1elWuI46+n26zO8ZA8px3zOJiOrooi5JF3DW9ZvBEBGRlElp/RwpBGWmmHqdrl8HLlwwHyQ5ubtPU6HB5m/2QvVF5czvd8R4H4cy+RCUQwORNqElAkMDHV4mKWIwZEcMhojILVmyfo6rW2WkxFiwtnix+VYjJ72eV05dwaqZu6DKv4mlB5vjlOZO95YCGnSptwvKruehfLwJWg9pDoWXsTSp8sJgyI4YDBGR23GHxQ7dhbFWo8oc2N135NdjUM08hILVdVF4vhVuwl+/rx4uY2DUTijvVdue+d3DMRiyIwZDROR2pL7Yobup3GrkwBWodZnfC+adh2prFHaWJ+r3eUGNYV4LcG/0LrS8Nxot33wY/g3q1HA2ctb1m7PJiIikyNbFDqU8rseVvL0dFjSWHi3FT+/vgmqJBsuKW+C8aKXf5wU1egTvxORmi5F+5BP4nj8FHAUwF8Cy19x+5WtPwWCIiEiKbFnsUEqDrT3cgZWHofr4MFRrg29nfu+u31dfcQn3xuxGhlLg3skpCP3zEDBkau0S3TLIdSh2kxERSZG1ix1ysLVD3bp2C7/O3QXV15Uzv9+R7HcIytYlUD5cH90fT4VvHV/tDnuM/ZJxkMsxQ3bEYIiI3JKp9XOqBjgcbO0Q5w9cwPL396BApcDyklSU4k5yUx/cQu8GO6DsfRnKp+PQ7J5Y4yep7dgvmQe5HDNERCR3mZnai52xVoHKs58sSVZaUqI9joOtTaqc+b3g1wZYX9YSGvTQ7w9XnMN98XsrZX5vb/6ktUl0q1Zr33tjbRbW5FNjF5tZDIaIiKTMVNqCyhczqWeWlzBd5veCvCtQ7Y5HsYnM7xmjw9B5tA2Z32uT6NYeQa6Mu9iswWCIiEjqzM2EsvWCK9MWg9M7z2LZe3uh+snXZOb3jHuuIX1CAmJ71DLzu7ncabouTF1erspqG+Sa6mKzZOC2zD4bDIaIiNydLRdcGbUYCI3An/P3Q/Vp5czvd16Lxl6noUzcB2WmP+55JhX1Gney35PXJtFtbVqVatPFJqPPhg4HUBMReQJLB1tXPtZTB+Wq1Shfugq7v9qIws1BmFmSiaOaGINDOtTZDWWnM1D+Q5f53cuxZbIl0a21Mwors3XgtsQ+G5xNZkcMhohIFiy54LrbzDMrumuObzqJXZM/R7tfP0RDzRn99hJE4wX8B9ca3wVl/3KkZzdHZPvGzqrBHbZ0PVkT5FaWlweMGGG+TLm5wEMP3SmfxD4bDIbsiMEQEcmGuQuuO6X5MNNdo8v8XvD5Gag2RSDu+h4swBAAApXbeQQAKBRQOLpVw1HjbGxpVbLlfZbgZ4NT64mIyHrmBlu7y8wzE9014vhx4O9/x6wmr+G100/gtCYFQAq8oMZiDEDVQAgA9LnfLZmGXpvyOmqcjSUzCquyZRyZu3w2HMDBnaTkdtRq7a+DvDztv2q1q0tERPZUm0G5lTnyb0UNg38VQkBAgYyTc3FWE4YglGFI1G9Yet8sxOCY6Yta5Wno9qYL3Kp2L+lmbeXn1/45dEHuQw9p/zUX0OkGbgN3utR0TA3cttdnww0xGKI78vO1/cVpadq+5rQ07X17fJGJSBp0LQZVL5A6CoW2C8bYVG8dB/+tUK8uqnF9HS8INEUJ/njic5y7HID5x7rh3ofDLTu5vVs1zM3aArQtUq74YalbtDMqynB7dLTxsUb2+Gy4KQZDpOWMXzaOwJYsIuvY0mJQmYP+VpQeLcX3k9bjkYRf8NSAQxY9pkOfIPjV89PecVWrhjULI7pCZiZw+LB2nE9urvbf4mLjXXe1/Wy4MyEDpaWlAoAoLS11dVGkqaJCiOhoIbRf2+o3hUKImBjtcVKycGH1ckdHa7cTyUlFhRCFhULk5mr/teS7auz7ExNT8/fHzn8r9q8oFu8NLhRp9bcIH9zUn6Y3Ck0/R+VbYWH1sikUzv07lptrWVlzc+37vI5ky2fDQZx1/eYAanLPvEa1WVmVtGS2wqzHsnXgri2Dcmv5t0KX+b3g60tQbY/F/lvxAOL0+3WZ3zMeDoZ4OxqKEyYG/wJAw4ba73tR0Z1y27q4YW144jgbWz4b7s6hoZZEsGXIDHf7ZeOuLVlSwlY1z7BwofGWEIVCe7P3+2nD34pz+8+L/z35i3gw5lcRgksGh/miXPQL3SRmPFAkDqw6bLxuplp6TH12nd2qUZsWKVta9GTGWddvBkOk/RJa2yTtSu5WXqlx9gWUHMMVPwos/O799drX4s17C0XP4G3CCxUGu8MVZ0VWwjoxf/J6UVpSeqcuxoICY4GNqbpW/uw6O8gwFbjV9J2y5geJjIMmBkN2xGDIDFf1tdvK3VqypIStap7DFT8KzPyt0ADiOJpUC4BaB+wV/+peKNbP2S4qyqt8tswFBbpA4OuvhWjYULqfXWtapKz5QSLzVlxnXb85m4zcbwaBJ/bRO4vUZ76Q5VyxQF6lvxWiyt8KDRQQUOBpfARf3MKghhvx8YNrcGT9cfx5PQlv/NoH3Z5oBW+/Sn9HLJmZpltfJyoKOHvWdNlc/dm1dNaWNVPx3XWWrxviAGrS0q1HYWwgZk1LvruCLSurkpaMV5iVPGsHtDv5R4Eu83vB3FBc8XsPT5e/ixjc+VtxEk2wOPIpjB4dhf9NVKNuIzOZ363Nqu4On11zq38Dlv8gKSqyPes8WY3BEN3hLjMIXDVrxBkcPcOLrWrSZMuMMCf8KLh+4Tp+nrEDqgU3oNqXiOOaJABJAPrgHUzAY/7/w4C7DqHlA82Q+H8jMM7f1/KTWzszzVM+u5YGa0VF7jfL1505tBPODm7duiVeeuklERcXJwICAkR8fLyYNm2aUKvVFp+DY4Y8lITWwrALZ4wNcLfxYXJQmwHttgzcNaPkjxNi9og1QtlogwjEVYPT1sEVMbjx7+LTR9aK45tP1qLSwvKxf19/bThmyB6fXVcOSLZ0rNe//82xkYIDqPVef/11ERYWJlQqlSguLhbz588X9erVEzNmzLD4HAyGPJinzLJw5gwvU8+lez53DSbdkT0GtNfyR4H6llps+GKneLlXoWgXuLtaEWK8j4lxLYvEsml/iGvnr9mp4sLyoCA83Pwx1nxPXD0g2dIfJKtWWfb6ePisWQZDt6Wnp4t//OMfBtsyMzPFww8/bPE5GAyRpLlihtfzzwvh7W34PN7e2u3kPPaaEWblj4LLJy+L/Bd+E/9IXCsivE4bftygFt3qbRdv9C8Uf87fJzRqjZ0qa6TMNQUF1twsDf6ksqyEJS16bMUVQjAY0svJyRGxsbFi3759Qgghtm3bJho1aiRyrWgaZDBEkubsKdJSuSCQU5eJKF5XIj4cUiQGhG0UfrhhcPoglIohUevFvMfWiTO7z9qhYhaqKSgw95o0bHinC83SrjEpLSthSYueA7pB3UpFhShVqRgMCSGERqMRL774olAoFMLHx0coFAoxffr0Gh9z48YNUVpaqr+VlJQwGCLpcua6SVK7IMidAwPhivIKse7jP8U/uxSKVP/91U6Z4HNYZLcrEqv+s1mUXy63e9UsZiwoqGk9IVtfFyku1mpJi5413aCeMmxACH29SwGnXL8lP5vsu+++w9dff43c3FykpqZi27ZtyM7ORmRkJLKysow+JicnB9OmTXNySYls5MxZMo7MQ8dcZ9az84ywS0dK8dN7u6Aq0GDZ4RRcEK31+7xRgZ4hO6HseQnKcU2RdG88FF6x9qqJ7YzNYj1+HHj4YfOPtWYavRSn5lsyFd/SWb625qiTIlO5Jx3JoaGWHURHR4uPPvrIYNtrr70mkpKSTD6GLUPkVhw5NqDqL8Wvv3ZMK5SrB6XquOMv41p2hexb/pd492/VM78DQjRQXBAjYn8RuU//Ks4fvOCc+tiDI1pxpNgyZC+e1PVdpfXaWS1Dkg+GQkNDxaxZswy2TZ8+XSQmJlp8Do4ZIslzxNgAYwGKJTNzrL0gSOUPsVQCMltY0RVy8+pNsfrdLWJyh0KR6PtXtZe9hd9B8XynQrHmg23i1vVbLqiMHTjiB4KnDkj2tK7vKkErg6HbsrKyRFRUlH5qfX5+vggPDxcvvPCCxedgMERuwR7rJulaRrKzLQt6avuHUyp/iKUSkNVGDa1almZ+P/jzYYeVwekc9QPB0wYke1qLV5UxlAyGbisrKxMTJ04UTZs2FQEBAeKuu+4SL730kigvt3zAH4Mhchu1uRhZmuG78gWgthcEKfwhlkpAZkcatUbs/OGAyBlYKHoE/Wky8/uC5yplfq8tW1rWHB08OWJhVU9brNXTElezZchxGAyRx6tpIUVTt6ozdmy5IEjhD7EUAjI7uFF6Qyx/faN4ulWRiPM5Wq34rQP2ipd6FIrfPt1RPfN7bdnSsuasbklHBFxSagGrLQ/5/OtV6c7kbDIiMq3yzK1GjUwndKzJ++9rM4HXZvaXFPJFSXGWkIVObT+DZe/vg+onX6w42RJX0VG/zx83cE/DHVDecx3pzySgaTddXjA7szZhKmB6to8um/qCBfabwWTJjCspnNNVPC1xdU25Jx2IwRCRuzE2hdYWUVG1vyBI4Q/xgQOWHSeBBJ5CI7Dtu31QfXYKqg3h+ONqSwCN9PubeJ2Csvl+KDP9cc/EluYzv9uDtcst2BI8keN4YuLqzExtQG2Pv3MWsioYKikpQUxMjKPKQkTm2GP9DXsGKK7+Q6xWA3Pnmj/Ohb+Mr527htUf7KyU+T0ZQLJ+f8c6u6HsfAbKRyPQbngSvHwaO7eAixdbdpyuZc2Ra1WRbUwFD9HR2u+fu60zBNxZX2n5ckCpdPjTWRUMJScnY/LkyXjxxRdRt25dR5WJiIyp6Re5pRwRoLjyD/G6ddpWKXMef9ypv4yPbTyJpTMOoGBVAH4+0wo30Fm/rw6uon/jncgYeBP3ZTdHk7YpAFKcVjYD+fna98gSupY1N+6W9GiWLs7oTry9nfYjxqpgaOXKlZg0aRI+//xzvPHGGxgzZoyjykVEVZn7RW4JRwUorvpDbOkFNzHRocXQVGiw6X97UPDFWag2N8a268kA7nTLNfU+hoyUQ1AOq4s+T7dEQP0uDi2PRXTBtSViYu5clKQwToyM86SxUE5mVTDUvXt3bNiwAf/973/x0ksv4YMPPsD777+PPnzxiRzPll/auq4r3RgORwYorvhD7MIL8+UTl7Fyxi6ofriFpQeTcUak6vcpoEHXeruQ0f08lE9EouUDiVB4Rdu9DLViTXBduSVRCuPEiOzMpgHUjzzyCIYOHYqcnBykp6djwIABePvtt9GsWTN7l4+IdGy5oLvzmAFLOPnCXLy2BKoP/oKqqC6KzrfCTXTV7wtCGe6N3gXlIDUGTUpGwxat7PKcDmNpcJ2dbfj5cfU4MSIHsHk2mRACAwYMwOXLl/HBBx/gxx9/xPjx4zF16lQEBQXZs4xEBFh24Y+KAubNA86c8YwxA+Y4+MJccaMCv3+xG6r/XkDBtmjsLm8G4M4kkgSfI8hodRjKh4LQ66mW8KvXzfa6OJulwfXgwdW3eeKAXZI1hRCWj8acPXs2Nm7ciI0bN2LPnj3w9vZG69at0bVrV7Rt2xbffPMN9u/fj0WLFqFjx47mT+gkZWVlCAkJQWlpKYKDg11dHCLb6WaTAcYv/PZc38WeHJ3R3thyAzExNl2Yq2d+D9Xvq5z5PWN8UzQfGA+Fl8JOlXAytRqIizPfqlZcbPq9cvT7SrLnrOu3VcFQTEwMunbtqr917NgR/v7+BsdMnz4dubm52Llzp90LaysGQ+RR7Hjhdwpj5Y2O1rbo2LO8tbgw7/+pGKpZR1CwNgTrLrWCulKjeQPFRQxquhsZf1Ng4KQUNIivb78yu5q7BtckG5IMhixx+vRpREZGQq1W2/O0tcJgiPQ85Zesu9TD1LpILr7Y3rp2C7/M3omCb0qh2hGLA7fiDfa38DuEjLYlUI5qgG6PpcInwIPXp3W34JpkxW2DISEE1q5di969e9vztLXCYIgAOK+FgrR03TCmZixZ0g1jR+f2nceP7++BapkXlpekogwh+n2+uIk+oTug7HMF6ePjkNA31uHlkRR3Ca5Jdtw2GJIiBkMk1RYKj1ZUBKSlmT+usNAhU/KFRmDX4oNQzTkO1fpQ/HY5FRrcucA3VJxFesJeKO/3wYBJLREUyYkfRFLjrOu3B7f9Et3GXEqu4YKVim9cuoE1H++E6rurUO25C4crEgHcWXCxTcA+KDucRMaYcHTKSoGXD9fCISIGQyQHzKXkGk5aEFGX+b3gJ1+sNJH5PaPfdaRPbIaYLg7K/E5Ebo3BEHk+5lJyDQctiKjL/F7w6Smo/miIjVdTUTnze6TXSSibH4BySAD6Tkh1TuZ3InJrDIbI8zGXkmvYcUHEa+eu4eeZtzO/70/EiSqZ3zvV3QVl57PazO8PJUPhxfeSiCzHAdTk+eyxuBzZzsap2yUbTmDpzINQ/azL/B6o31cHVzGgyQ4oB9y6nfk9woEVAGdbEbkIZ5PZEYMh4uJyLmZBMKGp0GDjV7uhmneuUub3O6pnfg9wTtm5JAORyzAYsiMGQwRAuovLybjVQZf5vWDRLSw7lIwzoqF+nwIadAvaiYzuF6AcG4XUwc2cn/rC3JIM338PhIfL8r0jcgYGQ3bEYIj0pBZ4yLDV4a+io1B9WAxVUT0UXWiFW/DT7wtGKQZG70ZGuhqDJrVAeFKY6wpqbtFIQPvZqbzavtTfO6l9/onMYDBkRwyGSJJkshBkxY0K/PbZLqj+dxGqP3WZ3+9o5ntYm/l9RAh6jk2FXz0/E2eyI0uCAksXjaxMyu+dDANvcn8MhuyIwRBJjsRSVdjbxeJL+On93VAVCPx4pEW1zO+96u+AsmcplOOaImnQXc4tnKVBQV4eMGKE9eeX4nsnk8CbPA+DITtiMESS4+JUFY6w78e/oJp1FKpfjGd+vy92N5QZLs78bk1QYEvLUGVSee88PPAmz8Z0HESezN4LQbpgLMjNKzfxy5xdUOXqMr/fBeBOK0+K/0Eo2xxDRlYouv4jBT4BPRxaHrOsTctibtFIc6SyiCdXYCcyi8EQkSvYcyFIJ44F0WV+L1jqjZ+OpaAM7fT7dJnfM9KuIP3peNzVpxmAZqZP5mzWBgU1LRppCaks4skV2InMYjBE5Ar2SlVhqtvn+HHt9lqOBdFlfi+YfRyq30Lx2+WWEOip399IcRbpzfZCeb8v+menIiiyg83P5XC2BAWZmdrXsGqwWXUWWWU2phlxGK7ATmQWxwwRuUptF4J0xFgQtRo3f/wZe/67EUWb6mLmkQdQrIk1OKRt4F4oO5yCcrQu87uXZed2tdqM06raDXn2LPDgg9p9Ul/EkyuwkxvjAGo7YjBEklWbhSDtOAj75LbT2DXpU7Rd+yHCNWf020sQjefxH1xplADlPTduZ36PNP+cUmTvoECqi3gawxXYyU1xADV5PrkuAFe13ocOAevXW/861GIsiNAIbM3bC9Xnp6H6oyGir+7DAvwfAMMgIRrHkKcYCcUnHnCxtGPiWADa12PwYPf4DJvq7ouOlmbwRuRkbBki13DkoF8pB1n2rLeVLUO6zO8FC25g6f5EnNBox4h4QY3DiEMUjsFoh5endaO4U4uOvUn5u0FkBLvJ7IjBkMQ4cgE4Yxe68HBg1ixg6FDbzmkv1tTbkouWBd0+FY2a4PM+X2PJ6npYfbalQeb3uriCAU124rHWf+C+nyaaL79U1s2xBwYFRG6BwZAdMRiSEEcuAGcq2NB5/nngP/+x7pz2Yk29Fy+2vPXIxFgQAUBAgSFYgEXQPsYLagz1yse9UTuQ0j8Krf/zMALC6lq+0nJuLvDQQ5bXmYiolpx1/XaTaSDkMaxZ68UaNS2op/P229rWF1ewtN5vvKENbqoeq5sqn59vuD0zE9fm/BfX6jY02FyCGAzBAizGYPQI2o6FbV/F9bBofKsZhtElr6HzF08ioG2y9nxSmnqtVmu7//LytP+amr4uFe5WXiIyigOoybkctQCcuWBDZ9w44IEHnN8lYml9Zs60aIXkv9Ydr5T5fRjUeAi9sA5NcBJlCEJQdAgeSFdg7qRLCN91EBgy1fRaRN99Z581j2xRubvqwAFg7lxtOXSknEiUiU+JPAaDIanztLEN1rZCWFp/S4ONs2ddk3bA0npfuGB63+3Wo9GB3+KrWyMBNNXvauZ7GO1bARkjk9HzyZbwreOr3aFWA/3MpKB49lng/feBYcPsM8vKUsaCiarstHik3Tl4sUsicjIhA6WlpQKAKC0tdXVRrLNwoRDR0UJo/+Rqb9HR2u3uqqJCWweFwrBeuptCIURMjPY4a+pfWGj8fMZuublOr7ZF9Q4Ls6j8w5ErvHFL9Km/Rbz7t0Kxb/lfpp/X0telsND46x0T45jP28KFpl+Lmj4TUqB7L92lvERuzFnXb44ZkirdL09Lx45InW5sxfffA48/fqdVorLKrRCLF1tX/169tLPGLGGvsS/WjBfRrXEDmKy3mDDBoqd9PPM8zh2+isKL7TB5cR80Hxhv+mBruiUzM4HDh7WzxnJztf8WF9u/hcOS8V2V6cZTffihNMbkOGrcGxG5jkNDLYlwu5YhT/vlaazFISysekuIrhXC1vp//735VgZ7vW62ttoZedz1kAjxefyrornPQXEU0UIN4y0mGlved2tahpzFmla8qjcptIzm5kq3BZLIwzjr+u0WwdCxY8fEyJEjRWhoqAgMDBRt2rQRmzZtsvjxbhcMSfECZitT3SEKhfY2bZr2olFYeOciX5v6P/98zUGUPS6k5upk5jnO7Dgllqd/IGaEThX3oUB4oUJ/iqH4VmgAobHx3NVY0y3pLJYGE6bKa6/30Vae9P0kkjgGQ7dduHBBxMbGitGjR4sNGzaI4uJisWrVKnHw4EGLz+F2wZCn/PK0tYWntvWfP1+Ihg0Nj7XX2Bcb6qRRa8T2BfvE9AGFonvQn0IBtcFDGinOiDGJa0X+C7+JsuNl9h+7owveqgZErgosatMy5KoArjIpBphEHspZ12/JzyZ76623EBMTgy+//FK/LS4uznUFcgZXrfti75lr1oytqDy7q7b1HzJEO33ekhWcra2vhXW6+ePPWL0tFKrvr0K1OwFH1M0BNNcf1jZwLzI6noJyTEN0HNUCXj6Vpq3bO+eV1PJS9epV81R+c0x9bpzF3jnOiMj1HBpq2UGLFi1Edna2GDJkiGjYsKFo27atmDt3bo2PuXHjhigtLdXfSkpK3KtlyBW/PB0xc83SFp5//9uwLs6ov631tbBOWfjCYFMArgllow1i9og1ouSPE7aXuzYqKrStMlW7JV3BVGuVNTddy6Cr6uXM2XdEMsVustv8/f2Fv7+/mDJlitiyZYuYPXu2CAgIEF999ZXJx7zyyisCQLWb2wRDQji3a6OWY2BMsqY7pGog4sj616a+FtapNwpFlNcJMbbFGlHw8gZx9exV7eOlFJC4mqmAdMwYyz4zppYDcOYga76fRA7FYOg2X19f0a1bN4NtEyZMEF27djX5GLdvGdJxxi9PR85cM9fCYy4QcUT9a1nfq6fKxLWgRtUHON++qaEQl/wbii1f7xQatcbwwa6+cEuRsWDC0pbB7793TBBPRJLBYOi2pk2bikcffdRg26xZs0RkZKTF53C7AdSVOfqXp6NnxljTHWIsELF3/W2o75H1x8Ss4WvEfQ3/EAG4Jh7AQqGGotoUeE1NF2FHtb55KnMtg/Pne9byE0RkFBddvK1Hjx7Yt2+fwbb9+/cjNjbWRSVyMm9v7SDRhx7S/mvvQZmOyhWmoxu8GxVl/lghqi9WZ+/6W1iPA9/8gX/3LEKbwH2I7R6Fcd/ejWVnO+EGArHVpxO+aDoNN4MNk6MqoqONp2GoaZFB3bbsbGksKFgTZyYlNfW50b3G4eFc+JCI7Ebys8kmTZqE7t27Y/r06Rg2bBj++OMPzJ07F3PnznV10TyDM2au6WZHTZ0KvP66+eNtDbwsYWE9Hv+sM9agDwDAC2p0D94JZfeLUD4ZjZSMBCi8XgbU/7Jsxpets+qkxBVJSWuaVZeXZ9k5HPlZIiKPIflgqFOnTli0aBGmTJmCV199FfHx8ZgxYwZGjhzp6qJ5BnPTnO2VsdzbG7jnHsuCIXsvGVCZmfpqoMAxRGM7WuPBmPVQpgvcm52M8KQ21c+la7Uyx9Gtb47myqSkpl5jVy0/QUQeSSGEsSugZykrK0NISAhKS0sRHBzs6uJIj+5iBxhe8HRrptjrYqdWA3Fx5gOv4mKHrNFScaMC6z/dhcMzF+PhQ1MBAF64Uw4NFFBAYGfW20ieNfFO5vfaKioC0tLMH1dYKL2WId17Zqply8HvmdlyueizRETO4azrt+THDJETmBufYa9f/RYkK7X3YnUXiy8hb8J6jIz7FY3qXEbvZ9og69D/YQgW4DgiDY71iomGYuFCtJr3nP0CIeBOa1TVOusoFEBMTO1b3xxBqklJXfBZIiLPJfluMnISe696XNPzOHA1ZKER2Le8GKpZR6H6pT5+KW0JNbrr94cqLuC+uN3IGNwYQRO2A0e3O7a+gHuvWOzKLj5zK4RLbWVtInJb7CYj17Bj6o+bV25i3Sc7ocq7jIIdcThUYTjTMNX/ADLaHYfykVB0fTQV3n4uCjqMDUKOiZH2hdtVXXzWDNi2dxoZIpIMZ12/GQyRWzq75xx+fH8vCpZ546fjqbiMO++rH8qRFrYDyrSrSJ9wF+LvjnFhSauQyoXb0nK4YmyOqQHb9h7DRkSSx2DIjhgMuT+hEdiRfwCquSeg+i0Mv19Jhag05C3C6wzSE/ZB+YAv+k1MRVBkkAtLK3HWTpN31gB7QLoDtonIJRgM2RGDIfd049INFH6wA6r516Dak4Cj6miD/e0C90DZ8XSlzO+cD2CWra0uzuric+eZd0Rkd866fnMANUnKyW2nsfT9/VCt8MPKUy1xDZ30+wJwHf0a7YCy3w2kZyciulMLAC1cV1h3Y24lbIVCuxL24MHVW12cNcDe3ddkIiK3xGCIXEpTocHWb/dB9flpFPzRCJuvpQCI0O+P9j4BZdJBKIcGIu3pVNQJ7+y6wrq72q6Ebekik7XBxRSJyAUYDJHTXT1zFT/P3AlVfjlU+5vjpMawhadz3Z3I6HoOyseboM3Q5lB4RZo+GVnOHVpdnLUiOhFRJQyGyCmO/nYcqpkHoVpdB6vPtkI5uuj31cNlDIjcBeXAW7hvcjIiWrZ0YUk9mDu0urjzmkxE5LY4gJocQn1TjT/m7Ybqq/NQbWmC7TeSDPbH+ZQgI+UvKIfXQ+/xLeEf7O+iksqIO6WwcMc1mYjI7jiAmtxO2bEyrHh/F1SL1Vj2VxLOilb6fZUzv2c8FY0WygQovCS0/o8cuFOri7MGbBMRgS1DVEuHVh+B6qPDUK2phzUXWuEW/PT7QlCKQU13aTO/T2qBsMRQF5aU9NjqQkRugusM2RGDIfvRZX5X/e8iCv6Mwd6bCQb7m/sWI6P1ESgfro8eT6TaN+Ep2Y9UVsImIqoBu8lIMi4WX8Ly93ajoEDgx6OpuCTa6Pf54BbubrADyrvLkP5ULJoPjAcQ77rCkmWcMU2eiMhNMBiianSZ3ws+PgrVr/Xxa5XM72GK87gvfg+Uf/PCwEmpCGna3oWlJSIiqh0GQwRAm/l97Sxt5nfVzjgcqrgLwF36/S39D0BpkPm9p+sKS0REZEcMhhxJ4uMyzuw6ix9n7IPqR13m9zstPJUzvysnJiCuZyKARNcVloiIyEHkFQytWweUlTknMLE2M7gTVM78XvBbGDZcSYXAnRaeCK8zUDbbB2WmH/pNTEW9xh1dUk4iIiJnktdsMgD6seiODExszQzuAOYyv7cP3ANlp9NQ/qMROoxMZuZ3IiKSDE6ttyOjwZCjAhPdKr+mEmI6YZXfE1tOYdnMAyhY4YdVp1riGurq9wXiGvpF7ICyXznSsxMR1ZEJL4mISJoYDNmR0WAIcExgUlQEpKWZP66w0G5TmzUVGmzJ3QvVF2eg2qjL/H5H5czvfZ9picDQQLs8LxERkSNxnSFnEAIoKdGOJbLXmitOygx+9cxVrJqhzfy+9EBznNSkANAGQQpo0Lnubii7nkPGE03QeggzvxMREZki72BIp5aBiQEHZgY/8usxLP3wUI2Z3zMGVWBQdhIzvxMREVmIwRBgU2BiUq9e2q43c5nBe/Uye6rKmd8LtkRix43mAO4MgI73OYqM1GIoh9fD3eNawj+4q/3qQUREJBPyDoasCEwsVsvM4LrM7wU/qLGsOBnnqmR+7xG8E8oeF6F8Upf5van9yu4KEl+LiYiIPJ98gyELAhObZWZqZ6kZW2fISGbwQ6uPoODDw1CtCcLaiy1xC930+6pnfm8DjyHBtZiIiEh+5DubLCbGaGBiVyZaPSpuVODXOTuh+voSVNurZ35P8vsLylZHkTGqPro/7qGZ3yW0FhMREUkTp9bbkf7FVKkQ7KwVqKu4cOgilr+3G6qluJ35vb5+ny7ze0bvy0gfF4vE/nFOK5dLSGAtJiIikj5OrXeEXr0AB76YlQmNwN5lf0H1SUmlzO899PvDFOeRHr8HysHeGJCdIq/M7+vWmQ6EAMcseUBERGSCvIIhB+cmq5z5vWBnHP6qSABwpwusVcB+KNudgDIrDF3GpMg387uT1mIiIiKyhLyCIaXyzv/tNFD3zK6zWPb+PqiWe2OFkczvfcO3Q5l2DenPJCCuZ3MAzWv1fB7BgWsxERERWUteY4ZQ+9xkQiOwfcF+qD49CdXvuszvd5KbNvY6jfRm+ytlfq9n/ERynlKuGzNkbi0mjhkiIpI1DqC2o9rmJrt+4ToKP9wJ1fzrUO1NQIk6ymB/+8A9yOiszfzefoQFmd85pfzObDLA+FpMnE1GRCR7DIbsyGQwpGMkaeqJLaewdMZ+qFb6m8z8njGgHPc9Y2Xmd04pv8NYUOiMJQ+IiMgtMBiyI7PBUG4uNEMf1Gd+L/gjAluutzA4JMb7OJTJh6AcGoi0CTZmfueU8urk3F1IREQ14tR6J3r7hbN47+GzOFUl83uXerug7Hoeysd1md+jaj6RuQu7lKaU2xqE2Dt48faufV0ZUBERUS3IOhjSQIFjiMaLx8ZDA2/Uw2UMjNoJ5b3q25nfW5k/iY4l44CkMqXc1jFLUhzrJMUyERGRWzEz0ld6cnJyoFAokJ2dXavzaKAdo5Pj9RKebvMLVr61BedK/bDgWDeM/qwnIlo2tPxkunFAVVt9jh/Xbs/P196XwpRyS8tqr8c5khTLREREbsetxgxt3LgRw4YNQ3BwMNLS0jBjxgyLHmdszFBZQEOUTZqKqNefgsLr9uBlW7pbrBkHBLh2SrmtY5akONZJimUiIiK7ctaYIbdpGbpy5QpGjhyJTz/9FA0aNLDpHIX3vYUr738KFBYi+MpJRE8fdycQys/XXlzT0oARI7T/xsWZb12wZhyQt7e2+wa4M3tMR3d/xgzHXbytKas9HudIUiwTERG5JbcJhsaPH4/09HT069fP7LHl5eUoKyszuAFAWt6TqJf9mLbFZ906IC8PKCrSTme3tbvF2nFAmZna54uqMhg7Otrx0+ptHbMklbFOtjwXU3oQEZEZbjGA+ttvv8WWLVuwceNGi47PycnBtGnTjO80NuDW29t4t5UQ2hab7Gxg8GDjLTa2jAPKzNSez9kzoGwdsySFsU62PhdTehARkRmSHzNUUlKCjh07YsWKFWjTpg0AoE+fPmjbtq3JMUPl5eUoLy/X3y8rK0NMTAxK//c/BD/yiPHAxxwjCzMCcK/UEraWVYp1lGKZiIjIrjhm6LbNmzfjzJkz6NChA3x8fODj44M1a9bggw8+gI+PD9RqdbXH+Pv7Izg42OAGAPjnP20LhADT3S32GAekVmu763TddkbqZBe2ltXVY52MkWKZiIjILUk+GLrnnnuwY8cObNu2TX/r2LEjRo4ciW3btsHbmovdiRO2F6Sm7pbajAOydeC2rWwtqyvHOpkixTIREZHbkXw3mTHmusmqMpuOoybWdLdYOzXflXnKpLICtT1IsUxERFRrTMchBdZ2t1iTWkKt1g7ktnXgdm3ZmgbDHukz7E2KZSIiIrfhlsFQUVGRbQ+MjNS2HphqDPP2NhyvEx3tuAzqUspTRkREJGNuGQzZ7K23gEce0ba6VA6IdC1AeXlAw4Y1d7fYq0uG6+QQERFJgryCob/9TTsOx1hiT0tagOyZFJTr5BAREUmCWw6gtla1AVi2tO7Ye7Az18khIiKqkbMGUMszGLKWo5KC6gIswHi3HaeHExGRjHHRRSlxVFJQS9fJcdaijERERDIkrzFDtnLkYGdzecrsOU6JiIiIqmEwZAlHD3Y2tU6OqXFKx49rt7MbjYiIqNbYTWaJXr20rTFVc2DpKBRATIz2OHsxtygjoF2UkV1mREREtcJgyBKuSArqqHFKREREZIDBkKWcnRSUizISERE5BccMWcPcYGd74qKMRERETsFgyFrOSgqqG6dkblFGe45TIiIikiF2k0mVK8YpERERyRCDISlz9jglIiIiGWI3mdQ5c5wSERGRDDEYcgfOGqfkDmxJsktERFQDBkPkPpiahIiIHIBjhsg96FKTVF2IUpeaJD/fNeUiIiK3x2CIpI+pSYiIyIEYDJH0MTUJERE5EIMhkj6mJiEiIgdiMETSx9QkRETkQAyGSPp0qUmqrsSto1AAMTFMTUJERDZhMETSx9QkRETkQAyGyD0wNQkRETkIF10k98HUJERE5AAMhsi9MDUJERHZGbvJiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLGYIiIiIhkjbPJnEWt5pRwIiIiCWIw5Az5+cDEiYaZ16Ojtasqc7FAIiIil2I3maPl5wNDhhgGQgBw/Lh2e36+a8pFREREABgM1UytBoqKgLw87b9qtfWPnzgREKL6Pt227Gzrz0tERER2w2DIlPx8IC4OSEsDRozQ/hsXZ11Lzrp11VuEKhMCKCnRHkdEREQuwWDIGHt1bZ08ad/jiIiIyO4kHwzl5OSgU6dOCAoKQqNGjXD//fdj3759jntCe3ZtNWli2XNaehwRERHZneSDoTVr1mD8+PH4/fffsXLlSlRUVGDAgAG4evWqY57Qnl1bvXppZ40pFMb3KxRATIz2OCIiInIJyU+tX758ucH9L7/8Eo0aNcLmzZtx99132/8J7dm15e2tnT4/ZIg28Knc2qQLkGbM4HpDRERELiT5lqGqSktLAQChoaEmjykvL0dZWZnBzWL27trKzAQWLACiogy3R0drt3OdISIiIpdSCGFscIw0CSEwePBgXLx4Eetq6KaaOnUqpk2bVm17aWkpgoODDTdWXRm6e3cgIUE7WNrYS6NQaAOZ4mLrWnS4AjUREZFVysrKEBISYvz6bUduFQyNHz8eS5cuxS+//ILo6GiTx5WXl6O8vFx/v6ysDDExMdVfTFMrQz/0EPDOO9r7xrq22KJDRETkcM4Khtymm2zChAlYsmQJCgsLawyEAMDf3x/BwcEGt2pqmj7/zjvAc8+xa4uIiEgGJD+AWgiBCRMmYNGiRSgqKkJ8fHztT2pu+rxCAXz7LXDoELB+Pbu2iIiIPJjkg6Hx48cjNzcXixcvRlBQEE6dOgUACAkJQWBgoG0ntXT6/Pr1QJ8+tj0HERERuQXJd5N98sknKC0tRZ8+fdCkSRP97bvvvrP9pFwZmoiIiG6TfMuQQ8Z3c2VoIiIiuk3yLUMOwZWhiYiI6DZ5BkO6laGB6gERV4YmIiKSFXkGQwBXhiYiIiIAbjBmyKEyM4HBg7kyNBERkYzJOxgCtIEPp88TERHJlny7yYiIiIjAYIiIiIhkjsEQERERyRqDISIiIpI1BkNEREQkawyGiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLGYIiIiIhkjcEQERERyRqDISIiIpI1BkNEREQkawyGiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLGYIiIiIhkjcEQERERyRqDISIiIpI1BkNEREQkawyGiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLGYIiIiIhkjcEQERERyRqDISIiIpI1BkNEREQkawyGiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLmNsHQrFmzEB8fj4CAAHTo0AHr1q1zdZGIiIjIA7hFMPTdd98hOzsbL730ErZu3YpevXph0KBBOHr0qKuLRkRERG5OIYQQri6EOV26dEH79u3xySef6Le1aNEC999/P3Jycsw+vqysDCEhISgtLUVwcLAji0pERER24qzrt+Rbhm7evInNmzdjwIABBtsHDBiA9evXu6hURERE5Cl8XF0Ac86dOwe1Wo2IiAiD7RERETh16pTRx5SXl6O8vFx/v7S0FIA2wiQiIiL3oLtuO7oTS/LBkI5CoTC4L4Sotk0nJycH06ZNq7Y9JibGIWUjIiIixzl//jxCQkIcdn7JB0Ph4eHw9vau1gp05syZaq1FOlOmTMHkyZP19y9duoTY2FgcPXrUoS+m1JSVlSEmJgYlJSWyGivFerPecsB6s95yUFpaiqZNmyI0NNShzyP5YMjPzw8dOnTAypUr8cADD+i3r1y5EoMHDzb6GH9/f/j7+1fbHhISIqsPkU5wcDDrLSOst7yw3vIi13p7eTl2iLPkgyEAmDx5MkaNGoWOHTuiW7dumDt3Lo4ePYonn3zS1UUjIiIiN+cWwdCDDz6I8+fP49VXX8XJkyfRsmVLLFu2DLGxsa4uGhEREbk5twiGAGDcuHEYN26cTY/19/fHK6+8YrTrzJOx3qy3HLDerLccsN6OrbdbLLpIRERE5CiSX3SRiIiIyJEYDBEREZGsMRgiIiIiWWMwRERERLLmlsHQrFmzEB8fj4CAAHTo0AHr1q2r8fg1a9agQ4cOCAgIwF133YXZs2dXO2bhwoVISUmBv78/UlJSsGjRIkcV32bW1Ds/Px/9+/dHw4YNERwcjG7duuGnn34yOGbevHlQKBTVbjdu3HB0VaxiTb2LioqM1mnv3r0Gx3na+z169Gij9U5NTdUf4w7v99q1a5GRkYHIyEgoFAr88MMPZh/jCd9va+vtKd9va+vtKd9va+vtKd/vnJwcdOrUCUFBQWjUqBHuv/9+7Nu3z+zjnPEdd7tg6LvvvkN2djZeeuklbN26Fb169cKgQYNw9OhRo8cXFxfjvvvuQ69evbB161b861//wjPPPIOFCxfqj/ntt9/w4IMPYtSoUfjzzz8xatQoDBs2DBs2bHBWtcyytt5r165F//79sWzZMmzevBlpaWnIyMjA1q1bDY4LDg7GyZMnDW4BAQHOqJJFrK23zr59+wzqlJiYqN/nie/3zJkzDepbUlKC0NBQDB061OA4qb/fV69eRZs2bfDRRx9ZdLynfL+trbenfL+trbeOu3+/ra23p3y/16xZg/Hjx+P333/HypUrUVFRgQEDBuDq1asmH+O077hwM507dxZPPvmkwbbk5GTx4osvGj3+hRdeEMnJyQbbxo4dK7p27aq/P2zYMHHvvfcaHDNw4EAxfPhwO5W69qyttzEpKSli2rRp+vtffvmlCAkJsVcRHcLaehcWFgoA4uLFiybPKYf3e9GiRUKhUIjDhw/rt7nD+10ZALFo0aIaj/GU73dlltTbGHf8fldmSb095ftdmS3vtyd8v4UQ4syZMwKAWLNmjcljnPUdd6uWoZs3b2Lz5s0YMGCAwfYBAwZg/fr1Rh/z22+/VTt+4MCB2LRpE27dulXjMabO6Wy21LsqjUaDy5cvV0t2d+XKFcTGxiI6OhpKpbLaL0tXqk2927VrhyZNmuCee+5BYWGhwT45vN+ff/45+vXrV22Vdim/37bwhO+3Pbjj97s23Pn7bQ+e8v0uLS0FgBqTsDrrO+5WwdC5c+egVqurZauPiIioltVe59SpU0aPr6iowLlz52o8xtQ5nc2Welf17rvv4urVqxg2bJh+W3JyMubNm4clS5YgLy8PAQEB6NGjBw4cOGDX8tvKlno3adIEc+fOxcKFC5Gfn4+kpCTcc889WLt2rf4YT3+/T548iR9//BGPPfaYwXapv9+28ITvtz244/fbFp7w/a4tT/l+CyEwefJk9OzZEy1btjR5nLO+426TjqMyhUJhcF8IUW2bueOrbrf2nK5gaxnz8vIwdepULF68GI0aNdJv79q1K7p27aq/36NHD7Rv3x4ffvghPvjgA/sVvJasqXdSUhKSkpL097t164aSkhK88847uPvuu206p6vYWsZ58+ahfv36uP/++w22u8v7bS1P+X7byt2/39bwpO+3rTzl+/30009j+/bt+OWXX8we64zvuFu1DIWHh8Pb27tatHfmzJlqUaFO48aNjR7v4+ODsLCwGo8xdU5ns6XeOt999x0effRRfP/99+jXr1+Nx3p5eaFTp06S+SVRm3pX1rVrV4M6efL7LYTAF198gVGjRsHPz6/GY6X2ftvCE77fteHO3297cbfvd214yvd7woQJWLJkCQoLCxEdHV3jsc76jrtVMOTn54cOHTpg5cqVBttXrlyJ7t27G31Mt27dqh2/YsUKdOzYEb6+vjUeY+qczmZLvQHtL8bRo0cjNzcX6enpZp9HCIFt27ahSZMmtS6zPdha76q2bt1qUCdPfb8B7WyNgwcP4tFHHzX7PFJ7v23hCd9vW7n799te3O37XRvu/v0WQuDpp59Gfn4+Vq9ejfj4eLOPcdp33OKh1hLx7bffCl9fX/H555+L3bt3i+zsbFG3bl39qPoXX3xRjBo1Sn/8X3/9JerUqSMmTZokdu/eLT7//HPh6+srFixYoD/m119/Fd7e3uLNN98Ue/bsEW+++abw8fERv//+u9PrZ4q19c7NzRU+Pj7i448/FidPntTfLl26pD9m6tSpYvny5eLQoUNi69atYsyYMcLHx0ds2LDB6fUzxdp6v//++2LRokVi//79YufOneLFF18UAMTChQv1x3ji+63z8MMPiy5duhg9pzu835cvXxZbt24VW7duFQDEe++9J7Zu3SqOHDkihPDc77e19faU77e19faU77e19dZx9+/3U089JUJCQkRRUZHB5/batWv6Y1z1HXe7YEgIIT7++GMRGxsr/Pz8RPv27Q2m5WVlZYnevXsbHF9UVCTatWsn/Pz8RFxcnPjkk0+qnXP+/PkiKSlJ+Pr6iuTkZIMvl1RYU+/evXsLANVuWVlZ+mOys7NF06ZNhZ+fn2jYsKEYMGCAWL9+vRNrZBlr6v3WW2+JhIQEERAQIBo0aCB69uwpli5dWu2cnvZ+CyHEpUuXRGBgoJg7d67R87nD+62bOm3qc+up329r6+0p329r6+0p329bPuee8P02VmcA4ssvv9Qf46rvuOJ2AYmIiIhkya3GDBERERHZG4MhIiIikjUGQ0RERCRrDIaIiIhI1hgMERERkawxGCIiIiJZYzBEREREssZgiIiIiGSNwRARERHJGoMhIiIikjUGQ0TklvLy8hAQEIDjx4/rtz322GNo3bo1SktLXVgyInI3zE1GRG5JCIG2bduiV69e+OijjzBt2jR89tln+P333xEVFeXq4hGRG/FxdQGIiGyhUCjwxhtvYMiQIYiMjMTMmTOxbt06BkJEZDW2DBGRW2vfvj127dqFFStWoHfv3q4uDhG5IY4ZIiK39dNPP2Hv3r1Qq9WIiIhwdXGIyE2xZYiI3NKWLVvQp08ffPzxx/j2229Rp04dzJ8/39XFIiI3xDFDROR2Dh8+jPT0dLz44osYNWoUUlJS0KlTJ2zevBkdOnRwdfGIyM2wZYiI3MqFCxfQo0cP3H333ZgzZ45+++DBg1FeXo7ly5e7sHRE5I4YDBEREZGscQA1ERERyRqDISIiIpI1BkNEREQkawyGiIiISNYYDBEREZGsMRgiIiIiWWMwRERERLLGYIiIiIhkjcEQERERyRqDISIiIpI1BkNEREQkawyGiIiISNb+HxqiMFuQwzXFAAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\n",
     "# Importing various packages\n",
@@ -1891,17 +1801,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[4.21639245]\n",
-      " [2.82985482]]\n",
-      "[4.15172236] [2.79589065]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "from random import random, seed\n",
@@ -1997,32 +1897,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[3.98919197]\n",
-      " [2.94015598]]\n",
-      "[[3.94925462]\n",
-      " [2.97087408]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from random import random, seed\n",
     "import numpy as np\n",
@@ -2319,15 +2194,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "gamma_j after 500 epochs: 9.97108e-05\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np \n",
     "\n",
@@ -2383,38 +2250,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Own inversion\n",
-      "[[4.5424657 ]\n",
-      " [2.40026896]]\n",
-      "Eigenvalues of Hessian Matrix:[0.29830651 3.89658408]\n",
-      "theta from own gd\n",
-      "[[4.5424657 ]\n",
-      " [2.40026896]]\n",
-      "theta from own sdg\n",
-      "[[4.55687658]\n",
-      " [2.41165766]]\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "# Importing various packages\n",
@@ -3100,29 +2936,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_188_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The max absolute difference is: 1.77636e-15\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "\n",
@@ -3182,16 +2996,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The gradient of f1 evaluated at a = 1 using autograd is: 3\n",
-      "The gradient of f1 evaluated at a = 1 by finding the analytic expression is: 3\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3232,21 +3037,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Evaluating at x1 = 1, x2 = 3\n",
-      "------------------------------\n",
-      "The derivative of f2 w.r.t x1: 12\n",
-      "The analytical derivative of f2 w.r.t x1: 12\n",
-      "\n",
-      "The derivative of f2 w.r.t x2: -4\n",
-      "The analytical derivative of f2 w.r.t x2: -4\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3301,16 +3092,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The computed gradient of f3 is:  [ 2.  3.  5.  7. 88.]\n",
-      "The analytical gradient of f3 is:  [ 2.  3.  5.  7. 88.]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3354,16 +3136,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The computed derivative of f4 at x = 2.7 is: 13.8759\n",
-      "The analytical gradient of f4 at x = 2.7 is: 13.8759\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3392,15 +3165,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The computed derivative of f5 at x = 2.7 is: 5.4\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3426,16 +3191,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The computed derivative of f6_for at x = 0.5 is: 3.95703\n",
-      "The computed derivative of f6_while at x = 0.5 is: 3.95703\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3471,15 +3227,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The analytical derivative of f6 at x = 0.5 is: 3.95703\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3500,16 +3248,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The computed derivative of f7 at n = 2 is: 1\n",
-      "The analytical derivative of f7 at n = 2 is: 1\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -3562,18 +3301,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'\\nimport autograd.numpy as np\\nfrom autograd import grad\\ndef f8(x): # Assume x is an array\\n    x[2] = 3\\n    return x*2\\n\\nf8_grad = grad(f8)\\n\\nx = 8.4\\n\\nprint(\"The derivative of f8 is:\",f8_grad(x))\\n'"
-      ]
-     },
-     "execution_count": 22,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"\n",
     "import autograd.numpy as np\n",
@@ -3608,25 +3336,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "AttributeError",
-     "evalue": "'ArrayBox' object has no attribute 'dot'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [23]\u001b[0m, in \u001b[0;36m<cell line: 11>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      7\u001b[0m f9_grad \u001b[38;5;241m=\u001b[39m grad(f9)\n\u001b[1;32m      9\u001b[0m x \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m1.0\u001b[39m,\u001b[38;5;241m0.0\u001b[39m])\n\u001b[0;32m---> 11\u001b[0m \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe derivative of f9 is:\u001b[39m\u001b[38;5;124m\"\u001b[39m,\u001b[43mf9_grad\u001b[49m\u001b[43m(\u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:20\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     19\u001b[0m     x \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mtuple\u001b[39m(args[i] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m argnum)\n\u001b[0;32m---> 20\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43munary_operator\u001b[49m\u001b[43m(\u001b[49m\u001b[43munary_f\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_args\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mnary_op_kwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/differential_operators.py:25\u001b[0m, in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[38;5;129m@unary_to_nary\u001b[39m\n\u001b[1;32m     19\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mgrad\u001b[39m(fun, x):\n\u001b[1;32m     20\u001b[0m     \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     21\u001b[0m \u001b[38;5;124;03m    Returns a function which computes the gradient of `fun` with respect to\u001b[39;00m\n\u001b[1;32m     22\u001b[0m \u001b[38;5;124;03m    positional argument number `argnum`. The returned function takes the same\u001b[39;00m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;124;03m    arguments as `fun`, but returns the gradient instead. The function `fun`\u001b[39;00m\n\u001b[1;32m     24\u001b[0m \u001b[38;5;124;03m    should be scalar-valued. The gradient has the same type as the argument.\"\"\"\u001b[39;00m\n\u001b[0;32m---> 25\u001b[0m     vjp, ans \u001b[38;5;241m=\u001b[39m \u001b[43m_make_vjp\u001b[49m\u001b[43m(\u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     26\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m vspace(ans)\u001b[38;5;241m.\u001b[39msize \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m     27\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mGrad only applies to real scalar-output functions. \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m     28\u001b[0m                         \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mTry jacobian, elementwise_grad or holomorphic_grad.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/core.py:10\u001b[0m, in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmake_vjp\u001b[39m(fun, x):\n\u001b[1;32m      9\u001b[0m     start_node \u001b[38;5;241m=\u001b[39m VJPNode\u001b[38;5;241m.\u001b[39mnew_root()\n\u001b[0;32m---> 10\u001b[0m     end_value, end_node \u001b[38;5;241m=\u001b[39m  \u001b[43mtrace\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_node\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mfun\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m end_node \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mvjp\u001b[39m(g): \u001b[38;5;28;01mreturn\u001b[39;00m vspace(x)\u001b[38;5;241m.\u001b[39mzeros()\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/tracer.py:10\u001b[0m, in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m trace_stack\u001b[38;5;241m.\u001b[39mnew_trace() \u001b[38;5;28;01mas\u001b[39;00m t:\n\u001b[1;32m      9\u001b[0m     start_box \u001b[38;5;241m=\u001b[39m new_box(x, t, start_node)\n\u001b[0;32m---> 10\u001b[0m     end_box \u001b[38;5;241m=\u001b[39m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstart_box\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     11\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m isbox(end_box) \u001b[38;5;129;01mand\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_trace \u001b[38;5;241m==\u001b[39m start_box\u001b[38;5;241m.\u001b[39m_trace:\n\u001b[1;32m     12\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m end_box\u001b[38;5;241m.\u001b[39m_value, end_box\u001b[38;5;241m.\u001b[39m_node\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/autograd/wrap_util.py:15\u001b[0m, in \u001b[0;36munary_to_nary.<locals>.nary_operator.<locals>.nary_f.<locals>.unary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     13\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m     14\u001b[0m     subargs \u001b[38;5;241m=\u001b[39m subvals(args, \u001b[38;5;28mzip\u001b[39m(argnum, x))\n\u001b[0;32m---> 15\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msubargs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "Input \u001b[0;32mIn [23]\u001b[0m, in \u001b[0;36mf9\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mf9\u001b[39m(a): \u001b[38;5;66;03m# Assume a is an array with 2 elements\u001b[39;00m\n\u001b[1;32m      4\u001b[0m     b \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m1.0\u001b[39m,\u001b[38;5;241m2.0\u001b[39m])\n\u001b[0;32m----> 5\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43ma\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdot\u001b[49m(b)\n",
-      "\u001b[0;31mAttributeError\u001b[0m: 'ArrayBox' object has no attribute 'dot'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import autograd.numpy as np\n",
     "from autograd import grad\n",
@@ -4324,7 +4034,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb b/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb
index c72bd0283..57a7b064c 100644
--- a/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb
@@ -283,40 +283,19 @@
    },
    "outputs": [
     {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lib/__init__.py:32: UserWarning: JAX on Mac ARM machines is experimental and minimally tested. Please see https://github.com/google/jax/issues/5501 in the event of problems.\n",
-      "  warnings.warn(\"JAX on Mac ARM machines is experimental and minimally tested. \"\n"
-     ]
-    },
-    {
-     "ename": "AttributeError",
-     "evalue": "module 'jaxlib.pocketfft' has no attribute 'pocketfft'",
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 5>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtime\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m----> 5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mtf\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m image\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/__init__.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 51\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/__init__.py:30\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m autograph\n\u001b[1;32m     29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m bitwise\n\u001b[0;32m---> 30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compat\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m config\n\u001b[1;32m     32\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m data\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/__init__.py:37\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Compatibility functions.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \n\u001b[1;32m      5\u001b[0m \u001b[38;5;124;03mThe `tf.compat` module contains two sets of compatibility functions.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     32\u001b[0m \n\u001b[1;32m     33\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     35\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m---> 37\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v1\n\u001b[1;32m     38\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m v2\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m forward_compatibility_horizon\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/compat/v1/__init__.py:47\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m layers\n\u001b[1;32m     46\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg\n\u001b[0;32m---> 47\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     48\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m logging\n\u001b[1;32m     49\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_api\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv2\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcompat\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mv1\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lookup\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/__init__.py:9\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m constants\n\u001b[0;32m----> 9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m experimental\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Interpreter\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpHint\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m authoring\n\u001b[1;32m      9\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01manalyzer\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m ModelAnalyzer \u001b[38;5;28;01mas\u001b[39;00m Analyzer\n\u001b[1;32m     10\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m OpResolverType\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/_api/v2/compat/v1/lite/experimental/authoring/__init__.py:8\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;124;03m\"\"\"Public API for tf.lite.experimental.authoring namespace.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msys\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01m_sys\u001b[39;00m\n\u001b[0;32m----> 8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mauthoring\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m compatible\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/authoring/authoring.py:43\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m\n\u001b[1;32m     42\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[0;32m---> 43\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m convert\n\u001b[1;32m     44\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite\n\u001b[1;32m     45\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmetrics\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m converter_error_data_pb2\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/convert.py:29\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01msix\u001b[39;00m\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lite_constants\n\u001b[0;32m---> 29\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m util\n\u001b[1;32m     30\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wrap_toco\n\u001b[1;32m     31\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtensorflow\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlite\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconvert_phase\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Component\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/tensorflow/lite/python/util.py:51\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     47\u001b[0m \u001b[38;5;66;03m# Jax functions used by TFLite\u001b[39;00m\n\u001b[1;32m     48\u001b[0m \u001b[38;5;66;03m# pylint: disable=g-import-not-at-top\u001b[39;00m\n\u001b[1;32m     49\u001b[0m \u001b[38;5;66;03m# pylint: disable=unused-import\u001b[39;00m\n\u001b[1;32m     50\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m---> 51\u001b[0m   \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_computation \u001b[38;5;28;01mas\u001b[39;00m _xla_computation\n\u001b[1;32m     52\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mImportError\u001b[39;00m:\n\u001b[1;32m     53\u001b[0m   _xla_computation \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/__init__.py:116\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     40\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mconfig\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     41\u001b[0m   config \u001b[38;5;28;01mas\u001b[39;00m config,\n\u001b[1;32m     42\u001b[0m   enable_checks \u001b[38;5;28;01mas\u001b[39;00m enable_checks,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     51\u001b[0m   numpy_rank_promotion \u001b[38;5;28;01mas\u001b[39;00m numpy_rank_promotion,\n\u001b[1;32m     52\u001b[0m )\n\u001b[1;32m     53\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mapi\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     54\u001b[0m   ad,  \u001b[38;5;66;03m# TODO(phawkins): update users to avoid this.\u001b[39;00m\n\u001b[1;32m     55\u001b[0m   checkpoint \u001b[38;5;28;01mas\u001b[39;00m checkpoint,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    114\u001b[0m   xla_computation \u001b[38;5;28;01mas\u001b[39;00m xla_computation,\n\u001b[1;32m    115\u001b[0m )\n\u001b[0;32m--> 116\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mexperimental\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmaps\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m soft_pmap \u001b[38;5;28;01mas\u001b[39;00m soft_pmap\n\u001b[1;32m    117\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mversion\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m __version__ \u001b[38;5;28;01mas\u001b[39;00m __version__\n\u001b[1;32m    119\u001b[0m \u001b[38;5;66;03m# These submodules are separate because they are in an import cycle with\u001b[39;00m\n\u001b[1;32m    120\u001b[0m \u001b[38;5;66;03m# jax and rely on the names imported above.\u001b[39;00m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/experimental/maps.py:26\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mfunctools\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m wraps, partial, partialmethod\n\u001b[1;32m     24\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01menum\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Enum\n\u001b[0;32m---> 26\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m numpy \u001b[38;5;28;01mas\u001b[39;00m jnp\n\u001b[1;32m     27\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m core\n\u001b[1;32m     28\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linear_util \u001b[38;5;28;01mas\u001b[39;00m lu\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/__init__.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2018 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     17\u001b[0m \n\u001b[1;32m     18\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m fft \u001b[38;5;28;01mas\u001b[39;00m fft\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m linalg \u001b[38;5;28;01mas\u001b[39;00m linalg\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01minterpreters\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mxla\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m DeviceArray \u001b[38;5;28;01mas\u001b[39;00m DeviceArray\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/numpy/fft.py:17\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Copyright 2020 Google LLC\u001b[39;00m\n\u001b[1;32m      2\u001b[0m \u001b[38;5;66;03m#\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Licensed under the Apache License, Version 2.0 (the \"License\");\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m     14\u001b[0m \n\u001b[1;32m     15\u001b[0m \u001b[38;5;66;03m# flake8: noqa: F401\u001b[39;00m\n\u001b[0;32m---> 17\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m     18\u001b[0m   ifft \u001b[38;5;28;01mas\u001b[39;00m ifft,\n\u001b[1;32m     19\u001b[0m   ifft2 \u001b[38;5;28;01mas\u001b[39;00m ifft2,\n\u001b[1;32m     20\u001b[0m   ifftn \u001b[38;5;28;01mas\u001b[39;00m ifftn,\n\u001b[1;32m     21\u001b[0m   ifftshift \u001b[38;5;28;01mas\u001b[39;00m ifftshift,\n\u001b[1;32m     22\u001b[0m   ihfft \u001b[38;5;28;01mas\u001b[39;00m ihfft,\n\u001b[1;32m     23\u001b[0m   irfft \u001b[38;5;28;01mas\u001b[39;00m irfft,\n\u001b[1;32m     24\u001b[0m   irfft2 \u001b[38;5;28;01mas\u001b[39;00m irfft2,\n\u001b[1;32m     25\u001b[0m   irfftn \u001b[38;5;28;01mas\u001b[39;00m irfftn,\n\u001b[1;32m     26\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m     27\u001b[0m   fft2 \u001b[38;5;28;01mas\u001b[39;00m fft2,\n\u001b[1;32m     28\u001b[0m   fftfreq \u001b[38;5;28;01mas\u001b[39;00m fftfreq,\n\u001b[1;32m     29\u001b[0m   fftn \u001b[38;5;28;01mas\u001b[39;00m fftn,\n\u001b[1;32m     30\u001b[0m   fftshift \u001b[38;5;28;01mas\u001b[39;00m fftshift,\n\u001b[1;32m     31\u001b[0m   hfft \u001b[38;5;28;01mas\u001b[39;00m hfft,\n\u001b[1;32m     32\u001b[0m   rfft \u001b[38;5;28;01mas\u001b[39;00m rfft,\n\u001b[1;32m     33\u001b[0m   rfft2 \u001b[38;5;28;01mas\u001b[39;00m rfft2,\n\u001b[1;32m     34\u001b[0m   rfftfreq \u001b[38;5;28;01mas\u001b[39;00m rfftfreq,\n\u001b[1;32m     35\u001b[0m   rfftn \u001b[38;5;28;01mas\u001b[39;00m rfftn,\n\u001b[1;32m     36\u001b[0m )\n\u001b[1;32m     38\u001b[0m \u001b[38;5;66;03m# Module initialization is encapsulated in a function to avoid accidental\u001b[39;00m\n\u001b[1;32m     39\u001b[0m \u001b[38;5;66;03m# namespace pollution.\u001b[39;00m\n\u001b[1;32m     40\u001b[0m _NOT_IMPLEMENTED \u001b[38;5;241m=\u001b[39m []\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/numpy/fft.py:19\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01moperator\u001b[39;00m\n\u001b[1;32m     17\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m---> 19\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m lax\n\u001b[1;32m     20\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m xla_client\n\u001b[1;32m     21\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mutil\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m safe_zip\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/lax/__init__.py:332\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    299\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (_reduce_sum, _reduce_max, _reduce_min, _reduce_or,\n\u001b[1;32m    300\u001b[0m                   _reduce_and, _reduce_window_sum, _reduce_window_max,\n\u001b[1;32m    301\u001b[0m                   _reduce_window_min, _reduce_window_prod,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    306\u001b[0m                   _upcast_fp16_for_computation, _broadcasting_shape_rule,\n\u001b[1;32m    307\u001b[0m                   _eye, _tri, _delta, _ones, _zeros, _dilate_shape)\n\u001b[1;32m    308\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcontrol_flow\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    309\u001b[0m   associative_scan \u001b[38;5;28;01mas\u001b[39;00m associative_scan,\n\u001b[1;32m    310\u001b[0m   cond \u001b[38;5;28;01mas\u001b[39;00m cond,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    330\u001b[0m   while_p \u001b[38;5;28;01mas\u001b[39;00m while_p,\n\u001b[1;32m    331\u001b[0m )\n\u001b[0;32m--> 332\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mfft\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    333\u001b[0m   fft \u001b[38;5;28;01mas\u001b[39;00m fft,\n\u001b[1;32m    334\u001b[0m   fft_p \u001b[38;5;28;01mas\u001b[39;00m fft_p,\n\u001b[1;32m    335\u001b[0m )\n\u001b[1;32m    336\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mparallel\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    337\u001b[0m   all_gather \u001b[38;5;28;01mas\u001b[39;00m all_gather,\n\u001b[1;32m    338\u001b[0m   all_to_all \u001b[38;5;28;01mas\u001b[39;00m all_to_all,\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    355\u001b[0m   xeinsum \u001b[38;5;28;01mas\u001b[39;00m xeinsum,\n\u001b[1;32m    356\u001b[0m )\n\u001b[1;32m    357\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mjax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01m_src\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlax\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mother\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m (\n\u001b[1;32m    358\u001b[0m   conv_general_dilated_patches \u001b[38;5;28;01mas\u001b[39;00m conv_general_dilated_patches\n\u001b[1;32m    359\u001b[0m )\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/jax/_src/lax/fft.py:145\u001b[0m, in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    143\u001b[0m batching\u001b[38;5;241m.\u001b[39mprimitive_batchers[fft_p] \u001b[38;5;241m=\u001b[39m fft_batching_rule\n\u001b[1;32m    144\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m pocketfft:\n\u001b[0;32m--> 145\u001b[0m   xla\u001b[38;5;241m.\u001b[39mbackend_specific_translations[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcpu\u001b[39m\u001b[38;5;124m'\u001b[39m][fft_p] \u001b[38;5;241m=\u001b[39m \u001b[43mpocketfft\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mpocketfft\u001b[49m\n",
-      "\u001b[0;31mAttributeError\u001b[0m: module 'jaxlib.pocketfft' has no attribute 'pocketfft'"
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mtime\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
     }
    ],
@@ -692,7 +671,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek34.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek34.ipynb
index 53b974273..6bc6c9558 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek34.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek34.ipynb
@@ -135,7 +135,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[38;5;241m100\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      2\u001b[0m y \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2.0\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m5\u001b[39m\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m0.1\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrandn(\u001b[38;5;241m100\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[38;5;241m100\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      2\u001b[0m y \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2.0\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m5\u001b[39m\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m0.1\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrandn(\u001b[38;5;241m100\u001b[39m,\u001b[38;5;241m1\u001b[39m)\n",
       "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined"
      ]
     }
@@ -319,7 +319,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek35.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek35.ipynb
index 0b4eb4f75..e8be6f76c 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek35.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek35.ipynb
@@ -403,7 +403,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb
new file mode 100644
index 000000000..7a94380ac
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek39.ipynb
@@ -0,0 +1,59 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f35930ac",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html exercisesweek39.do.txt  -->\n",
+    "<!-- dom:TITLE: Exercises week 39 -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cb567a0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Exercises week 39\n",
+    "**September 25-29, 2023**\n",
+    "\n",
+    "Date: **Deadline is Sunday October 1 at midnight**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "934324b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Overarching aims of the exercises this week\n",
+    "\n",
+    "The aim of the exercises this week is to aid you in getting started\n",
+    "with writing the report. This will be discussed during the lab\n",
+    "sessions as well. One of the lab sessions will be recorded.\n",
+    "\n",
+    "A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
+    "\n",
+    "Similarly, an example of an earlier project can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/ReportSample.pdf>\n",
+    "\n",
+    "Your task this week is to\n",
+    "1. Write an abstract for your project\n",
+    "\n",
+    "2. Write an introduction\n",
+    "\n",
+    "3. Include references\n",
+    "\n",
+    "Ashort feedback to the this exercise will be available after the deadline. And you can reuse these elements in your final report."
+   ]
+  }
+ ],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
index 64a0a00c0..be4c6b3dd 100644
--- a/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/linalg.ipynb
@@ -225,8 +225,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[-0.28587856 -0.73509675  0.35559283 -0.62819534 -0.15254784 -0.44792888\n",
-      "  1.5393681  -0.81784072  0.53476918  1.02055673]\n"
+      "[-0.1223405   0.96602098 -0.42045733  2.00897328  0.96178833 -0.30742211\n",
+      "  0.23867951 -1.84775931 -0.3804507  -0.47953891]\n"
      ]
     }
    ],
@@ -662,26 +662,26 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[0.99218609 0.13120126 0.8260149  0.70761641 0.8634474  0.47202234\n",
-      "  0.09862064 0.8970168  0.40947888 0.19121744]\n",
-      " [0.93969474 0.4378299  0.23405814 0.52872817 0.00229179 0.41050604\n",
-      "  0.846471   0.78027207 0.11551515 0.18573652]\n",
-      " [0.80515205 0.40984037 0.61970354 0.03608726 0.90793026 0.45494697\n",
-      "  0.41718305 0.77288474 0.94404545 0.09218919]\n",
-      " [0.24566623 0.18632646 0.82113506 0.01710429 0.88981061 0.77756468\n",
-      "  0.94073014 0.89779302 0.97936584 0.69051742]\n",
-      " [0.84924359 0.43533824 0.62420578 0.02185737 0.36336962 0.10056192\n",
-      "  0.19468989 0.96562567 0.770356   0.4756968 ]\n",
-      " [0.05851756 0.43471448 0.80088524 0.62083489 0.88778045 0.56821272\n",
-      "  0.7133574  0.10148978 0.54861905 0.45917334]\n",
-      " [0.15939618 0.47756853 0.08791994 0.87602519 0.11470382 0.67142502\n",
-      "  0.7600498  0.81709481 0.85895314 0.33874172]\n",
-      " [0.21561586 0.65011691 0.1897755  0.5538822  0.75747652 0.27898999\n",
-      "  0.35128114 0.27674224 0.47513129 0.59366475]\n",
-      " [0.5916751  0.82365318 0.16026316 0.533142   0.93265898 0.05881845\n",
-      "  0.10326551 0.95604667 0.8617319  0.74199799]\n",
-      " [0.21089449 0.0402861  0.12611267 0.49197115 0.59203799 0.74577306\n",
-      "  0.14491591 0.71135895 0.84723978 0.03416188]]\n"
+      "[[0.69846205 0.78851232 0.08308983 0.5305063  0.12815515 0.72072214\n",
+      "  0.67232869 0.76697449 0.58848856 0.9904943 ]\n",
+      " [0.75838023 0.80529041 0.6484163  0.10609258 0.41344691 0.48942943\n",
+      "  0.92662338 0.88338811 0.12254643 0.81520361]\n",
+      " [0.55042787 0.34048788 0.25737687 0.7565813  0.30552745 0.25529596\n",
+      "  0.44101674 0.95844886 0.86670783 0.3992021 ]\n",
+      " [0.62482386 0.98232786 0.5248769  0.48823898 0.944291   0.88340778\n",
+      "  0.96704933 0.5255844  0.38941883 0.29239286]\n",
+      " [0.65680942 0.65466708 0.96617085 0.42214481 0.99932624 0.96546053\n",
+      "  0.48953049 0.26725306 0.57937269 0.36135213]\n",
+      " [0.73623167 0.23284855 0.36113667 0.61429341 0.91951571 0.84545016\n",
+      "  0.37857094 0.76168988 0.96457138 0.61999335]\n",
+      " [0.89635517 0.52058686 0.41240055 0.94738767 0.74171774 0.96592507\n",
+      "  0.63880898 0.44499556 0.21026792 0.92965555]\n",
+      " [0.30230092 0.9347861  0.56187437 0.3860215  0.58467645 0.27058589\n",
+      "  0.67628977 0.01494766 0.30681968 0.30491305]\n",
+      " [0.00860818 0.97140208 0.86478154 0.68302636 0.72968415 0.5859337\n",
+      "  0.88898063 0.25024282 0.07427349 0.65046291]\n",
+      " [0.01924293 0.54705652 0.01611258 0.47220243 0.36688196 0.47846644\n",
+      "  0.17072424 0.48396466 0.7900928  0.28490342]]\n"
      ]
     }
    ],
@@ -800,13 +800,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.041129694365319464\n",
-      "4.025325212488352\n",
-      "0.010687707010849668\n",
-      "[[ 1.23319332  3.73704762  4.12446443]\n",
-      " [ 3.73704762 12.59095724 12.81409445]\n",
-      " [ 4.12446443 12.81409445 20.04983109]]\n",
-      "[30.70850263  0.10254846  3.06293056]\n"
+      "-0.0017018997030592974\n",
+      "3.9531810558360623\n",
+      "-0.018173592942955955\n",
+      "[[ 1.06833761  3.33062366  3.10248906]\n",
+      " [ 3.33062366 11.28977247 10.01231809]\n",
+      " [ 3.10248906 10.01231809 13.75855891]]\n",
+      "[23.52658256  0.07563718  2.51444926]\n"
      ]
     }
    ],
@@ -838,32 +838,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[1. 0. 0. 0.]\n",
-      " [0. 1. 0. 0.]\n",
-      " [0. 0. 1. 0.]\n",
-      " [0. 0. 0. 1.]]\n",
-      "  (0, 0)\t1.0\n",
-      "  (1, 1)\t1.0\n",
-      "  (2, 2)\t1.0\n",
-      "  (3, 3)\t1.0\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[15], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/linalg_44_1.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -902,25 +890,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The test matrix:[[ 1.  2.  3.]\n",
-      " [ 4.  5.  6.]\n",
-      " [ 7.  8.  9.]\n",
-      " [10. 11. 12.]]\n",
-      "This is the total mean summed over all elements:6.5\n",
-      "This is the mean for each column:[[5.5 6.5 7.5]]\n",
-      "This is the mean value for each row:[[ 2.]\n",
-      " [ 5.]\n",
-      " [ 8.]\n",
-      " [11.]]\n",
-      "This is the mean value for each row with keepdims false:[ 2.  5.  8. 11.]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"\n",
     "Simple code that tests various numpy functions\n",
@@ -960,19 +930,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Flatten  the matrix:[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]\n",
-      "Reshape the matrix to a one-dim array:[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]\n",
-      "[ 1.  4.  7. 10.  2.  5.  8. 11.  3.  6.  9. 12.]\n",
-      "[ 1.  4.  7. 10.  2.  5.  8. 11.  3.  6.  9. 12.]\n",
-      "[ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10. 11. 12.]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Ravel return a contiguous flattened array.\n",
     "print(f\"Flatten  the matrix:{np.ravel(a)}\")\n",
@@ -2126,7 +2084,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
index 9654f79a0..a692327b8 100644
--- a/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/project1.ipynb
@@ -140,26 +140,20 @@
    },
    "outputs": [
     {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_22981/39730396.py:11: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n",
-      "  ax = fig.gca(projection='3d')\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmpl_toolkits\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mmplot3d\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Axes3D\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/project1_6_1.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -732,19 +726,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'scipy' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [2]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mscipy\u001b[49m\u001b[38;5;241m.\u001b[39mmisc\u001b[38;5;241m.\u001b[39mimread\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'scipy' is not defined"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "scipy.misc.imread"
    ]
@@ -937,7 +919,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
index d905662e4..7b3c02138 100644
--- a/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/statistics.ipynb
@@ -415,18 +415,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/statistics_32_0.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmath\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m acos, exp, sqrt\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -1339,35 +1341,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "2.0543653729690416\n",
-      "[[ 8.75352505  9.52812155  6.26350283  2.23593659  5.0058263  12.34270689\n",
-      "   3.69987647 18.4524458   5.51178587  5.67743788]\n",
-      " [ 9.52812155 10.37126183  6.8177581   2.43379387  5.44879019 13.43490889\n",
-      "   4.0272773  20.08529655  5.99952195  6.17983246]\n",
-      " [ 6.26350283  6.8177581   4.48179077  1.59990347  3.58187211  8.83170827\n",
-      "   2.64741194 13.2034747   3.94390673  4.06243748]\n",
-      " [ 2.23593659  2.43379387  1.59990347  0.57113133  1.27865175  3.15273101\n",
-      "   0.94506946  4.71335815  1.40789038  1.45020332]\n",
-      " [ 5.0058263   5.44879019  3.58187211  1.27865175  2.86265211  7.05835037\n",
-      "   2.11582635 10.55229041  3.1519922   3.24672263]\n",
-      " [12.34270689 13.43490889  8.83170827  3.15273101  7.05835037 17.40355028\n",
-      "   5.21692581 26.01844727  7.77176703  8.00534085]\n",
-      " [ 3.69987647  4.0272773   2.64741194  0.94506946  2.11582635  5.21692581\n",
-      "   1.56383695  7.79934594  2.32968167  2.39969826]\n",
-      " [18.4524458  20.08529655 13.2034747   4.71335815 10.55229041 26.01844727\n",
-      "   7.79934594 38.89778737 11.61885405 11.96804878]\n",
-      " [ 5.51178587  5.99952195  3.94390673  1.40789038  3.1519922   7.77176703\n",
-      "   2.32968167 11.61885405  3.47057708  3.57488231]\n",
-      " [ 5.67743788  6.17983246  4.06243748  1.45020332  3.24672263  8.00534085\n",
-      "   2.39969826 11.96804878  3.57488231  3.68232235]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "from math import exp, sqrt\n",
@@ -1996,23 +1970,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.1999902359008225\n",
-      "4.487000566129411\n",
-      "1.3211480515121596\n",
-      "1.0120561022775605 9.785157020098348 24.0365416391166\n",
-      "2.9740940821517547 3.838584583553216 11.184094793957168\n",
-      "[[ 1.0120561   2.97409408  3.83858458]\n",
-      " [ 2.97409408  9.78515702 11.18409479]\n",
-      " [ 3.83858458 11.18409479 24.03654164]]\n",
-      "[30.9410965   0.08502185  3.80763641]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "from math import exp, sqrt\n",
@@ -2635,22 +2593,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/statistics_181_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "#!/usr/bin/env python\n",
     "import numpy as np\n",
@@ -2759,29 +2702,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-0.026121042099059435 1.0617129312534124\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/statistics_188_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "from math import exp, sqrt\n",
@@ -2837,7 +2758,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week34.ipynb b/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
index 2d131abfd..f91a2fc32 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week34.ipynb
@@ -985,8 +985,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[-1.79544237 -0.19322111  0.14623399  0.65045925 -0.73133982 -1.90092179\n",
-      "  0.45359479  1.04800573 -1.16171326  1.30577095]\n"
+      "[ 0.90148776 -0.63784548  0.61907743 -0.95073282  0.3897131   0.88123172\n",
+      "  0.68407077  1.02936353 -0.85538578 -1.44188631]\n"
      ]
     }
    ],
@@ -1424,26 +1424,36 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[[0.79725436 0.93166184 0.53462883 0.92250132 0.79313278 0.4185877\n",
-      "  0.21601417 0.21037404 0.98496212 0.89482188]\n",
-      " [0.15696119 0.72299619 0.71846708 0.7506246  0.74409239 0.1280756\n",
-      "  0.5316382  0.91236018 0.24479698 0.3435384 ]\n",
-      " [0.5342745  0.2369833  0.47356208 0.16499193 0.60378214 0.9920084\n",
-      "  0.80788856 0.36452684 0.23309661 0.33829607]\n",
-      " [0.7803076  0.17074761 0.15484848 0.82187419 0.69965466 0.85754328\n",
-      "  0.35700089 0.70856363 0.44993812 0.48802709]\n",
-      " [0.06875458 0.23106527 0.28230186 0.40805354 0.54632096 0.11033412\n",
-      "  0.51220693 0.07752967 0.58908017 0.78263078]\n",
-      " [0.62686358 0.14793475 0.11341291 0.46164895 0.32542732 0.42090072\n",
-      "  0.25033968 0.33199489 0.25137033 0.17009925]\n",
-      " [0.74260356 0.49932184 0.99035178 0.5146617  0.9859105  0.8990231\n",
-      "  0.38098948 0.10635754 0.21186069 0.07687896]\n",
-      " [0.92173899 0.87556429 0.04674926 0.70911476 0.43975616 0.37622356\n",
-      "  0.79994469 0.22524236 0.10951119 0.04316854]\n",
-      " [0.3521478  0.25186426 0.59164202 0.44214614 0.09497154 0.97558913\n",
-      "  0.40837841 0.56953559 0.36074377 0.95539206]\n",
-      " [0.33113182 0.3702755  0.31816439 0.83303886 0.51013506 0.6257439\n",
-      "  0.89881026 0.55805262 0.79700882 0.14010994]]\n"
+      "[[9.01367154e-01 4.99358923e-02 8.62083431e-02 4.87662496e-01\n",
+      "  4.35268384e-01 4.95778501e-01 8.47259540e-01 8.19492614e-01\n",
+      "  7.48029002e-01 6.23905282e-01]\n",
+      " [1.27137716e-01 2.21803999e-01 7.73335363e-01 8.12636533e-01\n",
+      "  9.98254070e-01 5.73014312e-01 2.20054803e-01 3.32763666e-01\n",
+      "  9.06059481e-01 8.89711757e-01]\n",
+      " [8.96925518e-02 7.63406517e-01 6.37309895e-01 7.34414668e-01\n",
+      "  5.05136701e-01 8.15223640e-04 8.94612568e-01 4.58800064e-01\n",
+      "  7.05353991e-01 1.57603741e-01]\n",
+      " [8.12532842e-01 9.31595458e-01 3.53618097e-01 9.13032740e-02\n",
+      "  7.90877850e-01 7.77836912e-01 2.21341535e-01 4.30426390e-01\n",
+      "  3.37060503e-01 8.73565723e-01]\n",
+      " [9.00991648e-01 5.91377887e-01 1.24999213e-01 8.88127749e-02\n",
+      "  7.49811765e-01 2.74541956e-01 6.70054572e-01 6.20486376e-01\n",
+      "  3.12715695e-01 9.93767143e-01]\n",
+      " [1.07972608e-01 9.20716385e-01 8.20068837e-01 5.64069531e-02\n",
+      "  1.06786283e-01 2.76784740e-01 7.16634263e-01 7.86140930e-01\n",
+      "  4.32839766e-01 9.78922154e-01]\n",
+      " [4.56496194e-02 9.39925712e-01 4.16339920e-01 8.51501448e-01\n",
+      "  6.50094775e-01 2.69132527e-01 9.01148802e-01 3.82213353e-01\n",
+      "  8.63686244e-02 4.94507958e-01]\n",
+      " [4.44878750e-01 5.09959399e-01 8.90303141e-01 1.35897374e-01\n",
+      "  2.21820632e-01 2.18969262e-01 6.93515781e-01 6.38299113e-01\n",
+      "  2.08291478e-01 4.53609787e-01]\n",
+      " [5.28044814e-01 3.39354674e-01 7.73240597e-02 3.69972328e-01\n",
+      "  4.52291156e-01 2.34048640e-01 7.34023583e-01 2.86689196e-01\n",
+      "  4.68794083e-01 9.14515024e-01]\n",
+      " [2.35728987e-01 5.58997922e-01 1.81586331e-01 7.01875673e-02\n",
+      "  4.86286714e-01 1.91892059e-02 1.99830074e-01 1.38493791e-01\n",
+      "  5.80880777e-01 9.24801038e-01]]\n"
      ]
     }
    ],
@@ -1557,13 +1567,13 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "-0.13314597157635316\n",
-      "3.42745728579187\n",
-      "-0.1549258803307933\n",
-      "[[ 1.0457893   3.16754123  2.39769983]\n",
-      " [ 3.16754123 10.50453066  7.29238177]\n",
-      " [ 2.39769983  7.29238177  8.3431023 ]]\n",
-      "[17.73772319  0.07333967  2.0823594 ]\n"
+      "0.19672699443907488\n",
+      "4.695047732333614\n",
+      "0.5139271024913812\n",
+      "[[0.9118261  2.86708608 1.95090925]\n",
+      " [2.86708608 9.97030515 6.26396287]\n",
+      " [1.95090925 6.26396287 6.36590624]]\n",
+      "[15.50830953  0.07327648  1.66645148]\n"
      ]
     }
    ],
@@ -1595,32 +1605,20 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[1. 0. 0. 0.]\n",
-      " [0. 1. 0. 0.]\n",
-      " [0. 0. 1. 0.]\n",
-      " [0. 0. 0. 1.]]\n",
-      "  (0, 0)\t1.0\n",
-      "  (1, 1)\t1.0\n",
-      "  (2, 2)\t1.0\n",
-      "  (3, 3)\t1.0\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[16], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_74_1.png"
-      }
-     },
-     "output_type": "display_data"
     }
    ],
    "source": [
@@ -1672,79 +1670,7 @@
     "collapsed": false,
     "editable": true
    },
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-       "      <th>First Name</th>\n",
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-       "      <th>Date of Birth T.A.</th>\n",
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-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>Frodo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2968</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>Bilbo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2890</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>Aragorn II</td>\n",
-       "      <td>Elessar</td>\n",
-       "      <td>Eriador</td>\n",
-       "      <td>2931</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>Samwise</td>\n",
-       "      <td>Gamgee</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2980</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "   First Name Last Name Place of birth  Date of Birth T.A.\n",
-       "0       Frodo   Baggins          Shire                2968\n",
-       "1       Bilbo   Baggins          Shire                2890\n",
-       "2  Aragorn II   Elessar        Eriador                2931\n",
-       "3     Samwise    Gamgee          Shire                2980"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import pandas as pd\n",
     "from IPython.display import display\n",
@@ -1778,79 +1704,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
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-       "\n",
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-       "      <th></th>\n",
-       "      <th>First Name</th>\n",
-       "      <th>Last Name</th>\n",
-       "      <th>Place of birth</th>\n",
-       "      <th>Date of Birth T.A.</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>Frodo</th>\n",
-       "      <td>Frodo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2968</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Bilbo</th>\n",
-       "      <td>Bilbo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2890</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Aragorn</th>\n",
-       "      <td>Aragorn II</td>\n",
-       "      <td>Elessar</td>\n",
-       "      <td>Eriador</td>\n",
-       "      <td>2931</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Sam</th>\n",
-       "      <td>Samwise</td>\n",
-       "      <td>Gamgee</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2980</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "         First Name Last Name Place of birth  Date of Birth T.A.\n",
-       "Frodo         Frodo   Baggins          Shire                2968\n",
-       "Bilbo         Bilbo   Baggins          Shire                2890\n",
-       "Aragorn  Aragorn II   Elessar        Eriador                2931\n",
-       "Sam         Samwise    Gamgee          Shire                2980"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "data_pandas = pd.DataFrame(data,index=['Frodo','Bilbo','Aragorn','Sam'])\n",
     "display(data_pandas)"
@@ -1874,21 +1728,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "First Name            Aragorn II\n",
-       "Last Name                Elessar\n",
-       "Place of birth           Eriador\n",
-       "Date of Birth T.A.          2931\n",
-       "Name: Aragorn, dtype: object"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "display(data_pandas.loc['Aragorn'])"
    ]
@@ -1911,95 +1751,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_7752/1326197715.py:6: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.\n",
-      "  data_pandas=data_pandas.append(pd.DataFrame(new_hobbit, index=['Pippin']))\n"
-     ]
-    },
-    {
-     "data": {
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-       "      <th>First Name</th>\n",
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-       "  </thead>\n",
-       "  <tbody>\n",
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-       "      <th>Frodo</th>\n",
-       "      <td>Frodo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2968</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Bilbo</th>\n",
-       "      <td>Bilbo</td>\n",
-       "      <td>Baggins</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2890</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Aragorn</th>\n",
-       "      <td>Aragorn II</td>\n",
-       "      <td>Elessar</td>\n",
-       "      <td>Eriador</td>\n",
-       "      <td>2931</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Sam</th>\n",
-       "      <td>Samwise</td>\n",
-       "      <td>Gamgee</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2980</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>Pippin</th>\n",
-       "      <td>Peregrin</td>\n",
-       "      <td>Took</td>\n",
-       "      <td>Shire</td>\n",
-       "      <td>2990</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "         First Name Last Name Place of birth  Date of Birth T.A.\n",
-       "Frodo         Frodo   Baggins          Shire                2968\n",
-       "Bilbo         Bilbo   Baggins          Shire                2890\n",
-       "Aragorn  Aragorn II   Elessar        Eriador                2931\n",
-       "Sam         Samwise    Gamgee          Shire                2980\n",
-       "Pippin     Peregrin      Took          Shire                2990"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "new_hobbit = {'First Name': [\"Peregrin\"],\n",
     "              'Last Name': [\"Took\"],\n",
@@ -2029,286 +1781,7 @@
     "collapsed": false,
     "editable": true
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-       "      <td>0.342680</td>\n",
-       "      <td>1.153036</td>\n",
-       "      <td>-0.252436</td>\n",
-       "      <td>0.981321</td>\n",
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-       "    <tr>\n",
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-       "      <td>0.514219</td>\n",
-       "      <td>0.221180</td>\n",
-       "      <td>-1.070043</td>\n",
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-       "      <td>0.255001</td>\n",
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-       "    <tr>\n",
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-       "      <td>0.435163</td>\n",
-       "      <td>-0.583595</td>\n",
-       "      <td>0.816847</td>\n",
-       "      <td>0.672721</td>\n",
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-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>-0.104411</td>\n",
-       "      <td>-0.531280</td>\n",
-       "      <td>1.029733</td>\n",
-       "      <td>-0.438136</td>\n",
-       "      <td>-1.118318</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>1.618982</td>\n",
-       "      <td>1.541605</td>\n",
-       "      <td>-0.251879</td>\n",
-       "      <td>-0.842436</td>\n",
-       "      <td>0.184519</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>0.937082</td>\n",
-       "      <td>0.731000</td>\n",
-       "      <td>1.361556</td>\n",
-       "      <td>-0.326238</td>\n",
-       "      <td>0.055676</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>0.222400</td>\n",
-       "      <td>-1.443217</td>\n",
-       "      <td>-0.756352</td>\n",
-       "      <td>0.816454</td>\n",
-       "      <td>0.750445</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>-0.455947</td>\n",
-       "      <td>1.189622</td>\n",
-       "      <td>-1.690617</td>\n",
-       "      <td>-1.356399</td>\n",
-       "      <td>-1.232435</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>-0.544439</td>\n",
-       "      <td>-0.668172</td>\n",
-       "      <td>0.007315</td>\n",
-       "      <td>-0.612939</td>\n",
-       "      <td>1.299748</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>-1.733096</td>\n",
-       "      <td>-0.983310</td>\n",
-       "      <td>0.357508</td>\n",
-       "      <td>-1.613579</td>\n",
-       "      <td>1.470714</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
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-       "          0         1         2         3         4\n",
-       "0 -1.749765  0.342680  1.153036 -0.252436  0.981321\n",
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-       "3 -0.104411 -0.531280  1.029733 -0.438136 -1.118318\n",
-       "4  1.618982  1.541605 -0.251879 -0.842436  0.184519\n",
-       "5  0.937082  0.731000  1.361556 -0.326238  0.055676\n",
-       "6  0.222400 -1.443217 -0.756352  0.816454  0.750445\n",
-       "7 -0.455947  1.189622 -1.690617 -1.356399 -1.232435\n",
-       "8 -0.544439 -0.668172  0.007315 -0.612939  1.299748\n",
-       "9 -1.733096 -0.983310  0.357508 -1.613579  1.470714"
-      ]
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-      "1    0.083527\n",
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-      "0    1.069584\n",
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-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>3.061679</td>\n",
-       "      <td>0.117430</td>\n",
-       "      <td>1.329492</td>\n",
-       "      <td>0.063724</td>\n",
-       "      <td>0.962990</td>\n",
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-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>0.264421</td>\n",
-       "      <td>0.048920</td>\n",
-       "      <td>1.144993</td>\n",
-       "      <td>0.035909</td>\n",
-       "      <td>0.065026</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>0.209789</td>\n",
-       "      <td>0.189367</td>\n",
-       "      <td>0.340583</td>\n",
-       "      <td>0.667239</td>\n",
-       "      <td>0.452553</td>\n",
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-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>0.010902</td>\n",
-       "      <td>0.282259</td>\n",
-       "      <td>1.060349</td>\n",
-       "      <td>0.191963</td>\n",
-       "      <td>1.250636</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>2.621102</td>\n",
-       "      <td>2.376547</td>\n",
-       "      <td>0.063443</td>\n",
-       "      <td>0.709698</td>\n",
-       "      <td>0.034047</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>0.878123</td>\n",
-       "      <td>0.534362</td>\n",
-       "      <td>1.853835</td>\n",
-       "      <td>0.106431</td>\n",
-       "      <td>0.003100</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>6</th>\n",
-       "      <td>0.049462</td>\n",
-       "      <td>2.082875</td>\n",
-       "      <td>0.572069</td>\n",
-       "      <td>0.666597</td>\n",
-       "      <td>0.563167</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>7</th>\n",
-       "      <td>0.207888</td>\n",
-       "      <td>1.415201</td>\n",
-       "      <td>2.858185</td>\n",
-       "      <td>1.839818</td>\n",
-       "      <td>1.518895</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>8</th>\n",
-       "      <td>0.296414</td>\n",
-       "      <td>0.446453</td>\n",
-       "      <td>0.000054</td>\n",
-       "      <td>0.375694</td>\n",
-       "      <td>1.689345</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>3.003620</td>\n",
-       "      <td>0.966899</td>\n",
-       "      <td>0.127812</td>\n",
-       "      <td>2.603636</td>\n",
-       "      <td>2.162999</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "          0         1         2         3         4\n",
-       "0  3.061679  0.117430  1.329492  0.063724  0.962990\n",
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-       "3  0.010902  0.282259  1.060349  0.191963  1.250636\n",
-       "4  2.621102  2.376547  0.063443  0.709698  0.034047\n",
-       "5  0.878123  0.534362  1.853835  0.106431  0.003100\n",
-       "6  0.049462  2.082875  0.572069  0.666597  0.563167\n",
-       "7  0.207888  1.415201  2.858185  1.839818  1.518895\n",
-       "8  0.296414  0.446453  0.000054  0.375694  1.689345\n",
-       "9  3.003620  0.966899  0.127812  2.603636  2.162999"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -2343,195 +1816,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
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-       "      <th>First</th>\n",
-       "      <th>Second</th>\n",
-       "      <th>Third</th>\n",
-       "      <th>Fourth</th>\n",
-       "      <th>Fifth</th>\n",
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-       "      <td>0.055676</td>\n",
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-       "    <tr>\n",
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-       "    <tr>\n",
-       "      <th>8</th>\n",
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-       "    <tr>\n",
-       "      <th>9</th>\n",
-       "      <td>-1.733096</td>\n",
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-       "      <td>0.357508</td>\n",
-       "      <td>-1.613579</td>\n",
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-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "      First    Second     Third    Fourth     Fifth\n",
-       "0 -1.749765  0.342680  1.153036 -0.252436  0.981321\n",
-       "1  0.514219  0.221180 -1.070043 -0.189496  0.255001\n",
-       "2 -0.458027  0.435163 -0.583595  0.816847  0.672721\n",
-       "3 -0.104411 -0.531280  1.029733 -0.438136 -1.118318\n",
-       "4  1.618982  1.541605 -0.251879 -0.842436  0.184519\n",
-       "5  0.937082  0.731000  1.361556 -0.326238  0.055676\n",
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-       "8 -0.544439 -0.668172  0.007315 -0.612939  1.299748\n",
-       "9 -1.733096 -0.983310  0.357508 -1.613579  1.470714"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.08352721390288316\n",
-      "<class 'pandas.core.frame.DataFrame'>\n",
-      "Int64Index: 10 entries, 0 to 9\n",
-      "Data columns (total 5 columns):\n",
-      " #   Column  Non-Null Count  Dtype  \n",
-      "---  ------  --------------  -----  \n",
-      " 0   First   10 non-null     float64\n",
-      " 1   Second  10 non-null     float64\n",
-      " 2   Third   10 non-null     float64\n",
-      " 3   Fourth  10 non-null     float64\n",
-      " 4   Fifth   10 non-null     float64\n",
-      "dtypes: float64(5)\n",
-      "memory usage: 480.0 bytes\n",
-      "None\n",
-      "           First     Second      Third     Fourth      Fifth\n",
-      "count  10.000000  10.000000  10.000000  10.000000  10.000000\n",
-      "mean   -0.175300   0.083527  -0.044334  -0.399836   0.331939\n",
-      "std     1.069584   0.965548   1.018232   0.793167   0.918992\n",
-      "min    -1.749765  -1.443217  -1.690617  -1.613579  -1.232435\n",
-      "25%    -0.522836  -0.633949  -0.713163  -0.785061   0.087887\n",
-      "50%    -0.280179   0.281930  -0.122282  -0.382187   0.463861\n",
-      "75%     0.441264   0.657041   0.861676  -0.205231   0.923602\n",
-      "max     1.618982   1.541605   1.361556   0.816847   1.470714\n"
-     ]
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-    {
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\n",
-      "text/plain": [
-       "<Figure size 1000x600 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_86_2.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x600 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_86_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "df.columns = ['First', 'Second', 'Third', 'Fourth', 'Fifth']\n",
     "df.index = np.arange(10)\n",
@@ -2571,23 +1856,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 0  1  2  3]\n",
-      " [ 4  5  6  7]\n",
-      " [ 8  9 10 11]\n",
-      " [12 13 14 15]]\n",
-      "    0   1   2   3\n",
-      "0   0   1   2   3\n",
-      "1   4   5   6   7\n",
-      "2   8   9  10  11\n",
-      "3  12  13  14  15\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "b = np.arange(16).reshape((4,4))\n",
     "print(b)\n",
@@ -2690,22 +1959,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_93_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "import numpy as np\n",
@@ -2859,22 +2113,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_101_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -2923,36 +2162,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The intercept alpha: \n",
-      " [2.18780801]\n",
-      "Coefficient beta : \n",
-      " [[4.72228205]]\n",
-      "Mean squared error: 0.37\n",
-      "Variance score: 0.83\n",
-      "Mean squared log error: 0.01\n",
-      "Mean absolute error: 0.47\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week34_103_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np \n",
     "import matplotlib.pyplot as plt \n",
@@ -3471,18 +2681,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "'                                                                                                                         \\nThis is taken from the data file of the mass 2016 evaluation.                                                               \\nAll files are 3436 lines long with 124 character per line.                                                                  \\n       Headers are 39 lines long.                                                                                           \\n   col 1     :  Fortran character control: 1 = page feed  0 = line feed                                                     \\n   format    :  a1,i3,i5,i5,i5,1x,a3,a4,1x,f13.5,f11.5,f11.3,f9.3,1x,a2,f11.3,f9.3,1x,i3,1x,f12.5,f11.5                     \\n   These formats are reflected in the pandas widths variable below, see the statement                                       \\n   widths=(1,3,5,5,5,1,3,4,1,13,11,11,9,1,2,11,9,1,3,1,12,11,1),                                                            \\n   Pandas has also a variable header, with length 39 in this case.                                                          \\n'"
-      ]
-     },
-     "execution_count": 29,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"                                                                                                                         \n",
     "This is taken from the data file of the mass 2016 evaluation.                                                               \n",
@@ -3517,21 +2716,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "Length of colspecs must match length of names",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [30]\u001b[0m, in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;66;03m# Read the experimental data with Pandas\u001b[39;00m\n\u001b[0;32m----> 2\u001b[0m Masses \u001b[38;5;241m=\u001b[39m \u001b[43mpd\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mread_fwf\u001b[49m\u001b[43m(\u001b[49m\u001b[43minfile\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43musecols\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m6\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[43m              \u001b[49m\u001b[43mnames\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mN\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mZ\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mA\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mElement\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mEbinding\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      4\u001b[0m \u001b[43m              \u001b[49m\u001b[43mwidths\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m4\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m13\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m9\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m2\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m9\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m3\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m12\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m11\u001b[39;49m\u001b[43m,\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m      5\u001b[0m \u001b[43m              \u001b[49m\u001b[43mheader\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m39\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m      6\u001b[0m \u001b[43m              \u001b[49m\u001b[43mindex_col\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mFalse\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[1;32m      8\u001b[0m \u001b[38;5;66;03m# Extrapolated values are indicated by '#' in place of the decimal place, so\u001b[39;00m\n\u001b[1;32m      9\u001b[0m \u001b[38;5;66;03m# the Ebinding column won't be numeric. Coerce to float and drop these entries.\u001b[39;00m\n\u001b[1;32m     10\u001b[0m Masses[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEbinding\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mto_numeric(Masses[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEbinding\u001b[39m\u001b[38;5;124m'\u001b[39m], errors\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mcoerce\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/util/_decorators.py:311\u001b[0m, in \u001b[0;36mdeprecate_nonkeyword_arguments.<locals>.decorate.<locals>.wrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    305\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(args) \u001b[38;5;241m>\u001b[39m num_allow_args:\n\u001b[1;32m    306\u001b[0m     warnings\u001b[38;5;241m.\u001b[39mwarn(\n\u001b[1;32m    307\u001b[0m         msg\u001b[38;5;241m.\u001b[39mformat(arguments\u001b[38;5;241m=\u001b[39marguments),\n\u001b[1;32m    308\u001b[0m         \u001b[38;5;167;01mFutureWarning\u001b[39;00m,\n\u001b[1;32m    309\u001b[0m         stacklevel\u001b[38;5;241m=\u001b[39mstacklevel,\n\u001b[1;32m    310\u001b[0m     )\n\u001b[0;32m--> 311\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/pandas/io/parsers/readers.py:871\u001b[0m, in \u001b[0;36mread_fwf\u001b[0;34m(filepath_or_buffer, colspecs, widths, infer_nrows, **kwds)\u001b[0m\n\u001b[1;32m    869\u001b[0m                     len_index \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(index_col)\n\u001b[1;32m    870\u001b[0m         \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mlen\u001b[39m(names) \u001b[38;5;241m+\u001b[39m len_index \u001b[38;5;241m!=\u001b[39m \u001b[38;5;28mlen\u001b[39m(colspecs):\n\u001b[0;32m--> 871\u001b[0m             \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mLength of colspecs must match length of names\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    873\u001b[0m kwds[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcolspecs\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m colspecs\n\u001b[1;32m    874\u001b[0m kwds[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124minfer_nrows\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m=\u001b[39m infer_nrows\n",
-      "\u001b[0;31mValueError\u001b[0m: Length of colspecs must match length of names"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Read the experimental data with Pandas\n",
     "Masses = pd.read_fwf(infile, usecols=(2,3,4,6,11),\n",
@@ -5967,7 +5152,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
index 71e93c686..fa5c6c0ea 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week35.ipynb
@@ -1519,7 +1519,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.9952714635635723\n"
+      "0.9947950318641428\n"
      ]
     }
    ],
@@ -1550,7 +1550,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "0.009039197557276654\n"
+      "0.010272505059533654\n"
      ]
     }
    ],
@@ -1585,31 +1585,23 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[6.11430166e-02 7.59428035e-03 7.64295978e-03 5.34442654e-02\n",
-      " 2.53861506e-02 7.46543658e-02 2.79339933e-02 1.32946226e-02\n",
-      " 3.80320028e-03 2.40474117e-02 4.36028477e-02 3.24382528e-02\n",
-      " 1.26022420e-02 5.06848116e-03 1.96793569e-02 1.04826413e-04\n",
-      " 9.25580178e-03 1.80413812e-02 1.22519792e-02 1.01505087e-02\n",
-      " 2.67180442e-02 6.71316703e-02 7.68415876e-03 3.33174939e-02\n",
-      " 1.43570786e-02 8.43459933e-03 4.11046407e-03 9.10453697e-04\n",
-      " 4.33142087e-03 7.64507671e-02 2.19696497e-02 1.18460525e-02\n",
-      " 4.35665906e-02 3.62818572e-02 1.61018347e-03 3.78738205e-02\n",
-      " 4.57031517e-03 3.11279984e-02 1.07745809e-02 7.09848429e-03\n",
-      " 2.30006341e-03 4.62535124e-02 6.70493970e-02 6.26624267e-03\n",
-      " 4.23399553e-02 1.88690267e-02 7.46184816e-03 1.75934097e-02\n",
-      " 3.60820168e-02 1.09322328e-02 3.16749353e-02 2.30626515e-02\n",
-      " 5.76196895e-04 1.51000420e-02 1.95456434e-03 1.22138768e-02\n",
-      " 2.52945186e-03 2.12804129e-03 3.32695433e-03 1.90886410e-02\n",
-      " 1.84291049e-02 1.78104004e-02 6.34498455e-02 1.50032818e-02\n",
-      " 3.43525003e-02 1.52033394e-03 3.95921014e-02 7.67148008e-02\n",
-      " 2.40893740e-02 6.75638425e-02 1.22105472e-02 7.72706640e-03\n",
-      " 3.00721135e-02 8.77081499e-02 1.40684484e-02 4.57081718e-02\n",
-      " 3.51190686e-02 7.42092776e-02 4.03105744e-02 1.08994018e-02\n",
-      " 1.37071826e-02 3.69106251e-02 1.94966662e-03 1.71112140e-02\n",
-      " 3.12669602e-03 3.01610677e-02 1.72139847e-02 2.75703556e-02\n",
-      " 2.23333773e-02 2.76892410e-03 8.05886306e-02 1.15545946e-01\n",
-      " 4.88029792e-02 4.59648068e-02 1.98750794e-02 2.69178261e-03\n",
-      " 1.07925220e-02 1.13151043e-03 5.00620642e-03 3.69871367e-03]\n"
+      "[0.01027068 0.05313438 0.04538489 0.01836177 0.02080937 0.01800647\n",
+      " 0.01875198 0.00467902 0.00753502 0.02005707 0.00232645 0.01531078\n",
+      " 0.03829802 0.00785147 0.04770861 0.04729106 0.01202626 0.05597075\n",
+      " 0.00759075 0.01536802 0.02241641 0.00274849 0.0097933  0.01440849\n",
+      " 0.05803407 0.03087398 0.0131244  0.0291341  0.03955471 0.04581495\n",
+      " 0.0096887  0.02838502 0.00331854 0.00917575 0.02232857 0.01026639\n",
+      " 0.01719879 0.04680163 0.03691034 0.05657464 0.01277062 0.02319192\n",
+      " 0.03410211 0.0114457  0.03498633 0.0345711  0.00908896 0.05115386\n",
+      " 0.01253218 0.00362237 0.03169296 0.06165423 0.0072295  0.00869224\n",
+      " 0.03849245 0.05269447 0.01539813 0.04350167 0.05006792 0.00862396\n",
+      " 0.02270315 0.0141736  0.00537237 0.02931659 0.02817395 0.025761\n",
+      " 0.05417012 0.01227    0.00370021 0.02342548 0.00361816 0.0400444\n",
+      " 0.02198873 0.00914991 0.01461902 0.04424899 0.00910613 0.0099676\n",
+      " 0.02701179 0.03971778 0.04524779 0.05279081 0.01519497 0.00134839\n",
+      " 0.04233422 0.01660753 0.05817493 0.0167955  0.01299388 0.00265975\n",
+      " 0.02189559 0.04726103 0.01705804 0.10695767 0.06613465 0.04663936\n",
+      " 0.00250484 0.02495131 0.01816794 0.01905766]\n"
      ]
     }
    ],
@@ -1660,18 +1652,19 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[ 2.04038959 -0.81343612  7.94304103 -3.83770135  1.70073443]\n",
-      "Training R2\n",
-      "0.9954441212986554\n",
-      "Training MSE\n",
-      "0.008653750612762521\n",
-      "Test R2\n",
-      "0.99255249100346\n",
-      "Test MSE\n",
-      "0.016970019460234076\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[7], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mos\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
     }
    ],
@@ -1928,416 +1921,7 @@
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-       "      <td>-0.276263</td>\n",
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-       "      <th>6</th>\n",
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-       "      <td>1.216290</td>\n",
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-       "      <td>-0.213103</td>\n",
-       "      <td>0.967809</td>\n",
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-       "      <th>9</th>\n",
-       "      <td>-1.557795</td>\n",
-       "      <td>-1.066837</td>\n",
-       "      <td>0.401842</td>\n",
-       "      <td>-1.213743</td>\n",
-       "      <td>1.138775</td>\n",
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-      "text/plain": [
-       "     0    1    2    3    4\n",
-       "0  0.0  0.0  0.0  0.0  0.0\n",
-       "1  0.0  0.0  0.0  0.0  0.0\n",
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-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import sklearn.linear_model as skl\n",
     "from sklearn.metrics import mean_squared_error\n",
@@ -2464,22 +2048,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_146_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -2537,40 +2106,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "MSE before scaling: 0.00\n",
-      "R2 score before scaling 1.00\n",
-      "Feature min values before scaling:\n",
-      " [1.00000000e+00 6.97906022e-03 2.43639284e-03 4.87072815e-05\n",
-      " 1.70037324e-05 5.93601008e-06 3.39931051e-07 1.18670072e-07\n",
-      " 4.14277718e-08 1.44624525e-08 2.37239927e-09 8.28205578e-10\n",
-      " 2.89126914e-10 1.00934327e-10 3.52362157e-11 1.65571174e-11\n",
-      " 5.78009660e-12 2.01783414e-12 7.04426744e-13 2.45915671e-13\n",
-      " 8.58492636e-14]\n",
-      "Feature max values before scaling:\n",
-      " [1.         0.99970894 0.99978365 0.99941797 0.99949266 0.99956735\n",
-      " 0.99912709 0.99920175 0.99927642 0.9993511  0.99883628 0.99891093\n",
-      " 0.99898558 0.99906023 0.99913489 0.99854557 0.99862019 0.99869482\n",
-      " 0.99876945 0.99884409 0.99891873]\n",
-      "Feature min values after scaling:\n",
-      " [ 0.         -1.71761101 -1.75770568 -1.12330033 -1.12591227 -1.12871842\n",
-      " -0.88613493 -0.884669   -0.88323026 -0.88182591 -0.75269037 -0.75050135\n",
-      " -0.74829661 -0.74607851 -0.74384949 -0.6652177  -0.66294408 -0.66064822\n",
-      " -0.65833132 -0.65599456 -0.6536392 ]\n",
-      "Feature max values after scaling:\n",
-      " [0.         1.71737253 1.75576555 2.20916295 2.23971032 2.26995402\n",
-      " 2.60543038 2.63162342 2.65743689 2.68286725 2.94273542 2.96631321\n",
-      " 2.98947894 3.01222822 3.034557   3.24159785 3.26297455 3.28391978\n",
-      " 3.30442964 3.32450054 3.34412923]\n",
-      "MSE after  scaling: 0.00\n",
-      "R2 score for  scaled data: 1.00\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -3105,43 +2641,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "True beta: [2, 0.5, 3.7]\n",
-      "Fitted beta: [2.08376632 0.19569961 3.97898392]\n",
-      "Sklearn fitted beta: [2.08376632 0.19569961 3.97898392]\n",
-      "MSE with intercept column\n",
-      "0.004113634617443139\n",
-      "MSE with intercept column from SKL\n",
-      "0.004113634617443147\n",
-      "Manual intercept: 2.083766322923899\n",
-      "Fitted beta (wiothout intercept): [0.19569961 3.97898392]\n",
-      "Sklearn intercept: 2.0837663229239043\n",
-      "Sklearn fitted beta (without intercept): [0.19569961 3.97898392]\n",
-      "MSE with Manual intercept\n",
-      "0.00411363461744314\n",
-      "MSE with Sklearn intercept\n",
-      "0.004113634617443131\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_181_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -3414,60 +2914,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n",
-      "\n",
-      "    The Boston housing prices dataset has an ethical problem. You can refer to\n",
-      "    the documentation of this function for further details.\n",
-      "\n",
-      "    The scikit-learn maintainers therefore strongly discourage the use of this\n",
-      "    dataset unless the purpose of the code is to study and educate about\n",
-      "    ethical issues in data science and machine learning.\n",
-      "\n",
-      "    In this special case, you can fetch the dataset from the original\n",
-      "    source::\n",
-      "\n",
-      "        import pandas as pd\n",
-      "        import numpy as np\n",
-      "\n",
-      "\n",
-      "        data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
-      "        raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
-      "        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
-      "        target = raw_df.values[1::2, 2]\n",
-      "\n",
-      "    Alternative datasets include the California housing dataset (i.e.\n",
-      "    :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n",
-      "    dataset. You can load the datasets as follows::\n",
-      "\n",
-      "        from sklearn.datasets import fetch_california_housing\n",
-      "        housing = fetch_california_housing()\n",
-      "\n",
-      "    for the California housing dataset and::\n",
-      "\n",
-      "        from sklearn.datasets import fetch_openml\n",
-      "        housing = fetch_openml(name=\"house_prices\", as_frame=True)\n",
-      "\n",
-      "    for the Ames housing dataset.\n",
-      "    \n",
-      "  warnings.warn(msg, category=FutureWarning)\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename', 'data_module'])"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.datasets import load_boston\n",
     "\n",
@@ -3521,32 +2968,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "CRIM       0\n",
-       "ZN         0\n",
-       "INDUS      0\n",
-       "CHAS       0\n",
-       "NOX        0\n",
-       "RM         0\n",
-       "AGE        0\n",
-       "DIS        0\n",
-       "RAD        0\n",
-       "TAX        0\n",
-       "PTRATIO    0\n",
-       "B          0\n",
-       "LSTAT      0\n",
-       "MEDV       0\n",
-       "dtype: int64"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# check for missing values in all the columns\n",
     "boston.isnull().sum()"
@@ -3570,30 +2992,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
-      "  warnings.warn(msg, FutureWarning)\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1170x827 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_199_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# set the size of the figure\n",
     "sns.set(rc={'figure.figsize':(11.7,8.27)})\n",
@@ -3621,32 +3020,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "<AxesSubplot:>"
-      ]
-     },
-     "execution_count": 20,
-     "metadata": {},
-     "output_type": "execute_result"
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1170x827 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_201_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# compute the pair wise correlation for all columns  \n",
     "correlation_matrix = boston.corr().round(2)\n",
@@ -3673,22 +3047,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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-      "text/plain": [
-       "<Figure size 2000x500 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_203_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "plt.figure(figsize=(20, 5))\n",
     "\n",
@@ -3747,18 +3106,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(404, 2)\n",
-      "(102, 2)\n",
-      "(404,)\n",
-      "(102,)\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.model_selection import train_test_split\n",
     "\n",
@@ -3789,24 +3137,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "The model performance for training set\n",
-      "--------------------------------------\n",
-      "RMSE is 5.637129335071195\n",
-      "R2 score is 0.6300745149331701\n",
-      "\n",
-      "\n",
-      "The model performance for testing set\n",
-      "--------------------------------------\n",
-      "RMSE is 5.137400784702911\n",
-      "R2 score is 0.6628996975186953\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn.linear_model import LinearRegression\n",
     "from sklearn.metrics import mean_squared_error, r2_score\n",
@@ -3849,22 +3180,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1170x827 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week35_210_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# plotting the y_test vs y_pred\n",
     "# ideally should have been a straight line\n",
@@ -4531,29 +3847,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[ 1. -1.]\n",
-      " [ 1. -1.]]\n",
-      "test U\n",
-      "[[0. 0.]\n",
-      " [0. 0.]]\n",
-      "test VT\n",
-      "[[0. 0.]\n",
-      " [0. 0.]]\n",
-      "[[-0.70710678 -0.70710678]\n",
-      " [-0.70710678  0.70710678]]\n",
-      "[2.00000000e+00 3.35470445e-17]\n",
-      "[[-0.70710678  0.70710678]\n",
-      " [ 0.70710678  0.70710678]]\n",
-      "[[-3.33066907e-16  4.44089210e-16]\n",
-      " [ 0.00000000e+00  2.22044605e-16]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "# SVD inversion\n",
@@ -5585,18 +4879,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.10790125813226321\n",
-      "4.340071371496255\n",
-      "[[ 1.04193203  3.08165104]\n",
-      " [ 3.08165104 10.18383522]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Importing various packages\n",
     "import numpy as np\n",
@@ -5634,18 +4917,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.08881497884574564\n",
-      "1.7086067479626619\n",
-      "[[1.         0.66080313]\n",
-      " [0.66080313 1.        ]]\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "n = 100\n",
@@ -5704,38 +4976,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[[-0.40620066 -2.01265755]\n",
-      " [ 0.01458611  0.37737221]\n",
-      " [-1.0895387  -3.65442354]\n",
-      " [ 0.2338675   1.12044974]\n",
-      " [ 0.4676059   1.54393936]\n",
-      " [-0.65891389 -3.16304863]\n",
-      " [-0.1715252   0.39197698]\n",
-      " [ 0.71142161  2.95511792]\n",
-      " [ 0.39214397  0.13069442]\n",
-      " [ 0.50655336  2.3105791 ]]\n",
-      "          0         1\n",
-      "0 -0.406201 -2.012658\n",
-      "1  0.014586  0.377372\n",
-      "2 -1.089539 -3.654424\n",
-      "3  0.233868  1.120450\n",
-      "4  0.467606  1.543939\n",
-      "5 -0.658914 -3.163049\n",
-      "6 -0.171525  0.391977\n",
-      "7  0.711422  2.955118\n",
-      "8  0.392144  0.130694\n",
-      "9  0.506553  2.310579\n",
-      "          0         1\n",
-      "0  1.000000  0.952387\n",
-      "1  0.952387  1.000000\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -5781,47 +5022,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "     0         1         2         3         4         5         6         7   \\\n",
-      "0   0.0  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000   \n",
-      "1   0.0  0.078974  0.081276  0.075889  0.077168  0.078540  0.065410  0.066474   \n",
-      "2   0.0  0.081276  0.084076  0.078336  0.079946  0.081655  0.067707  0.069028   \n",
-      "3   0.0  0.075889  0.078336  0.077460  0.078986  0.080616  0.069452  0.070737   \n",
-      "4   0.0  0.077168  0.079946  0.078986  0.080764  0.082653  0.070986  0.072476   \n",
-      "5   0.0  0.078540  0.081655  0.080616  0.082653  0.084809  0.072621  0.074323   \n",
-      "6   0.0  0.065410  0.067707  0.069452  0.070986  0.072621  0.064074  0.065378   \n",
-      "7   0.0  0.066474  0.069028  0.070737  0.072476  0.074323  0.065378  0.066854   \n",
-      "8   0.0  0.067637  0.070457  0.072132  0.074084  0.076150  0.066787  0.068441   \n",
-      "9   0.0  0.068906  0.072000  0.073644  0.075816  0.078110  0.068307  0.070146   \n",
-      "10  0.0  0.055734  0.057835  0.060872  0.062337  0.063894  0.057393  0.058645   \n",
-      "11  0.0  0.056683  0.058996  0.062016  0.063653  0.065390  0.058552  0.059951   \n",
-      "12  0.0  0.057722  0.060254  0.063260  0.065077  0.066999  0.059807  0.061359   \n",
-      "13  0.0  0.058854  0.061614  0.064609  0.066612  0.068727  0.061163  0.062874   \n",
-      "14  0.0  0.060083  0.063080  0.066066  0.068264  0.070582  0.062624  0.064501   \n",
-      "\n",
-      "          8         9         10        11        12        13        14  \n",
-      "0   0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  0.000000  \n",
-      "1   0.067637  0.068906  0.055734  0.056683  0.057722  0.058854  0.060083  \n",
-      "2   0.070457  0.072000  0.057835  0.058996  0.060254  0.061614  0.063080  \n",
-      "3   0.072132  0.073644  0.060872  0.062016  0.063260  0.064609  0.066066  \n",
-      "4   0.074084  0.075816  0.062337  0.063653  0.065077  0.066612  0.068264  \n",
-      "5   0.076150  0.078110  0.063894  0.065390  0.066999  0.068727  0.070582  \n",
-      "6   0.066787  0.068307  0.057393  0.058552  0.059807  0.061163  0.062624  \n",
-      "7   0.068441  0.070146  0.058645  0.059951  0.061359  0.062874  0.064501  \n",
-      "8   0.070213  0.072111  0.059993  0.061452  0.063019  0.064699  0.066500  \n",
-      "9   0.072111  0.074210  0.061443  0.063061  0.064793  0.066647  0.068629  \n",
-      "10  0.059993  0.061443  0.052305  0.053417  0.054617  0.055910  0.057300  \n",
-      "11  0.061452  0.063061  0.053417  0.054655  0.055987  0.057418  0.058952  \n",
-      "12  0.063019  0.064793  0.054617  0.055987  0.057457  0.059031  0.060716  \n",
-      "13  0.064699  0.066647  0.055910  0.057418  0.059031  0.060756  0.062599  \n",
-      "14  0.066500  0.068629  0.057300  0.058952  0.060716  0.062599  0.064606  \n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import numpy as np\n",
@@ -6905,7 +6106,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week36.ipynb b/doc/LectureNotes/_build/jupyter_execute/week36.ipynb
index d15ac0234..f0646a41d 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week36.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week36.ipynb
@@ -397,8 +397,8 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m<cell line: 3>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      2\u001b[0m X \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray( [ [\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m],[\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m4\u001b[39m,\u001b[38;5;241m5\u001b[39m],[\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m6\u001b[39m]])\n\u001b[0;32m----> 3\u001b[0m Xinv \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinlag\u001b[49m\u001b[38;5;241m.\u001b[39mpinv(X)\n",
-      "File \u001b[0;32m~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/__init__.py:313\u001b[0m, in \u001b[0;36m__getattr__\u001b[0;34m(attr)\u001b[0m\n\u001b[1;32m    310\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mtesting\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Tester\n\u001b[1;32m    311\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m Tester\n\u001b[0;32m--> 313\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mAttributeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmodule \u001b[39m\u001b[38;5;132;01m{!r}\u001b[39;00m\u001b[38;5;124m has no attribute \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    314\u001b[0m                      \u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{!r}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\u001b[38;5;18m__name__\u001b[39m, attr))\n",
+      "Cell \u001b[0;32mIn[1], line 3\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      2\u001b[0m X \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray( [ [\u001b[38;5;241m1\u001b[39m,\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m3\u001b[39m],[\u001b[38;5;241m2\u001b[39m,\u001b[38;5;241m4\u001b[39m,\u001b[38;5;241m5\u001b[39m],[\u001b[38;5;241m3\u001b[39m,\u001b[38;5;241m5\u001b[39m,\u001b[38;5;241m6\u001b[39m]])\n\u001b[0;32m----> 3\u001b[0m Xinv \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlinlag\u001b[49m\u001b[38;5;241m.\u001b[39mpinv(X)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/numpy/__init__.py:313\u001b[0m, in \u001b[0;36m__getattr__\u001b[0;34m(attr)\u001b[0m\n\u001b[1;32m    310\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mtesting\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Tester\n\u001b[1;32m    311\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m Tester\n\u001b[0;32m--> 313\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mAttributeError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mmodule \u001b[39m\u001b[38;5;132;01m{!r}\u001b[39;00m\u001b[38;5;124m has no attribute \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m    314\u001b[0m                      \u001b[38;5;124m\"\u001b[39m\u001b[38;5;132;01m{!r}\u001b[39;00m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;241m.\u001b[39mformat(\u001b[38;5;18m__name__\u001b[39m, attr))\n",
       "\u001b[0;31mAttributeError\u001b[0m: module 'numpy' has no attribute 'linlag'"
      ]
     }
@@ -4260,7 +4260,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
index 5586b0735..2e79f07db 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week37.ipynb
@@ -2018,12 +2018,19 @@
    },
    "outputs": [
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Bootstrap Statistics :\n",
-      "original           bias      std. error\n",
-      "  99.971  15.2789        99.9715        0.152907\n"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mtime\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m time\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
      ]
     }
    ],
@@ -2086,22 +2093,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_144_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# the histogram of the bootstrapped data (normalized data if density = True)\n",
     "n, binsboot, patches = plt.hist(t, 50, density=True, facecolor='red', alpha=0.75)\n",
@@ -2312,32 +2304,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Error: 0.013121574062587286\n",
-      "Bias^2: 0.012073649469946107\n",
-      "Var: 0.0010479245926411787\n",
-      "0.013121574062587286 >= 0.012073649469946107 + 0.0010479245926411787 = 0.013121574062587286\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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nfd0X39LSQnFxMYWFhWzbto3f/va3XHrppXzrW99i8eLFAIwZM4b29nb+/Oc/c/jwYV544QX++te/upxn5MiR1NfX89FHH1FeXk5jYyMjRowgLCzMPG7lypU88sgjAa3r888/53e/+x0HDhzgL3/5C//973+5/fbbAbjwwgs55ZRTuPrqq9m2bRtbtmxh8eLFnHPOOcyYMaPTP4uRI0eyfv16CgsLKS8vB/RamTVr1pCfn8+2bdv4+OOPuyR4BEHwjGF2Niol2qU2JNOPC6tN1bj3zV0yj0boMkGLkfr6enbs2MGOHTsAyM/PZ8eOHWYdwn333WdeSAGuuuoqkpOTue6668jLy2P9+vX8/Oc/5/rrr/dawNpb9HVf/OrVq8nMzGTkyJHMnz+fTz75hKeeeop33nnHrK+YOnUqTz75JI8//jiTJ0/mpZdeYunSpS7nmT17NjfddBNXXnklqamp/O53vyM1NZUVK1bw3//+l9zcXB577DGeeOKJgNb1f//3f3z11VdMmzaNRx55hD/84Q9cdNFFAKa3TGJiImeffTYXXngho0eP5tVXX+3Sz+Lhhx/myJEjjBkzhtTUVABsNhu33norEydOZP78+YwfP57ly5d36XkEQeiIsw28M0ZHTaGXyMjTH3/jc5CezKMRAkXRgpkPje5rcd5553XY/sMf/pAVK1Zw7bXXcuTIEZc2z3379vGzn/2Mzz//nOTkZK644goeffTRgMVIbW0t8fHx1NTUdEjZNDc3k5+fz6hRo4iI6Fw6ZfXuIh56N88lzJgZH8GShblDri9+5MiR3HHHHS4dPAOB7ngfCMJQ5b43d/LylmPcdv5J3DVvvLn9uY1HWLJyDxdNSudv17hGPm2qxvRH1lLd5H+q75++N5VLpw7r9nUL/R9f129ngm7tPffcc/GlX5zNugwmTJjA2rVrg32qXkP64gVBGMq4d9IYGDUjnroOt+RXBiREoOt1dwdK6lh/oIwfzh5JqFWmmAxGetxnZKAgffGCIAwFbKrW4cbL8BjpmKbx7sIaaJdhQlRol+vulryzh02HK8iMj+SSU4ZWtHqoIGJEcOHIkSN9vQRBEHoITynp9Nhwyuv1dv9RdsMzA0OMlNe30tJuIzzE4RUUaLTjutmjuhRl1jSNPSdqAMgrqhExMkiReJcgCMIQwFsLbond0CwxKpTocNf708SoUCJC9ctEsdtxRjeiL+IirMwYmdglI7SS2hZqm/XBod+U1PvZWxioSGREEARhAKJpGrXN7cRHhvrd19foC4OGVlsH23dFUciKj+RweQOF1U3kJDsiJ0Y34k0vbvP+vBpc/c8vzO870xhwoKTO/P83pSJGBisSGREEQRiA3PvGLqY89AG7jtf43dff6AuA1nbVYwtupr2915PXyPzJmZwzLqXD9rAQ/dLS0OJqZNgZIzRnMXK0ooHmto7miMLAR8SIIAjCAOOro5W8ulV3Qd5+rMrv/l0ZfZEV772IVdM09hfr0YpfXDSeP31vKi/dcDpxEZ6D7p0xQnMWI6rmMGgTBhciRgRBEAYQqqrx8HuOoZRVDf7ba7sy+sJwYT3hIbKyq7CG4tpmosKsXH/mKC6dOgyLRTELYj0RrBHafnudiDH66pvSOh97CwMVqRkRBEEYQLy78wRfH6s2v69q9D/40ig2La5p9lo3khQd5rEFN8v0GukYGflgTwkA545LIaLgMzi6gcSiGq63NrBfHcHn2sno8qNjN00g0RpV1Thoj4zMyEnkyyNVUsQ6SJHIyBDgwQcfZOrUqX29DEEQukhzm43frd4PwDB7xCIQMeJr9IXBbeeN8diC68tr5IO8YgDmHX4cXrgU1v+eCd/8nQdCX+LFsKVkUgEoXGddxRmWPCw4JnUHEq0prG6iodVGqFVhbm464Jq2EQYPIkb6kGuvvRZFUVAUhdDQUEaPHs3dd99NQ4PkRAVhKGFTNTYdqvDbAvuvDfkUVjeRFR/BzeeOAaCywb8YAb3Y9JkfnEqGl3bcZ9Yf9lhYmuWlgPVIeQMHSuoJoZ3zbJ93OE5RIFmpBeBsy25eCXuUDeG3Md+yJeABpEZKZnRKDLmZ+uT3g9JRMyiRNI2BaoOjG6G+BGLSIWc2WKz+j+si8+fP59///jdtbW189tln3HjjjTQ0NPDMM8+47NfW1kZoqP8WPkEQBhaBzsYqq2th+ScHAbhnwQRi7UWivgbVuTN/ciaqCrf8p2M7bmltCze/uI1nrp7C/Jh887MwM2MmAHUt7dQ2txEXoX8Ord2jC5fTLfuIVzzfQMUpDaBBDXpLcAaVLA9dxtenjg7ICM0ojh2XEcvYdN0d9oi9oyYitOc/n4XeQyIjAHkrYdlkeO5b8MYN+r/LJuvbe5jw8HAyMjLIzs7mqquu4uqrr+btt982UyvPPvsso0ePJjw8HE3TqKmp4cc//jFpaWnExcVx/vnn8/XXX7uc87HHHiM9PZ3Y2FhuuOEGmpsDq6QXBKF38WZE5qkF9sm1B2hotTElO4GFp2SREBUGBB4ZAT0C88j/8jw+pgEXWbYw7Y2zXT4Lo5+ZSnyYHqkxoiP1Le288+U3AMyzbPX6fPHoIqVG08WIRdEjJtP2PA6H1sGu1yH/M/1m0APf2FMy49JiSIsNJy4iBFWD/HKJHg82RIzkrYTXFkPtCdfttUX69l4QJM5ERkbS1qbf6Rw8eJDXXnuNN954gx07dgBwySWXUFxczKpVq/jqq6849dRTueCCC6is1CvTX3vtNZYsWcJvfvMbtm7dSmZmJsuXL+/V1yAIgn98GZE5t8C221Re2HSEV78sAODXl0zEYlFIsouR6gBqRgx8+Y1cZNnC8tBlpGoVrg/UFpHZpj/3iZomPswrYd6Tn7K7XCWMVuZZfYgRe8SklihzmwJQW6jXmPi5+dtviJGMWBRFYWx6LCB1I4ORoS1GVBusvgd8fRysvterau9utmzZwn/+8x8uuOACAFpbW3nhhReYNm0ap5xyCp988gm7du3iv//9LzNmzGDs2LE88cQTJCQk8PrrrwOwbNkyrr/+em688UbGjx/Po48+Sm5ubq+sXxCEwPFnRGa0wH7v75v59Tt7UDW4ckY2M0bqtRaJdjHS0GqjpT2wzyjvHSwaS0KfB/TohftjwxRdoCx5Zzc3Pr+VEzXNZMcq/Dv092Qq3lt03SMjXvFw82dTNbM+ZJxdhIyzp2o81Y18U1LH0vf30tja7vu5hH7J0BYjRzd2jIi4oOkK/ujGHlvCe++9R0xMDBEREcyaNYuzzz6bP//5zwDk5OSQmppq7vvVV19RX19PcnIyMTEx5ld+fj6HDh0CYO/evcyaNcvlOdy/FwSh7wnUiGzr0SpCrQq//lYuj11+srk9NiLErLsItG7EuYPFgkoGusg4WTlMllLpQYjoZNrFSEFlE1aLwk3njOGD/7uQOQm+vULi7JERo2bEOx1v/goqG2lpVwkPsTAiSY+snJTmPTJy75u7+Nunh3lre6Gf5xL6I0O7gLW+pHv36wTnnXcezzzzDKGhoWRlZbkUqUZHu/4Bq6pKZmYm69at63CehISEHlujIAjdT6BGZJnxEfxj8QwmD4t32W6xKCREhlLR0EplQyvpcf7PZ/iNTKlbzwOhz/Obth/wPzWZb1s3+DxumuUgL9rmMiVZZenV55CbFac/sOB38No1Xo8LODICuNz8jTrLFBwnpenRkE2HKiiv14f6uXuNnKhu4qujuhOtJ9t6of8ztMVITHr37tcJoqOjOemkkwLa99RTT6W4uJiQkBBGjhzpcZ+JEyeyefNmFi9ebG7bvHlzdyxVEIRuJBAjsshQC2vuOJs4L8PwEqPDqGhopSrAIlYrKs+P/oiT8v4CQImWCEC64ttS/nLrZ5xu2UvW5f/GYggRgNxFcMUL8O5t0NTxHEbNSGBixI795u9AsS5GYsJDOPPxj11SWofLG3j360IWThkGwP92Ogp9y+xTiIWBxdBO0+TMhrgsvNsAKRA3TN+vH3DhhRcya9YsLrvsMtasWcORI0fYuHEjv/rVr9i6VS8iu/3223n22Wd59tlnOXDgAEuWLGHPnj19vHJBENwJxIjskUsnexUigFnEWhVImiZvJfx+DGP3/gXF3tVSgqsY8T4tRmF4fDiWkXM6PpS7CH5+CK55B87+OUxYBOG6YDEjI37TNE7Yb/4O2OtCvvBSW/Ozl3eY3Ubv7XKIESN6IgwshrYYsVhh/uP2b9w/Duzfz3+sV/xGAkFRFFatWsXZZ5/N9ddfz7hx4/je977HkSNHSE/X/4CvvPJKHnjgAe655x6mT5/O0aNHufnmm/t45YIgeMKXEVlCVCjfmZHt8/iEKF2oVPrrqMlbqadTnKIXmgYlWgIAaejbPYuiAD4LLVYYcy6c/yv43gtwzxH44XvEn38HALWR2bB4JcRmdniWfDWD1bYZaJrrzd/+4lrfrwm92+hIeYOLPX6ZiJEBiaJpWmCjE/uQ2tpa4uPjqampIS4uzuWx5uZm8vPzGTVqFBERgeVgO5C3Uu+qcS5mjRum//HlLurCyoXeolveB4LQR9hUjS35lZTWNbPjWDX//vwI509I49lrT/N53L1v7OSVL4/xf3PH8bMLxnreSbXprbNuxfrVWjRTW/4BwP7wxYQrXrpQuvBZmF/ewHlPrCM6zMqeh+c7rBQAIw7z3ZYH+FKbwNKQf/L9q66D3EW02VQm/Hp1QJN9vz9zBC9vKSApOozKhlYy4yPYdN8FQa9V6Bl8Xb+dGdo1Iwa5i2DCJX3iwCoIgmC1KMwakwzA5sN658rEzFi/x5nGZ74iI166Bo16kUTqOgqRi36rfw528bMw3p5iami10WZTCc1dBFc873LzV6ClAfA76w0sGDmPBHSr+UCECMBn35QBcNXMETz9yUHK61vQNA1F8e/wKvQfRIwYWKww6qy+XoUgCEOcvCK9cNOYxeKLpGj9Yu+ztddLN6DX4tW4YXD6Td1yMxYX4bjE1Da1kRwT7nLzp9WVUPlKJKhQ1aLwxAf7efSykzkQxGTe41V6u/EPzsjh6U8O0mbTqGlqM4WaMDAY2jUjgiAI/Qibqpm1ErlZ3kPaBgFZwnvpBjTESJq7GOnGOrkQq4WYcF2Q1DY7RV/sN3/14y6lzTHIl5e+KGB3YY3pvBoZavVa3AsQE66vc/aYZDLiI8xIjBSxDjxEjAiCIPQT8ssbaG5TiQqzkpMU5Xf/gCzhza5BV0pxj4xY4LvPdXudnCEQapo6Rm+qGvRtkaFWFk3JQtPggXd2m4LskpMzAO/dRkYm51un6AMFU2PDASiV9t4Bh4gRQRCEfkJekX4RnpARiyWAqbaJ0QF007h0DTow0zT2Thq+82+YdFlwCw6AOB9ixFh3UnQY9188kagwK9sKqvlwbykAi6YO89htFGrVfzaNrTZCLAoXTdJFS0qMLs7Ea2TgMWhqRgZAU5DQg8jvXxgM5J3QxcjETP8pGnDMp6lu8OMzYpqT3Q5NuoW70dabHtYK332hxzoH4yP1y4xHMdKgi4ak6DAy4iO47YKxPPb+PrN4dVx6LBnxEczNzTC7jdJiI3hr+3Fe23ocgDPHppjpqlS7q215feDDA4X+wYAXI4Z9emNjI5GRkX28GqGvaG3VP3ysVumAEgYue4sCrxcB/SIOUNfSTmu7SliIj2C3UTh6ZAPkf0bJlnFQA2mXPwa5HdM43YWvNE2lXUQl2l/H9XNG8drWYxwuayAuIoT0OD3tYkVlliUPrCVgSWdPmmO93zrF8X+JjAxcBrwYsVqtJCQkUFqqh/WioqKkpWuIoaoqZWVlREVFERIy4N/SwhDGSNPkBhgZiYsIxaLotRPVja2k+ZtPY7HC6HNg9DmUbvkIaCY93n9tSlcwxEitx5oRe5rGbt4WFmLhkUsn88Nnt3Dm2BT9s9yDD9TY8HOBHxNmtTA311Gga9SMSAHrwGNQfHJnZOj5QkOQCEMPi8XCiBEjRIgKA5ayuhbK6lpQFBif4d9jBOzD8qJ0s6+qxjb/YsSOqmpmkWdGgMd0Fl+RkQpDjESHm9vmnJTChnvO191lTZM01zTsrOYNLLRMZsq0M8zzA6TE6OeRyMjAY1CIEUVRyMzMJC0tjba2wEZpC4OLsLAwLBapxxYGLkaKZlRKNFFhAX40qzYSQtupBCoPbYW0swNqy61sbKVd1VAUR2qjp4iLsIsRD14oZmQk2nX+TkZ8hO4cu/oePE3MCVPa+XPYX6DgLVAvNl+zERkRMTLwGBRixMBqtUrNgCAIAxIjRRNo8Sp73ob//R9JNbdymPFUr/4NfHGL3jnjpxi1pFYfPJcSE06ItWdFfHyU/24ao2bEBS/OsQ40qC3U97MbVqbGSJpmoCK3koIgCP2AvcHUi3zwa/jvD6GxnARFNwir1GL1i/dri/X0hg9Ka/WLtVEg2pOYNSPNngpYdTGS7EmMeHGO9bWfERmpaGhFDdBOXugfiBgRBEHoBxhtvX7FyO63YeNT5rdJdjFSjVFnosHqe/U0hxeMyEh6bM8PlfTlM2KkaRI9Wbd7cY71tV9SdBiKojvZVvmbZCz0K0SMCIIg9CI2VWPToQre2VHIpkMV2FSN5jYbh8r0eSw+23pVG6y6y2VTIvpxlZpT0auRvvBCiT0yEmjBa1fw2drrZHrWAdM51ltRuqLP0cmZbW4JtVpMYVMmqZoBxaCqGREEQejPrN5dxEPv5lFU02xuy4yP4NrZOaianq5Ii/WROjm6ERorXDYl2iMjVVqM674+0hwldfbISC+madzFSLtNNbd5rBkxnGNfW4wuSJzTLnaB4mGOTmpMOJUNrZTVtTAho5tehNDjSGREEAShF1i9u4ibX9zmIkQAimuaWfr+fkAvXvXZnu5BYBiRkSrc2oF9pDlKjTRNL0ZG6prbTWdVgOqmNjQNFAUSIkM9H5y7CK54HuIyXbfHZenbPRTqpsTqwkaKWAcWQYuR9evXs3DhQrKyslAUhbfffjvgYz///HNCQkKYOnVqsE8rCIIwYLGpGg+9m+ehSdX1fn9Cph9/EQ8Cw2NkJCrFJX3hTkkfFLAC1DkVsRr1IvGRob47enIXwR274YfvweX/0v+9Y5fXjqFU8RoZkAQtRhoaGpgyZQpPP/10UMfV1NSwePFiLrjggmCfUhAEod/hqfbDG1vyKztERDwR5q/N1sMEXqOA1SUycskffPqNFNsjI2m9UMAaarUQFaavxTlVU2m6rwbgc2Kx6u27J39H/9fHa3O4sEoB60Ai6JqRBQsWsGDBgqCf6Cc/+QlXXXUVVqs1qGiKIAhCf8Nb7ceShbnMn5zZYf/SOv9CBCA2ws9HsksdhS5+Eow0jVHAOvs2n9N3222qmcLojTQN6NGPxlabRzHisV6kC4gL68CkV2pG/v3vf3Po0CGWLFkS0P4tLS3U1ta6fAmCIPQHfNV+3PziNlbvLupwTKARiMnD4v3vZNZR6BESIzJSSzTN314B8x7xeXh5fSuaBlaL4tnfowcwXVidxYivTpouIC6sA5MeFyPffPMN9957Ly+99FLAQ8yWLl1KfHy8+ZWdnd3DqxQEQfBPILUfD72b1yFlM3NUEpnxEV6bVAFCLAqzx6QEtpDcRayeu5ZbQh9mSesPzWc/+91Yj2LImRIzRROOxdI7s5wcw/LazW1VwaRpgiBFXFgHJD0qRmw2G1dddRUPPfQQ48aNC/i4++67j5qaGvPr2LFjPbhKQRCEwPBX+6EBRTXNbMmvdNlutSgsWZgLeHfNmD85A2uA4mD17iJufulrVtWdxLvabPOspXUtXqMzBqYY6aUUDXg2PqvooTSNREYGJj0qRurq6ti6dSs//elPCQkJISQkhIcffpivv/6akJAQPv74Y4/HhYeHExcX5/IlCILQ1wRa++Fpv/mTM3nmB6fqQ+DcUID7Lp4Y0Ll9RWcMPEVnDErsF+l0X34m3Ywnr5EqX1bwXcCIjFQ2ttJuU7v13ELP0aOmZ3Fxcezatctl2/Lly/n44495/fXXGTVqVE8+vSAIQrcSaO2Ht/3mT85kbm4GW/IrKa1rZt3+Mt7aXsiZY1MYlhAZ0LmDic7MGpPc4fHe9Bgx8CRGKht9GJ51gaToMCwKqJpeJNubESCh8wQtRurr6zl48KD5fX5+Pjt27CApKYkRI0Zw3333UVhYyPPPP4/FYmHy5Mkux6elpREREdFhuyAIQn/HqP0ormn2GJlQgIz4CGaOSvJ6DqtFYdaYZGyqxmPv7wPgytMCr4sLJjpTWN3E6t3FfOfU4cRHhWJTNXYdrwGgpV3FpmoBp4a6gkcx0qBHaJKivRiedRKrRSE5JpyyuhZK61pEjAwQgk7TbN26lWnTpjFt2jQA7rrrLqZNm8YDDzwAQFFREQUFBd27SkEQhH6Ar9oP4/slC3MDusCv/6aMoppmEqNCmZsb4FA4govOLF21l0fey+P/PfM5L2w6wpmPf8y6A2UAvLb1GGc+/rHfgtfuID5Sv++tdUnT2CMj3VzAClLEOhAJWoyce+65aJrW4WvFihUArFixgnXr1nk9/sEHH2THjh2dXK4gCELf4q32IyM+gmd+cKpHnxFPvPalXph/2bRhhId4N/Fyx19njoLueXLayEQ2HdLn2Bwua+DX7+wJqh25O4mP8hQZMWpGur92RYpYBx4yKE8QBCFI3Gs/0mL11Iy/iIhN1diSX8nhsno+yNPnzFwxw56iUW36ILz6Et32PWe2R6dRIzpz84vbOoyPM1iyMJejlY1UNLQSFmJBVTXaPRS0auji5aF385ibG3g3T7C4p2maWm00tdkASOzmNA1ASoxM7h1oiBgRBEHoBEbtR6B4cm0NtSocrWhgYtU6WH0P1J5wHBCXpbutepjBMn9yJn+56lR+9c5uM8IAEB5i4U/fm8r8yZm8vEVPl49JjWZvUZ3XdfkreO0O3E3PDMOzUKtCTHj3X4ZMS/g6sYQfKMjUXkEQhB7Gm2trm03j7f/8Fe21xa5CBKC2SLd9z1vp8XyP/C/PRYgAZCVEmmkiw+tkRFJUQGsMtDC2M5imZ/ZBeabhWXSY7ynFncQclieRkQGDiBFBEIQexJcviILKA6HPo/nydF19r57CseNN2ADklzeY9R+GGJme472zx5meHJrncGBtQ1U1x1yaHiheBefIiIiRgYKIEUEQhB7Ely/I6ZZ9ZCmVPj6INagt1GtJCNzwrKCikcLqJkIsCt+fmR1QwauvduSuYjiwqhrUt7Y7Jvb20GwciYwMPESMCIIg9CC+0h8XKl8FdpJ6vdjVn+EZ6PUfr3yp14tMGhZPbERot7Ujd5aIUCvhIfrlpqaxrccm9hqkSDfNgEPEiCAIQg/iLf2hoPL/QjYEdpIY3Yck0LqO7QXVAJxuj3Z0VztyV3DuqKlq7BkreAMjMlLT1EZLu83P3kJ/QLppBEEQehBvrq2nW/aRrHjvcjGJStHbfAm8ruNoRYP+3CMdqZfOtiN3F/GRoZTWtVDb1OYYktdDNSPxkaGEWBTaVY2K+layArTaF/oOiYwIgiD0IM6urc6kUR3YCU65wvQb8Wd4BpAQFcqJmmYUBU4b6VoHYrQjXzp1GLPGJPeaEAG3yEgP14xYLIq4sA4wRIwIgiD0MEaaJDLUYWJWSkJgB4+/2PyvLzt6c/f0WPNfw/m0P+AsRnq6gBUgJdZufCZ1IwMCESOCIAi9wPzJmZyUFgPA9XNGcvt1P0SLy8K7rFAgbpiZonE+j6f6D6NAdG9RLUCPdsd0Bk81Iz0pRsyOGhEjAwKpGREEQegFbKrGgRK9RmRxdjkjm/fCqdfCuqXQwdjdLlDmP+bREt5T/cdrW4/x1vZCapvbgf4nRuI8REZ6qmYEnLxG3NI0hiV/X9TNCN4RMSIIgtALHKlooKVdJZJWRrx1KSh28RGZCCjQVOnYOS5LFyIerOAN3O3oP9pb4vL4zJH9U4xUN7VR1ag7sfZomsZDZMSTJX9mfARLFub2SkeR4B0RI4IgCL3Avi8/BqyMUwqwKE5RkKZqQINz74fkMT6H5PnC2bNjVEo0aXE956jqC2+RByNNc7yqCZt9aF9PDMkzcERG9CiM4VzrbhhnTC7urRZnwTMiRgRBEHoa1cb+LR8AC5hoKXB70D47d9tzcMeuoEWIgXPKo6+iIr4iD4YYOVKutx3HhIcQHtK51xoIzpERX861vTW5WPCNFLAKgiD0NOufYG9rKgDjlWMednC1fe8MiU6dM6f1Qb2It5k5RuThUKleL3O8qhHo2agIOCIjZfUtfp1rnScXC32DiBFBEIROYFM1Nh2q4J0dhWw6VGGmHjqg2uCL5ezTRgAwQXGPjDhRX+L9MT84p2lO72Ux4i/yAPDa1uOAPp8GICk6vEfXlGYXIyeqmyiobAjomJ6cXCz4RtI0giAIQbJq5wl+9c5uKhvazG1eCyGPbqS+sZljWhoAEyyeIiN27LbvnSEnOQpFgVHJ0QxP7F3H0UAiD4brqkFSD3ugjEyOZnRqNIfLGsg74XC6taAy07KPNKopJYEt6gRU+315T04uFnwjYkQQBCEIlq7K42/r8ztsL/JWCFlfwn4tG4AMKkhU6j2fODKpg6dIMGTGR/LOrXNIiQlHUXq37qEzEYWeGpJnYLEoXDd7JL9+Zw+fHiglIy6cqfWf8UDo82QpjnTMCS2Jh9sW83Xs2f2uHXooIWkaQRCEAFm1s8ijEDHQ0AshXVI2MensU3UxMt5XVOT0mzpdvGpwyvCEPpnD0pmIQlIPeowYfPvU4cRGhHCkopEbckpZHrqMDFzrQjKoZHnoMpafelyKV/sQESOCIAgBYFM1fvXObr/7dSiEzJnNvtCJgI96kcgkOPvu7lhmn+BvZo4CZMSFE2Z1XHKSYnpejESHh/C903QhuH5fMYoC7nrDooCiKEzb87he39NJ6prbKKpp6spyhzQiRgRBEAJgS36l6RzqD5e0hcXK/lg9/TLRW2Rk4Z+6HBXpS3zNzDG+f3DRJOIiHZUBvREZAVg8ayQWBT5rG89BdZjHfZRu6Gb6/j82c+7v18lgvk4iYkQQBCEAgqmLcE5baJrG3lq9WHN8rNs54obBFS/4dFodKHibmZMRH2HW0RgurNDzNSMG2UlRzB2uRzz+bbvI986d7GZSVY29RXW0tKum5b9BwF1XQxwpYBUEQQiAQOsikqJDXQohT9Q0U9fcTohFYcwda6Bws37R66TTan/G08wc59kv8U5iJLmXxAjAdVNjWXOskTdtZ/GLkFdJULy0+naym6m6qc0UGSeqHYJT7OcDRyIjgiAIAWDURfjj0UsnuxRC7i/Wp+ielBZDWFgojDoLTv6O/u8gEiIGxsycS6cOY9aYZJefRXwfREYATj/jLCaGFNJMOK/YzvOwh+cJyYHinJopqtbrRvyZwK3eXdSp5xqsiBgRBEEIAKMuwle/xazRSVx8SpbLtr1Feth+QkZsD65uYOAsRnqrZgRAsYZw3Uw9EvF8+zzaNedLn+8JyYHgLEZO1DQFZALXoetqiCNiRBAEIUCMuoj0OFf30Ogw/SKWV1RHTWOby2P7inUxMj4jzue5h0JtgSFGLIqrMOkNFi24mOQIjROk8KE63fFAXBZc8XyX6naMYXygp2nEfj54pGZEEAQhCOZPzmRseiwX/OFTwkIsPHfdTKbnJLLwzxvYX1LHX95ex/0n15g1IfuK9DTNhEzvkZGhUltgCJDEqDAsvezpERFq5f/NGM0/N+Tz6Um/YP6ptd1Wt1Ne5xQZqW4KuNhZ7OcdSGREEAQhSCrsd8JZ8RHMGpNMWIiFeydXA/DPnc3c/PJONj77C5r/OJXDZXpkZKKXyMhQqi0wxUgv1os4M2NkIgDbqyK6tW7HJU1T3URqTGBzd8R+3oGIEUEQhCAx7miNybDkreTcDYu5wvoJKhbeV0/nqrZfcUHZ/2HTFOLDtA6pHQhswNxgqi0wxEhv1os4MzVbFyMHSupoaGnvtvNWOKVpGlptTMyM82sClxkfIfbzTogYEQRBCJIye1g+LTZCd+1cfQ+KovG70H+wJuwXXG39kCiaKSQVgPHaYRRN7XCeoVZbcM74VM4YncQPZuX0yfNnxEeQEReBqsGuwhrXB1Ub5H8Gu17X/w3CjdXd6KykrtmvCdyShbliP++E1IwIgiAESaldjKTGhuuunbUnzMfGW47zG8uz3BPyMm/YzmadOoUbeB+OTtPTAi7nGVq1BWmxEbzy41l9uoap2Qms3lPMjmPVnDE6Wd+YtxJW3+PyeyQuC+Y/HlBhq7sYKapuNoud3WuBMgZhLVB3IGJEEAQhSEprncSIF9fOOKWJ60LWcB1r9A0e9gu0ZkBqC7qPqSPsYqSgWt+QtxJeWwzuybLaIn17AJ02RjdNSkwY5fWtFNq9RvyZwAkOJE0jCIIQJGX1RpomPHDXTg/7BTJgTmoLupdp2QkA7DhWbabYOggRcGxbfa/PlI2maWZk5ORh8QAuA/N8mcAJDkSMCIIgBElprR52T4uL0FtD47LoWB1g4N3dM5ABc1Jb0L2cPDweq0WhuLaZ4rwNrqmZDvgfoFff0k5Lu2o/dwLgagkvBEbQYmT9+vUsXLiQrKwsFEXh7bff9rn/m2++ydy5c0lNTSUuLo5Zs2axZs2azq5XEAShzzEKWFNjwvXW0PmP2x/xIil8uHsGMmBO6D6iwkIYl657vuw4WhHYQT4G6BkpmqgwK2NSowG9vVcIjqBrRhoaGpgyZQrXXXcdl19+ud/9169fz9y5c/ntb39LQkIC//73v1m4cCFffPEF06ZN69SiBaGvsKma5H+HOG02lcpG/QKUVr0dKsr0FMx3V6CtuQ/F6U5bi8tCmf+Y35oDqS3oXaZmJ7C3qJbttbHMD+QAH6m4CnuKJiUmnKyESEC3hBeCI2gxsmDBAhYsWBDw/suWLXP5/re//S3vvPMO7777rogRYUAxVFwyBd9U1LeiaWDFRtKrl4Ki1xY0RaTzcNs15LdGkEY1pSRwrHkKv1ZPDuiCZ9QWCD3PtOwEXt5SwI7aaJoiMwhvLMaT7lM1aInKINLHAL1yU4yEmWKkuKYZVdV63WV2INPrNSOqqlJXV0dSkveCrJaWFmpra12+BKEvGUoumYJvSr/+AIAUarAojsLHiKYSftP+BPHUs1KdzWY1lxO1bfL+6IdMHZEAwK7CWpa0LgZ04eGM8f1DbYux+bhUlpmdNOGkx4ZjUaDNpnVo9xV80+ti5A9/+AMNDQ1cccUVXvdZunQp8fHx5ld2dnYvrlAQXBlqLplDDZuqcfkzG7l+xZdomp/foWqj7NO/A5CmVLs8pCh6hcjS0H9iQS9olPdH/2RMagwx4SE0ttp4rWEqN7fdQTGuN8jFJHNz2x28Uj+Vpav28vf1hzyey5hLkxwTTojVQnqcXvtzwoeZndCRXvUZefnll3nwwQd55513SEtL87rffffdx1133WV+X1tbK4JE6DOCccmUMPvAo6imia+OVgF6MaJp8e6J/M8obdE/Nt3FCOiCJIl6TrfksUmdDMj7oz9itSicMjyejYf0AtY16kzWtsxgpmWfmWLbok5Atd+v/2tDPhpw8cmZDE+McjlXRYNRzKxb3GfGR1BU08yJ6iam2tuIBf/0mhh59dVXueGGG/jvf//LhRde6HPf8PBwwsMDGzQkCD3NUHPJ7C36SzFwdWOb+f9vSut8i5GvnqWUBABSPYgRg1lKHpuY7LJN3h/9i6nZCaYYAVCxsFnN9bivEdM6Ut7YQYyU19nTNPb3TVZCJNsKql06avrLe70/0yti5OWXX+b666/n5Zdf5pJLLumNpxSEbkNcMruf/lQMXNXoGHJ2sLSe2WNSPO+o2uDgR5Rp3wUgjWrvJ/VwnZH3R/9i2gh9aF6IRcGmah7TsACRoRaa2vS0W355PWeOdX1/lDt10wCOjhq710h/eq/3Z4KuGamvr2fHjh3s2LEDgPz8fHbs2EFBQQGgp1gWL15s7v/yyy+zePFi/vCHP3DGGWdQXFxMcXExNTU1nk4vCJ3CpmpsOlTBOzsK2XSoolvz8+KS2b30t2LgKufISEm99x2PboTWekq1BMB3ZGST0x22vD/6J0YKxRAi3v6+DSEC8Nj7+zq8Pw0xkhytp2my7H4xRTVN/e693p8JWoxs3bqVadOmmW25d911F9OmTeOBBx4AoKioyBQmAH/7299ob2/n1ltvJTMz0/y6/fbbu+klCEOd1buLOPPxj/n+PzZz+ys7+P4/NnPm4x932x+6uGR2H/2xGLjaKTLyTWmd9x3txlf+xEi9Fs4Xquv7Rd4f/Y/U2HCGJUSiAXdcOLaD6RyABZUwHGK1obW9g4ioqHdN02TaIyOF1U397r3enwk6TXPuuef6rDhfsWKFy/fr1q0L9ikEIWCMOw/3d6Rx59FdDpYygbN76I/FwFUNjovNwVIfkRG78VWZXYx4KmAF+Fv7t8zCR3l/9G+mjkigsLqJUKuFDfecz5b8Soprmnjkf3s5rWkDt4S8w6WtvzH3H60UMU45zkPvRjA3N4M2m0pdSzvglKaJ18VIQUUj1U1tHZ/UjhQ2uyJTe4UBi7+7bAX9zmNubka33JWKS2bX6Y/FwM41I+X1rVQ2tJJkD7m7kDMbLTaLsuYEwLMY0SKTmH31Y5zU0CbvjwHAtOwE/reziB3Hqk3TuU2HKjitaQPPhC5jrW06ALE0UEc0J7Rk1obezS11sCV/KtlJuvAIs1qIi9Avp1kJeoTFlxBxRgqbdWRQnjBgCeYuu7uQCZxdI9AiztSYcP63s4hjlY09vCLXNA34iI5YrNSc/zithAK66ZkrCsrCPzFrbJq8PwYIU50m+BoR/9LaBpaEPg/ALm00AHMt27Bio5lwSklgSegLlNY2mHNpUmLCUBT9d50UHUZ4SOCXVils1hExIgxY+uNdtuCbQIuBVQ1u/c827n9rV4+vybmAFXzXjZRlnQdAvNJIhOJ0XNwwuOJ5vzNohP7F5GHxhIdYKKtrIa9Id/o+qXEXWUolFgW+1sYAcKrlAMOVMgAKyCBLqeCkxl3mXJrkGEc7uKIoZkdNUnSoFL4HiIgRYcAiLbcDj0CLgQ+U6IKgJ6afundeGWma0Sn6xFVfHTWldrfNtNQ0+OF7cPm/9H/v2CVCZAASEWrl3PGpAKzeXQzAxFg9GqdpsFPVIyNTLIcZoZQCcFRNN/dznkvjTKa9GHbRlCxACt8DQcSIMGDp6ZbbnmwX7gztNpUn1x5g06EAx573U4xiYPfuhYz4CLPguMCenqlrbu/W5/bUebXnhH5HfNpI/X3iq4jViLKlxobDqLPg5O/o/1qs3bpOofdYYC8uXrVL75CxxGYAcFRLp4YYwmhlvFLASEUXK0e0DHO/cqe5NM4YkZHU2Ai/73VBRwpYhQGLcZd984vbUMClkLWrdx790ajoi/xKnvroG97fVcTau87pkzV0F/6KgY/1gBjx1nlliMyIUP3ezGeaxoiM+HJpFQYU509MI8xq4VBZA9+U1DE2ZzbEZbGjahQAucpRwhQbOYre2n1US9fTcjmzKdu1D3C09RoYXiOF1U3cet5JUvgeABIZEQY0gdxlB0t/NSoy7soPlzfQ0m7rkzV0J76KgY/axUhTm412m+rtFAHjq/PKwLgzLqltocZLJ0RprV2MxEnqb7AQFxHKWXZX1VW7ivUo1/zHzRTNVIs+IM9FjMx/DCxWKhr0yEiyW/eVERkpsqcZpfDdPxIZEQYcmqaZlevQvS23vd0uHAyVdj8Mm6qRX97AhIy4Xn3+3kJVNZcumvqWdhKiPLTaBoG/zivQR8EnRYdR2dDKwdI6pud0TO8ZNSOpMRIZGUzMn5zBR/tKeX93EbdfOBZyF/F1kgXK4BTLYQBGGmIkZCTaxEtQcEzsdZ9nlOlmCS/4RyIjwoDi92v2cdpvPmR/sWsovbvuPPqiXThQqhocLagHfNmWD3DK6ltoaXdEQ7ojVRNoR5WRfvFWxGqmaeJEjAwm5uamE2JR2Fdcx+GyetpsKnuq9TqgKd/+OVz+L7Kv+SuKAnVtCpX2v0X3uTQGw+xeIydqur8Ae7AiYkQYUKzeXUx5fSu/W72vR87fn9uFK51ty0t82JYPcArcvEW6Q4wE2lEVH6l7iKw/UOaxYNmlgFUYNCREhZkuqO/vLuZASR3NbSqx4SGMmnIOnPwdIsaeTYY9PWekEY00jbsYybS7sNY1t1PXHJj52VBHxIgwYNA0zYxafLSvlO0FVd12bqNzJtCLfF+0C7tGRgavGDla4S5Guv5h7q/zCsCi6EXCAKt2F3ucbyQFrIOXi0/W68ve313EzuO6od3Jw+OxOEVZc5KjADha0UC7TTXbwpPdWnujw0NMYesvPSjoiBgRBgx1Le00tjoKN59ce6Bbzuvc7vn0J4d87tuXRkWVDc6Rke5P03gr2uxteiIy4svfxMA9EOJesNzcZqPWvpZU8a4ZdMzLTceiwO7CWt7beQKAKXaHVoORyboXzZGyeir3foam6SI2MaJja3emU0eN4B8RI8KAodh+hxERaiHEovDZN+UB12548wzx1jnjib42KnKeoXKkons7ap7fdIQpD33A/3ae6HNvFXcL+PqW7mnv9dZ55Q33yapGVCQ8xDGHRBg8JMeEc/ooPVXz+UHdy2fK8HiXfXLsYqTg89coe+1nACRp1VifOhnyVrrsO8zsqJHISCDIX5QwYDAEw8jkaE7NSeQ/XxTwxAf7efXHZ7h017jjzTPk15dM5JH/7fXZ7ulMX09grXSaLqtqcLisgYmZ3dNRs/WInvL6xRs7aWhxiJy+8FY5WtEAQIhFoV3VujXn7t559eqXx9hoN5GzoDLTso/t6km0EIaCiobFLFgOs88bSY0N9/l+EwYuF5+cwabDDlNB98hITtMewMqR1jgqQvS/vRSlBmqL4LXFLiMBMo0iVomMBIRERoQBg9Gznxkfwc/OP4mwEAtb8ivNuxhP+PIMueU/2wOKiPz0vJN4+UdnsOGe8/tMiGiaZkZGhifqd1zdWTdinMtZiEDfeKsUVOq/57HpsQBmaqS7cO68MoajnaQcY0v4zbwS9ijTLXr67/6Ql7jIsgXQC1fL7MWrUi8yeLloUgaGzkyNDTcLVgFQbeTs/BOge42Uo0dNUpRazDja6ntB1f+Gssz2XhEjgSBiRBgwGMIhIz6SzPhIrpo5AoA/rN1vXlSc8ecZEihj02P63KiotrndTJkY9SrdVTdiUzWvFujuqYqeprG13WyXzLVHfbrbEt6Zsjpd4C22riVF0QXZWKVQf0xL4JnQZVxk2UJabIRjLo3Uiwxa0uIimJGTCMCU4QmuEbCjG8lp3A1AJXHkq/qNiWN6swa1hXB0I+CoL9lbHPxNQ38bRdEbiBgRBgxGzYhRGHbLeWOICLWwvaCadfvLOuwfiNFVIPSHi4/RSRMdZmVyln5H5su2PBi25FfS7uPDrje9VYzi1ehwK/Utenqmp1ojbapGTYUe8UnEIcZOsouRg9owAB4Ke4GZOfFmzYi09Q5ubjhzFCEWhcumZbk+UF9CjNJsio+vtLGAPU3jth84Zh3tK66l2qneyx+e5id56uwabIgYEQYMRbVGZEQXB2mxESyeNRKA363Z3+HuoateIP1pxLfhMZIYHcY4e/qiuyIjxbWBhZF7w1vl7e26EGhosbFmj/6h/sa2453+IFZVjfve3Mm/NuR3eGzLoTLiNH1IXqLi+FmOsxwH4BttOBYFMqjAemyTwwpexMigZv7kTL75zQK+dYqbGInRp/Xm2Afm7VBPAjyIEft+qbHhnJQWg6bB5sOBCfn+OoqiNxAxInSKvggjFtvdDLPshkIAN50zhriIEPYW1fLql8dc9u+OiEZ/GfFtREaSosMYlx4D6B01zW1d76iJCQsNaL+ejhCt3l3EXz893GF7c5va6Q/i/SV1vLzlGL9fs69DKs925HNqNd03IkFxRJmMNM1xLYVGzS486ktMMSbuq4MfjwXK9gF6xoyaRvS/h2RqjaPMAXoGZ4zWb2Q2H/Y/aTuQtHJvpUv7AhEjQtD0VRjRUTPiuCgmRYdxx4XjAHjig/3UNDpC+v6MrozIx/KrTiU6zNUnwKLA01dN6zcjvg2PkcSoMFJjw4mLCDE7arrKyJQon4/3RoTI+CD2RWc+iIvt0bTmNtUc926QSjXV6FEm58hIklJHMjVoWDis2X//MemU1UuaZkhjH6CXYyl12axHRuyfMvYBegazRusD+AIRI/15FEVvIGJECIpVO4u4qQ/CiPUt7WYho7tPxDWzchibFkNlQyt//NBhhObL6MrZM+TiUzK5MFcPrX7rlExi7Rf6iNCORkZ9RaVTZERRFEeqphvqRqoavddk9Ja3Sk99EJfWOs7pbj6VkT2aNru7gXPNCDjqRl61ncvr1gW8XTWSwir9+P5QQyT0EbmLGHnGt102pSo1EJfl0tZrcPpoo26kzsVB2RP9eRRFbyBiRAiYVTtP8NOXt3l8rKfDiEbxamxECDHhrvY4oVYLSxZOAuCFzUd57ctjZvpobm6GR6OrjPgInvnBqWbko8J+13zBxDSumJENwH+3Hu/219FZzJoR+/Tasd1YN1LZ0GL+311vuP+ceoqe+iA26jwAjle5mqnVpp4KQBitRNLi8phRN/KCbR53N1zDHa/tNEWbpGmGNjlTznL5PuWKp+COXR2ECOgza8am6WnVL/J9R0cCFbmDVQyL6ZkQEKt3F3HLf7b73Mf57tUYOtVduHfSuHPm2BSmZsez41gNv3hjp7ndMO3acM/5ptFVWqyecnC+0zc7JWIi+O6MOP61IZ+P9pVQUd9Ccj8YF++oGdHrO4y6ke7wGnFOX0SFhfCPxTO8/px6ip76IC5xEi9GZAPVBkc3Un20FIjQoyJuL/E662oqtVgaEiegJo9D0zRUTWP6iMRBezEQAmNksmta85uwXFKx4C2OesboZL4prWfz4Uqfot5IKxfXNHusG1HQbw76Q0F9TyBiRPBLIPl8Z3oijFhkL17NcCpedWb17iJ2HKvpsN1IH/m7uzdHgceGMSEjjlOGx7PzeA1v7zjBDWeO6oZX0DUM99XEaD0y4kjTdEdkxCFGGlrbOWN0Uq87jM4clURabLjp5eGJztStuEZGmnTL7tX3QO0JqmwnA/eRaG2CyCRocqSARsW085dLZsCky4J9KcIgZ/PhChQc0eBrnt3i06l41phkXth81G/diJFWvvnFbS7nh74fRdEbSJpG8Euwfh2B3DlqmkZFfUvAKR0zMhLX8dy+xFIg6aN2m2qmQVLtUZDvTh8OwH+3HvNoqNbbGO6rSUaaxh76PdoNHTUV9Y4LtqbpxZ69jdWi8IMzRvjcpzMfxCVO4qbw2BHdsrtWH4JWhf4zTNBqUJoq4dz74fJ/wQ/fQ7n7gAgRoQNG6637J4KvmjlDQO8rrnMR/p7wNj+pt9KlfYlERgS/BBPp8Hf32tJuY9WuIlZ8foSvj9dw0zljuHfBBL/ndfcYcSaY4kdP6aPKhlY0Tb8gGjUZi6YM45H/7WVfcR17TtQyeVh8h+N6E+fWXtA7OuIjQ6lpauNwWQO5WZ2fUVPh9gHZ0NpOZFjvF+8aUa+wEAut7a6CaOm3J3fqg7jMqYD1eHEJhDouI9WavZOGOkCBbc/puX9L/ylcFvoP/lpvFeCRlbuYG/UN1oZS3W8kZzYpMeGMS4/hQEk9XxyuYMHJvt/H7vOTejNd2peIGBH8EkyO3Nvda0V9Cy9sPsqLmwvMlAjA2rzigMRIsTGXpn4P5Jfovfz2i0ZpXbM55CyNag5qmeRpI3EvBPAmqozUQHJ0GBb72uOjQrloUgbvfn2CN7Yd73MxYkRuDDGid9TE8OWRKr4preuaGHFreW1ssWEPGvQqBRV6gel3pw/nW6dkUVrXzP1v7aKhxWa6WQaDqmouaZ9CWzxaCObsETMyotTjYuU96iwPZxOGOv5ueuZZtrCk5Xmszzt1fMVlwfzHOWP0aA6U1LM5ADECjvlJQwlJ0wh+MQqrfGFRYPlV3sOIV//zC5Z9+A3l9S2kx4Vz87ljADhc3kCDtxHxqg3yP4PV91F0UC+ezdj2JDz3LVg22RzZPaFqHRvCb+OVsEd5KuxpVoX/ko/D7mIMhS6n85ZtMetF3ApVF56iv5Y1u4v7NFXTblOpaXKtGQFHR01Xi1jdQ8cNrT03C8YXhhV8TnKUOcjOiFR1ZlheVWOri819A5FUO6msak3/v0tbr93KWxDc8RUhvsiyhWdCl5GBW+u5fZrvrDDdzC9QJ9ahiIgRwS/Ofh3eePr707j4FM9CpLG1nX32YVF/vHIKG+45n3vmTyAtNhxN02c3dCBvpS44nvsWbF5OkU2PTGQq9j9mY2T3B79m3Ke3kqG4/pGPtpTwYfjP+U3IPwlDv9j+47OO7p7g6KRJcTOzOntcKlFhVk7UNPP18Y7Fsb1FTVObKaQSIh1uqUbdyIEutvdWNLgWjTb2sRgZkeToVoiN0F9vZ4blldiLV1MiNFKoBqBQSzEfrzLSNE7uq4aVtyC44y1CbEFlSejz+v87BIXtwy33PALojsAvbT46ZIbfBYOIESEg5k/O5O554zpsz4yP4K8/OJWL3ec4OHGkXL/IJESF8v+mDSfUqr/tJtlTC3tOOIkR1QbrHofXrjELDZu0MNMp0yE6NP1r09MoaB7fyIoCV4d8zKqw+wHIO1FNy6r79WiL6ij6NFpbU90iIxGhVs6bkAbA+304E8IoXo2PDCXE6nilRkeNt4m7gaCqmhkZSYnRoxANLYEXxN784ldc9pfPu0XAOMRItLkt1u4pU98JMWLcyaa2n2C4og9SPO4sRow0DfV4svIWBGe8OTrPtOwjS6n0IEQMNJLrDxBj0cXxL9/ePWSG3wWDiBEhYNzbav9y1alsuOd85k/O9Dmr5kiFbllujNQ2MOow9hTaxUjeSvjjJFj3W5f9ijW9XiCKZuJwNa5C89/5MUY5QSTNaFgo3PxGhzSPIzIS1uHYBZMzAH2A29vbj3fbHU1RTRO7CwOLthhtvUnRrusbm971jprqpjaMlzMsUY9IBCosKupbeH93MTuOVfPmtkL/B/igrrnNFEXZSY73WWxEiPl4sBhtvelqGcOUcgCOa6nm42aaxqgZcbPyFgRnvDk6p9mjbv5IVV2jt0Nh+F0wiBgRAuZohesclJzkKKwWxe+smvxy/bhRKa5ixIiM7D5RowuD1xZDXcc/zCK7GMlQKumM/YWiQLb9zviYpkc6qD2hP1/eSrNmxD0yAnq9Bugh/zte/brb7miuX7GVy/7yeYefqSccc2lcB9qlxoSTEBWKqsGhss5FRwz31biIEOLtKaBAIyP7ix3pjX9/no/aBZF2rFIvUE6KDjNTM+AsRjqTprEPtlOqzMiIS5oGpzTNGbd4dNAUBGc8td6WkhDQsaGK63t4KAy/CwYRI0LAHKlwjUqU1bUENPL6SLnnyMikLD0ycqCkjtb37wePTXNQjC5GMpXOF385xEiq6wOr76XcCOe71Yys3l3Ena9+3XE9XbyjKa1tZm9RLe2qxt4iD/UyblS5ddIYKIpi1o10NlVjpKiSY8LNYYGBRkb2OxXOHipr4LOD5Z1aA0BBpf4eca4XAYgxxIi3ImcfGJ006VQz3EdkJIF6GH9x8IsWhiTzJ2ey4Z7zeflHZ/Cn703l9ut+iBaXheZlJKeqwQktmW+0YR0eG+zD74JBxIgQMAX2u3ijdbektjmgkddGZMR9OuzwxEjiIkJos2l8U+P9rWhERjIVDw6GSmBv4WxFn7R53EWM6O2cZVXVgGtkpCfHeW8rqDL/f7yqyceeOs4Te90xUisf7i3pVArJOHdydBhRYfqFv6HVERnxlX4zIiMRofrv4N+f5wf13M54Kl4F5wLW4NM0ZmQkUjPFiBEZadOs1KE/V2JcjNSKCEFhtN5eOnUYs8amsWPSvfaRAa77Gd8/1HaNl8o2ncE6/C4YRIwIAWNERibb0yvbC6oDMhszLMvdIyOKopj+GHvUkV7PY9SMZLq3zaHArJ8GtHbjYtQhMgKUN+oX35Sa3bDrdcj/jC2HynpsnPdXRx1i5Fhlo489ddwNzwxW7y7iw7xiAN79uqhTKSTDfTUpOozocHtkxB6F8Jd+Mzqkfnb+WBQF1u0v63SExrsYCTJNY7SD73qd0nL9d54249IONSPV6O9FBZX4+Q9IrYjQaWyqxi3bhnNz2x1mFNegmGRubruDNepMn+eQeUdieiYESHVjq+l1cWpOIl8frzHnxfjDOG6kW80IwOSseDYfriRPy/F6vKNmxCkyEjdMLzjMXQTDT4N3b4OmKi9ngOFmZCTNZXubZqWqRY/0pK68GhT9Yjo1Ip2LLN/3+yHy+cGyoN0RXcRIIJERY2KvkxjxZ0sdqHW04b6aHBPuEhnxd/6/XD2Nb+xpmnm56WwvqObDvSWs2JjPo5ed7Pd53TlqF7ojkrsQGXGaOwNQ2vwUkEJaJAy7fCm8DLVEU6tFmu6rcWEK1skLg16vIBgYZmhFzGRtywzTfLGUBLaoE1B93PMP9uF3wRB0ZGT9+vUsXLiQrKwsFEXh7bff9nvMp59+yvTp04mIiGD06NH89a9/7cxahT7EiIqkx4Wbd68t7f47WQySosPMAklnJg2zF7FaxtNhdKqdYk13IsyMaNcLDX/4nuvI7txF8PND+myRyESP5/BcM6JQEaHPQwmhnXgcxaQRzaU8E7qMiyxbfL6upz85xPRH1vKnDw8ElCJpbrOxu9BRJxJUZMSepunOFJLhvpocHWbWjNS3tPs9/5KVe2hotRFmtTAyJZrr54wE4I2vCqlpDD6lYqSrshPdxIjR2uuvZsQogLYLEVVTKLMXFqZ/fAfRoY4C4MIL/kLV/L8AkBjbUSALQjA4p1hULGxWc1mpzmazmouKBQsqZ1jyWGTZaN4UwdAYfhcMQYuRhoYGpkyZwtNPPx3Q/vn5+Vx88cWcddZZbN++nfvvv5/bbruNN954I+jFCn2H0fWRkxxtFnqqmuax795AwWHS5T5228AoYt2rjUTVFDwJEiNNk3Hd8zB/qW7X7R5Wt1jh3Ht0UfLD93TREuWwUzZqRiqJo0ELtz+PRpmqi6FkarEojsuvggYK/Cb0WS61bGC6sh9vBbbVTW388cNvmP7oWr8pkt2FNbTaVELsHz7Hq5r8urtWNrq6rwYzi8cfhuFZckwYUfYL/7HKRr/nL6vTRczo1GhCrRZmjUlmQkYsTW02XvmywO/zupxP0zhht/sfluDaPh5Qmka16RERp99PFTG02QO/KdTA6nsZnqifuzDlTKriJwKQ4KEORxCCwVeK5SLLFhd36NusbwGQQvWQGH4XDEGLkQULFvDoo4/y7W9/O6D9//rXvzJixAiWLVvGxIkTufHGG7n++ut54okngl6s0HcYxmUjk6PMQs/y+laPfffO3589Ti8Y9JSiARidEk14iIWGdoUjC56DONc/zJbYEZRjd19NCOAu1mLVxcr8pXD3N6YwiYuOIt5u+31cS9VnRpx7P+XN9hSN0tHzwwKkKLX8KWw5b4Q/xGnKfvtr8xwRqm5s89tlY6RozhybgqJAU5utw6A6dxw1I7qwC7TYLZD9jMhIklNkpLYp8MjGhAw93aEoCtfPGQXAcxuPmC3RgVDZ0EpLu4qiQHq8a0dTQA6sRzeaERGDUi0BgGRqCFPaobaQYWH6e/h4VSPVRuorqmO0ThCCwZsZmieLeKMIP0mpY8OiehEiTvR4AeumTZuYN2+ey7aLLrqIrVu30tbm+UOvpaWF2tpaly+hb3GOjBi26WV1LX5HXoda9QvcqGTPQiLEamFipr2INXIG3LFbFxD2Ue6lP9wIQHiIhYRgLxxuwmR4iv48x877s57mSR5DmaYLnRQPYsSdhdZNAJys5HtN32j4TpEYYmTW6GQy4vSfmb9UTZVbN02gxW6B7Fdhuq+Gm5GRYBpyxmc4BvQtmppFUnQYJ2qa+SAv8BkvRhQmJSac8BDXiFdAkREP3jQlmp6uS1Mc9TnDw/XoS2F1E1VGtEkiI0IX8WSG5s0i3rAnKNKSsb53h4sT9FCnx8VIcXEx6emu8x7S09Npb2+nvNyzL8HSpUuJj483v7Kzs3t6mYIfnF1UjTRNfUs7ja3tHfruX/7RGaYzq3mcl8gIuNnCGwLi5O/AqLMoqtMvGpnxESidcTwzsFjJTteLV4+FjdKfJyadMnvUJVWp9nuKi6xfArBTG8PDIc/yl5BlzLLsxuIWKfGWItE0zWzrnZ6TaNZH+CpibW1XTY8No5vG252YgYL+8wqkKM5s7Y1xREZCrIrf8xtppvEZjsFzEaFWrjxN/1tdvbvY73MbGCmaLA/DGGPC/Tiw5q2E1fd12FxqipFqc9uwJH2tx6uaTO8WSdMI3YH7TZk3i3gjMlJHFHWNTbBeMgQGvdLa634RMXLk3i4u9913HzU1NebXsWPHenyNgm+Mboec5Chiw0MID9HfOuX22gGXvvsxyWZB1hEv7qvOGHUje050jE4YHTvukZfOYNiMG26f5MymLFQ3IkrBf2QkXalmkqJ7aWzSTuaSkC28HPZbdobfwM+sb7iIEk8pkoLKRsrrWwm1KkweFs9w+3qOV3mPjBjpBIsCcfaUhTdbaufvAymKs6mai6Ga0U3T2GrzeX4NvV4IXCMjALn2KFexj5oTd0wx4lYvAo7X3NKu0upeMG0UrTZ2vKkxXDHTlSqMuTPDRuuvqbC6ieoGIzIiaRqhe3C+Kbt7drzHfaKVFuLshfLFWhJsfEqiI3Z6XIxkZGRQXOx6l1RaWkpISAjJyckejwkPDycuLs7lS+g76prbzHB+TnIUiqKY0ZGyeu8XnVq347zhHBlxL+Y0QviZ8R0vVMGSnWREIuwXf4uV8vQ5gOeaEU+cZdkFwHqbo301Rmnh/0Lf4OvwH7HA8gXgOUVipGgmD4snItTKcCMyUumIjLibjBlW9YlRYVicxIW/9FggueiqxlZzGnBSlKvPiK/z//qSiaia3uniHs1It6eeimsDFyO+fseGAyu4RUc8FK06Y6ZpjLkh8x9juKfISLRERoTuw7gpmzFpotd9jOhIkZYErfUSHbHT4z4js2bN4t1333XZ9sEHHzBjxgxCQ+WuZCBgREVSYhxzQ1Jjwzle1WR2Vbig2uDoRo4cLQUiSHGbN+LO+IxYrBaFyoZWimubXS5Kxh12t0RGzIu/IxJRbkkBKkmJsoDvOlJAFyN/tS1ig3oymobLrJxYpYnloX/iRetlzBzV0V7cECPTRyTa1+MaGVm9u4iH3s1z6WQxilYTPVw050/OZG5uBve/tYtXvzzG2WNT+Pd1MwNuEzSKVxOi9GnA7g6sxvm35FdSWtdMWqye+nlvp14sOi4jtkN0M8NJjGiaFlBqrdCMjHT8HVstClFhVhpbbdS3tJNsuOR6KFp1xihgTQ9vg+88D7mLGGYvzK1saOWEPeImkRGhR8iZDZEJ0FTd4aFMpZL92giK7JYFfPEMnH33kDfeCzoyUl9fz44dO9ixYwegt+7u2LGDggK9ne++++5j8eLF5v433XQTR48e5a677mLv3r08++yz/Otf/+Luu+/unlcg9DiOFI0j1WJ01JTZ79xN8lbqE3Gf+xb5H/0DgJGt+80JuZ6ICLWaM1b2FLoWKxtpmsxuECNma6dTO60xsTf1ij/phbPf/gdEpXg9x3TLASJooZREDmjDPe7zA/VtrGvu1Z1AnUKwphjJsYuRJIc48jbjx5jY6w2rRWHWaP1Drc2mBeVXYLb12oWOGRlxmk3jKf1m2MCPt3fSOJMWp78vWttV0+zOH8Zr9pSmAaci1sYW012V/E99ntOIjKROX2T60cRHhprnOlCsd1ZJAavQI1iscPotHh8yIiMnDDHSVKWL6yFO0GJk69atTJs2jWnTpgFw1113MW3aNB544AEAioqKTGECMGrUKFatWsW6deuYOnUqjzzyCE899RSXX355N70Eoac5YnbSOFItqU4dNSZuxlNHtQwARqoF5oRcb+Q6T/C1Y1M10168prGty5MtjbRIXUu7eaE0BsWlxkXqhbOnXAHf+iPeDNgilDZOt+wF4DO1o9OootiP/OKv8Ny34I+TYN3j1G173byIu4uRwuomHly5x0vCQedYZaPX129cxE8E6Ihr4DA803+XRmSkzaZ1rM9wwngdEzyIkYhQq9n1FGiqpqjat+A0omq1Ly3Wf6Zv3ADrf+/znGVGZCTZtYjX8DFptbceB92hJQiBcvbdENaxVs7oqHGxjq8PvPtssBK0GDn33HPRNK3D14oVKwBYsWIF69atcznmnHPOYdu2bbS0tJCfn89NN93UHWsXegmzrTfJKTLiLkY85PCPqLoYGaXYa4ZW3+u1WMsoYt1dWMumQxU8/O4eTvvNhxwq05/7D2sPBD13xZ3IMCsp9ojOscomWtptpihJcRqSR+4iuOJ5iPTcjXKWZTfgWYx0oK4I1v2WHW/9EQ3ItlSQdvwDQE9phFgU2mwaxbUtPk/T0q56NTEzLuJFNc2oQQg2504agKgwR5jYOTriXsdizKQZl95RjIBTqiaAItZ2m2qKFq+REVV/vvoG/261AJoGpdhrRsad5vLYcDeHV4mMCD2GxQqzb++wORO3yAhATHqH/YYaMptG8IthBe88dbeDGPGQw883IiNKMcaEXI5u1CMQbhhFrJ/sK+HDvZ7vEoKdu+KJ7KRIyutbOFbVaF6EQ61KR6v63EUw4RK9uGzzcmiuNh86y7ITgC/UibRoIYQr/oe4faWNA2A6e+G1Z+CK57HmLiIrIZKCykYUVE73M9PCm4lZRnwEiqKnRioaWs3fjT+ch+TpPwcLYSEWWttVGlptJER5rmMx8BQZAb2IdV9xHaV+BJb+mlpQNf134Dw12US1EVN7ABhvTtn1RxWxpvtqalzHSdHOiBgRepSz79ZrQpzmZpmRES0JvdMrS6ZGI1N7hQBwNjwz6FAzsn9Vh+OOuIgRO17CkUao3ubjxj7YuSuecC5iNYRUSky450JLw2L+F4f1uTd2xinHSaOKZsL5Sh0X0PMa+023HNA32KNERrvxr0JeNC2jXwl7lK/Cb+I26xuk2LtBzlF2cFL9No+RpVCrhXR7947RJhsIzkPyDAyvkcaWdq91LAabD1d43J5urxsJJE1j1ASlx0W4dAuZHN1IXLv+QV6nBdZRVRI9HtBFVliI60ecsxgJD7EQGTa0iwaFHsZihYVPuWxydNPYIyPzHxvyxasgYkTwQ1OrjRL7He5IDzUj5XUt+gVy56sux9Vo0VSh3zm7iBEP4UibqvG7NfsDWk8wc1c8YXqNVDWabbN+IwmGKLniBYhMRFHgTHuLbyCpGpumsEM9CYBTLd/gHCXKRh/gV4fbHbtSz12hbzDRotdfXRqykUkf/gB+P8a19ka1Qf5nZNqtzk9UNRAozkPyDIy6kbpm78PyDLyJwowg2nsLq+0pGqODSrXBoXXw8aPw0aNweB2xiv7a6vEhRs76ucO1d9FLAKR5+L06z76RqIjQK+Qu0j874rIAR2SknkhqL3veMfBziCNpGsEnBfY22PjIUBe3SqPGoqyuBe3TJ1AaXe+SjRRNGlVEK/boSVSKx3Ckv8Fvngh0Pos7Rs2A3pbsiIwEhJG6yf+Ms955nTdL4TP1FO7hVZ+HfaMNp44oomlivOJk4FdXxPCi9cACjmtpHo+ttI+6T0Svm6CpCl67Rv9wA71Op/YEWa0/YzuzOLHyIQj5VkAfcO41I+DoqPnqaJXf34khCmeNcfULSrfXsJQGEhkx23rDYd3jsPFP0OoqqGK4GoA6zTXlUq1F8/9aH2aWZQ+/HX2Omf4r2ar/jA3PE2eca0akeFXoNYzPjqMbiaovIf51qGmB4szzEBctHYmMCD5x2MC7XgiMaEKrTaV23Z86HucpRXPKFR7DkZ0RFoHOZ3HHOU1jRkYCFSOgr3/Mucz5kW5UtEfLoULzXDthsEMdA8AUyyFCFKculYYyslsP6etRUz0eW2U/d5JS5/rAytt0UWKv0xlmtAs2hfrtXDIob3CtGQFHZKSkC8P4Ao6MqDaKjh0GIDPvWVj32w5CBDAjI7VuNSNfqBPJ1zJ52XY+xQmnmtsNkekxMpIokRGhj3AadZGZqP9dB5NWHeyIGBG8YlM11h/Q0wjR4SEuIfmIUKvp2WAMm3Mm3+iksTiJkfEdjcAgOGERzNwVT2SbFuxNlBqRkdjgL0ppsRFMyIhFw8Krk/7GwTGL0fDsB1qo6UJjtGJ0Aun25ESnMlzRf77HNc9ipNKe6krCTYw0V7l828G7wEfnknlupyF5BkbNSErVDs6w5BFCO7Msu7kr5DXutLxGCK7Fup5+d6YLa42HAlZ7WonV98ETYynM0/0VslTvXVKx6B/Y7pGRfE0vYtaw8Od1h81uH6OLx1NkJDEq1OwaSoyWyIjQNxgdcMGMTRjsSJpG8Ih7F8XGQxWc+fjHLFmYa3aypIbbqGvW3S5PwrWTpkNkJG6Y14pxY/BbcU2zzxqFYOaueCMrIRKLorfK7ivSL/BBRUacyE6MZF9xHb/bBr9jPhdZkng47AXScU1ZFdvbTDOUSsermP8YRCaSrZQCUEQybZqVUMUhIJq0MJrR15boHhlxf10uYsR35xJAm02l2j651oyM5K0k6theYDJx+/7LK2EfY9MUrIr+WynVEvhjyxVYULnJ8g7vxFzBzJx4XVzUl+j1QDmzTRFQ0dBCW1sbocc36y3Oh9bBgf+5uFIaRXzG+j0Ri+eakfyQ0Rja6KUvCnjpC72+JtSq/4wbWtqxqa5GcIqiMCwhkm9K62VIntBnZJreQCJGDESMCB0wuijchYFLa63lS1IbDnGYcebkW2ecxYgGKD4qxo3Bbze/uM0cxOaJjPgIFzHUGUKtFjLjIymsbmJnYTUAKQG2wjqzencRa/eWumxbo87kw+YZnGbZx31nJjAlqhK2raC4XI/ipFOlF7HNf0zPIas2UuOiCS9rpYUwirRkRiiOcxpRkTDaiMb3h9YwRR8W5+Jd4MNIyZjNoij2dIXdsC66/WYAGtEFhcXpt7Ff1R1nRyrF/CLsv9ylrsL6hzCXtkXiski+6HFCLCG0qxply84iq2Gv13UUafrPJtOXGFGMyEikXqiaNgFi0vnqTRs0d0zrtNlbsv698Qir9xR3eM8MT9TFiFjBC32FMdOpSNI0JpKmEVywqZrXLgpj27q3n0V77RpSVf0CUu4hTXNE07tmRirFPNn2HVarp3XYxxlvg9mSokO5Yc5IXv7RGWy45/wuCREDo26guU2v3wg2MmL8jDw+hoUv1Fxu+no0trN/ge22XRyNOgWAlhk3Ybttp6O41GJFWfC4mao55paqqXIqXnXuPNY8/HKMyEIZibRo9nsMH0ZKRidNYlQYVlTTsC5K0UVPgz0i4/y8+7URgN7aDBDS3uAqRABqi7D8dzFpofp5iuu8W8I3a6FU2IVsIJGROqJg9Dlw8new5ZzJ4XL/nUNFdgHtbJY3Y6QugCZneZ6sKgg9TYa9eyyYgZKDHYmMCC7462xRUPlF23JQIFWpBhzW2wZVWgw16LNmwmllue0y0t7NY25uhs/0irfBbJ1NyXgjOzHKpTU42MiIv5+R0X789McHeeXLAop0R3t+tRn+svdT1zv13EVkZ73HocKOYsTspHFK0Wiafv4aYoinAcUuEROpIxw9wlKsJZMTH+LTSMmlrdfJsM6IwDRqHestCu1RlxznomSPr14hvbWAE4w1Z8R4wkjRRNFMPN6Fhdnaq8SYr2nd/lKCsZp56N08zp+QzldHqxiWEMFfrjqVeZMyAj+BIHQjRmSkQwGrfcioc9pzqHiQiBgRXPDX2XKr9W2SFP3q6hAjrneYRltvBhU83v59bFi8toG6Ywxm60mMIlaDgFt77QTa/fPHDw902ObJRTY7eyQUHuX4iMugaodZU2H4tDh30lQRw31tNwLw17A/gT2xpSh6quawlsUJLZmc+ff5/BAzh+TFhEF9obk9Cn17Ax3FSIWmNyGmKrUdHnNF0+tjNPyIEUeKxtdw3xijgNWaYL6mvCJ/a3BejS4Oz1j6kVm0C3oRYVfTfoLQGTKcRjiY063zVpqt+iZxWTD/8SHhRSJpGsEFX50tFlSuD1ltfp+KPtSujASX/Yx6kRZCWaPONLd31hsEOs5H6crQvGwnr4mwEAtxEcFp8s62FYNnF1nDFfRY3FT4+WE2zFnBba0/5Y/t3wagXIvjqbbL+H7r/cxo+Str1JmsUWfy5cxlEOe4kJpFrDPv9/vh5TIkzymdE614j4xU2h0RkvyKEUhX9PRNsea966lQS3FZtzdiI3WxWN+umLN3Wtq8D/LzhrMQAYcw7Mq8I0HoDJn2NE1jq43a5vYOQ0ZNaosCbtUf6EhkRHDBV2fLTMs+Eu1REfAeGdlqtz6vcrPz6exF3NN8lK7c1RrTckGvF/FoBe+DQLt/vOHsIjtrTLK5nmOVjWCxYh19Nis/cnR6HNBG8KRtRIfz2MYvhPnXmGHdzK1xsL+NE1ET/K7BxfAsZ4p+B1ZbRBSuNSPOlNsjI8kELkZ8Rkbw0UkTFgNjLoDTbiB22CxYshZNg4bWdmIjQumOzJ2eUNKFob8UoiB0J5FhVhKjQqlqbKOoqoF4tyGjDuzv0tX36qZpgzhlI5ERwQWjs8UTF1q2unyfqtgjI041IzZNYbVtpst+XfEG8TYfpSt3tc7zSTrTSePrZxTM5cyIFJlGbFV6OsIQO95w+Xk6GSllDR8JwIka/xX6Fc6GZxarHgoG0y230UeaJtn+e/eOQoZdqJbgXYwYnT9GJ01zWCKccQv88D24twCufB5Gn0NEeBhhVv2jqq5Z7+U1hjfqz9Z5ujpeQBA6i1HEWvTNto4RERecWvUHMSJGhA7Mn5zJ8qunuXzIX2TZwg1OKRpwiJFK4rBp+t5btfFmOB+65g0SSGdPZ4bmpcdFmF4UqTGd85owu3/iXMVMRnwEd144NqBzGJEio4alrK6F5jZbQGLH08/TmLtyotp/OsxM0xj1MrmL4IrniYrSz9Fgpmn051A1xaxhSfbpeaLvnz75HMB3msYQIwdtWXyv9Vds/+4WmL9UF1dud4AxEY6ZOQD59k6am84Z3aEDqzN0JYUoCJ3BbO+t8Cfu7XgYRjqYEDEieGTysAQ0IMSi8IfvTOKphFc67JNELQoqKhYqiEMD3rbNcdknIz7CpVgzGALtWgn2rtZqUcwLt98heT6YPzmTz++9wLQ///UlE9lwz/n89PyxZMZHeL1jd48UxUeGEhOuX2yf33SETYcqmJubwdi0mA7H+vp5ZpliJJDISMcheeQuIvryvwDQGH+SHqH4VSksXkntuO/Qbs/qJtnTNFpkEkS6RT7isuCK50k/X/crKcGzGKnSYtitjgLgPW02R2NPZeYYzy60gOn2W9fchqZpphj5zvThbLjnfF7+0RlcNjWrw3FJAbqsdqUOSBA6Q2aC3YW1vePfuUc2Lx/UtSNSMyJ4ZM8J/YIzPiOWy5OPQWPHds4QRSWZOsqJp0xLIIVaPgk/HxrhR2eN4vwJ6V1qzQ30brUzd7XZSVEcqWgMupPGHatFYWx6DMW1zcRHhZmv1TBxc8dTZGPNnmKa23Tn1d+u2gfotuwNrfq2Ry+bTGxEiN9WZ+PD7UR1k6NC3wuVnsQIEBWhf99giXa4t44+h7eLRsCuPKzY+HnbTZSSwLGwKfx6YS7zY/I7tCJmtOgRjAYtgrrvv8vhg3t5Z+NOKrU4ikniC3UCmtO9kL/ImSlGWtopq2+hvqUdi6L/Ho0OrDNGJ7HnRC3flNbz3enD+fapw5mek8g5v//Ea32Pgi7wOjteQBA6i1HEeoJUe82Wr1QNDPbaEYmMCB4xWidzM+N8OnmmOBWx7sj9BcWNCtFhVv5v3nhmjUnuUlFgoHernbmrnWk3vpqanRD0se4YUZbjVY46BiONY6SDDNwjG0ZNTLtbqskQIhefnMEPzsjh0qnD/P48s+wfbg1Ghb4PjCGByW5pqmj7oLzGFoct/erdRTxoN3mzYWWlOpvNai4natu4+aWvWd1wEpz8HZf0SnR4CLH2aE9J4qlMueQnzPz+r/gi9kI2q7kuQuSp7031GzmLDdcjHHXN7Rwu06MiwxOjCA9xfCgrisJjl5/Md6cP59cLc5k1JpmwEIuZ8nL/yXXHeAFB6CxGXVhRbbNZs+WbwV07IpERwSN59sjIpKw4n06eqUoN+zS9iHWj7TSglQsmphMR2nXl7q9rxd9drU3VvBqo/fT8k/j+6SO6HBkBhxgprHJNj8yfnEli1B5K61q4e944puckuazBV02MwfaC6g7zVbwRGWYlKTqMyoZWTlQ3ER/pOUXR2q6atRfJ0a6v3xgi19Da7rJGT/jrRkmPj6CutJ6S2mZOSotxMbXbcayKx1fvJzEqlEVTh/n8XYFzzUgbDfaoy6iU6A5rmp6TxPQc1/eDIQzdO7K6Y7yAIHQWZ68Rchfpxdubl/s9Tq05MSijCCJGBI/sNSIjWfGQM8Js/XRvP0ulGoDS8BGsOqZfyBZM7h5nS18za/zd1fprB1YUpVuECMBwp0nAzrTZVMrsEYgrTsvuEMHxVxMD+gfVH9ceYM5JKQGlvDLjI0wxMjHTUUjc2q6y9UglH+8r5eP9+vwbq0XpIFii7dGM5jbVFAiB1u24m9Wlx4VzsLTeZTKpkVJpamu3rzcyoNZtI02zp7CW4lr95zwyuaMY8UZvufsKQqAYkcyiarvx2fiLAxIj1W/fzdGSZqZd9MOeXmKvMhgFltBFqhtbKbQXQU5o2Q173oJTr8VxL+zA6Kj5NGYBx6uaiAy1cu74tG5bi7eZNb4KOXuiHdgXwxL01txCt8LRsroWNE0vAk6J7ih8Aq11efqTg3z/H5s58/GP/a7dvYhVVTWWrzvI9EfWctU/v+CfG/I5XNZAiEXhmjNysLhdjI3ICEBja3uX6naM6b0lHh4zOn5CLIrH31VRTTM3vbiNVTv1PHqVvcblP1sK+HifPsvnre3Hg/pdGkIokJSXIPQ0xmdaU5uNmqY2yJmNFpeF5qdZPUGrZcrG29i+5rneWGavIZERoQNGvcgISzlxr1zleCAyCdBchqOlRmpQD1tK9D+gc8enEhnWvcVVwdzV+msH7gmTK8O35ER1k0tKxRiClR4X0eGiD8HXuniykndnmNNo8qqGVu56bQef7Ncv3snRYZw7Po3zJ6Rx1rgU4iI6pnHCQyxYLQo2VaOx1daluh2jy6jEQ2SlyO6FcrCs3mea6qcvb+eGY9Xma3Cmtrnd789DEPorEaGOtGpRTTObDzewrvEH/Fb7HRq4GPuVagnE0UCE0oZFAVWDzE0PYbvgaqwhg+MyPjhehdCt5G3fBFjI5bDrA4YIOfd+SB4DMemkVo+EV3eauyw4uWcuCoHOrOlKWqGzpMdFEGJRaFc1SuuazSp54yKcHuc5HRSsk2sgYirL3lGz8WA5K3ecoLC6ifAQCw9fOonvTs/2KIqcURSFqDArdc3tNLS0m2v09jP1VbdjREY8TSY1IiONrbYOjzmjavCPz/J97iMOqsJAxUirvvf1CZavO4TGVKosd/Db0H8RqrXzrm0Wr9nO5WvtJC60fMU/w/4A6EIlgwr2fLGGSXMu6eNX0T1ImkZwRbWRt1tvSc21HHV70H7J3PYcTPp/MOosUuMcbqZhIRbOn9B9KZrO0JPtwN6wWhSzrda5iNW4gBvixNNx3jo9vOHPW8V4rq+P11BY3cTI5CjeumUOV542wq8QMTA7alo7b8AGTmma2pYOjwXihRII4qAqDGSMjpoXNh81b0jWqDO5tOURZrYs55ftN/K1dhIA69VTaNNco85NVYUMFkSMCK4c3Uheiy4ochV3MQLu7WVpTqZhZ49NNc27+oqebAf2haO913GRLXFK03jDW02MP7yJKee5OwsmZ7DyZ2eSmxXncV9vRIXbO2rsXSvzJ2eabpHO+DO0M15TiYfIiL/C3WARB1VhIGLcPLi34h8njWbCGasc51chLxJDI62Eclhz/VuLTBzWa2vtaSRNI7jQXFPCQU13ssy1HPG+o917xLkjpbu6aLpCV9uBO8vwxCig0qWI1UhPZMT77tpxron5/GAZT39yyO/zeRNTpwyL56fnnUR2UiRXzMgOeggguEZGDFra9Sm5j337ZCLDrAF1oxjpqdK6FpdaGlXVzJqR1Nhwyuo6Rk6CRRxUhYGIEVHtiMY/Qp/gfGU7Vgustp3GVm08e7UcxnMcVYNSJZkJp1/Uq+vtSSQyIrhwsDWFdkJIoI5MfIS+7d4j8ZGhjE6NJiUmnAsnevcj6S18pT560uTKk/GZcfef4SVN44xRE3Pn3PFBWcm7Y7Eo3H3ReK48bUSnhAh49hqpbNS7Wc6fmBZwN0pqTDgWRT/eGMwHUN7QQptNQ1HgQS8poEDpyhBGQehrvA/EVHjddg6KvVjVSJnnqTkY/ohFs5YMmuJVEDEiuJGHPi8k13IUz9cyBeKG6bbf6AWP79w6hw/uPJv4qMDmgPQ0nWkH7irDEr2naTJ8pGnc6Ssx5YzhNWK4sFY3tqLZPwCTogIfLBhitZiRs5IahxgxilfTYyO45JQsll81jc68HHFQFQY6c8akMCkrjojQjpfiNepMbm67g2KSmGhPme/VRlCqJPP17KcGnc/I4JFVQreQV1wPwCTlKHizGpv/mMtshFgPLaJ9TW+bXBntvUYBq6ZpptlXMGIE+t4x1D0yYgzVS4gKJcQa3P1LRnwEpXUtFNc2czLxAByt0O3cjRD1xadk8TQKt/zH+yyfq2Zm89KWYx3OLQ6qwkAmLS6C/912lumNBK6fuB+oM1nbMoOfTmyEvbAz5BRS7ssj48SXsOt1l3lQAx0RI4ILhg187qwFcOAT1+FNcVm6EMld1EerC45A24G7g+FOxmeaplHd2GbWWaR5ae31RV86hrrXjJhzbKIDj4oY6LUcNWb9jE3V+Ounesv49BGOib8Xn5LJXy3eBdick1JcxMjffjCdC3PTJSIiDAr83YCcOz6Npx9YTU0rVD51NmkN+x0Hx2Xps20GyOeyN0SMCCaqqjkG5M04Fy7erXfNuE1kFTqSER+BRdELPcvqW6io16MJSdFhnZ7T05tiyhn3bhpzwm8n7PON4t1Suxh5besx9hbVEhcRwi3nneSyry8Bpqp6jYmmQVxECPMmpXe6JkYQ+iP+bkBGx2kcrFHYUxtBmvNHSm0RvLYYrnh+QAsSESOCybGqRupb2gkLsTA6NRosFscYecEnYSEW0uN0c7DCqiaqm9qA4FM0/QH3yIghrDoTGTFef3FNM7XNbTyxRr+ju/3CcSR5OJ83AWaxKMSEh1DX3M6o1BgRIsKgxOsNiGpjYvMODjKNvdoIzuNrpwftdoir74UJlwzYG0YpYBVMjBTN+PRYQoOsDRCc6kaqm0z31WD9Q/oD7pGRCiNNExO8GEm1+9DsKqzh/jd3UdHQyujUaBbPygn6XLH2wtrRHqb1CsKg5uhGcm37AMhTR3rYQfd/sh35vFeX1Z3IFUcw2WPUi2QGZ5Il6DgbnxWZVvADT4x0iIwYaRoPw/58sXp3EY+/r3+A7iuu472d+lC7BZMzOiV2jULpUSJGhKFGfYlLR403HvqP/2Ga/RURI4LJZwfLAZiSndC3Cxmg6MZnekeN0dbr3Ueg/9Khm8ZI0wQRGTG6Ayob2zo89pdPDnXqAzMlVn/+cekxQR8rCAOamHRyLQUA5GuZNGme/xYPNEb3yGTy3qBTYmT58uWMGjWKiIgIpk+fzmeffeZz/5deeokpU6YQFRVFZmYm1113HRUVFZ1asNCRw2X1vLKlAFX1Pm6tsqGVVbuKvO5zorqJr49VoyhwYW7fzpcZqDi8Rhod7qsDMTLi5jNSGWRkxNfkZHAM+7P5eL964v6LJ3Lvggn9wlxPEHqVnNmkxkWRQg0qFvZr2S4PaxqUa3FsVccBnfv76muCFiOvvvoqd9xxB7/85S/Zvn07Z511FgsWLKCgoMDj/hs2bGDx4sXccMMN7Nmzh//+9798+eWX3HjjjV1evKBz/1u7uPfNXbzy5TGv+/z8v19zy0vbeG7TEY+Pr9lTDMCMnMQuW2vbVI1Nhyp4Z0chmw5VDLg/is5ipGkKq5tMj5H0QRAZKbe7p3oqOPVEMJOTg2FSVjw3nTMmaK8TQRjwWKwoCx5noj06sld1TdUoCqQotawPv4N5li0Dcnhk0H/VTz75JDfccAM33ngjEydOZNmyZWRnZ/PMM8943H/z5s2MHDmS2267jVGjRnHmmWfyk5/8hK1bt3Z58QK02VS2F1QD8MqXngXh8apGPt5fCsB/vihA0zqKg9W7dTFy0aSuzZdZvbuIMx//mO//YzO3v7KD7/9jM2c+PnDzmMEw3MmFtXgAp2nMyIhbN01KgGmavpicLAiDntxF5E6cBECe5rkAPINKngldxkWWLXyRX8GPn9/qMi+rPxOUGGltbeWrr75i3rx5LtvnzZvHxo0bPR4ze/Zsjh8/zqpVq9A0jZKSEl5//XUuueQSr8/T0tJCbW2ty5fgmf3Fdaa51s7jNew5UdNhn9e2HjftvL8prWebXbwYlNe38OURXUXP78KwO6NOwP2uuLimecDmMYMhyx4ZaWy1UW2vlRiIBaxmZKSlnTabSo29TTlQn5G+mpwsCIOdiZNPBWCnOhpPAWfDA3BJ6At8vLeED/JK+Pun/gdv9geCEiPl5eXYbDbS011ztunp6RQXF3s8Zvbs2bz00ktceeWVhIWFkZGRQUJCAn/+85+9Ps/SpUuJj483v7Kzs73uO9TZedxVfLzmlqqxqRr/3apvM+7SX3WLoKzNK0HV4ORh8WYRZrD4qhMwtg3EPGYwRIRazVZWgMhQK3ERA8/Kx7mbpspeL2JRICEyMNt/Y3JyZ4f9CYLgmdwsvdPxoDaMjtOrdCwKpFPJ4VL9Jv6jfaUeo+H9jU4lX90NhzRN82pClJeXx2233cYDDzzAV199xerVq8nPz+emm27yev777ruPmpoa8+vYMe+1EEOdr49VAzBluD73463thTS3OUa/rz9QRlFNMwlRofz+O1MAePfrIuqaHV0ORoom2KiIc23Iis/ze6ROYKBh1I2AfsEdiOZcps9Iaztl9Y56EUuA1uv9YdifIAxGRqdEE2bRaCCSY1qq1/32a9nU2z/ij1c1cbC0vpdW2HmCEiMpKSlYrdYOUZDS0tIO0RKDpUuXMmfOHH7+859zyimncNFFF7F8+XKeffZZioo8h+3Dw8OJi4tz+RI88/XxagBuPncMwxIiqW1uN8UFwMtb9CjIt6cNZ85JyYxOjaapzWZ6PtQ0tbHxkN7SG0y9iHttyCP/2xvQcYO9TsCoG4GBmaIBR2RE0xwTdoP1GOmLycmCMNgJsVoYn6TfLHirGwH4yt5VY/DRvtIeXVd3EJQYCQsLY/r06axdu9Zl+9q1a5k9e7bHYxobG7FYXJ/GatV/mAMhdNSfaWxt50BJHQDTRiTy3enDAXj6k4NsOlRBUXWT+Sb83sxsFEXhe6fpKS+j8+bjfSW02TTGpsVwUlpg/g3eakMCYbDXCWQ5RUasFmVApqUinWbpFFQ2AoF30jgzf3ImG+45n5d/dAZ/+t5UXv7RGWy453wRIoLQBSaM0P9+8lTPYkTVYL16CuCoIfl47yATIwB33XUX//znP3n22WfZu3cvd955JwUFBWba5b777mPx4sXm/gsXLuTNN9/kmWee4fDhw3z++efcdtttzJw5k6ysrO57JUOQPSdqUTVIjwtne0EV/7FHQQ6W1vP9f2zmvCfWYVM1po1IYFx6LADfPnU4IRaFr49Vs7eoNugUjT8PCW8MhTqB1buLeGWLox5nw8HyAdlJZLEoZhHrMbsY6YwVPDhmbVw6dRizxiRLakYQusDq3UWsySsB9MiI+72O8f1n6sku3289Wkl1Y2tvLbNTBC1GrrzySpYtW8bDDz/M1KlTWb9+PatWrSInR1dpRUVFLp4j1157LU8++SRPP/00kydP5rvf/S7jx4/nzTff7L5XMUQx6kUy4iO4+cVtlNa1uDzebO+y2VdcZ14QU2LCmZurp9RWfH6ETw+UAYGnaPx5SHhiKNQJGNGi2uZ2l+0DtZMoyp6qMcRISicm9gqC0H24f8Z8rk6mGNebu2KSubb1FzTj+veqavDJ/rJeW2tnULQBkCupra0lPj6empoaqR9x4mcvb+fdr08QGx5CXUu73/3/as/Vr9tfyrX//tLcnp0UyfqfnxdQseU7Owq5/ZUdQa0zMz6CJQtzB2143qZqnPn4x15FmoIuGDfcc/6AEWPn/P4TjlY0MjYthm9K67lr7jhuu2BsXy9LEIYk3j5jFFROt+wjjWpKSWCLOgHVS4xhzphkXvrRGb2xXBcCvX4PvL5DwcSIjAQiREBvrZ2bm8FZY1PJio/ghP2NPX9SRsBdH4HWfPz6komkxIaTFqunZgbKRbgzBOM46nE8eD/EjIxUdS1NIwhC1/H2GaNhYbOaa35vQSWdSkpIIoMKSkk0xcn2Y9W021TTwdimamzJr6S0rrlffE6LGBmgVDa0msWFgeJ8QfzujGz+9NE3QHAtvYaHRHFNs8e6ESMKcO2cUYNagDgzGB1Ho+01I81teqov2G4aQRC6j0A+Oy6ybGFJ6PPc0Ho3JVoSD4S+wFTLQZa0LmatNpPGVhvbj1Vz2sgkVu8u4qF381wETl9HsGXIwwBlp72l15PduIKKFRspVHOGJQ8LqvmY8aa+4rRsYsJDGJMazbTsxICfVzwkOjIYHUejwl3vUyQyIgh9h7/PjossW3gmdBlRWhP7NH1uzQzLATKo5G9hy8gJ0f2dPtpb2m+dskWMDFC+PqY7r55uj1QYXGTZwufht7Et/Cd8Hn4br4Q9yobw27jIsgVwvKmHJUTy4V3n8MbNswM2szIQDwlXBqPjqBEZMUjuRGuvM0N1eKIgdAe+PmMUVJaEPg/A19pYNCyMUEpIU6rN1t6fhf8P0K0c+qtTtqRpBihGZGRKdgLzJ2dw84vbmGdXx+DoLwfH8KT7Q3/BzFEXO7Z3YYjb/MmZzM3N6Fc5x77CiBbd/OI2FHD5Qx+o0SKjZsQg0Lk0nuiPIWFBGEj4+owJo510qrAosFUdD8AM5YD5uEWBC9vXY1Wu4UCJbyfWvqxvk8jIAETTNNN5VRcjmTxz9RQeCtPVsfs1zzE86XmsTimbriIeEg4GW7QoOtwRGQm1Kp2esdNfQ8KCMNDw9hnTQhgfq9MA2KrpzqszLPtd9klQGpieYiNQ+qK+TSIjAwD3qufhiZGU17cSYlHIzdRbpeZXvARUepudhEWByKZiOLoRRp3Ve4sfQgymaJFzZCQpOqxTM3b8DU9UcHR4DcSfkSD0Nu6fMWvzSnhvZxH/ts3nXMvXbFdPAuA0NzECcP7oKLaUtXTY7om+qG8TMdLP8RTiTojSp6dOyIwlItQKeSth3W8DO2F9SU8sU7BjRIsGOs41I0md7KQZjC3PgtDXOH/GzBiZxPu7i9moTuZN21k0E0489YxRTjgdoUBcFuefMYPHvvjc57mNbsi+qG+TNE0/xluIu7pRH8eYGBUGqg1W3xP4SWM8DzQUBGecu2lSOtlJMxhbngWhPzEsIZKLJumf6Y+2/wDQu2gsihGPtEcc5z/GmPR4wqyOS35/64YUMdJPCWQGzM7j1diOfA61J3zs5UTcMMjxPNBQEJxxjox0tpNmMLY8C0J/4/o5owCoIwqA6c4pmrgsuOJ5yF2E1aIwPEkf5HnHBSf1u/o2SdP0UwKZAVPT1M6hw4cY53MvJ+Y/Bhar//2EIY9zZKSzaZpADfIGUsuzIPQ3puckcvKweHYV6nYPp118A8RepkfBc2a7fOaPSIricFkD6fGRbLjn/H5V3yZipJ8ScIhbSwhMjJx7P+Qu6tKahKGDS2TER5rGl6X0YGx5FoT+hqIoXDdnJHe99jVhVgsnn3Y2hHq+6cxJ0qMnRysa+119m4iRfkqgoWvryDmwKwtqi8BbUiduGJx9d/ctThj0OHfTeKsZCcQ/xGhHdN8vQ3xGBKHbWDgli53HaxiTFqM3NXhhRHI0AAWVDb21tIARMdJP8RfiBrur55hUmP84vLYYvN1/SnpGCBJnnxFPaRqjuNr9vWn4hzjnngdTy7Mg9EdCrRYeXDTJ734j7JGRYOea9QZSwNpP8TUDxsAMcecu0ouU4tzuMp2KlwQhGJwjI+5pGn/+IdDRUloM8gSh78lJdqRpNK1/jWSQyEg/xluIOzrMyh+umOIa4s5dBBMu0U3N6ks8Fi8JQqA4R0ZS3CIj4h8iCAOT7ERdjNQ1t1Pd2EZiF2dOdSciRvo5Roh71a4ibntlO5oGb986h7HpsR13tljFXVXoFmLCvUdGxD9EEAYmkWFW0mLDKa1roaCyUcSIEBxWi8I3JXVoGswanexZiAhCNxIbEcrd88YRYrUQHe76MSH+IYIwcMlJjqK0roWjlY1MyU7o6+WYiBgZALTZVF758hgAV58xoo9XIwwVfnr+WI/bxT9EEAYu2UlRfHmkioKK/tVRIwWsA4CP9pZSWtdCSkwY83Iz+no5whDHV3G1+IcIQj9DtUH+Z7Drdcj/jJxE3YW1v3XUSGRkAPCfL44C8N0RDYQd+1wKU4U+R/xDBGEAkLcSbfU9KE4jQ0aEXQJczdEKESOCDyrqWwgNsRAXoU/mLfhiJeu/0YXH9w/+HA6X6i278x+Xll2hTxH/EEHox+StRHttMRqaSwQzu/kAAAUlFX2zLi+IGOlHvLOjkDtf3YGqQWxECMMi21CrTwDZnGXZyQhLqb5jbZFuciYeIkIf098spQVBAFQbTe/+nHBNw/3eYKRSAkBxo0ZzSysR4f2jo0bESB/hPtPDalH4+X93YvhE1TW3s69ZAbIB+IH1Q6ejNUCB1ffq3iKSshEEQRDs2I58TmRTsUfHzGRqiaaJBiIp2PM54049r/cX6AERI32Ap5keFgVUDebmpvPkFVMozvuc4289QKGWQpTSwjzLVrezaFBbqJucibeIIAiCYMfXNHdFgWyllH1aDlsOnGDcqb26NK+IGOllvM30MCIi3zolg9iIUGJDyxlr/dr/CetLun2NgiAIwsDF3zT3HKWEfVoOBxpjem1N/pDW3l7E10wPg8fe36/P9IhJD+ykge4nCIIgDAmsI+dwQktC9XKxGaHo9YelocN6cVW+ETHSi/ib6QFQUtPIvk2roK4IolLwPiZPgbhhepuvIAiCINiZOSaVp0JvBOggSFRNT9MAtNn6z7A8SdP0Iv5mdVxk2cKS0OfJWlvp50x2gTL/MSleFQRBEFywWhTOvex6bvlPKw+EPk8WjmtKMcmstOk3sf3J+EzESC/ia1bHRZYtPBO6LLATxWXpQkTaegVBEAQPzJ+cCVfdxHdXziG7/mvSqKaUBI7FTOEn88ey9Z08CiobUVUNSz/wBhIx0ot4m+lhQWVJ6PP6/729J6JSYP5SiM0UB1ZBEATBLw5jwukuxoSqpvHQu3tpaVcpq28hPa7vh1pKzUgv4jzTw5mZln1kKZXehQhAY7kuREadJUJEEARBCAjDmPDSqcOYNSYZq0Uh1GohK0EXIP3FFl7ESC9jzPSIDHX86NOoDuxgaeMVBEEQuoERSVEAHO0n03tFjPQB8ydnMiZN7+++/syR/OSSADtipI1XEARB6AZGJEUDcKyfFLGKGOkDVFXjYGk9ANecMZJJs+brRanSxisIgiD0MLb2diLqCgDYuf8gtvb2Pl6RiJE+4VhVI81tKuEhFj1UZrHqU3iBjoJE2ngFQRCE7mH7mucof3Qcpx1cBkD1iW8of3Qc29c816fr6pQYWb58OaNGjSIiIoLp06fz2Wef+dy/paWFX/7yl+Tk5BAeHs6YMWN49tlnO7Xg7samamw6VME7OwrZdKhCdz/tYQ6U6FGRMakxjnHruYv0Kbxxma47x2XJdF5BEAShy2xf8xxTNt5GqlbBCPv03mNaGqlaBVM23tangiTo1t5XX32VO+64g+XLlzNnzhz+9re/sWDBAvLy8hgxYoTHY6644gpKSkr417/+xUknnURpaSnt/SAs5GlgXWZ8BEsW5uo92j3EgZI6AMZnxLo+kLtIn8J7dKNerBqTLm28giAIQpextbeTtekhQLeQGIHuwlpBPI1EEE0zIzf9EtsFV2MN6X3Xj6AjI08++SQ33HADN954IxMnTmTZsmVkZ2fzzDPPeNx/9erVfPrpp6xatYoLL7yQkSNHMnPmTGbP7tv6B2Ngnbs9e3FNMze/uI3Vu4t67LkNMTI2tBx2vQ75n4Fq0x+0WPX23ZO/I228giAIQrew74s1pFNhWkjEKU0kol+LjmrpKAokUseW5+7vk/UFJUZaW1v56quvmDdvnsv2efPmsXHjRo/HrFy5khkzZvC73/2OYcOGMW7cOO6++26ampq8Pk9LSwu1tbUuX92Jr4F1xraH3s3rsZTNgaOFAIzb/ht44wZ47luwbDLkreyR5xMEQRCGNk1VhR22OadqDCYce6lPClqDEiPl5eXYbDbS011bTNPT0ykuLvZ4zOHDh9mwYQO7d+/mrbfeYtmyZbz++uvceuutXp9n6dKlxMfHm1/Z2dnBLNMv/gbWaUBRTTNb8v3NiAme9t0rOVSl/6LHK8ccD9QWwWuLRZAIgiAI3U5kYscJvcb03qOa45qeSD37vljTa+sy6FQBq6K4dnxomtZhm4GqqiiKwksvvcTMmTO5+OKLefLJJ1mxYoXX6Mh9991HTU2N+XXs2DGP+3UWfwPrgt0vYFQbR1c9QSuhRNLMMKXc6UF7FGb1vY6UjSAIgiB0AxNOv4hqol225dgjI0edIiMA4YdW9dq6DIISIykpKVit1g5RkNLS0g7REoPMzEyGDRtGfHy8uW3ixIlomsbx48c9HhMeHk5cXJzLV3fia2BdZ/YLmKMb+aYuDICxSiEWxT0NpEFtoV7AKgiCIAjdhDUkhOOp57tsuzrkIz4Mu5sHQl5w2T7m8Iu9HqUPSoyEhYUxffp01q5d67J97dq1XgtS58yZw4kTJ6ivrze3HThwAIvFwvDhwzux5K5jDKzzYTFGZrw+UKhbqS9hv6a/5nEWz0IM4MChg73aaiwIgiAMfnLnLHT5PlOp5CTLCSKUto4793KUPug0zV133cU///lPnn32Wfbu3cudd95JQUEBN910E6CnWBYvXmzuf9VVV5GcnMx1111HXl4e69ev5+c//znXX389kZGR3fdKgsB5YJ0XizGWLMx1eIB0FzHpHFDtYkTxLkYe+Lic21/Zwff/sZkzH/+4Rzt7BEEQhKGBJT4roP0U6PUofdBi5Morr2TZsmU8/PDDTJ06lfXr17Nq1SpycnIAKCoqoqCgwNw/JiaGtWvXUl1dzYwZM7j66qtZuHAhTz31VPe9ik5gDKzLiHdNxWTER/DMD07tGZ+RnNl8o4wCYKwHMaJqcEJLZos6wdzWG63GgiAIwhAgZzbEZXnsJPVILw5nVTRN6/d5gNraWuLj46mpqen2+hGbqrElv5LSumbSYvXUjK+IiKpqXP/cl7TbNFZcdxoh1sD1XGu7Su6vV9GuKXwefptLAasKoMHNbXewRp3pcpyCLpI23HN+90drBEEQhKFD3kp47ZrA9v3he7rfVRcI9Po95GfTWC0Ks8Ykc+nUYcwak+z3Yn+orJ51+8vYcLCcD/KCU41HKhpo1xRiQjWy4sJcHivWkj0KEejZVmNBEARhCJG7CL77HKqPy7+qQVNkRq8OZx3yYiRYthVUmf9fsfFIUMeazquZiSh37tZV5+X/YsOcFZzZ8iePQsSZbm81FgRBEIYctomX8kvrXaiaLjycMb5/qG0xtl6UCCJGgmR7QbX5/y35lewtCtwd9kCxLkbGpcW62L5bR5/tU6UadHursSAIgjDk2JJfycsNp3Jz2x0U49o1WowepX+lfmqvRuN7fxrOAMcQIykx4ZTXt/DcxiM8dvkpAR1rTOsd5zYgz2g1Lq5p9lhYZNSMdHursSAIgjDkMKLsa9SZrG2ZwUzLPtKoppQEtqgTzJvj3ozGS2QkCOqa2zhQqkc3Hr50EgBv7yikurE1oOONY8elx7hs77NWY0EQBGHI4RxlV7GwWc1lpTqbzWquS5S+N6PxIkaC4OtjNWgaDE+MZMHkDCZmxtHcpvLql/7t6pvbbBwpbwBgXHpsh8f7pNVYEARBGHL0mfGnDyRNEwTb7cWr00YkoigK187O4Z43dvH8pqPceNZon5GLw2UNqBrER4aSFhvucZ/5kzOZm5sRVKuxIAiCIASDEY2/+cVtKOBSHtBX0XgRI0Gw/Vg1AKeOSADg0qnDWPr+Pgqrm/hwbwkXTcoA4Otj1Tz2/j52Fdagahqqppm27uPSY7wOFQRHq7EgCIIg9BRGNP6hd/NcpthnxEewZGFur0fjRYwEiKZpLpERgIhQK1eels3fPj3McxuPMGV4Ar9bvZc3t5/wep4LJnoeKCgIgiAIvUl/isaLGAmQoxWNVDW2ERZiITfT4SJ3zRk5/GP9YTYequC8339IU7v+S7zc8ik/CllFdGw8nHMPlnFzCQ+xkBLjOUUjCIIgCL1Nf4nGixgJEMPsbHJWHGEhjrrf4YlRXDgxnQ/ySmhqV5iu7OeB0BeYYjkMgNZwHGXVYoh5Xne+EwRBEATBBREjAWL4ixgpGmd+ffF4Yg7/j3Ntm1ho2YRzSYiChoaCsvpemHCJbnYmCIIgCIKJiJEA2X7MqBdJ6PBYdt0OnuRJ8KIzFDTHOOYuDh0SBEEQhMGG+IwEQFOrjb1FumHZqR4iI2pdcUDnCXQ/QRAEQRhKiBgJgJ3Hq7GpGulx4WQ6m5KpNsj/jMID2wM6z966qB5aoSAIgiAMXCRN44RN1Ty2OBn+ItOydbMzVBt8+jvY9DS01pNtP17TwJOFiKrpw4cORp3MpF57NYIgCIIwMBAxYmf17qIO5i+ZdvMXh79IAuSthLdvgtYGj+dxFySOcczXcG1cdE8tXxAEQRAGLCJG0IXIzS9u6zAxt7immZte3EZchP5jmqbugdeu8XoeRdHFiMs5SObhtmvYGXu2TN0VBEEQBA8MeTFiUzUeejevgxABh19/bXM7IRaFk7/6pd/zGVGRp9ovY6M6mS/t45ifkam7giAIguCRIV/AuiW/0iU1443RkY1E1hcEfN6D6nA2q7mkxUfJ1F1BEARB8MGQj4yU1vkXIgCnN38GoYGf94rzZvD90WfI1F1BEARB8MOQFyNpsRFeH5ugHGWqcohKYrjeujrwk0alcOYFi8RtVRAEQRACYMiLkZmjksiMj6C4ptmlbsSCyrNhvyeDSoIObFz8BxEigiAIghAgQ75mxGpRWLIwt8P2mZZ9ZCmdECKzb4PJl3XL2gRBEARhKDDkxQjA/MmZPPODUwmzOn4caVQHdQ4tPBa++xzMe6SbVycIgiAIgxsRI3bmT84kOSYMgDsuHMtPLpkd0HFvtM/h+633c6b2LKu103tyiYIgCIIwKBExYqel3UZxrd5Z84Mzcpg0az7EZQGe8zSqBie0ZH7efjOb1MmcqG3j5he3sXp3US+uWhAEQRAGPiJG7ByrbELTIDrMSnJ0mF6AOv9x+6OugsTZ4l21/wiN4teH3s3DpnqyUBMEQRAEwRMiRuwcq2wEIDspSh+GB5C7CK54HuJcDcuKSebmtjtYo8502a4BRTXNbMmv7I0lC4IgCMKgYMi39hocrdAH3+UkR7k+kLsIJlwCRzeydc9enthYwxa7xbs3AjVSEwRBEARBxIjJUXtkJCfZw2RdixVGnUWbmsvmDZv9nsuXkZogCIIgCK5ImsZOQYUuRkYkRXndxzBI82Y9ogCZ8REynVcQBEEQgkDEiB1HZMS7GHE2SHMXJMb3S2Q6ryAIgiAEhYgRQFU1CuxiZERDHux6HfI/A9XWYV/DIC0j3jUVkxEfIdN5BUEQBKETSM0IUFrXQmu7ihUbWW/9P1DsIiQuS2/vzV3ksv/8yZnMzc1gS34lpXXNpMVGyHReQRAEQegknYqMLF++nFGjRhEREcH06dP57LPPAjru888/JyQkhKlTp3bmaXuMo9s+AGCYUk6o4hQNqS2C1xZD3soOx1gtCrPGJHPp1GHMGpMsQkQQBEEQOknQYuTVV1/ljjvu4Je//CXbt2/nrLPOYsGCBRQUFPg8rqamhsWLF3PBBRd0erE9gmrj6MbXAchRStwetJuXrb7XY8pGEARBEISuE7QYefLJJ7nhhhu48cYbmThxIsuWLSM7O5tnnnnG53E/+clPuOqqq5g1a1anF9sjHN1IQaM+k2aEUuphBw1qC+Hoxt5dlyAIgiAMEYISI62trXz11VfMmzfPZfu8efPYuNH7xfrf//43hw4dYsmSJQE9T0tLC7W1tS5fPUZ9CUe1dMCbGHHsJwiCIAhC9xOUGCkvL8dms5Genu6yPT09neLiYo/HfPPNN9x777289NJLhIQEVi+7dOlS4uPjza/s7OxglhkcMekUaGmApzSN636CIAiCIHQ/nSpgNWe32NE0rcM2AJvNxlVXXcVDDz3EuHHjAj7/fffdR01Njfl17NixziwzMHJmU4DejjvCoxhRIG4Y5Mzu8IhN1dh0qIJ3dhSy6VCFDMgTBEEQhE4QVGtvSkoKVqu1QxSktLS0Q7QEoK6ujq1bt7J9+3Z++tOfAqCqKpqmERISwgcffMD555/f4bjw8HDCw8ODWVqnqW1VqdJ0C/gRSpnbo3aBNf8x3RLeidW7i3jo3TyKahxzaDLjI1iyMFe8RgRBEAQhCIKKjISFhTF9+nTWrl3rsn3t2rXMnt0xchAXF8euXbvYsWOH+XXTTTcxfvx4duzYwemnn9611XcDhg18SoRGTHyi64NxWfrUXjefkdW7i7j5xW0uQgSguKaZm1/cxurdRT26ZkEQBEEYTARtenbXXXdxzTXXMGPGDGbNmsXf//53CgoKuOmmmwA9xVJYWMjzzz+PxWJh8uTJLsenpaURERHRYXtfcdQuRrLTEuGm3XrXTH2JXiOSM7tDRMSmajz0bh6eEjIaeizloXfzmJubId4jgiAIghAAQYuRK6+8koqKCh5++GGKioqYPHkyq1atIicnB4CioiK/niP9iaOVDQDkJEWZ03l9sSW/skNExBkNKKppZkt+JbPGJHfnUgVBEARhUNIpO/hbbrmFW265xeNjK1as8Hnsgw8+yIMPPtiZp+0RjhkzaZKjA9q/tM67EOnMfoIgCIIw1Bnyg/KMNE1Okvdpvc6kxUb43ymI/QRBEARhqCNixBAj/7+9e4+Nsl7zAP6d6WXKpTNcepkWsFTUIlQMtJYOoYBAaxE5BRNB5HSHYIwQwRRN3AKJQLKGQgTWDVA0shijQlfbeiBgpSf2gkuRQoZQnIDusUD30FKL9GJZQNpn/xg7OsylM0Nnhnfm+0nehP76e2eep0+gD++8v9870r1mJCN5BPRa542GCpZVNRnJIwYiPCIioqAXsk/t7ekVnPifNlzt+D8AwKhhg9w6r9Lcglt3HT+npu921Y0LJvDmVSIiIjeF5JWRivPNmL71G+T/5ynI78tiFu35736X5PYt6W2/+ZvD7w8bHIHiv07hPiNEREQeCLlmxNEeIYNwCxm/VuGjzz5BRcP/OjzP1ZLePppwNbIn6Ac4YiIiouAWUs3IvQ3F46pLAIDp6vP4j8hdOBj5b5hcOgM93//N7tz+lvQCQEvnbZxq/GWAoyYiIgpuIdWM/LmheEZ9Cga1GYDtA/Ji5TrUnxsB8yGbc7mkl4iIyDdCqhnpaxTU6MXGiI+tT+t9SNVqnWO977SiEOj940ZVLuklIiLyjZBqRvoahQz1BSSqfsHa8FLsiNiDLHWDzTwVBOj8p2Vr+N9lJI9Agi4KztbIcEkvERGRd0KqGelrKOLQDgCYqL6M58O+RbK6xfEJv/7x8U2YWoWNCyYAgF1DwiW9RERE3gupZqSvoWjFMPdOGBoPwHLja90/ruP23V4UzH0M8fdseqbXRXFJLxERkZdCbtOz3NQEYOlSXCstttys6vBChgrQJgJJ01BxvhmbD5ttVtLotRqsnfsoxsYMQVy05aMZXhEhIiLyTkhdGemT+8RoxLywEyqVCuLsQ5fcIlSYW+32JAGAa5238e9//xGacDUM40ayESEiIroPIdmMAEDYxDyoFn8Mlfaej1a0icDij9EzfoHTTc76xjYfNqOn19U2aERERNSfkPuYxsaEvwDj51tWzfx6zXKPSNI0QB2GU/+47nKTMwHQ3HELpxp/gWHcSP/FTEREFGRCuxkBAHUYkJxlN8xNzoiIiPwjZD+m6Q83OSMiIvIPNiNOcJMzIiIi/2Az4gQ3OSMiIvIPNiMu5KYmoPivU6DXcZMzIiIiX+ENrP3ITU1A9gQ9TjX+gtauW9zkjIiIaICxGXFDmFrF5btEREQ+ErrNSG+Pw/1FiIiIyL9CsxkxHwIq/hXovPrHmDYRyN1q2QiNiIiI/Cb0bmA1HwL+619sGxEA6Gy2jJsPBSYuIiKiEBVazUhvj+WKiKsnzlQUWuYRERGRX4RWM3L5hP0VERsCdP7TMo+IiIj8IrSakV+vDew8IiIium+h1YwMjR/YeURERHTfQqsZSZpmWTXj6okz2lGWeUREROQXodWMqMMsy3cBOH3iTG4R9xshIiLyo9BqRgDLPiKLPwa09zxXRptoGec+I0RERH4VmpueTfgLMH4+d2AlIiJ6AIRmMwJYGo/krEBHQUREFPJC72MaIiIieqCwGSEiIqKA8qoZ2bNnD5KTkxEVFYW0tDQcP37c6dyysjJkZ2cjNjYWWq0WBoMBX3/9tdcBExERUXDxuBkpKSlBQUEBNmzYAJPJhKysLMybNw9XrlxxOL+2thbZ2dk4evQozpw5g6effhoLFiyAyWS67+CJiIhI+VQi4uipcU5NnToVU6ZMQXFxsXXs8ccfx8KFC7Flyxa3XmPixIlYsmQJ3n77bbfmd3Z2QqfToaOjA1qt1pNwiYiIKEDc/f3t0ZWRO3fu4MyZM8jJybEZz8nJwYkT7j1crre3F11dXRgxYoTTObdv30ZnZ6fNQURERMHJo2akra0NPT09iI+3fXZLfHw8Wlpa3HqN7du3o7u7G4sXL3Y6Z8uWLdDpdNZjzJgxnoRJRERECuLVDawqle1W6iJiN+bIgQMHsGnTJpSUlCAuLs7pvHXr1qGjo8N6NDU1eRMmERERKYBHm57FxMQgLCzM7ipIa2ur3dWSe5WUlODll1/G559/jrlz57qcq9FooNFoPAmNiIiIFMqjZiQyMhJpaWmorKzEokWLrOOVlZXIy8tzet6BAwewYsUKHDhwAPPnz/c4yL57bHnvCBERkXL0/d7ud62MeOjgwYMSEREh+/btE7PZLAUFBTJkyBC5dOmSiIgUFhZKfn6+df5nn30m4eHhsnv3bmlubrYe7e3tbr9nU1OTAODBgwcPHjx4KPBoampy+Xve46W9gGXTs23btqG5uRmpqanYuXMnZsyYAQBYvnw5Ll26hOrqagDArFmzUFNTY/caRqMRH330kVvv19vbi6tXryI6Otqte1Pc1dnZiTFjxqCpqSlolwwzR+UL9vyA4M8x2PMDmGMw8EV+IoKuri4kJiZCrXZ+m6pXzUiwCIX9S5ij8gV7fkDw5xjs+QHMMRgEMj8+m4aIiIgCis0IERERBVRINyMajQYbN24M6mXEzFH5gj0/IPhzDPb8AOYYDAKZX0jfM0JERESBF9JXRoiIiCjw2IwQERFRQLEZISIiooBiM0JEREQBFXLNyDvvvINp06Zh8ODBGDZsmFvniAg2bdqExMREDBo0CLNmzcL333/v20Dvw40bN5Cfnw+dTgedTof8/Hy0t7e7PGf58uVQqVQ2R2Zmpn8C7seePXuQnJyMqKgopKWl4fjx4y7n19TUIC0tDVFRUXj44Yexd+9eP0XqPU9yrK6utquVSqXChQsX/Bix+2pra7FgwQIkJiZCpVLhyy+/7PccpdXQ0xyVVsMtW7bgqaeeQnR0NOLi4rBw4UJcvHix3/OUUkdv8lNaDYuLizFp0iRotVpotVoYDAZ89dVXLs/xZ/1Crhm5c+cOXnjhBaxatcrtc7Zt24YdO3Zg165dqK+vh16vR3Z2Nrq6unwYqfdeeuklnD17FhUVFaioqMDZs2eRn5/f73m5ublobm62HkePHvVDtK6VlJSgoKAAGzZsgMlkQlZWFubNm4crV644nN/Y2Ihnn30WWVlZMJlMWL9+PV5//XWUlpb6OXL3eZpjn4sXL9rU69FHH/VTxJ7p7u7Gk08+iV27drk1X4k19DTHPkqpYU1NDV577TWcPHkSlZWVuHv3LnJyctDd3e30HCXV0Zv8+iilhqNHj0ZRURFOnz6N06dPY/bs2cjLy3P6H2u/18+zx+QFj/3794tOp+t3Xm9vr+j1eikqKrKO3bp1S3Q6nezdu9eHEXrHbDYLADl58qR1rK6uTgDIhQsXnJ5nNBolLy/PDxF6JiMjQ1auXGkzNn78eCksLHQ4/6233pLx48fbjL366quSmZnpsxjvl6c5VlVVCQC5ceOGH6IbWACkvLzc5Rwl1vDP3MlRyTUUEWltbRUAUlNT43SOkuvoTn5Kr6GIyPDhw+XDDz90+D1/1y/krox4qrGxES0tLcjJybGOaTQazJw5EydOnAhgZI7V1dVBp9Nh6tSp1rHMzEzodLp+462urkZcXBwee+wxvPLKK2htbfV1uC7duXMHZ86csfnZA0BOTo7TXOrq6uzmP/PMMzh9+jR+++03n8XqLW9y7DN58mQkJCRgzpw5qKqq8mWYfqW0Gt4Ppdawo6MDADBixAinc5RcR3fy66PEGvb09ODgwYPo7u6GwWBwOMff9WMz0o+WlhYAQHx8vM14fHy89XsPkpaWFsTFxdmNx8XFuYx33rx5+PTTT/HNN99g+/btqK+vx+zZs3H79m1fhutSW1sbenp6PPrZt7S0OJx/9+5dtLW1+SxWb3mTY0JCAj744AOUlpairKwMKSkpmDNnDmpra/0Rss8prYbeUHINRQRvvPEGpk+fjtTUVKfzlFpHd/NTYg0bGhowdOhQaDQarFy5EuXl5ZgwYYLDuf6uX/iAv2IAbNq0CZs3b3Y5p76+Hunp6V6/h0qlsvlaROzGfMndHAH7WIH+412yZIn1z6mpqUhPT0dSUhKOHDmC559/3suoB4anP3tH8x2NP0g8yTElJQUpKSnWrw0GA5qamvDuu+9ixowZPo3TX5RYQ08ouYarV6/GuXPn8O233/Y7V4l1dDc/JdYwJSUFZ8+eRXt7O0pLS2E0GlFTU+O0IfFn/YKiGVm9ejVefPFFl3PGjh3r1Wvr9XoAli4xISHBOt7a2mrXNfqSuzmeO3cO165ds/vezz//7FG8CQkJSEpKwo8//uhxrAMlJiYGYWFhdlcIXP3s9Xq9w/nh4eEYOXKkz2L1ljc5OpKZmYlPPvlkoMMLCKXVcKAooYZr1qzBoUOHUFtbi9GjR7ucq8Q6epKfIw96DSMjI/HII48AANLT01FfX4/33nsP77//vt1cf9cvKJqRmJgYxMTE+OS1k5OTodfrUVlZicmTJwOwfM5fU1ODrVu3+uQ9HXE3R4PBgI6ODpw6dQoZGRkAgO+++w4dHR2YNm2a2+93/fp1NDU12TRg/hYZGYm0tDRUVlZi0aJF1vHKykrk5eU5PMdgMODw4cM2Y8eOHUN6ejoiIiJ8Gq83vMnREZPJFNBaDSSl1XCgPMg1FBGsWbMG5eXlqK6uRnJycr/nKKmO3uTnyINcQ0dExOlH8X6vn09ui32AXb58WUwmk2zevFmGDh0qJpNJTCaTdHV1WeekpKRIWVmZ9euioiLR6XRSVlYmDQ0NsnTpUklISJDOzs5ApNCv3NxcmTRpktTV1UldXZ088cQT8txzz9nM+XOOXV1d8uabb8qJEyeksbFRqqqqxGAwyKhRowKe48GDByUiIkL27dsnZrNZCgoKZMiQIXLp0iURESksLJT8/Hzr/J9++kkGDx4sa9euFbPZLPv27ZOIiAj54osvApVCvzzNcefOnVJeXi4//PCDnD9/XgoLCwWAlJaWBioFl7q6uqx/zwDIjh07xGQyyeXLl0UkOGroaY5Kq+GqVatEp9NJdXW1NDc3W4+bN29a5yi5jt7kp7Qarlu3Tmpra6WxsVHOnTsn69evF7VaLceOHRORwNcv5JoRo9EoAOyOqqoq6xwAsn//fuvXvb29snHjRtHr9aLRaGTGjBnS0NDg/+DddP36dVm2bJlER0dLdHS0LFu2zG752Z9zvHnzpuTk5EhsbKxERETIQw89JEajUa5cueL/4B3YvXu3JCUlSWRkpEyZMsVmuZ3RaJSZM2fazK+urpbJkydLZGSkjB07VoqLi/0csec8yXHr1q0ybtw4iYqKkuHDh8v06dPlyJEjAYjaPX1LIO89jEajiARHDT3NUWk1dJTbvf9OKrmO3uSntBquWLHC+m9MbGyszJkzx9qIiAS+fiqR3+9IISIiIgoALu0lIiKigGIzQkRERAHFZoSIiIgCis0IERERBRSbESIiIgooNiNEREQUUGxGiIiIKKDYjBAREVFAsRkhIiKigGIzQkRERAHFZoSIiIgCis0IERERBdT/A5AXg33lDaS1AAAAAElFTkSuQmCC\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_160_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -2413,110 +2380,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 0\n",
-      "Error: 0.32149601703519115\n",
-      "Bias^2: 0.3123314713548606\n",
-      "Var: 0.009164545680330616\n",
-      "0.32149601703519115 >= 0.3123314713548606 + 0.009164545680330616 = 0.3214960170351912\n",
-      "Polynomial degree: 1\n",
-      "Error: 0.08426840630693412\n",
-      "Bias^2: 0.0796891867672603\n",
-      "Var: 0.004579219539673834\n",
-      "0.08426840630693412 >= 0.0796891867672603 + 0.004579219539673834 = 0.08426840630693413\n",
-      "Polynomial degree: 2\n",
-      "Error: 0.10398646080125037\n",
-      "Bias^2: 0.10077114273548984\n",
-      "Var: 0.0032153180657605116\n",
-      "0.10398646080125037 >= 0.10077114273548984 + 0.0032153180657605116 = 0.10398646080125036\n",
-      "Polynomial degree: 3\n",
-      "Error: 0.06547790180152352\n",
-      "Bias^2: 0.062082386342319454\n",
-      "Var: 0.0033955154592040923\n",
-      "0.06547790180152352 >= 0.062082386342319454 + 0.0033955154592040923 = 0.06547790180152355\n",
-      "Polynomial degree: 4\n",
-      "Error: 0.06844519414009445\n",
-      "Bias^2: 0.06453579006728322\n",
-      "Var: 0.003909404072811221\n",
-      "0.06844519414009445 >= 0.06453579006728322 + 0.003909404072811221 = 0.06844519414009444\n",
-      "Polynomial degree: 5\n",
-      "Error: 0.05227921801205679\n",
-      "Bias^2: 0.04818727730430286\n",
-      "Var: 0.004091940707753925\n",
-      "0.05227921801205679 >= 0.04818727730430286 + 0.004091940707753925 = 0.05227921801205679\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 6\n",
-      "Error: 0.03781367141738902\n",
-      "Bias^2: 0.03365768507152769\n",
-      "Var: 0.0041559863458613296\n",
-      "0.03781367141738902 >= 0.03365768507152769 + 0.0041559863458613296 = 0.03781367141738902\n",
-      "Polynomial degree: 7\n",
-      "Error: 0.027609773491022394\n",
-      "Bias^2: 0.022999498260366198\n",
-      "Var: 0.004610275230656182\n",
-      "0.027609773491022394 >= 0.022999498260366198 + 0.004610275230656182 = 0.02760977349102238\n",
-      "Polynomial degree: 8\n",
-      "Error: 0.017355848195593312\n",
-      "Bias^2: 0.010331721306655165\n",
-      "Var: 0.007024126888938144\n",
-      "0.017355848195593312 >= 0.010331721306655165 + 0.007024126888938144 = 0.01735584819559331\n",
-      "Polynomial degree: 9\n",
-      "Error: 0.026605727637184558\n",
-      "Bias^2: 0.010018312644139219\n",
-      "Var: 0.016587414993045335\n",
-      "0.026605727637184558 >= 0.010018312644139219 + 0.016587414993045335 = 0.026605727637184554\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Polynomial degree: 10\n",
-      "Error: 0.021592704588021178\n",
-      "Bias^2: 0.010516485576646504\n",
-      "Var: 0.01107621901137467\n",
-      "0.021592704588021178 >= 0.010516485576646504 + 0.01107621901137467 = 0.021592704588021174\n",
-      "Polynomial degree: 11\n",
-      "Error: 0.07160048164232538\n",
-      "Bias^2: 0.014436800088896381\n",
-      "Var: 0.05716368155342902\n",
-      "0.07160048164232538 >= 0.014436800088896381 + 0.05716368155342902 = 0.0716004816423254\n",
-      "Polynomial degree: 12\n",
-      "Error: 0.11547777218876518\n",
-      "Bias^2: 0.016285782696017142\n",
-      "Var: 0.09919198949274803\n",
-      "0.11547777218876518 >= 0.016285782696017142 + 0.09919198949274803 = 0.11547777218876518\n",
-      "Polynomial degree: 13\n",
-      "Error: 0.2284246870217162\n",
-      "Bias^2: 0.01975416527168255\n",
-      "Var: 0.20867052175003364\n",
-      "0.2284246870217162 >= 0.01975416527168255 + 0.20867052175003364 = 0.2284246870217162\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_162_3.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -2622,49 +2486,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "============================\n",
-      "Underfitting vs. Overfitting\n",
-      "============================\n",
-      "\n",
-      "This example demonstrates the problems of underfitting and overfitting and\n",
-      "how we can use linear regression with polynomial features to approximate\n",
-      "nonlinear functions. The plot shows the function that we want to approximate,\n",
-      "which is a part of the cosine function. In addition, the samples from the\n",
-      "real function and the approximations of different models are displayed. The\n",
-      "models have polynomial features of different degrees. We can see that a\n",
-      "linear function (polynomial with degree 1) is not sufficient to fit the\n",
-      "training samples. This is called **underfitting**. A polynomial of degree 4\n",
-      "approximates the true function almost perfectly. However, for higher degrees\n",
-      "the model will **overfit** the training data, i.e. it learns the noise of the\n",
-      "training data.\n",
-      "We evaluate quantitatively **overfitting** / **underfitting** by using\n",
-      "cross-validation. We calculate the mean squared error (MSE) on the validation\n",
-      "set, the higher, the less likely the model generalizes correctly from the\n",
-      "training data.\n",
-      "\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1400x500 with 3 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_165_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"\n",
     "============================\n",
@@ -2812,22 +2634,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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Uv3OZ+exxqY+X4ylCHhtZ5fsf4VXM08+Nx9OQS+ndqVjbmkSPA2FGZFLCWmjUqFHccccd11yna9euTJw4sUbyCCHUWRZ/npd6j2Xs+3/gE3HloSFuRkyX5vhnX8An6wIJ83+v8v0LyyeFigm6UiGxcOFC7O3tmTp1Kq+99ho6ne6yx9q10rNeCHFjlh5IBaBvc/9q2b/e2YlDncsGbSyY/2O1HENYNilUzMCXX37J8OHDmTlzJs8++ywATZs25ezZsxUenTt3VpxUCGFOLpxMpXTHTnSakX6RvtV2HKfhwwBouHUtJYaiajuOsEy1s1DJy7v6o7Dw+tctKPjvdW/S1KlTGTduHD/88AMPPfRQ+XIbGxvq1atX4WFnZwdAXFwc3bt3x8HBAU9PTx555BFyc6/e4z4vL4/7778fZ2dnfH19+fDDD286txDC9CV9OY8l3z3FL0vfwdu1+gYoDB96G5mOrtTJz+LwT0ur7TjCMtXOQsXZ+eqPu++uuK6399XX/fccNMHBl69zE55//nnefPNNli5dyt3/znUV+fn59OnThzp16rBr1y5++eUX1q5dy7hx4666zaRJk/jrr79YvHgxq1evZv369ezZs+emsgshTJ/tihUAFLdtV63HsdHbkRjTA4C8HxZU67GE5ZHu1yZqxYoV/P7776xbt47u3btf9npcXFyFyQEjIiLYuXMn8+fPp6CggO+++w4np7LRJWfOnMmAAQN477338PHxqbCf3NxcvvrqK7777jt69iwbkunbb7/F3796rlcLIUxDYU4ejeO2A+A1rGpvS74S+3uGwLpfCdu8htLiErn7R1y32vlJucZlEKytKz5PS7v6ulb/apA6ebLSkf4tKiqKixcv8sorr9CmTRtcXFwqvN64cWOWLFlS/lyv1wNw6NAhmjdvXl6kAHTs2BGj0ciRI0cuK1SOHz9OUVERMTEx5cs8PDxo3LhxlZ2LEML0HP15KVHFhaS5eBLas1O1H6/J8DtY9FkfVgVF82BSOu0a+fz3RkJQWwsVpxuYx6K61v0P9evXZ9GiRXTr1o0+ffqwcuXKCsWKnZ0dYWFhl22nadpVZz290nKFc1IKIRQq+LXsVuGk9t3w/vcfXdXA1l7PpknvsDo2lZDjGVKoiOtWO/uomInAwEA2bNhAWloavXr1Ijs7+z+3iYiIIDY2lrx/dOTdsmULVlZWNGrU6LL1w8LCsLW1Zfv27eXLMjMzOXr0aNWchBDCJNXfsQEA/e0DauyY3cK9Afjr8DVaqoX4FylUTJy/vz/r168nPT2dXr16kZWVdc31hw8fjr29PSNHjuTgwYP89ddfjB8/nhEjRlx22QfA2dmZBx98kEmTJrFu3ToOHjzIqFGjsKqBv7CEEGqk7kvAPz2VEp0VYcNqrlDp0siLyPPH6LtoNmfj5I8hcX3k28gM1K9fnw0bNnDp0iV69uzJpUuXrrquo6Mjq1atIiMjgzZt2jBo0CBuvfVWZs6cedVt3n//fTp37sztt99Ojx496NSpE9HR0dVwJkIIU7A5346h90zhq2FP41y3To0d193RjqmbvubJLT+Q/O1PNXZcYd50mhl3UsjOzsbNzY2srCxcXV0rvFZYWEhSUhIhISHY21ff+ABC/JN87oQ5GPfDXpYeOMuEWxvyZM/LLwlXp22PTCJmzgcciIwh6sDWGj22MB3X+v7+N2lREUKIWsRo1Nh6PB2ATg3r1vjx6907CIBGh/ZQcCmnxo8vzI8UKkIIUYuc2LiT8b9/Qu/kfbQIcK/x4wd3bsM5d2/sS4o48uNvNX58YX6kUBFCiFrk4s+/MXrPHzyesBJb65r/CtBZWXGqfVcADL//UePHF+bH4gsVM+6CI8yQfN6EqXPYugmAgk5dlGWwH1h2p1HQjg1oRqOyHMI8WGyhYmtrC5TNfSNETfn78/b3508IU2IsKSXkyH4APPrcqixHo2EDKbK2wSk/h+SEE8pyCPNgsSPTWltb4+7uTtr/hsB3dHS86oitQtwsTdPIz88nLS0Nd3d3rP89FYMQJuDUpp2EFOaSb2tPgxoYNv9qHNxdeOalb1ic78JrubaMUJZEmAOLLVQA6tWrB1BerAhR3dzd3cs/d0KYmrQV6wgBjodFEqm3U5oluHNbSlcfZUviRUa0D1KaRZg2iy5UdDodvr6+eHt7U1xcrDqOsHC2trbSkiJMmvWWLQDktmmvOAl0DKvLB6uPsvX4RUpLjVgr6NgrzINFFyp/s7a2li8QIUStZ59yEgCXHt3UBgEi67vxyqZv6J6wheOt59Hotu6qIwkTJSWsEELUAqcz87ntnvfp8tjXNBjYU3UcbKytaFl4keBLZ0n/fbnqOMKESaEihBC1wO6TmaDT4d60EY6uzqrjAFDUpSsALpvXK80hTJsUKkIIUQvsPJkBQJugmpuE8L/Uu/s2ABomHqAwO1dxGmGqpFARQohaYOikEcz+9S06W2erjlIuMKYlaa510ZcWk/jrKtVxxL+czy5kw9ELZOQVKc0hhYoQQli4S8lnaX58P70St9Ms3F91nHI6KytOtYwBIHf5SsVpxL/tXr6ZGW9+x9PfblOaQwoVIYSwcCeXrQUg2SsAjxDTKVQA6FZ2t0+dXWq/DMXl6n49i8XznuGR9fOU5pBCRQghLFzh5rIi4FzTVoqTXM7/zj4c8/Bnl0cIeYUy3pUp8TgcB4C+XVulOWrFOCpCCFGbOe7fC4DWpo3iJJfzjQqn46RvOXOpgJCULDo1rKs6kgAMRcVQUABAve4dlWaRFhUhhLBgmtFI8PF4ADy7q5vf51rahngAsCMpXXES8bejafn0fPAzbnl+Ib7Nw5VmkUJFCCEs2OldcbgW5mKwtiWoq/qh86+kXYgHNqUlnNmyW3UU8T8HzlwCIDjMH52V2lJBLv0IIYQFO3b8LOfqR2Dn7EBze73qOFcUY1/IgY+GYm00UvjMHdi7OKmOVOvFnc4CyqY6UE1aVIQQwoJtcA5g8H1T+W3qN6qjXFVgszDy9Y7oS4s5sfwv1XEEcO/zo/jhxxfoUHBWdRS1hUpJSQkvvfQSISEhODg40KBBA9544w2MRqPKWEIIYTH2n74EQItA0xmR9t90VlacatoagKyV6xSnEYU5eTQ5cYAOyQcIDfNTHUftpZ/33nuPL774gm+//ZamTZuye/duRo8ejZubGxMmTFAZTQghzF6RoZiTSefA2p7m/u6q41xTSadOsGMNzju3qo5S6yVv2EEjYymZjm7Ua9pQdRy1LSrbtm1j4MCB9O/fn+DgYAYNGkSvXr3YvVs6VAkhxM06tW4rez4YzMIFkwnydFQd55q8+5fN6ByaeIDiQoPiNLVb5p+bAEgOjVDekRYUFyqdOnVi3bp1HD16FID9+/ezefNm+vXrd8X1DQYD2dnZFR5CCCGuLGP9JqzQsHNxRqfTqY5zTUG3tOWSgwuOxYWcWLVRdZxazWr3LgDyW7ZWnKSM0kLlueee45577iE8PBxbW1tatmzJxIkTueeee664/pQpU3Bzcyt/BAQE1HBiIYQwH1a7yr5w8lqY3oi0/2ZlY01Sk7KcmdJPRal6hw8A4NgpRnGSMkoLlZ9++ol58+bxww8/sHfvXr799ls++OADvv322yuuP3nyZLKyssofKSkpNZxYCCHMh9eh/33hdDTN8VP+7eJdQ5na+X6W1W+hOkqtlXUmjYALZd+tQb26KE5TRmln2kmTJvH8888zbNgwACIjIzl16hRTpkxh5MiRl62v1+vR601zHAAhhDAluRczCTx/CgD/3qbxhfNf6o28l89yAnEpseE1o4a1lWlfrrJERw6fIj8kGp+SXJoEqb/jBxS3qOTn52P1r4461tbWcnuyEELcpJS/tmGFxnk3LzxDzOMyeRNfF5z1NuQUlnDorPRBVGE77owa8jpfTP1RdZRySguVAQMG8Pbbb7Ns2TJOnjzJ4sWLmTZtGnfeeafKWEIIYfaytuwA4GyI2nlaboSNtRXd3I3cdmgjp39fqTpOrbQ/5RKASd3OrvTSzyeffMLLL7/M448/TlpaGn5+fjz66KO88sorKmMJIYTZ2+/iy+lmt+LeubPqKDdk+P6VtF/yMbsv9oHHh6qOU6toRiOnDiWBzokWge6q45TTaZqmqQ5RWdnZ2bi5uZGVlYWrq6vqOEIIYTL6zNjI4XM5zB4RTa+m9VTHuW4Hv/uVZiPv5py7N/Uyz6uOU6ukxh7Cr2UESR5++J5Jwt7ertqOdSPf3+pHchFCCFGlDCWlHEvLBaCZCUwqdyNC+nenRGdFvUtpnE9IVB2nVjm7ej0AJc6u1Vqk3CgpVIQQwsIcjz9J6Pkk6uqt8HWzVx3nhjh5unOyfhgAp5euVZymdineuh2AjKbNFSepSAoVIYSwMLk/LWTV1+P46tc3TX5E2itJj4oGoGTjZsVJahe3g7EAWLUzrXF3pFARQggLo+3dA0B+eITiJJVj3fkWADz3y7xvNaUov5CQU4cB8OllWh2wpVARQggL434kHgC7NtGKk1SOf/8eAASfOUZe+iW1YWqJk+u2YF9SxCUHFwLayqUfIYQQ1aTEUETQ6WMAeHc2rSb861WvWUMm3/sqt4z5iv2ZJarj1AoZq/8C4GSj5uisrRWnqUgKFSGEsCCnt8diX1JEnp0D9VtHqY5TaTn9b+esqxd7TmWqjlIrbHEP5ruW/Unvc5vqKJeRQkUIISzIxY3bAEgOaIiVjWn9ZXwjWgfVAWC3FCrVTtM0frIP5pVej+H8yEOq41xG6ci0QgghqlbJnr0AZIc3U5zk5rTxseex7b/Q4o8TGO//y6yLLlN3OrOAtBwDNlY6mge4q45zGSlUhBDCgiwLv4XNGUaibzO9Jvwb0TjAk5CtP+FYXMiJzbto0NU8+9uYg6N/7SD6dAK61tHY25peQSiXfoQQwkJomsZSx0BmdhiG14A+quPcFBu9HSdCy1qFLqz8U3Eay+b05SwWzX+WZ9Z/qzrKFUmhIoQQFiItx0BmfjFWOgjzdlYd56bltmoLgNXWrYqTWDavA2Xj7tjd0klxkiuTQkUIISzEye376XV0G+2tc02yCf9GOXYvG3jML36v4iSWKyctneCzJwAIuO1WxWmuTAoVIYSwENrixcxe/DZPr/1KdZQqEXzbrRjRUT/jLBePnVQdxyKdXP4n1pqR1Dr18GrcQHWcK5JCRQghLITNwYMAFDU17zt+/ubqU5eTfmVfnil/yASF1SF33UYAUiNaKk5ydVKoCCGEhfA4UTZXi0Mr0/3SuVEXIltRaGPH+cNJqqNYJJc9ZTMml7aPUZzk6uT2ZCGEsADFhQb8z50CwKdTa8Vpqs6F518mMvJemgZ7Yd73MZmeovxCQhPjAPC5rZfiNFcnLSpCCGEBTm+Pxc5YQq6dI/UiG6uOU2WiIkMptrYlPjWLwuJS1XEsSty5HO655x0+7P0IQbeYbnErhYoQQliA9G27AEgJCENnZTn/tQd4OODloqe4VONAyiXVcSzK9lNZxPo1JnH4IyY3EeE/Wc6nWQgharHiffsByA6znNYUAJ1Ox8Tjf7Hqq8cpfe9d1XEsyo6kDADaNfBQnOTapI+KEEJYgEVt+jPf4EH/2023U2RlhTrpaHwxmdgd21VHsRglhiL6fv4mdeo1pt1jpj09gbSoCCGEBdhS4sLSJp3xurWz6ihVrk6PLgAEH92PsUT6qVSFE6s3cc/upby5dhbhfm6q41yTFCpCCGHmLuUXcTarEIBG9VwUp6l6IT1vodDGDveCHFK271MdxyJkLF8DwInwlljZmvbFFSlUhBDCzJ3cvIeHd/xK30vHcLW3VR2nytk52nMiJAKA8yvWKU5jGRy2bQagsOMtipP8NylUhBDCzBlWrubF9V/z6I5FqqNUm6z/TVCokwkKb1ppcQkNDpe1THn2M93xU/4mhYoQQpg5XVzZoF0F4U0VJ6k+jl3L/vKvd1AmKLxZSeu24GLIJ0fvSIOeHVXH+U9SqAghhJlzO3YIALuWUYqTVJ/gAT057lGfbb7hXLyUpzqOWUv/YxUAJxq3wNrE+6eA3J4shBBmzVhSSsCZEwDU7dBGcZrq41bfh0EvzicxLZdZZ3Lo7e6kOpLZyo8vK2wLOndTnOT6SIuKEEKYsbOxCTgWF2KwtqV+G8ttUQFoHVwHgD2nMhUnMV+GklIev+VR2j7+LR6PPaQ6znWRQkUIIczY+S3/GzrfNxgbvZ3iNNUrOsgDK2MpqTv3q45itvYlX6KguBSjry8NmwSpjnNd5NKPEEKYMcOBgwBkhjRSnKT6tdMbOPDRMOxKiyl8egD2LnL550ZtSbwAQMewuuh0OsVpro8UKkIIYcYW3zKIt0uDGN65EZbbQ6WMf0QIGbZ6nIsKOLxyA+GD+6mOZHZ6PnEfrYs1Clq8pzrKdZNLP0IIYcbis0s5WC8Mz3YtVUepdjorK5LDWwBwad0GtWHMUPb5izRN3EeXpL20aBqoOs51U1qoBAcHo9PpLnuMHTtWZSwhhDALRqPG8Qu5AIR5OytOUzMM7comXdTvlAkKb9Txn5dirRlJ8QqgXqT5XCpUWqjs2rWLs2fPlj/WrCmbe2Dw4MEqYwkhhFk4l3CcF5fNZMT+lQR6OKqOUyPce3YFIPjIfjSjUW0YM1O0cjUAZ1qb/iBv/6S0j4qXl1eF5++++y6hoaF06dLliusbDAYMBkP58+zs7GrNJ4QQpuzi5h2M2LecpHoh2Fh/ojpOjWjQqzOFNnbUyc8ieUcsgTGtVEcyG767yub30fcx/WHz/8lk+qgUFRUxb948Hnjggav2RJ4yZQpubm7lj4CAgBpOKYQQpiP/f3f8ZASFKU5Sc+wc7TkR3ASA88v/VJzGfJyLO0rghRRKdVY0GHyb6jg3xGQKld9++41Lly4xatSoq64zefJksrKyyh8pKSk1F1AIIUyM1eHDABQ1ClecpGYl3T6UaZ2Gs9EjRHUUs3Fq/kIAjjZohpuv13+sbVpM5vbkr776ir59++Ln53fVdfR6PXq9vgZTCSGE6XI7mQiAbbMIxUlqlv1DD/Cx7W4aGJ14WnUYM7Gz0J6ioBZY9eitOsoNM4lC5dSpU6xdu5Zff/1VdRQhhDALmtGIb+pJADzatlCapaZFB5UNpX/iQh4ZeUV4OFn2iLw3y1BSyueuEeQPe4ul4zupjnPDTOLSz9y5c/H29qZ///6qowghhFm4mHgSV0MepTori5/j59/cHe1o7VBE7yNbObx2q+o4Jm9XUib5RaV4u+hp6ueqOs4NU16oGI1G5s6dy8iRI7GxMYkGHiGEMHnndscBcKZuffROtePW5H96dtM8Zv32Drp581RHMXmH/1iHV24GXRp5mc2w+f+kvFBZu3YtycnJPPDAA6qjCCGE2dgb0pyoCQuY9dQ01VHU6Fg2Foj7vl2Kg5i+nu89y65P72dweoLqKJWivFDp1asXmqbRqJH5jJInhBCqJablkG3vjGuLZqqjKOHbtxsADU4ewpCXrziN6TqzJ56gtGRKdFaE39lTdZxKUV6oCCGEuHHH0v43dL5X7Rg6/9/82zYn3ckdfWkxJ5avVx3HZJ3+cREAR8Ka4+pTV3GaypFCRQghzNBDHz/Hq2tnEW5r+O+VLZDOyopTTaMBuLRyreI0pst+zSoAcrqbZ2sKmMjtyUIIIa7fpeSz9IjfBEBe/e8Up1GnuOMtsHMdTjvkzp8ryb2YSXh8WR8en2F3KU5TedKiIoQQZubsjn0AnHP3xsnTXW0Yhbz6l7UShB3dT3Fh7WxZupaj3y5EX1rMGU8/gju3UR2n0qRQEUIIM5Oz9wAA5/1DFSdRK7hLO168cxK9HvyUg+fzVMcxOaW//QZASude6KzM9+teLv0IIYSZMSaU3WZaENpQcRK1rGysOT9wCKcPnWfnyUxaBnmojmQyikuNPNlhNG3cwnnwUfO97APSoiKEEGbH8UTZHD+6prVrjp8rad+grDjZkZShOIlp2ZmUwWmdAxvb9aFJzw6q49wUKVSEEMLMeKccB8C1Ze0aOv9K2tdz5MGdixnywTOUFpeojmMyVsefA6BHEx+srcxvNNp/kks/QghhRnKzcrEtKus46tuupeI06oUHevDklh9xLsrn2J9bCevdWXUk5TSjke4vjMHeuyExg15SHeemSYuKEEKYkePZJUSPn0+P53/GPaCe6jjK2ejtON64OQAXl61RnMY0HFu5iS4JW5iwZQHtG/mojnPTpFARQggzciwtF3Q66ob4q45iMvJjOgGg37pZcRLTcPH7HwE43DwGe1fzH7lYChUhhDAjiX8Pne9t/l9AVaVO71sBCD60F2NJqeI0amlGIwFrlgJgvOtuxWmqhhQqQghhRtp98BJfLXydDueOqI5iMhr06UK+rZ46+dkkb9mjOo5Sx9dsxj/9DIU2doQ/fK/qOFVCChUhhDAjYQd2cOvxXQQ6WauOYjLsHO05ERYJwPk/VilOo9aFr74HIKFlJ5zr1lGcpmpIoSKEEGaiMCcPv/RUAOq1a6E2jInJadcRg7UNF5POqI6ijGY0ErS27LKPNmSo4jRVR25PFkIIM3F29wFCNCPZeic8w4JUxzEp+icn0NzjFhzdXelr1LAy87FDKiPu8GlOezXA3pBPxIPDVMepMtKiIoQQZiJjVywAqX4hZj13S3VoFhGElZMTGXlFHD6XozqOEktO5PL4nS/w+uercajjqjpOlZFPuhBCmImiuLI5frKDwxQnMT12Nla0CykbTn/r4XOK09Q8o1FjedxZAPq2sqzWNilUhBDCTOiPHgbA2KSJ4iSm6e7cEyyb+wRtnhytOkqNO7h5Hw4nEnHW29C1sZfqOFVK+qgIIYSZyCzRkWPngENUM9VRTFJERCAN0k6Qn3mGovxC7BztVUeqMQVvTWHdmoWsGvQo9ra9VcepUtKiIoQQZqCk1MiYPhOJnPgzHncNUB3HJAV3aUeGkxuOxQaO/bFWdZwaU5iTR5ONKwCoP9CyihSQQkUIIcxCckY+xaUaDnY21PeUUWmvxMrGmqSo9gBkLV2pOE3NiZ81H1dDHufcvIgYdrvqOFVOChUhhDADfw+d38DLqVbeenu9Srt3B6DO1o2Kk9Qc63llg7wl9b0LKxvLGwhQChUhhDADzp/MYO2cMTy4Z4nqKCbNf1DZZbGwpHhy0tIVp6l+F48n0+zAVgD8xj2sOE31kEJFCCHMgF3CQcIyTuNrU7sn3fsvfi2acNrTDxvNyPFFy1XHqXbHPpqDjWbkaFATgjpGq45TLeSuHyGEMAPuJ48BoJc7fv7TsS592XnkBBfybGmhOkw1068q64uTOchyRqL9NylUhBDCxBlLSvE7dwoAzzYt1IYxA8Vvvs1T3+0m0OjII5qGTmeZfXriTmcx5PYX6XdsB68/YZmXfUAu/QghhMk7n5CIU3EhRVY2+EVLi8p/6RDqiZ21FckZ+Zy4mKc6TrX5YWcyxda2MHQI7oG+quNUGylUhBDCxKXtjAUg1csfW72d2jBmwElvQ9vgOjRJO8HBxZY5nkpubgF/7EsB4J62gYrTVC8pVIQQwsQVxMYBkBEUqjiJ+XgsYRUr5j5Bg4+mqI5SLeLf/ojlnzzA40kbyuc4slRSqAghhIk7U2JDvHcD8iMiVUcxG/6DbgOg8ZG95KVfUhumGnjM/4bArPN09rK12D44f5NCRQghTNwPzXvTf/THZEycpDqK2QiMaUmqhy92pSUkLvhDdZwqlbh8Aw1TjlBkbUPjSWNVx6l2yguVM2fOcN999+Hp6YmjoyMtWrRgz549qmMJIYRJ0DSNY/8blTbMS4bOv146KytS2nYGwPCHZRUqmdM+BuBA+57UCfJTnKb6KS1UMjMz6dixI7a2tqxYsYKEhAQ+/PBD3N3dVcYSQgiTcSErn5y8Qqx0ZcPni+tnP7Ds8k/Qjg1oRqPiNFUj81QqURuWAuA43vJbU0DxOCrvvfceAQEBzJ07t3xZcHCwukBCCGFi0pau4dC0Iexu1Br7Kf1VxzErjYYNxDDOlnqX0jixfgcNuseojnTTDr81jZiSIo75N6LJ4L6q49QIpS0qS5YsoXXr1gwePBhvb29atmzJnDlzrrq+wWAgOzu7wkMIISxZXmwc+tJinPQyPueNcnB34VBk2WzKZ7//WXGam1dsKCL0528ByHzoMXRWyntv1AilZ3nixAk+//xzGjZsyKpVqxgzZgxPPPEE33333RXXnzJlCm5ubuWPgICAGk4shBA17FACAAVhjRQHMU/p459i+NC3eKfZANVRbtqKwxd5ZOBkfm3dj6hnHlEdp8YoLVSMRiOtWrXinXfeoWXLljz66KM8/PDDfP7551dcf/LkyWRlZZU/UlJSajixEELULKfjiQBYN41QnMQ8tRraj+0NWhJ/oYCTZj5K7debk4j1a0zylOnonRxVx6kxSgsVX19fIiIq/vI1adKE5OTkK66v1+txdXWt8BBCCEtW70wSAO7RzRUnMU91nOyIaeAJwKr4c4rTVN7eUxnEplzCztqK4e2CVMepUUovenbs2JEjR45UWHb06FGCgmrXP4IQQlxJ1pk06uZmAODbvqXiNObrDm/oNmsO4auzYe+fquNUSsnQe3izyIakRyfg5aJXHadGKS1UnnzySTp06MA777zDkCFD2LlzJ7Nnz2b27NkqYwkhhEk4u2MvbsB5Ny98vCx7mPTq1DXcG4/dS7BCI+3QcbybmNdUBCc37KTtjtW0RkdKszdUx6lxSi/9tGnThsWLF/Pjjz/SrFkz3nzzTWbMmMHw4cNVxhJCCJNwKqeU5Y06EN+8o+ooZq1uoxCONiibdTppzjzFaW7chZfLipPYNt0I6hitOE3NU36/22233cZtt92mOoYQQpicXZ4hfHnnC4zuGEx31WHM3KU+t8FncTgvWwLTXlUd57ql7kug5eYVALi89rLiNGrUjpuwhRDCDCX+PXS+twydf7MCHx4BQJOj+0g7dFxxmuuX8sLr2GhGDjRtR8N+XVXHUUIKFSGEMFGXEpNA02jo7aI6itnza9GEQ6FRWKFx4pMvVce5LucTEmmxZjEA1pMnK06jjhQqQghhgvIysvj93WHETx9MQ32p6jgWIXvQUAC8lixSnOT6HJ/0GvrSYg6FRhFxj/kPWFdZUqgIIYQJSt0eC4DBTk8dPy+1YSxE+LgHSHX1YkO9JhxJTlcd55pOpefxRMMBfNH2LrS336k1w+VfSe09cyGEMGFZe/cDcNavgeIklsPNvx6vfryMN3o8wuL4C6rjXNOMtYlctHdh66PPETG0dk9GKYWKEEKYoOKD8QDkNghTnMSy3B3tD8CivacpLjUqTnNliUnn+W3faQAm9WqsOI16UqgIIYQJsk88CoAW3kRxEsvSPdwHL0cbGsXtYPdPK1XHuaLcQUP54ccXeMAtl0h/N9VxlFM+jooQQojL1U0pu4XWqUWU4iSWxc7Gig+Or6DLTx+xPyEG7u2nOlIFB79fTMu9GyjRWeHXUS77wU20qJSUlLB27VpmzZpFTk4OAKmpqeTm5lZZOCGEqI0Mefn4XjwDgE+7FmrDWKDQx0cDEBm3nXNxRxWn+X8lhiKcnnsGgD19hxLUuY3iRKahUoXKqVOniIyMZODAgYwdO5YLF8o6JU2dOpVnnnmmSgMKIURtk5yayZy2d7Ey4ha8GoeojmNx/Ns1J75xNFZoJL0zTXWccntenkrI2RNk2TvT+PMPVccxGZUqVCZMmEDr1q3JzMzEwcGhfPmdd97JunXrqiycEELURkcLrHiv6yi+eHxKrb4ttToVjXkMgCa//0DBpRzFacpmym706fsAHBrzNO6BvooTmY5K/QZs3ryZl156CTs7uwrLg4KCOHPmTJUEE0KI2ioxreyLU4bOrz5RY0eS6uGLe0EOB975WHUcDj80njr52Zz0CSZ6Su0dhfZKKlWoGI1GSksvHynx9OnTuLjIUM9CCHEzcvfuxys3k4ZeTqqjWCxrWxuSRzwMgO83szCWqBv9d9fhVJz27QEg9/1p2NrrlWUxRZUqVHr27MmMGTPKn+t0OnJzc3n11Vfp18+0elALIYS5ufejyez6dATtjuxUHcWiNXtpItl6J3J1NmzYEq8kQ2FxKc8tPcodIz7k68kzaTbiTiU5TFmlbk+ePn063bp1IyIigsLCQu69914SExOpW7cuP/74Y1VnFEKIWqOkqJj655MB8GrdXHEay+Zctw5zP/6JN44bCY/NosstGlZWuhrNMPPPY5y4mIeXuxN3P/lIjR7bXFSqRcXPz4/Y2FgmTZrEo48+SsuWLXn33XfZt28f3t7eVZ1RCCFqjbOxh9CXFlNgo6delIxKWt3uvK8nzvZ2HDqbzar4czV67MRlf6F/83XsSop5c2BT3Bxta/T45qLSA745ODgwevRoRo8eXZV5hBCiVkvfGUsAkOoTSKitjMlZ3dwd7RjdKYQ5K+I4+sYH9PrhPaxr4H3PSUvH8f7hjM84SxM3a3o0u6Paj2muKtWi8u2337Js2bLy588++yzu7u506NCBU6dOVVk4IYSobQri4gDIDApVnKT2eLBDEMu/m8iEhdPY/fLUaj+eZjRy5M77qJ9xlrPuPrSZLWOmXEulCpV33nmnfPyUbdu2MXPmTKZOnUrdunV58sknqzSgEELUJjaHDwNQ3ChccZLaw81Jz/n7HgCg0SfvkXW6ei8B7XptOq23rqREZ0XWV9/iVl+6TFxLpQqVlJQUwsLKZvT87bffGDRoEI888ghTpkxh06ZNVRpQCCFqE/eTxwDQRzZVnKR2af3eiyTVC6FOfjaHH55Qbcc5+sc6oqa8AMCuB58k/K7e1XYsS1GpQsXZ2Zn09HQAVq9eTY8ePQCwt7enoKCg6tIJIUQtomkaX7YcwJetB+LRub3qOLWKjd6O/A+mA9Bu5c/EfbOoyo9xPiERj3uHYF9SRGzzTrT7/L0qP4YlqvQ4Kg899BAPPfQQR48epX///gDEx8cTFBRUpQGFEKK2OJtVyE/hXXi35yPUbxmhOk6t03T4QHb0HgyAz4QxVXoJ6FJ+Ee/MWou+qICkeiGErV2ClY11le3fklWqUPn000+JiYnhwoULLFq0CE9PTwD27NnDvffeW6UBhRCitkhMK5t9PriuE7bWMsePCpE/ziHFKwDv7IvsGTmeUqN20/vMKSxm5Nc7+d0hkHEPvo9+xTKc69apgrS1Q6XuwXJ3d+eDDz7gwIEDpKWlsWTJEgCio6OrNJwQQtQm6dv3EH06gcDgNqqj1FqOddw48813bB73FE83vZOBSxN47fbK9xfKSErhrc9Wst/ajzqOtrz45P34+chUMzeiUoXKypUruf/++0lPT0fTKlabOp3uivMACSGEuLb6875k0ZpFbDM+BmO6qo5TazXs15Wji5eS+eM+vtl6Ejd7Gyb2aHjDM1mf2rIHqzvu4NWcTE4/NI1Xxg+lkRQpN6xSbYvjxo1j8ODBpKamYjQaKzykSBFCiMpxPZEIgG2k9E9RrX9zP17oV3aLeMGU99jZbxhF+YXXta1mNLL7rY/x6taJgIunKXBw4oPhrWlW3606I1usSrWopKWl8dRTT+Hj41PVeYQQolbSjEZ8U5MAcI+WOX5MwSOdQ/E+l8yAqd9irRk50XAvJbNm0+i27lfd5vjqTRRMfIrWh3YDEN84Gp+lC6kXFlxDqS1PpQqVQYMGsX79ekJDZeREIYSoChmnzuBZkIMRHfXbtVQdR/zPHUO6se/8VwQ/P5EGqcdhwK3EN2xJ7h134dahLbqWLcnWrNmfcommEx4kZt96AAzWtuwd8ThtZ39QI0PyWzKd9u9OJtchPz+fwYMH4+XlRWRkJLa2FSdSeuKJJ6os4LVkZ2fj5uZGVlYWrq6uNXJMIYSoDvHzf6fpfXdwxsOX+umpquOIf8lIOs2J+8fQYssKbDRj+fJbH/qc454BADy98XvG7FjI/nY98Pt0Gn5yi/lV3cj3d6XKvB9++IFVq1bh4ODA+vXr0en+f1psnU5XY4WKEEJYitz9ZXP8XAxoQH3FWcTlPEL88di0lPMJiZx4/1Ocdu+g3qlE6jjYUt/dgSa+rrjGPM2lJlNo3ShEdVyLUqlC5aWXXuKNN97g+eefx+oGe0ELIYS4gvgEAApCGykOIq7FJ6IhPnNnlD9fqC5KrVGpQqWoqIihQ4dKkSKEEFXk9+jeLC12o2t/mftFiH+qVKUxcuRIfvrpp6rOIoQQtdZafX2+b3UbdXp0UR1FCJNSqRaV0tJSpk6dyqpVq4iKirqsM+20adOuaz+vvfYar7/+eoVlPj4+nDtXvVNsCyGEKcnKLyYtxwBAQ29nxWmEMC2VKlTi4uJo2bLs9rmDBw9WeO2fHWuvR9OmTVm7dm35c2trmaRJCFG7JO89yN1x6zgf2gQXe9v/3kCIWqRShcpff/1VdQFsbKhXr16V7U8IIcxN/orVfLh8OgeatgceVh1HCJOivDdsYmIifn5+hISEMGzYME6cOHHVdQ0GA9nZ2RUeQghh7rSD8QDkh8kdP0L8m9JCpV27dnz33XesWrWKOXPmcO7cOTp06EB6evoV158yZQpubm7lj4CAgBpOLIQQVc/x+FEArJrKAGFC/FulRqatLnl5eYSGhvLss8/y1FNPXfa6wWDAYDCUP8/OziYgIEBGphVCmLXz7t74ZF3g8KIVhN/VR3UcIapdtY9MW12cnJyIjIwkMTHxiq/r9Xr0en0NpxJCiOqTnZaOT9YFAHzbRytOI4TpUd5H5Z8MBgOHDh3C19dXdRQhhKgRqdv2ApDm4ombn5fiNEKYHqWFyjPPPMOGDRtISkpix44dDBo0iOzsbEaOHKkylhBC1Jic3fsBOO/fQHESIUyT0ks/p0+f5p577uHixYt4eXnRvn17tm/fTlBQkMpYQghRYzZFdOCTwa/TPSqASNVhhDBBSguVBQsWqDy8EEIod6DQho0Nounds5nqKEKYJJPqoyKEELVN4vlcABp6uyhOIoRpMqm7foQQojbJTb/E0CWzSawbSEOvHqrjCGGSpFARQghFUrft5YltP3HRuQ51nKeqjiOESZJLP0IIoUjWnv/d8VNf7vgR4mqkUBFCCEVK4srm+MkJlTl+hLgaKVSEEEIRh2NHANDJHD9CXJUUKkIIoYh3ynEAnFtGKU4ihOmSQkUIIRTIz8yiXsY5AHzbt1KcRgjTJYWKEEIokLojFis0Mh3d8AjxVx1HCJMltycLIYQCBzyDefCR2XR2LeVN1WGEMGFSqAghhAKJ6QWcquOH1j5QdRQhTJpc+hFCCAVk6Hwhro+0qAghhAJ9vpxCuM6RJne9pDqKECZNChUhhKhhhdm53LnlN6w1Ixc831IdRwiTJpd+hBCihp3Zvg9rzcglBxfqhgSojiOESZNCRQghaljmrlgAzvqFoLOS/4aFuBb5DRFCiBpWsv8AANlhjRUnEcL0SaEihBA1zOHoobIfmkWqDSKEGZBCRQghapjPqUQAXFq3UBtECDMghYoQQtSgnPRLeGRnAFD/lnaK0whh+uT2ZCGEqEFHc40Me+oXooszWFDfW3UcIUyeFCpCCFGDjpzLpdjaFrsmzVRHEcIsyKUfIYSoQUfOZQMQXk+GzhfiekiLihBC1KCO014hMiMbl+gXgCaq4whh8qRQEUKIGqIZjbTZvY46+dkcc3lZdRwhzIJc+hFCiBqSfuwUdfKzKdVZ4d8hWnUcIcyCFCpCCFFDUrfsBuBM3frYuzorTiOEeZBCRQghakj+nlgALgY3VBtECDMihYoQQtQQ6/iDABiaNFWcRAjzIYWKEELUEPcTRwHQt2iuOIkQ5kMKFSGEqAGlpUZKDEUY0eEV00p1HCHMhtyeLIQQNSA5s4C+oz7G3VjEntZRquMIYTakRUUIIWrAkXM5APgH1MXaxlpxGiHMh8kUKlOmTEGn0zFx4kTVUYQQosr9Xag09nFVnEQI82ISl3527drF7NmziYqS5lAhhGVq/faz/HzsKBe8nwOkM60Q10t5i0pubi7Dhw9nzpw51KlT55rrGgwGsrOzKzyEEMIc+Cfspe3pBALc9KqjCGFWlBcqY8eOpX///vTo0eM/150yZQpubm7lj4CAgBpIKIQQN6cwOxf/C6cB8O3URnEaIcyL0kJlwYIF7N27lylTplzX+pMnTyYrK6v8kZKSUs0JhRDi5iVv3Im1ZiTDyY26DYNVxxHCrCjro5KSksKECRNYvXo19vb217WNXq9Hr5dmUyGEebm0dRcAZ4Ia42GlvCFbCLOirFDZs2cPaWlpREf//wyipaWlbNy4kZkzZ2IwGLC2llv4hBDmzxgbC0Bek2ZqgwhhhpQVKrfeeitxcXEVlo0ePZrw8HCee+45KVKEEBbD7WgCADYtW6gNIoQZUlaouLi40KxZxb8unJyc8PT0vGy5EEKYK6NR46TenTrOHtTt1E51HCHMjkmMoyKEEJYqOSOfxwY8i52NFQkdo/97AyFEBSZVqKxfv151BCGEqFIJZ8vGewqv54KNDJ0vxA2T7udCCFGNjpy8AECErwydL0RlSKEihBDVqNvLY9k5cwS9ju9QHUUIsySFihBCVCPfk0fwzsvEt4G/6ihCmCUpVIQQoppknkrFJ6vs0o9/F7njR4jKkEJFCCGqyZkN2wE47emHi5eH4jRCmCcpVIQQoprk7tgNQFqDcMVJhDBfUqgIIUQ1sY47AIChaZTiJEKYLylUhBCimngeOwSAQ9tWipMIYb5MasA3IYSwFIXFpfwZ0Jw0G0eCO7dXHUcIsyWFihBCVINjabm81e1B3B1t2RcRpjqOEGZLLv0IIUQ1SEgtGzo/wtcVnU6nOI0Q5ksKFSGEqAapew/iZMiniQydL8RNkUJFCCGqQZ/3niVuxlB6JW5XHUUIsyaFihBCVLESQxFBKYlYoeHbvoXqOEKYNSlUhBCiiiVv2YNDiYFcO0f82zRXHUcIsyaFihBCVLGL67cCcCo4HCsba8VphDBvUqgIIUQV03btAiC7mbSmCHGzpFARQogq5n44DgDbtm0UJxHC/EmhIoQQVai40EBwSiIA9bp1VJxGCPMnI9MKIUQVSjyTyY/dHyQq/RSDWjdTHUcIsyeFihBCVKED6UV83+o2OoR6MthKGq2FuFnyWySEEFUo7kwWAJH+boqTCGEZpEVFCCGqkOPyP2hS6kKUT6TqKEJYBJ2maZrqEJWVnZ2Nm5sbWVlZuLrKfBpCCLWK8gvB1QW70hLO7D5I/eimqiMJYZJu5PtbLv0IIUQVSd64A7vSErLsnfFr2UR1HCEsghQqQghRRdL/3ARAcoMIdNKRVogqIb9JQghRRax27AAgt5UM9CZEVZFCRQghqki9Q/sBcOwsA70JUVWkUBFCiCpwKfksARdSAAjq3VVtGCEsiBQqQghRBU6tWg9AilcA7oG+asMIYUFkHBUhhKgCG70b88GQN+ge4MRo1WGEsCDSoiKEEFVg58ViNoW0wmbQ3aqjCGFRlBYqn3/+OVFRUbi6uuLq6kpMTAwrVqxQGUkIIW6Y0agRm3IJgJYB7kqzCGFplBYq/v7+vPvuu+zevZvdu3fTvXt3Bg4cSHx8vMpYQghxQ5L3HOTxlV/S69Qewuu5qI4jhEVR2kdlwIABFZ6//fbbfP7552zfvp2mTWXoaSGEeUj7YzWP7VhIQsYxbKxfUR1HCItiMp1pS0tL+eWXX8jLyyMmJuaK6xgMBgwGQ/nz7OzsmoonhBBXpW3fDkBW82jFSYSwPMo708bFxeHs7Ixer2fMmDEsXryYiIiIK647ZcoU3Nzcyh8BAQE1nFYIIS7nFb8PAH2nDoqTCGF5lM+eXFRURHJyMpcuXWLRokV8+eWXbNiw4YrFypVaVAICAmT2ZCGEMtnnL+Lk64O1ZuTC4eN4NW6gOpIQJu9GZk9WfunHzs6OsLAwAFq3bs2uXbv46KOPmDVr1mXr6vV69Hp9TUcUQoirSlqyhuaakTMevtSXIkWIKqf80s+/aZpWodVECCFMWf669QCkRslEhEJUB6UtKi+88AJ9+/YlICCAnJwcFixYwPr161m5cqXKWEIIcd1sE/43nEKnW9QGEcJCKS1Uzp8/z4gRIzh79ixubm5ERUWxcuVKevbsqTKWEEJcl8LiUu697QXqtz/NNyP7qY4jhEVSWqh89dVXKg8vhBA3ZX/KJYqMGrlBDQgMra86jhAWyeT6qAghhLnYdTIDgLbBHuh0OsVphLBMyu/6EUIIc9XipQl8mpFNacSLqqMIYbGkUBFCiEooMRTRcs96nIoKOO4r4zgJUV3k0o8QQlTCybVbcSoqIFvvRHDXdqrjCGGxpFARQohKuLhyLQBJ4S2wtpXGaSGqixQqQghRCfqtWwDIbyfz+whRnaRQEUKIG1RiKCI0fhcAngP6KE4jhGWT9kohLFRG0mlSVm8kraCEPY3bciHHQInRyKC572FrZwP+/jg0b4Z/7y54hshM5Dfi2Ir1hBvyyLJ3JrR3Z9VxhLBoUqgIYSEKc/I4/N2vFP26GL/9O/FPP4MHsNM/gi+GTy1f78Utq/HOy6yw7Qm/UM5370vA+IfxbxtVw8nNT8LxNAp9G1ESGERr6Z8iRLWS3zAhzJimaew+mYHxgQeJ3LKKFsWFFV4/5R1IQcNwRnUIxsfVHjsbK44UTeT4mdPYJZ/CM+kowedP0iD1OA3mzeTQqqWMfncBj3VrSNsQD0VnZfoWOIey8/5pvHV7BK1VhxHCwkmhIoQZys3J5+f95/lhZzLH0nL5IjUNx+JCzrl5capTT+wH3kZwv1sJqu9NENDlnxt3eqXCvjKSTnN83iL0Py/g65BO/HX0In8dvUivMA9eamZPYPuWNXlqJi/PUMK+5LIWqU6NvBWnEcLySWdaIcxIRtJptg1/nKJ6fnw970+OpeXiYGvN4Yef5PDiVfhknKPd0vk0f/ge3Opf35eoR4g/bV6eQFTcNiZ+/Rr3tA3ExkpH/QVzqdepLdsfepoSQ1E1n5n52LfnCPr8PPzrOBDk6ag6jhAWT6dpmqY6RGVlZ2fj5uZGVlYWrq4yMqSwXOlJKSROfJHmy3/GocQAwHc9RqB7803uaOGHi71tlR7v+IVczt8+mA7bVwJwJKQp7ksX4xPRsEqPY4623zGS1kvmsfaecfSZ/5HqOEKYpRv5/pYWFSFMWPb5i2wb/jgOjRvRfsn3OJQYSAwMZ9/0Lxm+/GtGtA+q8iIFINTLmZgty9j1xgyy7Z1pnBSPTdu2JCz4o8qPZW58dm7GRjPi1aKJ6ihC1ArSoiKECSosLuX7jYn0v7sLfllpABwNbILh1ddoNmoQOqua+xvjzJ54Cm+/g9DUY5TorNjz3Nu0m/J8jR3flFw8dpK6DUMAyDx5hjpBfooTCWGepEVFCDNVbChi/o5TdHn/L95ec5yFEd045RPEvulf0jDpIJEPDKnRIgWgfnRT/OL3srtjX2w0I63fe5EfvluNGf+NU2knFywB4Jh/QylShKghctePECbAWFLK3ve/wPfDd/ij1zjOB0ZR390B/w/ewr9NMEGKx+pwcHcheuNSto0Yx28ZNvyUUMzJFYeZ3DccnU6nNFtN0i1fDsCFDl0JU5xFiNpCChUhFNKMRg589RPOr71C69RjADy+93f6jB3GPe0C0dtYK074/3RWVsTM/4z4TSdg2SFmbzyBdV4uz94dXeOtPCqUGIpouK9sfp86Q+9SnEaI2sPy/3cRwkQdXriCQ41b0fyRewlNPUaO3pFtoyYSvWUlozqGmFSR8k8P3dKAd++KxDsnnTsfG8SOkU+ojlQjji5ehWthLpmOrjQc0EN1HCFqDWlREaKGHT6XTep9D9F93S8AFNrYETvwPsKnvUVMoK/idNdnWNtA/H87R6P0ZJj3KdtdXGj/2RTVsarVajyY3+tx2vg4cIcMmy9EjZEWFSFqyIkLuTz5Uyx9P9rEEodASnRW7Oh5N1kH4mm/8CvczaRI+Vund55l20NPA9D+83fZPeVTxYmq17LUEua37If100+pjiJErSKFihDV7OSGnezu2Je59z3H4n1n0DQoGTqU1G17abd6IT5NzLdbZsycD9h+5ygAol6eSMJPy9QGqiYpGfkkpuVibaWjcyMv1XGEqFWk/VKIanJ8zRayXnqVFjv/JBgNXxcvzg+9j/G9Ioj0d1Mdr8q0/flL9sacotXuv/AbfQ8pQRsIsLD5gY7MnMv9e+K40Os23ByqfoA9IcTVSYuKEFVIMxo5+P1i9rfoRGivTrTauQ4rNPa26U7BwkXMfiDGoooUACsba5qs+Z2jQU1wL8ghY/gosguLVceqUgHffM4ba2cx6twe1VGEqHWkUBGiChhKSvlldwoLewyn2f130Xz/Fozo2BPTm6S/ttNq5zrCet2iOma1cXB3wWPdSv5q2olHez/FkwtiMRotY0C4tEPHaZwUD0CDh+9TnEaI2kcu/QhxE87sOciSg+f5KkXjYq6BFv5t6G+7mLied+L3yvNEt2uuOmKNqRsaiOfKP8j4YhvrDqfx0bpEnuzZSHWsm5Y0Zx7ewOGQZoSHh6qOI0StIy0qQtygovxC9nwwm7iIttRvHYnLjA+5mGugnqs9vR8YSFHyadot+5GAWlSk/C3K352372gGwJHPvmHfp98rTnTznJeVDZuf1XeA4iRC1E7SoiLEdTAWl3Do52XkffM9jTevIrowt2w5OhraFPHFfa24tYkPttZS+w9uHUDRb0sY/tsUcpc7ktyqKYExrVTHqpSLx04SnhgLQMBDctlHCBWkUBHiKkpKjew5lcmahPMMGDeE5qfiy19Lc/HkxG2DCZw0nnYtIxSmNE1DXnqIhJ+/JCIxlot33k1e/D6cPN1Vx7phxz7+ivaaseyyj/w7C6GEFCpC/EP2+YskfreQkmXLGX/LI6QVl024V8c3gpBzJznSqRcOI0fQZNgAvGV00quytdfjvXwxF1pFE3z+JHsGDKPV5uVmNyfQmYTjFFtZk3XXYNVRhKi1dJoZz9WenZ2Nm5sbWVlZuLq6qo4jzFBhTh7Hf19D9qq1uG3fTNiJeOyMJQCMGvQasZExdG/sTf8gRzpF+qN3clSc2LwcXriC0KEDsDWWsn3CK7Sf8brqSNftWFouPaZtwLMwh9XP9cDTt67qSEJYjBv5/pY/CUWtkpFrYP+ZLGKTL6EtWsjYL1+jaWnFMT+SvQJIvaUHT43pQ0TXNthIv5NKCx/Ul+3jXqD9x28S/cnbHO7UnvBBfVXHui6/x54BoHmLUClShFBIChVhkTSjkfRjpzi7dS95u/Zgu3cPvkfj+Cz6Dua16g9Ao2I3niot5qKzByej2mLs0pX6d/UjsHUkgYrzW5J2019jz84dRG9fzfpZP+PZuzteLnrVsa6ptLiEXau2g21dBrbwUx1HiFpNaaEyZcoUfv31Vw4fPoyDgwMdOnTgvffeo3HjxipjCTNSYiji3LlMThVbc/xCLmlxR+j3/nP4nTlB3YIc/v13cIuzR9nqNYQW/u60CmxK8kMxBLRrQV0z6zthTnRWVoQv/YmXJ33G997NWf/jXuY92M6kW6riv13IgmmjWBfekY5vblAdR4haTWmhsmHDBsaOHUubNm0oKSnhxRdfpFevXiQkJODk5KQymjARuYYSzl/MpuCvjRSeTKbk9Bl0J5NwOJ2Mx7kUfDLPsyGqJy/2HgeAkyGfZ47tB6BUZ0Vq3fpcCArD0KIVLrd0oGfPWxjk+89J5YJr/qRqISdPd0a++wS/ztzM9hMZvL/yEJP7N1Ud66pKv5gFgFPDEOxtrRWnEaJ2U1qorFy5ssLzuXPn4u3tzZ49e+jcubOiVKK6aJpGrqGES/nFZGblwZ9/UpR2kdILFzGmp2OVno71pUwcLqaxNyCC9zoMJ9dQgkNRIYemD7rqfgOyLxDq5USwpxON6rmw0+8LPJtHUD+mFQEuTgTU4DmKqwvzdub9wc15ddZauj/2PPuemkjLiQ+qjnWZC0dOELl3IwD1nh6vOI0QwqT6qGRlZQHg4eFxxdcNBgMGg6H8eXZ2do3ksnSa0UhJUTGG3HyK8wowoKPQyRVDiZGiAgO2e3ZRkl9AaUEhxoICSgsKMBYY0AoLyPAJ4FiLDuQWlVCUnUP/mW9gk5+LTUEedvl56AvzsS/Mx8FQwKpGMUzqOwEAu5Jijn447KqZLhRBbnTZ3Tc2Ls4c9m9MibMzhZ7eFAcEYd0wDKcmDanbvAmdGjVgnc0//urtE16t75eovH6RvjhnbKddykFyn3uClPatTG6m5WPvfkKMZuRQaBRNurRVHUeIWs9kChVN03jqqafo1KkTzZo1u+I6U6ZM4fXXq//2xkNns9m2dDNN/lwCmgZGDdDQGY2gaWhGjUMde3K6cQs0NDxSkmi77Afg/9f9ezudpnGgQy8SI9tj1DQ8ziXTY9Gcste1/+2z7A1AZzSyp31P9rfujoZGnbRUBs2fBhrl+9QZjejQ0JUa2d76Vv6M6UepUcP94lkmzXkZK2MJ1qWlWBlLsSotxdpY9vMfrXozq9sISowaHpcusnTmA9gYS7E2GrHWjNgCf09eP79Fn/JLKW4FOez/+J6rvle/RXThwwFlPUFsS4t5dfOyq67rmZsJgL2tFXXcXDgUFIHR3gGDmzvF7h4Y69RB5+mJjb8fHuGN+bNTDN6u9jjrbeD1wzfzTypMSMzc6STs3kpEYiwX7ryb/IR9ONYxjRmlDXn5NFz4HQB5o0yvtUeI2shkCpVx48Zx4MABNm/efNV1Jk+ezFNPPVX+PDs7m4CAqm/YP3o+h60rt/PAr7Ouus7SfEfmXyz7z7XDyf2MX/7jVdddVerOT4b6ALQ6c4TJG/646rrrbbxYpm8CQHjaKd7es/6q625xqs92n/YABGZm0ij50FXXtb2UycXcIgBsio04Fhuuuq7eWIqTnTV6W2tcHVw47VmfYls7Suz0lNjaUWpnR4mtHqOdHcYmrbinbQCOdjY46W3Ylj8ZKxdnrN1csXFxxcbdFX0dN/QebjTz8eJwgN//X/OfHH/VDMJy2ert8F76KxejWxNyLondA+4heuNSkxgMbv/UL2ibm0GaiydRTz2iOo4QAhMZ8G38+PH89ttvbNy4kZCQkOverroGfIs7ncXGX/8kes0i0OlAp0OzsgJ06KzKnh/p2JOz4S3Q6aDOuRQiV/0K/3sNndX/frYCnY6UVh240Kysedsp/TyN1ywp3w86HVhZlf98oWlL0pu2QKfTYZ+dSfCfywAdWOnQWVmDDtDp0NnaktuwCblNo7Cx0mFjKMBr91Z0NrZY2dpiZWuDla0NOhsbrGxt0Xy80QICsLHSYa1p6FNPY2Vjg7WdDVZ2ttjY2mLn4oydkwPWNtJ5UFS/hJ+W0eie27HRjGx/6nXaf/iK0jyaprE3vC3RR3ez/dFnaf/Fe0rzCGHJbuT7W2mhomka48ePZ/Hixaxfv56GDRve0PYyMq0Q5m37+JdoP/NtiqxsOLFwGeF39lKWZf2RNB6Zs5VBiZt47ovncatwd5gQoirdyPe30rbWsWPHMm/ePH744QdcXFw4d+4c586do6CgQGUsIUQNaffRG+xteyvJ7vV4bcNpLuZe/ZJkddI0jelrjlJkY4vDww9KkSKECVHaoqLT6a64fO7cuYwaNeo/t5cWFSHMX+7FTIbN2sbBHI2YBp58/2DbGh8MbtPa3YxedQZbez0bn+1m8iPnCmHuzKZFRdO0Kz6up0gRQlgG57p1mPHwLTjaWbPtRDpz5v1Vo8c3lpRSf+Qw1n05hud98qRIEcLEqO9mL4So9cK8XZg6KIoHdy7moQd6s+/juTV27N1vzKBB6nHqFORwx52dauy4QojrI4WKEMIk3BblR0+XImyNpTSaNJbEZdXfspJ1+hwNP3wTgIQHxuNW36fajymEuDFSqAghTEb0T3M42KQ1TkUF1B1yJ8nb9lbr8Q4/+AR18rM4WS+Y6GmvVeuxhBCVI4WKEMJk2NrrCd64msSAxtTJz8KuX1/OJyRWy7HivllEu9W/AJA37SNs7aVvihCmSAoVIYRJca5bB88Na0nxCqDepTSKO3cldX/VTqGQkXQa3/FlI8/u6D2YpvfcXqX7F0JUHSlUhBAmxyPEH5u1q0n18MU/PZUFL83k+IXcKtl3SamRl5YkEOsTykmfYKIWfFUl+xVCVA8pVIQQJsk3KhybzZv4dOBYPm7al6GztrEvOfOm9qlpGi8uPsjys8WMG/YaRWvX4eDuUkWJhRDVQQoVIYTJ8m4SyrB5H9LUz5WLuUU8MmMN296eWal9GUtK+f2Zqfy86xRWOvjk3mgaNWtQxYmFEFVNChUhhEnzdNaz4JH29G7syYeL3yXmpfHsbdeTjKTT172Pgks57LulH3dMe57Jf83ljYHN6BkhtyILYQ6kUBFCmDwXe1s+H9EG265dKLayptXOtVhHNGHbo8+Sn5l11e00o5G4r38mI7Qx0dtXU2RlQ8vbu3Jf+6AaTC+EuBlK5/q5WTLXjxC1z7GVG7B68EEapB4HIM/OgYQOPcl56FG8u3ZEb2NF3v6DFP7+B16/LyT0TNntzefdvLgwczbN7rtDYXohBNzY97dNDWUSQogqEdanC6UnD7PrnZn4fvI+/umptFm/hCdcGrMkruzvrgd3/cbLf34JgMHaln19h9D0q49o5u2pMroQohKkUBFCmB1rWxvavDoR7eUnSPhlBdnzF1DSrh11NT1GTSO5cQv2XeqCoeMthD/zOO0DfVVHFkJUklz6EUIIIUSNupHvb+lMK4QQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWjeoAN0PTNKBsumghhBBCmIe/v7f//h6/FrMuVHJycgAICAhQnEQIIYQQNyonJwc3N7drrqPTrqecMVFGo5HU1FRcXFzQ6XRVuu/s7GwCAgJISUnB1dW1SvdtCuT8zJ+ln6Olnx9Y/jnK+Zm/6jpHTdPIycnBz88PK6tr90Ix6xYVKysr/P39q/UYrq6uFvsBBDk/S2Dp52jp5weWf45yfuavOs7xv1pS/iadaYUQQghhsqRQEUIIIYTJkkLlKvR6Pa+++ip6vV51lGoh52f+LP0cLf38wPLPUc7P/JnCOZp1Z1ohhBBCWDZpURFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEEEIIYbKkULkOt99+O4GBgdjb2+Pr68uIESNITU1VHatKnDx5kgcffJCQkBAcHBwIDQ3l1VdfpaioSHW0KvX222/ToUMHHB0dcXd3Vx3npn322WeEhIRgb29PdHQ0mzZtUh2pymzcuJEBAwbg5+eHTqfjt99+Ux2pSk2ZMoU2bdrg4uKCt7c3d9xxB0eOHFEdq0p9/vnnREVFlQ8SFhMTw4oVK1THqhZTpkxBp9MxceJE1VGqzGuvvYZOp6vwqFevnrI8Uqhch27duvHzzz9z5MgRFi1axPHjxxk0aJDqWFXi8OHDGI1GZs2aRXx8PNOnT+eLL77ghRdeUB2tShUVFTF48GAee+wx1VFu2k8//cTEiRN58cUX2bdvH7fccgt9+/YlOTlZdbQqkZeXR/PmzZk5c6bqKNViw4YNjB07lu3bt7NmzRpKSkro1asXeXl5qqNVGX9/f9599112797N7t276d69OwMHDiQ+Pl51tCq1a9cuZs+eTVRUlOooVa5p06acPXu2/BEXF6cujCZu2O+//67pdDqtqKhIdZRqMXXqVC0kJER1jGoxd+5czc3NTXWMm9K2bVttzJgxFZaFh4drzz//vKJE1QfQFi9erDpGtUpLS9MAbcOGDaqjVKs6depoX375peoYVSYnJ0dr2LChtmbNGq1Lly7ahAkTVEeqMq+++qrWvHlz1THKSYvKDcrIyGD+/Pl06NABW1tb1XGqRVZWFh4eHqpjiCsoKipiz5499OrVq8LyXr16sXXrVkWpxM3IysoCsNjfudLSUhYsWEBeXh4xMTGq41SZsWPH0r9/f3r06KE6SrVITEzEz8+PkJAQhg0bxokTJ5RlkULlOj333HM4OTnh6elJcnIyv//+u+pI1eL48eN88sknjBkzRnUUcQUXL16ktLQUHx+fCst9fHw4d+6colSisjRN46mnnqJTp040a9ZMdZwqFRcXh7OzM3q9njFjxrB48WIiIiJUx6oSCxYsYO/evUyZMkV1lGrRrl07vvvuO1atWsWcOXM4d+4cHTp0ID09XUmeWluoXKmz0L8fu3fvLl9/0qRJ7Nu3j9WrV2Ntbc3999+PZsKD+t7o+QGkpqbSp08fBg8ezEMPPaQo+fWrzDlaCp1OV+G5pmmXLROmb9y4cRw4cIAff/xRdZQq17hxY2JjY9m+fTuPPfYYI0eOJCEhQXWsm5aSksKECROYN28e9vb2quNUi759+3L33XcTGRlJjx49WLZsGQDffvutkjw2So5qAsaNG8ewYcOuuU5wcHD5z3Xr1qVu3bo0atSIJk2aEBAQwPbt2022KfNGzy81NZVu3boRExPD7Nmzqzld1bjRc7QEdevWxdra+rLWk7S0tMtaWYRpGz9+PEuWLGHjxo34+/urjlPl7OzsCAsLA6B169bs2rWLjz76iFmzZilOdnP27NlDWloa0dHR5ctKS0vZuHEjM2fOxGAwYG1trTBh1XNyciIyMpLExEQlx6+1hcrfhUdl/N2SYjAYqjJSlbqR8ztz5gzdunUjOjqauXPnYmVlHg1tN/NvaK7s7OyIjo5mzZo13HnnneXL16xZw8CBAxUmE9dL0zTGjx/P4sWLWb9+PSEhIaoj1QhN00z6/8zrdeutt152B8zo0aMJDw/nueees7giBcq+6w4dOsQtt9yi5Pi1tlC5Xjt37mTnzp106tSJOnXqcOLECV555RVCQ0NNtjXlRqSmptK1a1cCAwP54IMPuHDhQvlrKu+br2rJyclkZGSQnJxMaWkpsbGxAISFheHs7Kw23A166qmnGDFiBK1bty5vAUtOTraYfkW5ubkcO3as/HlSUhKxsbF4eHgQGBioMFnVGDt2LD/88AO///47Li4u5a1jbm5uODg4KE5XNV544QX69u1LQEAAOTk5LFiwgPXr17Ny5UrV0W6ai4vLZf2J/u6/aCn9jJ555hkGDBhAYGAgaWlpvPXWW2RnZzNy5Eg1gVTecmQODhw4oHXr1k3z8PDQ9Hq9FhwcrI0ZM0Y7ffq06mhVYu7cuRpwxYclGTly5BXP8a+//lIdrVI+/fRTLSgoSLOzs9NatWplUbe2/vXXX1f8txo5cqTqaFXiar9vc+fOVR2tyjzwwAPln08vLy/t1ltv1VavXq06VrWxtNuThw4dqvn6+mq2traan5+fdtddd2nx8fHK8ug0zYR7hAohhBCiVjOPzghCCCGEqJWkUBFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEEEIIYbKkUBFCCCGEyZJCRQghhBAmSwoVIYQQQpgsKVSEsEBdu3Zl4sSJqmNcUXp6Ot7e3pw8eRKA9evXo9PpuHTpUrUet7LH+eabb3B3d7+hbdq0acOvv/56Q9sIIa5MChUhxH86e/Ys9957L40bN8bKyuqqRdCiRYuIiIhAr9cTERHB4sWLL1tnypQpDBgwwOJmtv6nl19+meeffx6j0ag6ihBmTwoVIcR/MhgMeHl58eKLL9K8efMrrrNt2zaGDh3KiBEj2L9/PyNGjGDIkCHs2LGjfJ2CggK++uorHnrooZqKrkT//v3Jyspi1apVqqMIYfakUBHCwmVmZnL//fdTp04dHB0d6du3L4mJiRXWmTNnDgEBATg6OnLnnXcybdq0Cpc7goOD+eijj7j//vtxc3O74nFmzJhBz549mTx5MuHh4UyePJlbb72VGTNmlK+zYsUKbGxsrjnzeHp6Ovfccw/+/v44OjoSGRnJjz/+WGGdrl27Mn78eCZOnEidOnXw8fFh9uzZ5OXlMXr0aFxcXAgNDWXFihWX7X/Lli00b94ce3t72rVrR1xcXIXXv/nmGwIDA8vfi/T09AqvHz9+nIEDB+Lj44OzszNt2rRh7dq1FdaxtramX79+l+UWQtw4KVSEsHCjRo1i9+7dLFmyhG3btqFpGv369aO4uBgo++IeM2YMEyZMIDY2lp49e/L222/f8HG2bdtGr169Kizr3bs3W7duLX++ceNGWrdufc39FBYWEh0dzdKlSzl48CCPPPIII0aMqNAyA/Dtt99St25ddu7cyfjx43nssccYPHgwHTp0YO/evfTu3ZsRI0aQn59fYbtJkybxwQcfsGvXLry9vbn99tvL34sdO3bwwAMP8PjjjxMbG0u3bt146623Kmyfm5tLv379WLt2Lfv27aN3794MGDCA5OTkCuu1bduWTZs2Xd+bJ4S4OmXzNgshqs3f084fPXpUA7QtW7aUv3bx4kXNwcFB+/nnnzVNK5vSvX///hW2Hz58uObm5nbNff+bra2tNn/+/ArL5s+fr9nZ2ZU/HzhwoPbAAw9UWOevv/7SAC0zM/Oq59OvXz/t6aefrpChU6dO5c9LSko0JycnbcSIEeXLzp49qwHatm3bKhxnwYIF5eukp6drDg4O2k8//aRpmqbdc889Wp8+fSoce+jQoVd9L/4WERGhffLJJxWW/f7775qVlZVWWlp6zW2FENcmLSpCWLBDhw5hY2NDu3btypd5enrSuHFjDh06BMCRI0do27Zthe3+/fx66XS6Cs81TauwrKCgAHt7+2vuo7S0lLfffpuoqCg8PT1xdnZm9erVl7VYREVFlf9sbW2Np6cnkZGR5ct8fHwASEtLq7DdPy87eXh4VHgvDh06dNllqX8/z8vL49lnnyUiIgJ3d3ecnZ05fPjwZfkcHBwwGo0YDIZrnq8Q4tpsVAcQQlQfTdOuuvzvAuLfxcS1truWevXqce7cuQrL0tLSygsGgLp165KZmXnN/Xz44YdMnz6dGTNmEBkZiZOTExMnTqSoqKjCera2thWe63S6Csv+PqfrufPmn+/Ff5k0aRKrVq3igw8+ICwsDAcHBwYNGnRZvoyMDBwdHXFwcPjPfQohrk5aVISwYBEREZSUlFTo35Gens7Ro0dp0qQJAOHh4ezcubPCdrt3777hY8XExLBmzZoKy1avXk2HDh3Kn7ds2ZKEhIRr7mfTpk0MHDiQ++67j+bNm9OgQYPLOv/ejO3bt5f/nJmZydGjRwkPDwfK3q9/vv7v9f/ON2rUKO68804iIyOpV69e+Zgw/3Tw4EFatWpVZbmFqK2kUBHCgjVs2JCBAwfy8MMPs3nzZvbv3899991H/fr1GThwIADjx49n+fLlTJs2jcTERGbNmsWKFSsua2WJjY0lNjaW3NxcLly4QGxsbIWiY8KECaxevZr33nuPw4cP895777F27doKY6707t2b+Pj4a7aqhIWFsWbNGrZu3cqhQ4d49NFHL2upuRlvvPEG69at4+DBg4waNYq6detyxx13APDEE0+wcuVKpk6dytGjR5k5cyYrV668LN+vv/5KbGws+/fv5957771iq82mTZsu61wshLhxUqgIYeHmzp1LdHQ0t912GzExMWiaxvLly8svk3Ts2JEvvviCadOm0bx5c1auXMmTTz55WV+Sli1b0rJlS/bs2cMPP/xAy5Yt6devX/nrHTp0YMGCBcydO5eoqCi++eYbfvrppwr9YyIjI2ndujU///zzVfO+/PLLtGrVit69e9O1a1fq1atXXkhUhXfffZcJEyYQHR3N2bNnWbJkCXZ2dgC0b9+eL7/8kk8++YQWLVqwevVqXnrppQrbT58+nTp16tChQwcGDBhA7969L2s5OXPmDFu3bmX06NFVlluI2kqnVeZitBDCoj388MMcPny4Wm6vXb58Oc888wwHDx7Eysoy/1aaNGkSWVlZzJ49W3UUIcyedKYVQvDBBx/Qs2dPnJycWLFiBd9++y2fffZZtRyrX79+JCYmcubMGQICAqrlGKp5e3vzzDPPqI4hhEWQFhUhBEOGDGH9+vXk5OTQoEEDxo8fz5gxY1THEkIIKVSEEEIIYbos8wKxEEIIISyCFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiTJYWKEEIIIUyWFCpCCCGEMFlSqAghhBDCZEmhIoQQQgiT9X+fZkvEqg05YAAAAABJRU5ErkJggg==\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_169_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import matplotlib.pyplot as plt\n",
@@ -2938,149 +2745,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:   1\n",
-      "Mean squared error on training data: 446033.51374050\n",
-      "Mean squared error on test data: 455173.80460179\n",
-      "Degree of polynomial:   2\n",
-      "Mean squared error on training data: 114550.54637219\n",
-      "Mean squared error on test data: 129963.83146596\n",
-      "Degree of polynomial:   3\n",
-      "Mean squared error on training data: 9054.61775176\n",
-      "Mean squared error on test data: 10572.87627342\n",
-      "Degree of polynomial:   4\n",
-      "Mean squared error on training data: 302.15313054\n",
-      "Mean squared error on test data: 433.26292364\n",
-      "Degree of polynomial:   5\n",
-      "Mean squared error on training data: 3.64316192\n",
-      "Mean squared error on test data: 7.23528337\n",
-      "Degree of polynomial:   6\n",
-      "Mean squared error on training data: 3.56589683\n",
-      "Mean squared error on test data: 10.50427787\n",
-      "Degree of polynomial:   7\n",
-      "Mean squared error on training data: 0.47313680\n",
-      "Mean squared error on test data: 1.53738247\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:   8\n",
-      "Mean squared error on training data: 0.04926746\n",
-      "Mean squared error on test data: 0.14629156\n",
-      "Degree of polynomial:   9\n",
-      "Mean squared error on training data: 0.02546675\n",
-      "Mean squared error on test data: 0.11202337\n",
-      "Degree of polynomial:  10\n",
-      "Mean squared error on training data: 0.02424794\n",
-      "Mean squared error on test data: 0.22467274\n",
-      "Degree of polynomial:  11\n",
-      "Mean squared error on training data: 0.01594452\n",
-      "Mean squared error on test data: 1.07641937\n",
-      "Degree of polynomial:  12\n",
-      "Mean squared error on training data: 0.00805074\n",
-      "Mean squared error on test data: 0.04295757\n",
-      "Degree of polynomial:  13\n",
-      "Mean squared error on training data: 0.00781918\n",
-      "Mean squared error on test data: 0.56965674\n",
-      "Degree of polynomial:  14\n",
-      "Mean squared error on training data: 0.00465099\n",
-      "Mean squared error on test data: 0.28443039\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  15\n",
-      "Mean squared error on training data: 0.00420072\n",
-      "Mean squared error on test data: 568.47202442\n",
-      "Degree of polynomial:  16\n",
-      "Mean squared error on training data: 0.00325450\n",
-      "Mean squared error on test data: 48.97690235\n",
-      "Degree of polynomial:  17\n",
-      "Mean squared error on training data: 0.00242954\n",
-      "Mean squared error on test data: 2.52775466\n",
-      "Degree of polynomial:  18\n",
-      "Mean squared error on training data: 0.00219194\n",
-      "Mean squared error on test data: 429.23643365\n",
-      "Degree of polynomial:  19\n",
-      "Mean squared error on training data: 0.00154860\n",
-      "Mean squared error on test data: 238.16356503\n",
-      "Degree of polynomial:  20\n",
-      "Mean squared error on training data: 0.00140849\n",
-      "Mean squared error on test data: 1345.68592431\n",
-      "Degree of polynomial:  21\n",
-      "Mean squared error on training data: 0.00119699\n",
-      "Mean squared error on test data: 1836.21110005\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  22\n",
-      "Mean squared error on training data: 0.00092904\n",
-      "Mean squared error on test data: 1182.64316482\n",
-      "Degree of polynomial:  23\n",
-      "Mean squared error on training data: 0.00089187\n",
-      "Mean squared error on test data: 3886.35846425\n",
-      "Degree of polynomial:  24\n",
-      "Mean squared error on training data: 0.00083346\n",
-      "Mean squared error on test data: 1346.92651068\n",
-      "Degree of polynomial:  25\n",
-      "Mean squared error on training data: 0.00079910\n",
-      "Mean squared error on test data: 7697.35412147\n",
-      "Degree of polynomial:  26\n",
-      "Mean squared error on training data: 0.00075597\n",
-      "Mean squared error on test data: 1078.81597834\n",
-      "Degree of polynomial:  27\n",
-      "Mean squared error on training data: 0.00068088\n",
-      "Mean squared error on test data: 3189.20355156\n"
-     ]
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Degree of polynomial:  28\n",
-      "Mean squared error on training data: 0.00063364\n",
-      "Mean squared error on test data: 692.24085321\n",
-      "Degree of polynomial:  29\n",
-      "Mean squared error on training data: 0.00063862\n",
-      "Mean squared error on test data: 3073.63180447\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/626635268.py:73: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(trainingerror), label='Training Error')\n",
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/626635268.py:74: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(testerror), label='Test Error')\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_171_6.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -3192,30 +2857,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/var/folders/td/3yk470mj5p931p9dtkk0y6jw0000gn/T/ipykernel_10727/3817475779.py:63: RuntimeWarning: divide by zero encountered in log10\n",
-      "  plt.plot(polynomial, np.log10(estimated_mse_sklearn), label='Test Error')\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_174_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -3320,36 +2962,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[1.79934087 0.47179152 5.01549939]\n",
-      "[1.79909592 0.47176716 5.01550546]\n",
-      "  \n",
-      "test MSE of OLS:\n",
-      "1.13943111290393\n",
-      "  \n",
-      "test MSE of Ridge\n",
-      "1.1395235273363686\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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E0wtce71oKsqBVJj9BwM8/kKpJPGZEEII93AuiAgkkVusOwD44cL0gLycTE4r7mpdNflmvYTVpKEoCjToCj41UM6fhX2/urtaQgghKiCHblDZ0wzAXdo6zIqDCL0+B4ya+T6vmo9HSVTvqkjwkRtVc2U8Zft37q2LEEKICmlzVDwJ522AQX9tDQBzHLfkWV4Bgv3KxrJbCT7y0mJQ5t+HV8PZI26tihBCiIrHOXzSWtlHfTWWFMPKr462uZZ1Zlgf27sJmlr6861L8JGXKnWhXmcA/lv3PwZ8sUn2exFCCFFinMMn95sy530scrQnBc9cywb5eTD9gZb0CAsusfpdDZlwmp8Wg+HwGjwi5/J3cmt+2e7DdTUru7tWQgghKoDWof408rVze/rfAMx1dMlRprKnmU8HtaRtvYAy0ePhdFU9HxMmTEBRFEaNGuU6ZhgG4eHh1KhRA09PTzp37syePXuutp4lLvpsKpE+N2G3VsbPdpKb1V0s3nmCyJhEdkcnEn021d1VFEIIUY5pqsLkJv/iodjYp9dip1HfdU658Ofdu5vRoUFgmQo84CqCjy1btvDFF19w3XXXZTk+adIkPvzwQ6ZOncqWLVsICgqiW7duJCcnX3VlS1LHiavp9dlWvk3JHF+7X1tNfEoGvaasp/fU9a7lT0IIIUSxMAyaxC4A4DdLdy7O7Ch7wyzZXVHwce7cOQYNGsSXX35JlSpVXMcNw2Dy5MmMGTOGu+66i7CwMGbOnElqaiqzZ88uskqXBOd+L85urq7qdgI5C8h+L0IIIUpAzHb4LxI0K6OefZ05j7fl4/ubM+fxtqx/6ZYyG3jAFc75GDFiBHfccQe33norb7/9tut4VFQUcXFxdO/e3XXMarXSqVMnNmzYwNChQ3NcKz09nfT0dNfjpKQkAGw2Gzab7Uqqlyfn9Qpy3TvCqlHXvw39phts0xtyg3qAe7V1THP05aehbWhaw7fI61eaFKatKjppq4KTtiocaa+CK09t5dANftwWjf/qd7kDcDTujW7xplVtAF8AdIcd3XFl1y+utirM9QodfMydO5ft27ezZcuWHOfi4uIAqF69epbj1atX5+jRo7leb8KECYwbNy7H8eXLl+Pl5VXY6hXIihUrClTu+DkAE3McXbhBPUB/bTXTHb1Zv349R72LpWqlTkHbSkhbFYa0VeFIexVceWmrdYcz+ChjHSiwMb0RZ37/vchfo6jbKjW14HMhCxV8HD9+nGeeeYbly5fj4ZF3BjVFyTrxxTCMHMecXnnlFZ577jnX46SkJGrVqkX37t3x9fUtTPUuy2azsWLFCrp164bZbL5s+djENL6J2sQR3+5kJM2mjv0kPb3+pXaT+zAMg0BvKzfUqVLmJvoURGHbqiKTtio4aavCkfYquPLQVvO2HufNxXsxgLuUTXib0zisB/HI3iaAwhu9m9C/Va2rfp3iaivnyEVBFCr42LZtGydPnuSGG25wHXM4HKxbt46pU6eyf/9+ILMHJDj44ljUyZMnc/SGOFmtVqxWa47jZrO52N5ABb127UAz60Z3IeJYAjF/9SY0ag53GSt4bF5jV5lgPw/G9m5Spsfe8lOcv4fyRtqq4KStCkfaq+DKals5dIPXFv6Dc1LpAEvmooZ5ji5k6JnTM19b+A8D2oQW2Q1vUbdVYa5VqAmnXbt2Zffu3URERLj+tGrVikGDBhEREUG9evUICgrK0pWTkZHB2rVrad++fWFeqlRYGhlL1w/WMvCrvxm+L3NVz836ZgJIdJWJS0xj2KztLI2MdVc1hRBClHGX7kR7rXKU5uohbIbGz46b8yxXlhWq58PHx4ewsLAsxypVqkRAQIDr+KhRoxg/fjwNGzakYcOGjB8/Hi8vLwYOHFh0tS4BSyNjGTZrO8aFx/8YdYjQ69NcPcTd2jq+cPQGMrcwVoBxi/fSrUlQuRyCEUIIUbwu3Yl2oPYHAMv0VpzGL89yZVmRp1cfPXo0o0aNYvjw4bRq1YqYmBiWL1+Oj49PUb9UsXHoBuMujLtdavaFDX0GaKvgkrMGmfNDyktEKoQQomQ5U6l7kUY/7S8AZju65lmurLvq9Opr1qzJ8lhRFMLDwwkPD7/aS7vN5qh4YhNzRpe/OtrxumkWoep/tFP3slFvmuV8eYlIhRBClKzWof4E+3lw07nV+CjnidKrs1FvkqVMWdmxtiBkY7lc5BVEpOLBIkfm3JXM3o+syktEKoQQomRpqsLY3k0YdGHIZY7jFoxLvqIVys6OtQUhwUcu8gsinEMvt6lb8CfrsqLyEpEKIYQoeT0CTnK9ehgbpiwTTYPLeCr13Miutrlwdn/FJablmPexxwhllx7KdWoUd2vr+NLRC4CHO9QtNxGpEEIIN9g6AwCtaR+mtryNk8lpVPPJHGopb98v0vORC2f3F1y6jc9F3ztuBTJnJCvovNzjGro3CWJhRAwbD53BoWcPWYQQQoi8RR6O5vz2uQCorR6mXf0A+jYPoV39gHIXeID0fOSpR1gw0x9oybjFe3NMPl3saMeYCxNP26t7+Gq9B6fP7XedL++Jx4QQQhQdh24QseR/hBnniTPXpGrtjmjurlQxk56PfPQIC2b9S7e4dhKcOqAFgd5WGtSsTmydvgAM0v7g9LmMLM+TxGNCCCEuJ/psKp+vPUSb8Su57r/5AHyV2ok2E/7g87WHiD5b8L1Syhrp+bgMTVVoVz/A9bhb0+pYNBX9vyrw2Vy6q1upxllOUsVVRhKPCSGEuJyOEzNTqIcph7nOGkW6YeJnx02cPZfBhCX7mLBkH0fevcPNtSwe0vNRSFaThqIobE4JYrN+DSZFp7+2Okc5STwmhBAiO4dusPHQGeZvj6aSNXNwxbm8dqnemrNc3FC1sqe53M4hlJ6PK3QyOY1V9q60tuxngGkV0xx9ceQySieJx4QQQkDmth3Z5xH6kuLKaDrLfmuW8gnnbWyOis/S+15eSM/HFarm48FSvTXxhjc1lHg6qxF5lhNCCFGxOfcLy76A4S7tTzyVDPbrNdliXJPjeeX1BlaCjyvUOtQffz9ffnJ0Ai52mzkplK9UuEIIIa5MXvuFgeH67pjluJXckjuU1xtYCT6ukKYqjOxS35XxtLO6k5rKKdd5AxjZpb5MNhVCiAour/3C2qr/0FCNIcWwMt/RMcu58n4DK8HHVRizYA9HjGD+dIShKgb3Z9vvZcyCPW6qmRBCiNIir6GTB7SVACxwdOQcXq7jzlvW8rSXS3YSfFyFyf2bY1KVC91l0F9bjQUbACZVYXL/5m6snRBCiNIgt6GTqpzlNnULgOs7xCmoHO7lkp2sdrkK/VqE0KCaN/2m2IgzqhCknKWHuoVFensWjOhAWIifu6sohBDCzXLbL6y/tgaz4mCb3pB/jDr4VzLzeq+mBPmWz71cspOejyJgx8RsR1cABpuWu7k2QgghSpPs+4Wp6AwwZQ7Tf2+/FQUYf2cz7mxRfvdyyU6Cj6sU4G2hqreVndX6oismblT/pX2lWAK8Le6umhBCiFIiLMSPl3s2JsDbwi3qDkKUM8Qb3mzyvImXezaucD3lMuxylYL9PFn/chcsmoryU2/YM5/vrtuF5veYu6smhBCilHCmUgd4wJw50fRHRydOpFPuU6nnRno+ioAz5To3ZgYcWuSPkJbo5loJIYQoLZwLFOoocdys7gJwDddXxAUKEnwUpTodoOq1YEuFiDnuro0QQohSol+LEBaM6MAD2kpUxWC143qOGkEALBjRgX4tQtxcw5IlwUdRUhS48VEAEv+cTrcP1jBr09FyuzGQEEKIglPs57lPWwPAt47uKOV/XmmeJPgoYivMnUnBA7+UI1Q98zevLYik48RVLI2MdXfVhBBClCDnDrYLI2LYeOgMwccW46ekEqsG0a3PQJqF+FHV21ohFyjIhNMi9P2mI4xZ8C9vmm7iQdMKBmsr2KCHEZuYxpOztvNOv6YMalvX3dUUQghRzHLuYGuw3HMq/kBQ1xEMbFuPAW1CyXDoWE05d0Qv76Tno4g4dMOVTv07RzcAuqnbCOKMq8yYBXtkCEYIIcq53HawbaXsp5FxhDTDzCrPzO8IRVEqZOABEnwUmc1R8a5/HzBqstHRBJOiM8j0R57lhBBClC957WD7oGkFAAsdHXht2YkKfyMqwUcRyb5x0ExHdwAGaKuwkpFnOSGEEOVHbjvYVuUsPdXNQOZE09jEtAp/IyrBRxHJvnHQCv0GYowAApUk7lA35VlOCCFE+ZHbDeZAbRVmxcFWvRF7jLp5lqtIJPgoIs6Ng5wcaHxvz9ypcIhpOWAQ7Je5YZAQQojyKfsNpgk7Ay8Mv39r755nuYpGgo8i4tw46NJl23McXUg3zFyvHqaFcpCxvZtUiA2DhBCiosp+g3mbupXqSgKnDD+W6K3zLFfRSPBRhHqEBTP9gZauHpCz+LLI0Q6AqQ224Odpca33ruiTjYQQojzSVIWHO9R1PR5iWgbAbMct2C5kt3i4Q90KfyMqeT6KWI+wYLo1CWJzVDwnk9MIzXgBfl9HteNL6fflUk5RGYBgPw/G9m5Cj7Bg91ZYCCFEkRrbuynBvh4sXLqE1up+bMbFYfhXezbmiU713VxD95Oej2KgqQrt6gfQt3kIJ7wasVVvhBk7A7WLy27jEtMYNmu7ZD4VQohyqH2DQB6+0Ovxu96GU1RxHRcSfBQr53rvmRcmGQ0y/YEZO4BrDfi4xXtlCEYIIcqZqmoifbQNAFg7DqdZzYqbSj03MuxSjJzrvZfQmjijCkFK5lrvRXp7IDMAca73blc/wL2VFUIIUWSq/zsPsGOE3ECP23pzW3ejwqZSz430fBQj5zpuOya+t3cF4CHT0jzLCSGEKAccNtjyFQBKmycz/67AqdRzI8FHMbp0HfccR1fSDRMt1YNcrxzMs5wQQogybu9COBcH3tWhST9316ZUkuCjGF2aeOw0fiy+MNzy8CW9H5J4TAghyo9d0Qn8u+j9zAetHgWTzPHIjQQfxciZeMxphr0HAHeof1OdzLz+knhMCCHKj7//XEEj2z84FBO0etjd1Sm1JPgoZj3CgplwZxiqAnuMuvytN8asOHjQtIIJd4ZJng8hhCjjos+msjs6kciYRGr8+y0AS2hPZKKV3dGJRJ9NdXMNSx9Z7VICBrSpQ98WIUQcS0D5dxhsfobhPn+itKzm7qoJIYS4Sh0nrgYyd6/9y/oXKPBZWncip6x3lTny7h3uql6pJD0fJcTLYqJ9g0Ba9xgMlWujnI+HXT+4u1pCCCGu0uT+zVEVGGxageXC7rWRRj0AVCXzvMhKgo+SpmrQemjmvzdNB0MSjAkhRFnmYVYxGxkMupDF+n/2nq5zupF5XmQlLeIOLR4AcyU49Q9vT/2MXdEJ7q6REEKIK+DMZH2ntp4AJZloI5DleqssZSSTdU4SfLiDZ2VoMQiAtifn8cv2GPfWRwghxBXJzGR9nke0JQDMsN+Gg6zJxJyZrMVFEnyUMOes6H/rDATgVm0HERHbiIxJlFnRQghRSjl0g42HzrAwIoaNh864ejJOJqdxs7qLRmoM5wwPfnB0yfX5ksk6K1ntUsKcs6IB/mduQVdtB3dmLKLXlIt7u8isaCGEKD2WRsYybvFeYhMvBhDBfh6M7d2Eaj4ePHqh1+MHR2eS8cr1GpLJOivp+ShhzlnRAP9zZE5Kuldbhx/nZFa0EEKUMksjYxk2a3uWwAMgLjGNJ2dt53+//E4nbRe6oTDDcVuO5ytIJuvcSPBRwjzMKs55Rxv0pvyj18ZLSWeQ9ge6AUfPpOTo1hNCCFHynJNJc/skdh67JfFnAJbrrYg2qmcp48xdLZmsc5LgowQ538gXKXxpvx2AIaZlmLHz0coDPDM3ggFfbqLjxFUsjYx1T2WFEKKCy5xMmvdcjSokcZeWmUgso9VQAryz7uMS5OfB9AdaSibrXEjwUYJyeyMv1tvzn1GZ6koCvdUNWc7FJaYxbNZ2CUCEEMINLjdJdJD2Bx6KjV16KE9v9OT0uQwAPr6/OXMeb8v6l26RwCMPEnyUoNzeyDZMzLRnjhM+ZloCl3TwOf8la8SFEKLk5TdJ1IKNIablAHxt7wkomFSFyf2b07d5CO3qB8hQSz4k+ChBeb2Rv3d0JdWw0kQ9Sjt1b5ZzBrJGXAghSpJzWW1c4nn8K1nILYToq/1FVSWRE4Y/v+ptAVgwogP9WoSUbGXLKFlqW4Jah/oT7OdBXGJalglMiXjzo+NmhphW8Lj2Gxv1pjmeK2vEhRCi+OW2rDY7BZ0ntN8AmGHvgUMxkeusVJEn6fkoQZqqMLZ3E4AckfTXjp7ohsItWgT1lZwZT2WNuBBCFK+8ltVm10ndSUM1hhQ8adhzBM1C/Kjqbc0x4VTkTYKPEtYjLJjpD7QkyC9rMHHUCGKFfgMAj2q/ZzlX1ccqa8SFEKIY5bes1sm/kpmP+jfn41qZK1y82j3KfR3DWDiiA+tf7kKwn2fJVLYckODDDXqEBbP+pVuY83hbPr6/ueu4c9nt3dp6Akl0HT+VnC4Tl4QQohhdblktQHyKjfq2g/j9txFDNbE9+H4WRsSw6XA8JlW+TgtD5ny4iaYqtKufmVLdMOC5HyLYalxDhF6f5uohHjQt40P7fagKfHhfc/dWVgghyrmCzqs7tfwDAJbTjqGzjwHHgIvp1mVpbcEUKlSbPn061113Hb6+vvj6+tKuXTuWLFniOm8YBuHh4dSoUQNPT086d+7Mnj17irzS5U2/FiEsGtkRUPjM3huAwdpKPElj/vAOVPf1kKynQghRjAoyr64Gp+lk+xOAT873yHJO8jIVTqF6PmrWrMm7775LgwYNAJg5cyZ9+/Zlx44dNG3alEmTJvHhhx/yzTff0KhRI95++226devG/v378fHxKZYfoLxZYbQiSq9OqPof92lreXSmrytxDUh0LYQQxSGv1YiXesS0FJOi85ejKXuM0CznDDIXEoxbvJduTYJkqPwyCtXz0bt3b26//XYaNWpEo0aNeOedd/D29mbTpk0YhsHkyZMZM2YMd911F2FhYcycOZPU1FRmz55dXPUvNwK8LVT1ttI0pAqnmj0OwGPa75w9dz5LOYmuhRCi6OW3GhHAh1T6a5m7kn/pyH3nccnLVHBXPEPG4XAwd+5cUlJSaNeuHVFRUcTFxdG9e3dXGavVSqdOndiwYUM+VxIAwX6erH+5CwtHdOCGPiOIx5da6iluV//OUk6yngohRPHIazUiwCBtJT7Kef7VQ1ijX5/vdSQv0+UVesLp7t27adeuHWlpaXh7ezN//nyaNGniCjCqV8+6q1/16tU5evRontdLT08nPT3d9TgpKQkAm82GzWYrbPXy5bxeUV+3qKiA3a6z+WgyWx3deUb7iSfNv7Lc3pbssXj8ufNsOniy2Jbglva2Kk2krQpO2qpwpL0Krqjaqus1gXRueBPbjp7l9Ll0Ar2teKp2an43HIDP7b1xfh6bVYPcRlcCvUyl+ndWXO+rwlxPMQyjULfPGRkZHDt2jISEBH7++We++uor1q5dS0JCAh06dODEiRMEB1+cj/D4449z/Phxli5dmuv1wsPDGTduXI7js2fPxsvLqzBVK1fM9mS673kWk57B/JCXmHaqGX3q6NT2dnfNhBCiYvGJWcMtJ7/mhOFPp/TJ2NEwUHihmZ1a8pnskpqaysCBA0lMTMTX1zffsoUOPrK79dZbqV+/Pi+99BL169dn+/bttGjRwnW+b9++VK5cmZkzZ+b6/Nx6PmrVqsXp06cvW/nCstlsrFixgm7dumE2m4v02kVpc1Q8j8zcwhh1Jg9qy1mnX8eDGS+jKQamSwbKvh5yY7H2fJSFtioNpK0KTtqqcKS9Cq7Y2kp3wPR2mBMO85XXoxyuP4Q5W45jABYVlAs9H84OkI/6N+fWa6vndbVSobjaKikpicDAwAIFH1ed58MwDNLT0wkNDSUoKIgVK1a4go+MjAzWrl3LxIkT83y+1WrFarXmOG42m4vtP1txXrsotG1QDV8vD744dzuD1BXcrO7iWuUo/xh1cDgyy1T1sdK2QbVin1Fd2tuqNJG2Kjhpq8KR9iq4Im+rvUsg4TCGhx+PPh2O4uHLTY2qMm7xXuKSLt44l8WViEXdVoW5VqGCj1dffZWePXtSq1YtkpOTmTt3LmvWrGHp0qUoisKoUaMYP348DRs2pGHDhowfPx4vLy8GDhxY6B+iItNUhVPJ6UA1ftfb0FvbxFDTYkbZRrrKSNZTIYQoZoYBf00GQLnxcfDIvJvv2awG3ZsGszkqnpPJaVTz8aB1qL98JhdCoYKP//77j8GDBxMbG4ufnx/XXXcdS5cupVu3bgCMHj2a8+fPM3z4cM6ePUubNm1Yvny55Pi4ApP7N+e5HyL4zN6H3tomeqmbeF+5j2ijmmQ9FUKIYrYrOoEF83/gjTPbQLNCm6FZzl+apVoUXqGCj//973/5nlcUhfDwcMLDw6+mToLMrKcNqnnTawqsdVxHJ20XT2i/8Yb9YRaN7EhYiJ+7qyiEEOXWL9tj6HRyFmhAi0HgXc3dVSpXZCecMmC6ow8A92lrsmw4J4QQ4uo5dIONh84w468ovt90lJ3HE/gnYgNdtJ04UPm3/kPsjk4k+myqu6tabsjGcqWYM+tpql9bTjmuo2rCLkZ4riDA+053V00IIcqFpZGxjFu8N8eOth+Z54MGSxytGTkzGogG4Mi7uWc3FYUjwUcp5sx6atFUlP0vw9yBPGRZgWLNADzdXT0hhCjTlkbGMmzW9hx7udRS/qO3uhGAz+y9ADCpCu/fm39mU1FwMuxSyllNGoqiQKOeULUxSnoy23/5kG4frmXWpqOSYl0IIa6AQzcYt3hvrpvIDdV+xaTorHVcR6RRD4AFIzrQr0VIyVayHJPgo6xQVXbVfQiAWvtncOxkPK8tiKTjxFWyyZwQQhSQc37HRyv25xhqAajKWe7V1gLwqb1vrpvMiasnwUcZ8f2mI9z1Zw2ijUCqKonco60DMndQfHLWdr7fdMS9FRRCiFJuaWQsHSeuYsCXm5i6+lCuZR4z/Y5VsbNVb8RmozE1/T2p6m0lwNtSwrUt3yT4KAMcusGYBXuwY+JLe+Zkp6HaYjQcrjJjFuyRIRghhMiDc35Hbr0dTn6c4wFtJZDZ6wEKE++6jvUvdyHYT+bZFSUJPsqAzVHxrn/Pc3TmjOFDbfUUvS5MiMqtnBBCiEz5ze+41EPaMiop6fyj12aN3pxgPw/a1AvAatJKpJ4ViQQfZcDJ5IuRehpW/mfvCcBI00IU9FzLCSGEyLQ5Kj7fHg8AL9J42JS5+7qz12Ns7yaSMr2YSPBRBlTz8cjy+DtHd5IMLxqqMdymbs2znBBCiILdmA3Q/qCykkKUXp0d3jcz/YGWZWqTuLJGgo8yoHWoP8F+FwOLZLyY4bgNgJGmBYBBsF/mxkZCCCGyutyNmQUbT5h+A+Ab9U6mDW5NSGUvyWhajCT4KAM0NbP779LOvxn2HqQYVsLUI3RRI6R7UAgh8uC8gcvrE/JebS3VlQROGP7MSWtP30//ovfU9XScuLpE61mRSPBRRvQIC2b6Ay1dPSAJ+DDLcSsAHwUtp0fTIHdWTwghSi3nDRyQIwAxYWeYaREAX9h7kXEh8bdJVZjcv3kJ1rJikfTqZUiPsGC6NQlic1Q8J5PTCDHVx5i/ksrxOzm05Xdeiwjgldsbc13Nyu6uqhBClCrOG7js+7g86LWRmvppThl+zHHc4jq+YEQH2T28GEnwUcZoqkK7+gEXDxwbApu/QPnzAzaeep5ftsdI8CGEELnIfgNXrZKJlotegWT4wtGLdCwoChiSMqnYybBLGRZ9NpV99R7GUEzUS95GS+VfFu88QWRMomz/LIQQuXDewPVtHkK71DVYk49yFl8iqt/FO3eG0SzETzKalgDp+SjDnJOh3jV15H7TGp4yzeeRlEb0mrLeVUa2fxZCiFzoDlj3HgA+XZ7hh5u7oigKA1vXJsOhS2KxYiY9H2XY5P7NMakK0x19sBsqXbSdXKccBEBTFAa3rc3GQ2ck7boQQlxiV3QCH095D84cAI/KmNo8kbl7OKAoigQeJUCCjzKsX4sQFozowFEjiIV6BwCeNs0HwGEYfLfpGAO+3CQ73wohxCXmbzvObWdmZT5oOxw8fN1boQpIgo9yYqqjHw5Doau2g2bK4Szn4hLTGDZruwQgQogKK/psKrujE4mMSSR550Iaq8c5hxd7aw+QOXJuIHM+yrgAbwtVva14+zXm9zMd6c2fPG36hcdtL7jKGGSubR+3eC/dmgRJMjIhRIVzMWGYwa+WH0GFb+zdef+L3a4yMkeu5EjPRxkX7OfJ2tGd6Xt9MB+l98VhKHTTttNUicpSzgBiE9P4aMW/Mg9ECFHhOOfIdVO3EaYe4ZzhwVcXNumUhGIlT3o+yrilkbGXJM2pwSK9PXdqfzHK9AuP257PUX7q6oNMXX2QYD8PxvZuIhsnCSEqhH4tQmhQtRLKFy8D8I3jNhLwASShmDtIz0cZtjQylmGztmfJ1jfV3g/dUOimbaOpciTP58o8ECFEReNzZBlN1aMkG558Zb8dRUag3UaCjzLKoRuMW7yX7IMnh4wQFuvtAHja9Euez3c+b9zivTIEI4Qo/3SdGhGTAfjdqw8v3tlOEoq5kQy7lFGbo+Kz9Hhc6hP7nfRWN3KbtpUm9iPsNermWs45D2RzVHzWlO1CCFHe7PsV8+m9GFYf7nvqXRQvf0ko5kbS81FGnUzOPfCAzN6PX/W2ADxr+vmqriWEEGXdruPxHPvlDQCUNsNQvPwz/y0JxdxGgo8yqpqPR77nP7bfdWHly7YceT8Key0hhCjL9q36ntr2KNLUStBuuLurI5Dgo8xqHepPsJ8Hec2XOmSEsOBC1tPnTD/mWkYBgv08aB3qXzyVFEIIN3ElFYs+S8uoLwD41ridyHhVkoqVAjLno4zSVIWxvZswbNZ2FMgx8RQgqskI7Ps30EXbSUv7v2w3GrnOOYOWsb2bSNIxIUS540wqdoe6iU8tx0gyvJia1p3xsvFmqSA9H2VYj7Bgpj/QkiC/rMMmQb5Wpg9qwQsDbkdrMQiAlz2yrnwJ8vNg+gMtJc+HEKJcmty/ORbV4FnTTwB87ehBEpUASSpWGkjPRxnXIyyYbk2C2BwVz8nkNKr5ZA6jOHszlE6jYedcWuu7+OLmNN7bF8iQ9nW5r1Utth09y8KImBzPEUKIsq5fixBaJSyl5toTnDW8+Z/9dtc5SSrmfhJ8lAOaquS9VLZybWj5IGz9H432fsKB0y/yxz//8enqg1mW6krGUyFEWeLQjSw3XS1q+mQtYM+g2vaPAPjc0YtkvFAUMCStUakgwUc5F302leSGT3DNjlnUPRdBBzWS1fub5SjnzHgqQzFCiNIu67YSmepUsfJc40sKRczCknycM1RmW/V7ead1Q+ZtOU5sQpokFSsFJPgo55yTrsaaOvOwaRnPm37kr4wwyLZOJvvOt0IIURo5t5XI3oHxX1JmILLyn//oeW0grH0PAL/uL/FDu64oiiJJxUoRmXBazjl3cpxm78t5w0JL9SBd1e25lr0046kQQpQ2eW0rAVm3jJg55Q1IPgG+NTG1fhTlwiYuklSs9JDgo5zr1yKEBSM6cIrKzHD0AOAF0w8o6Hk+RzKeCiFKo/y2lXBKOZfEHYlzMh90ehFM1hKomSgsCT4qkM/tvUgyvLhWPU4fdUOe5STjqRCiNMrvxkg34Pg5GKwuI1BJ4jhBRFbrJQnFSikJPiqAAG8LVb2t1A4J4RulDwDPmX7ChD1LOcl4KoQozfK7MbLpCl/sTmeo6VcAPsi4i16f/k3vqetdc99E6SHBRwUQ7OfJ+pe7sGhkB67tN5pThi911JP019a4ykjGUyFEaZf/thIGT5oW46eksl+vySK9PQCqgiQUK4Uk+KggrCYNRVHo1rw+p1o8BcDTpl/wIB2QjKdCiNLPua0EZF+vByHqWR7WlgLwnr0/+oWvN90AD7N81ZU28hupgJr0egbDrxbVlQQe1JbTo2kQ61+6RQIPIUSpl9e2EiO0+XgqGWzVG7JSb5nl3KvzdzN/RwwbD53BoUuWsdJA8nxUMNFnUzmbYqNK81HUXPs8w0yL6RfVg39iG2AYUKWSmZpVvNxdTSGEyNOl20r8dfAUv65Zz31q5ryOSbb7yd4vEp9i49l5EYBkcy4tJPioYJwTr1Sqs8wSQkM1hvsyfqHXFLOrjOz0KIQo7TRVoZJVY9me/3je9CMmRSfW53oiMhrnvs33BZLNuXSQYZcKxpl0TEflPft9ADyiLaEaZ2WnRyFEmfLL9hgsp3bTW9uEbijsq3EvymXmy1+ajEyGYNxHgo8Kxpl0DGC53oqteiM8lQxGmX5mwYgO9GsR4uYaCiFE3qLPprI7OpHImEQW7zzBaNM8ABbr7dmj1y7QxnGSzdn9ZNilAlMUhXdt9/OT9U3u09ZwOOEghNzg7moJIUQOzl1sB3y5yXWsnbqHTpZd2AyN9+33cHx34b7SJJuz+0jPRwXkTDrWLMSPO/vdw9+WNpgUndo73nd31YQQIoelkbF0nLgqS+ChoPOyKTON+mzHLRw3qqMqBial4EMpks3ZfaTnowJyJh2zaCqKomCEfowxvT0eB3/n4LaVvL7Nmxe7N3B3NYUQIs9dbHupm7hePcw5w4Mp9rsAeC7MQYsb23LynI23fvuHsykZuc49VcjMbSTZnN1Hej4qKGfSMQCl2rUoLR4AwLJqHBsPn2ZBRKw7qyeEEHnuYmvB5prr8Zm9N2cUP9e51qH+3NmyJuPvDANyJiOTbM6lgwQfguizqfxzzUh0zYPaKbu4Vd3Ob7vjOH4OImOSZFMmIYRb5LWL7WBtBbXUU8QZVfjKcTuhAZUI9LbgczFjQJ7JyCSbc+kgwy7ClfvjRVN3RpgW8ZJpLj1SmvP+bhPv784cY5XcH0KIkpbbhFBfzvGUaT4AH9rvIQ0rT3dtwK2Nq/LH8qVZyl6ajOxkchrVfDKHWqTHw/2k50O4cn98Zu9DvOFNQzWG+7XMgEST3B9CCDfJbULocNMiKisp7Ndr8pOjEwDVfT2xmnL/OtNUhXb1A+jbPIR29QMk8CglJPgQrtwfyXgx2X43AM+afsKbVH4e2kZyfwgh3CL7LrYhnOJhbRkAE+wDMFAJlomjZZIEHyKLOXpXDunBBCpJDDMtcnd1hBAVkEM32HjoDL/uOsHtYcGuCafPm3/Eqtj4y9GUNXpzDGBkl/rSm1EGyZwPAWTm/gj0tuLrUYk//UdS/9gYHtWWcEYfAwS4u3pCiApiaWQs4xbvzTHRtJlymLu09UBmr4dz3cqYBXsY1LZuCddSXC3p+RAA7DyegEmFw6dTCP+3Ln/r1+Kh2EhZMpYBX2xiV3SCu6sohCjnnDk9cq5wMXjd/B0Avzg6EmnUA5D9qMowCT6E6z98XFL6hSMKEx2DAGh0cikpUZuZtvqQbMIkhCg2eeX0AOipbqa1up/zhoVJtv6u47IfVdlVqOBjwoQJ3Hjjjfj4+FCtWjX69evH/v37s5QxDIPw8HBq1KiBp6cnnTt3Zs+ePUVaaVF08voPv9sIZZ9P5gZ0Y8zfs3RPLG3Gr+TztYck74cQosjlldPDSgavmGYD8IWjF3EEXHbnWlH6FSr4WLt2LSNGjGDTpk2sWLECu91O9+7dSUlJcZWZNGkSH374IVOnTmXLli0EBQXRrVs3kpOTi7zy4url9R/epis8fOp+0gwzbdR93KZu5fS5DCYs2efKCyKEEEUlr03eHtKWUftCQrHP7L24r1VNmoX4UdXbSoC3pYRrKYpKoSacLl2aNYHLjBkzqFatGtu2bePmm2/GMAwmT57MmDFjuOuuzFz7M2fOpHr16syePZuhQ4cWXc1Fkch7V0eDWAL40nEHT5kW8Krpe1ZnNCcDM5U9zTh0Q2aYCyGKTG45PQJIZKRpAQDv2fpzHg/ubFGTtvX8yXDoWE1aCddSFJWrWu2SmJgIgL9/5hrrqKgo4uLi6N69u6uM1WqlU6dObNiwIdfgIz09nfT0dNfjpKQkAGw2Gzab7Wqql4PzekV93bIs0MuEVcs5ympSDFLsCtPtfbhPW0Md9SSPaEv4n9Gb8xkZbDp4UtbWXyDvq4KTtiqcitReLWr6UKeKlf+S0jAAuw7PaT/ho5wn0qjL70oH6lSx0qKmD3a7HRWw2XTX8ytSW12t4mqrwlxPMQzjimYRGoZB3759OXv2LH/++ScAGzZsoEOHDsTExFCjRg1X2SeeeIKjR4+ybNmyHNcJDw9n3LhxOY7Pnj0bLy+vK6maKALHz8H7u00oGNyp/smHls84Z3jwQ71JBFSu7O7qCSHKofh0SLnw/fXHPzH8pL2Kphj8UvNVTng2ppIZ/K3uraPIW2pqKgMHDiQxMRFfX998y15xz8fIkSPZtWsX69evz3FOyTYbyDCMHMecXnnlFZ577jnX46SkJGrVqkX37t0vW/nCstlsrFixgm7dumE2my//hApi5T//8ey8CADXxFOzYuBjNkixwWKjAw/qK2iuHsL34M+M1p/g6yE3Ss/HBfK+Kjhpq8KpaO3V8PXlF/5l8J35ezTFYInjRp47GOYqc+Ct7rk+t6K11dUorrZyjlwUxBUFH0899RSLFi1i3bp11KxZ03U8KCgIgLi4OIKDL+4YePLkSapXr57rtaxWK1ZrzlDWbDYX2xuoOK9dFvW8riaKqmVN7KPB+BscvLJFI0PXeNM2mF+s4dylrmOBuSdT1gTwqpeV62pWdmvdSxN5XxWctFXhVJT2mty/OS/8uJOubOEmLZJ0w8x4+0AgM6fH+/def9l2qChtVRSKuq0Kc61CrXYxDIORI0fyyy+/sGrVKkJDQ7OcDw0NJSgoiBUrVriOZWRksHbtWtq3b1+YlxIlrEdYMOtfuoU5j7flkQ51ATCpuJa0bTcascDRAVUxeMP8HZsOn+GX7THuq7AQotzp1yKEhUNv4DXTLAC+cNzBcSPzxlVyepQvher5GDFiBLNnz2bhwoX4+PgQFxcHgJ+fH56eniiKwqhRoxg/fjwNGzakYcOGjB8/Hi8vLwYOHFgsP4AoOs7dH9vVD+DGOn5kRG3Lcv4Ly4PcYWyjUfoeeqsbWbzTyj031MQwoEolMzWryBwdIcTVCdz1BdXVU8Qa/kyz90FR4MpmJorSrFDBx/Tp0wHo3LlzluMzZszgoYceAmD06NGcP3+e4cOHc/bsWdq0acPy5cvx8fEpkgqLknHrtdX5PQq+HnIjp1PtPDM3gr0pPnyi9eJ580+8Yp7NrSkt6TXl4pyfj+9vTjWfzB0mZRmuEKIwdkUn8PnidXxyeioA3/s+ymsdWzFvy3FiE9Ikp0c5U6jgoyALYxRFITw8nPDw8CutkyhFWof6YzabMQx44cedfOHoRX/TGmoqpxlmWsQH9vtcZZ+ZGwFAsJ8HY3s3oUdYcB5XFUKIrH7ZHsNtJ6ahaWnotdry/MOvoqgqA1vXlpwe5ZDs7SIKpF+LEBaM6EA6Ft6yDQbgCe1X6ihxOcrGJaYxbNZ2lkbGlnQ1hRBlSPTZVHZHJxIZk0h0xEr6aBvRUTjc6g0iTyQTfTYVRVEk8CiHrirJmKiYluutWOu4jk7aLsaavuUR24s4t7eGzOW6CjBu8V66NQmSIRghRK6cWzWo6Pxq+R+oMMd+C2PmJACZQ7pH3r3DfRUUxUZ6PkSB7Y5OQFXAQCHcPoQMQ+MWLYKu6vYcZQ0gNjGNzVHxJV9RIUSZMLl/c0yqwiBtJU3UoyQaXrxvvxfIXFo7uX9z91ZQFBsJPkSBLI2M5dX5kegXpv1EGcF85ci8Ixlr+hYrGbk+L++9Y4QQFV2/FiGM7RLIi6YfAHjP3p+zZCaXHH3bNbK0thyT4ENclkM3GLd4L9mnG0+19yPW8Ke2eoqh2q+5Pje3zaKEEBWXQzfYeOgMCyNi+HjlAbzWvYmvkspuvS6zHV1d5cYv2SfzxsoxmfMhLmtzVPzFzKeXSMWDd2yDmGqZwnDTQn7RbyLaqOo6X9XHKinYhRAuSyNjs2RSvlHZx4/WP9ENhddtj6Bnux+WeWPll/R8iMvKb+jkV70tGxxN8FBsjDV9m+XcqeR0NkfF49AlQ5AQFd3SyFiGzdruCjw0HLxpngHAXEdnIowGOZ4j88bKLwk+xGXlP3Si8Ib9IWyGRjdtG93UrVnODvhyEx0nruL3XSdcXa0bD52RgESICiS3oduHtGVcqx7nrOHNe/b+eT5X5o2VTzLsIi6rdag/wX4exCWm5Zj3AXDQqMmXjjsYblrEWPO3rE8P4zwXA5bYxDSGz96R5TmSiEyIiiP70G01zjLK9DMAE+33uyaZ5kbmjZVP0vMhLktTFcb2bgJcms0jqyn2OzmuV6WmcppnTPMve01JRCZExZG99+I18yx8lPNE6PWZ5+ic63MUMm9SZN5Y+STBhyiQHmHBTH+gJUF+We9CqvlY8fUwERzoz1j7EAAe1X6nkXI83+s5e1DGLd4rQzBClHOX9l7crO6kj7YRh6Hwmu1hjFy+hpw3OWN7N5HJpuWUDLuIAusRFky3JkFsjornZHKaaxM5u66zZHcso+alsNRxIz20Lbxt/pr+Ga/n+sHidGkisnb1A0ruBxFClCjn0O3ZxETeNn0NwEzHbUQa9XItHyTDsuWeBB+iUDRVyREoaKpGdV9PAMbZHuQmdRet1f3co63jxzy6VC8lE8qEKN+cQ7eH5o6mtnqKWMOfDy5kMnV69taG1A2sJDtjVxAy7CKKhHNcNpYAPrLfA8Crptn4k3TZ58qEMiHKt13RCfyxdi1Pmn8DYKxtCClk3rCoCky4M4xnbm1E3+YhtKsfIIFHBSA9H6JIaKrCwx3qMuOvI3zjuI27tT+5Vj3Ga+ZZPGcbnutzFDK7V2VCmRDl2/xtx+n/3wdoqgN7o5481Hokd5xLp6q3lea1K+Nlka+iikZ6PkSRGdu7Ka/2bIwdEy/bHkM3FO7S1nOzujNHWZlQJkT5Fn02ld3RiUTGJKJFfEcr9V9S8eDQDWPx8TBzQ50qtG8QKIFHBSW/dVGk2jcIBGCX0YBvHLfxiGkp75i+ZoD5I6JTLsa6MqFMiPKt48TVAFQlgZXW70CB92338vWMw8BhAI68e4cbayjcSXo+RJEK8LZQ1dtKs5p+VOoZzkm1KrXUUyy57k/e7hdGw2revN0vjPUv3SKBhxDl2OT+zTGpCmPNM/G7sHHcTEd3AEyqwuT+zd1bQeFW0vMhilSwnyfrX+6CRVNRFAWj6jSYfS8+EV+S2qg1B056cvDkORlqEaKc69cihBYp66mz8m/shsrLtidwoAGwYEQHwkL83FxD4U7S8yGKnNWkoSiZwUVM1Y4k1O8Lhs7N+9/ChJ3FO08QGZPI7uhEos+murm2Qohicf4sNf4aA8Dnjl7sMeqiyD2HuEB6PkSx6jhxNQH0YKX1DxorR3hc+53PUvrQa8p6VxkZ9xWi/NgVncCE3/fxqffX+J8/xVFqsKr6w7zTuj7zthwnNiGNAG+Lu6sp3EyCD1GsJvdvzgs/7uRt2wN8YPmMUaafWa7fwCEjBJOq8P6917u7ikKIIvTL9hiUI2vxt8wDIPjBr/gptD2KojCwdW0yHDpWk+bmWgp3k+BDFKt+LUJoUM2bXlN0+jg20EnbxSTzF9ybMZYFI26WcV8hyoHos6mcTbGhGwZLth/kR9OXAJy+9kFiLWFUSThPzSpeKIoigYcAJPgQJUbhFfvjLFNHc4N6gIe1pcDN7q6UEKIIOJfVArxmmkNt0ylijAC67+hEyo7MIVYZXhWXkgmnotg5l98GhtRjb9iLALxo/oHkE/sZ8MUmdkUnuLeCQoir8nCHugDcoOznEW0pAGNsj7pSqDvPC+EkwYcods7ltwtHdKDNPc9h1OuMBxnUWPsCmw6f4pftMe6uohDiCjl0g6WRcXiQzvvmz1AVgx/tN7NGb+4qszQyDoduuK+SotSR4EOUCOfy2+iE8+y/8R0cJi/qnNvJg9oKWXorRBm2OSqe2MQ0RpvmEar+R6zhz1v2wVnKxCamsTkq3k01FKWRzPkQJco5NvyA1p+3zTN4yTSXNanN6TUlw1VGxoaFKBscusEv26NprfzDI6bM4ZaXbY+TRKUcZU8mp5V09UQpJj0fokQ5Uy5/7+jKRkcTvJR03jN/hoouKZeFKEOWRsbSceIqft12kPfMnwMwx96FtXruy+cP/HeOjYfOyPCLACT4ECWsX4sQFozogIHKi/ahnDM8aK3u5zHtNxaM6EC/FiHurqIQ4jK+33SEJ2dtJzYxjZdMc6mjniTGCOAd+6A8nzN19UEGfLmJjhNXsTQytgRrK0ojCT6E28QYVXnzwtjw86Yfscbvd3ONhBCX49ANxizYA0A7dQ8PmZYDMNr2BOfwuuzz4xLTGDZruwQgFZwEH6LE7Y5OQFXAAH5wdGalowVWxU7g8qfYffSkLL8VohRzThz1JYUPzNMBmGXvyl96swI93znoMm7xXhmCqcAk+BAlamlkLK/Oj+TiZ47CK7bHiTe8qZK8jyM/j2Xj4TOy/FaIUso5cfRN8wxqKPFE6dUZn89wS24MZAVMRSfBhygxDt1g3OK9ZL/XOUVlxtgeBeD2xDm0UA7I8lshShmHbrDx0BkO/JdMb3UD/bQN2A2VZ20jSMXjiq4pK2AqLllqK0qMMx9AbpbobZjv6MCd2l98aJ5Gr5QJsvOtEKXE0shYxi3eS2xiGsGcYan1awA+dfQjwmiQo7x/JTPxKbbLXreaz5UFLaLsk54PUWIud5cz1jaEE4Y/oep/vG76FkCW3wrhJs6ejjcX73GtbFHQec/8GX5KKhF6PabY++V4ngK83TeMYD8PlDyurQDBfh60DvUvxp9AlGbS8yFKzOXucpLw5tmMEcyxvM39pjWs0Ztzc99HURTYeOgMrUP90dS8Ps6EEEXl0p6OSz2sLaOjtofzhoVnbSOwZ/sKCfbzYGzvJvQIC0ZVFYbN2o4CWYZanf+Dx/ZuIv+fKzAJPkSJaR3qT7CfB3GJaTnmfTj9bVzLdEdvRpgW8a75S3rOr08sAUDWDzYhRPFYGhnLsFnbc/wfvVY5ykumuQC8Yx9ElHHx/+HILg3o0CAwyw1Cj7Bgpj/QMkcQEyT/jwUSfIgSpKkKY3s3yfVuyKlOgBdxoaPYuSuS69XDfGieziDbq+iorvwA0x9oKR9cQhSDvCaFe5LGFPMUrIqNPxwtmOW4Ncv5htW9aVc/IMf1eoQF061JEJuj4jmZnEY1Hw/pwRSAzPkQJcx5NxTkl3UIJtjPgykDmvPHc51Yuv8sz9hGkGJYaaft5QntVyAzWDGA1xfukfwAQhSDvCaFv276jgbqCf4zKvOibShkm82R35Cqpiq0qx9A3+YhtKsfIIGHAKTnQ7hBfndDGw+d4VRyOqcIJtw+hPfMX/C86Uc26E3ZZdQH4FRyOpuj4nO90xJCXLncJoXfrm5ioGk1uqHwrG048fhmOS8TR8WVkJ4P4Ra53Q05dIO/Dp52lfnR0YnfHK0xKw6mmKfgw8V8H0siY2WTKiGKWPYejBBO8a75KwCmO3qzQQ/L8RyZOCquhAQfolRw7pA5dfXBS45mZj89rleljnqSCeavcM4U+XbjUdmkSogi1jrUn6o+VgA0HHxs+RRfJZUdegM+st+TpWyQr5XPZP6VuEISfAi3c86uz22sOYlKPGV7Cpuh0UvbxEBtVZbzskmVEEVHUxVOJacDMMr0M63Uf0kyPHnKNjLLsto5j7flr5e7SuAhrpgEH8Kt8ppdf6kIowET7fcDMNb0LdcqR13nZJMqIYrW5P7N6azu5CnTAgDG2B4l2qgGgKpknpeJo+JqSfAh3Cq/lOuX+p+jJ384WmBVbEw1f4IXF5/j3KTqm7+iJAAR4ir1qwdf+XwBZO5Wu1hv7zq3aGRH+rUIcVfVRDkiwYdwq4JuLGWg8oJtKLGGP/XVWN42f032TCFv/faPzAER4grtik7ggc/XkzL7QUzpZ4nU6/KWYzAAinRyiCImwYdwq8JsLHUWX57KGIndULlLW59j/gfIHBAhroRDN/h09SE6Hp9Opf+2olt8eM38IteEVOWdO8NoFuJHVW8rAd4Wd1dVlBOS50O41eVSritAdV8roBCXlMZWozGT7P151TyHsaaZROp1Xfk/ILMvRCFzDki3JkEyLi1EPqLPpvLbrli+/PMw16du5ElLZkK/l+1D6daxDX2a16CWfyUGtq5NhkPHatLcXGNRXkjPh3ArZ8p1yJ4z8eLj8D5NCe/TxHX8C0cvljlaYVXsTLN8TGWSszzPOQdkc1R88VVciHKg48TVTFiyD8+U43xg/gyAr+09+CG1Je8t/5ebJq0BQFEUCTxEkZLgQ7hdXinXg/w8XPu49AgLZsKdYWR2ZCi8YHuSKL06NZXTfGz+FBU9x3ULOp9EiIrIoRtU9jTjQTqfmydTWUlhh96ACfaBrjKVPc0yiVsUCxl2EaVCQTagGtCmDn1bhDB701He/n0fw2zPMt/yBp20XTxt/MLkbEmQCjOfRIiKZnNUPAnnM/jI/BVN1KOcMnwZlvEMtku+FhLO22QrA1EspOdDlBoF2YDKy2Li4Y71ANhn1OYV22MAPK3Np7O6I0tZ2W9CiNztik7gjYWRPKQt407tL+yGysiMZ4gjZ5AhPYiiOEjwIcocTVV4uENdABboHfnOfiuqYvCJ+VNClcxVLg93qCuTTYXIwy/bY6hyagtjTN8DMN4+iL+Na3MtKz2IojjIsIsok8b2bkqwrwfjl+zjTfuDNFaPcaP6L1+aP+DPTnN4uGtTd1dRiFIl+mwqZ1NsKApsitjNd5ZPMCsOFjja87WjR47yCpnzrqQHURQHCT5EmdW+QSAAdkwMy3iWRdYxNFBPUO3om+w6/hUTlvzLK7c35rqald1bUSFKgY4TVwNgJYN5lklUVRP5R3cOXWbtJXQ+kh1rRXGRYRdRZgV4W6jqbaVZTT+evbMD71d+gzQs+B77g4Tfwtl4+Ay/bI9xdzWFKBUm92+OSYWJ5i9orh7irOHNUNuznCfnsMqlK82EKA7S8yHKrGA/T9a/3AWLpqIoCjc37E9shE7ouue4OW4mt6t+LN5p4Z4bamIYUKWSmZpVvNxdbSGKjUM3cl0xtis6gXlbjvNZ3XXcemIDNkNjuO0ZjhnVAXi5xzVcX6tKnivNhChqhe75WLduHb1796ZGjRooisKCBQuynDcMg/DwcGrUqIGnpyedO3dmz549RVVfIbKwmjSUCxtP3DRpNV2WB/Gl/XYAPjB/Ro3UffSasp7eU9e7up2FKI+WRsbSceIqBny5iWfmRjDgy02uvY5+2R5DpSPLuSXmcwDG2R9ko35xXtS7S/eTeD4j35VmQhSlQgcfKSkpXH/99UydOjXX85MmTeLDDz9k6tSpbNmyhaCgILp160ZycnKu5YUoKpndygrv2gew1nEdnkoGX1o+oDrxmFSFyf2bu7uKQhSLpZGxDJu1PccO0bGJaTw5azvbt/zFZPOnqIrBt/ZuzHJ0y3GNcYv3SkIxUWIKHXz07NmTt99+m7vuuivHOcMwmDx5MmPGjOGuu+4iLCyMmTNnkpqayuzZs4ukwkLkpV+LEBaM6IADjZG2p/lXDyFIOcv/LO+z6Inm1KtaiQFfbGJXdIK7qypEkXHoBuMW7811bySAABKZqkzCW0njL0dT3rQPzrWcbEkgSlKRzvmIiooiLi6O7t27u45ZrVY6derEhg0bGDp0aI7npKenk56e7nqclJQEgM1mw2azFWX1XNcr6uuWR2W1rex2OwDnFC8esb3IAssbhKlHSFz1NB9UeY2Nh8/w09bjNKrqxbajZzl9Lp1Abys31KlyxV3NZbWt3EHaqnAK0l6bo+KJP3cea7atVxw6aEYGX1k+oLZ6iiN6dYbbnsGOCTAwKaBlu/08mZiCzeZbxD9FyZD3VsEVV1sV5nqKYRhX3M+mKArz58+nX79+AGzYsIEOHToQExNDjRo1XOWeeOIJjh49yrJly3JcIzw8nHHjxuU4Pnv2bLy8ZHKgKJyEdHh/t0ZlC7SrrnP2xCGmGu9gVWzM0O9gXMYgvE0GT17rAKCSGfytbq60EEXo2DlYdFSlT207PeM+pcG5LSQYlbgrYxyHjczP5Rea2anl7eaKinInNTWVgQMHkpiYiK9v/kFssax2cU4AdDIMI8cxp1deeYXnnnvO9TgpKYlatWrRvXv3y1a+sGw2GytWrKBbt26YzeYivXZ5U5bb6u7eOhZNQVEUGr6+nBfVoXximcrD6m/8qwUxx34L7++++Na3aoYrr8FH/Ztz67XVC/V6ZbmtSpq0VeHk114r//mPd5fsIy4p6zwPuw4OQ8Fj3480MG0h3TDxRMazFwIPA1D4eI/GpR19ClDd14Nlo24us5NN5b1VcMXVVs6Ri4Io0uAjKCgIgLi4OIKDL64PP3nyJNWr5/6BbrVasVpz3nqazeZiewMV57XLm7LYVqp2cbnhiC4N+HytQqgtlmfNP/O26Wv+M6qwSm/pKp/uyPywVYA3f9tP97CQK/oALott5S7SVoWTvb2WRsYyfPbOC/M8cr5XH9BW8LjpNwBetA1ls9HkwpnMsjb94nOc/3rljqZ4WC1FX/kSJu+tgivqtirMtYo0yVhoaChBQUGsWLHCdSwjI4O1a9fSvn37onwpIXKVfbnhp6sPUtnLzMeOu/jB3glNMfjU/AnNlYM5nmsgk+5E6Xe5CaZd1B2MM30DwHu2+1ikd8j3epJQTLhDoXs+zp07x8GDFz+4o6KiiIiIwN/fn9q1azNq1CjGjx9Pw4YNadiwIePHj8fLy4uBAwcWacWFyM653DD7h/LpcxmAwqv2R6mmJNBZ28n/LO9xd0Y4R4ycH7iyi6cozTZHxedYUuvUQjnANPPHaIrBPHtnPnX0zfM6lT3NfDqoJW3rSV4PUfIK3fOxdetWWrRoQYsWLQB47rnnaNGiBW+88QYAo0ePZtSoUQwfPpxWrVoRExPD8uXL8fHxKdqaC3GJy90NAhiqieG2Z9ilhxKgJDPTPJFAEnOUk108RWmWV3BcX4nha8t7eCoZrHFczxj7I+Q2JKNc+PPu3c3o0CBQAg/hFoUOPjp37oxhGDn+fPPNN0DmZNPw8HBiY2NJS0tj7dq1hIWFFXW9hcgiv7tBJ4cOqXjwSMZojurVqKOe5GvLJCpxPks52cVTlGa5BcfBnOE7ywSqKOfYoTdgmO0ZHBc6tgO9s87jkGEWURrI3i6iXCjoUEmnhoGsPQBDbC/xsyWc69QovjR/wMO20aRj4eEOdeVOUJRqrUP9qepj5VRyZn6kyiTzreVdaijxHNRr8HDGi2hWb8ICKxGXmMb8Ee05Hn9e9m0RpYoEH6JcKOhQyZOdG9ChQSDjl8BDGS8x2/IO7bW9TGUKUV0+xcvLi24frmVI+7oMaF1bPqRFqaOpiivw8CSNry3v0VCNIdbw58GMl0nAB9LtLBrZgQyHjtWkyYaKotQp0tUuQrhL61B/gv08chnhzqQAwX6Zd33tGwQCEGnU47GMF0gzzHTTtlHzz9G8vmAXB06e47UFka5NuYQobSb3b46HksEX5g9pqR4kwajEgxkvc4JAVCXzvKIoWE3a5S8mhBtI8CHKBU1VGNs7M5dB9gDE+Xhs7yZoqkKAt4Wq3laa1fSjT797ed3yIjZD43ZjHeGmmXBh2qpzU67vNx0pqR9DiHztik5gwBebqO9vZnPD77hJi+Sc4cHDGaM5YNQEYNHIjvRrEeLmmgqRvzI77OJwOAqdl95ms2EymUhLS8PhcBRTzcqH4mors9mMphXP3ViPsGCmP9CScYv3Zpl8GuTnwet3XIufp4WFETFU8/Fg7ejOeJo1dAPGzA8jXR3GZPOnDDGtIAVPJtn74wxbxizYw/2t68gQjHC7X7bHsPnwSdT5E/FNWEWaYeYx24vsMBqiKHDlm2UIUbLKXPBhGAZxcXEkJCRc0XODgoI4fvx4nuneRabibKvKlSsTFBRULL+DHmHBdGsS5MpwWs3Hg7MpGbz1W9aAJNjPg7G9m+DnmbkSYJHeHh97Ku+Yv2a4aRE2ND6y3+sqvzkqnnb1A3DoRpZry8oYUdzi0yEyJgmz2cSvEdFMMn9B04Q/0VUzzxkvklCtNe+0q8O8LceJTUgjwLvsZykV5V+ZCz6cgUe1atXw8vIq1BeYruucO3cOb29vVFVGnPJTHG1lGAapqamcPHkSIEsK/qKkqQrt6gcAmYnHRszOmXgsLjGNYbO280iHuq5j3ztuxYKNsebveMY0H91Q+dhxNwBbj8aTeD4jR69KsJ8Hb9xxTbH8HEIAjNtugu2bUNB52zSDu01/YjdUhqeNZLkeBueTGdSmDgNb13ZNMBWitCtTwYfD4XAFHgEBAYV+vq7rZGRk4OHhIcHHZRRXW3l6egKZ+/1Uq1at2IZgIP/EY5nba8H8iJgsx2c4eqKi87r5e541/4wDlamOO/njn5N8uPzfHNeKTUxj1LwIJrXO7B1p26CaDM+IIuHsZRvcwMHsQwpvaf9joGk1uqHwnG04y/UbURX48L7mADLBVJQpZSr4cM7x8PKSZWNlmfP3Z7PZijX4uFziMQOIT7HhX8lCfEqG6/j/HHdgQucV8xxeMP+Ijsr0433zzZ4K8MjMLfh7ezK2dxNJ4CSuytLIWMYt3svp5POEVjKYYPof92lrcBgKz9uGsUjP3CtLN8DDLDdSouwpk+9ama9RtpXU76+gicf6Na+RY4XM547eTLL1B2C0eR4jtV/gsuHHxeEcWaIrCsOhG2w8dIaFETF8vPIAw2ZtzwycDZ3Hz3/lCjyetQ1ngd4xy3PHLd6LQ5eZpqJsKVM9H0IURkETj3VrEkTrUP8c8zmmOfoCBqPNP/C8+Se8lHQm2u8nt/0ynJzDOeMW76VbkyAZghGX5ezlyN5Lp6Lzrulz7tbWYzdURtlG8KveLsfznTsxO+c5CVEWSPAhyi1n4rG4xLRc+ywUMpfhOtNNd2sSxKZDZxgxezsJ5zOH+KY5+pGGlTfM3zHMtBhP0hlnfxAjn05DA/lCEBfltkLKGZTmtROzBRsfmqfRS/sbu6HytG0kv+tt83wN2YlZlDVlctilLHrooYdQFAVFUTCbzVSvXp1u3brx9ddfo+t6ga/zzTffULly5eKraDlSmMRjzvKqqrgCD6evHT151fYouqHwkGk575q+QuXi70w3MpdDZidfCGJpZCwdJ65iwJebeGZuBAO+3OTKnJvXhGhP0vjK/D69tL/JMDRG2J7ON/AA2YlZlD0VNvi4dIx146EzJTJm2qNHD2JjYzly5AhLliyhS5cuPPPMM/Tq1Qu73V7sr18ROROPBfll/XDOa2fPvAKG2Y6uPG97Eoeh0N+0hk/MU7GQGaTYdCVzOWQ28oVQsTl7NbIPpzjnBU1ddSDHOV/O8Z3lXW7WdpNqWHnENppleus8X+PSbQOEKEsq5LDL0sg43vrtn1yTThXnKgWr1UpQUBAAISEhtGzZkrZt29K1a1e++eYbHnvsMT788ENmzJjB4cOH8ff3p3fv3kyaNAlvb2/WrFnDww8/DFyctDl27FjCw8OZNWsWkydPZv/+/VSqVIlbbrmFyZMnU61atWL7ecqK3BKP5bWzZ34Bw3z9Js7brHxinkIvbRNVSGao7VnO4Ul1z4u9H5cO54iKqSDLvGf8dSTL8UAS+c4ygWvVYyQaXjycMZrtRsNsz7oot947IcqKCtfz8cf+M4yYvSPPu5GSXqVwyy23cP311/PLL78AoKoqn3zyCZGRkcycOZNVq1YxevRoANq3b8/kyZPx9fUlNjaW2NhYXnjhBQAyMjJ466232LlzJwsWLCAqKoqHHnqoRH+W0syZeKxv8xDa1Q/I88P6chvULdVb84htNOcMDzpoe5hreZtqJPDfeQXdkC+EiiavHtSCLPO+dHivjhLHT5ZwrlWPccrwo3/GG2w3GgEK99Vz5Pp+zKv3ToiyoEL1fDh0g0krD+d7N+KOVQqNGzdm165dAIwaNcp1PDQ0lLfeeothw4Yxbdo0LBYLfn5+KIri6kFxeuSRR1z/rlevHp988gmtW7d2ZSkVBeOcJzJs1nYUcl9c+5fejPszXmOGZRJh6hF+soTzoO1ljhhBBHpbeKxjKBl2w7WPzA11qrDt6NnL9rqIsiW3VSrOHtR0e8HmcSkKtOBfvrR8QICSzHG9Kg/YXuGokfn/W8OgQ3WDBUegSiULA9vUoW5gJXkfiTKvQgUfW47E819yRp7n3bVKwTAM1zDK6tWrGT9+PHv37iUpKQm73U5aWhopKSlUqlQpz2vs2LGD8PBwIiIiiI+Pd01iPXbsGE2aNCmRn6O8yGuDumo+VtJsDuoGVmJXdD3uzhjHd+YJ1FFP8pNlHI9lvEDEuQa8u3R/luupSuakVKeSGOITxSuvVSrOHtRRtzbM9XnZdVe28LF5Kh6KjV16KI9mvMgpKrvOP9O1PqT+y4yHbpTsuaJcqVDDLieTc1mSkGu5kl2l8M8//xAaGsrRo0e5/fbbCQsL4+eff2bbtm18+umnAPnu4JuSkkL37t3x9vZm1qxZbNmyhfnz5wOZwzGi8HqEBbP+pVuY83hbPr6/OXMeb8vGV7qy5bVbWTiiA5P7N+eEEsTdGePYrdclUElinuUteqkbc1wr+1xmSURWtl1uPgfAnM3HCPLNe/gO4GHTUqabJ+Oh2FjpaMH9Ga9nCTxe7dmYYZ0bAEgvhyh3KlTwUc3HWsByJbdKYdWqVezevZu7776brVu3Yrfb+eCDD2jbti2NGjXixIkTWcpbLJYcW9zv27eP06dP8+6773LTTTfRuHFj1+Zt4srlNk/EatJQFIV+LUJYMKIDp8kcn1/paIFVsTHVMoWnLpMN1XlGMlOWTQWZzxGXlM6A1rWBnMu8TdgJN33DWNO3qIrBLHtXhtqeI5XMz516gZUI9LbSu3mNYvoJhHC/ChV83FjXn+o+ljzvRop72Vp6ejpxcXHExMSwfft2xo8fT9++fenVqxcPPvgg9evXx263M2XKFA4fPsx3333HZ599luUadevW5dy5c/zxxx+cPn2a1NRUateujcVicT1v0aJFvPXWW8XyM4iczisePGF7ni/tPQF43vwTH5qnu5bi5ubSIT5RthS0Z7RuoFeOZd5+nGOmeSIPmZYDMNF2P6/ZH8GBhqbA5P7N+eP5Tvz1cheC/TyLpf5ClAYVKvjQVIXRt9YDCpZ0qqgtXbqU4OBg6tatS48ePVi9ejWffPIJCxcuRNM0mjdvzocffsjEiRMJCwvj+++/Z8KECVmu0b59e5588kn69+9P1apVmTRpElWrVuWbb77hxx9/pEmTJrz77ru8//77xfIziIsCvC1U9bYSVsOXe+oZvGMfzCu2R7EbKndp65ljeZtqnM33GpKIrOwpaM/o6eR0ujUJYv1Lt3Bb0yAaKNGs8A6ng7aHFMPKExnPMt3RB+enz8KRHenXIkR2pxUVgmIYRqnq901KSsLPz4/ExER8fX2znEtLSyMqKorQ0FA8PAo/NKLrOklJSWw4luqWPB9libOtfH19UdWijVGv9vdYmqTbHSi6gyVLlvDcJg2HodBB3c0088f4KamcNCozPONpthqNc33+yC4N6NAgsMKM6dtsNn7//Xduv/12zGazu6tzRRy6QceJq/JM23+pQG8LT9xUj71rf+Atx8f4KOc5awnm/uRn2G/UzlL21Z6NeaJT/SzHykN7lRRpq4IrrrbK7/s7uwq12sWpR1gQt4UFFyjplBD5sZo0bLbMlUU1K3tw9Gw6f+nN6JPxNp+bP6Kxepw5lnd40z6Y7xzdyN7nNnX1QaauPkiwnwev33EtVSpZ5T1ZyhVkObZT/Lk00la8yWTTAlBgk34tw5Ke4Sw5P5jHL9lH7QAvuQESFUKFDD7g4mRCIYrKyz0bM2z2TgCOGkHclTGOieYv6K1t4i3zNzRXDzHG9ghp5Jz4HJuYxvDZO7Icy603Lr9NykTJyWs59qUCSORj81Q6ansA+Nbejbfsg7Hl8bEruyGLiqRCzfkQojjdem11JtwZhvN7IxUPnrI9xVu2QdgNlbu1P1loeZ2GSnSBrpd9SW5+m5SJkudcjv36HdfmONdK2cdv1lfpqO0h1bDydMYI3rA/nGfgATIJWVQsEnwIUYQGtKlD5LjbmP1YGwa3rY2mKPzPcQeDba9wyvDjGjWaRZbXuF9bRf4d9lmX5P6+K/9NyiQAcQ9NVUi1XVz6rqLzpLaIuZa3CVLOclCvQZ+Mt1ikdyjwNWUSsqgIJPgQooh5WUy0bxDIW/2asXBkRwA26k3pmf4u6xzN8FQyeNf8FVPNU/AhNd9rOe+GX1sYmW9SK8kZUvzy2sclMiYJgGDO8L15PC+b52JSdBY52tEn420OGjUBuD0sKM9rX0p2QxYVQYWd8yFESVIUOG34McT2Ek/ov/GC6Qd6aZu4XjnEC7Yn+dvI2XV/qfiU0rctQEWS2z4uzpUsW4/Ec7u6iQnmr/BTUkkxrIyzP8gPjs44JxgH+VqZfH8Ltk9aRVxS7pmWZTdkUZFIz4cQxciZC6RZiB9v9Q1DVVQ+d/Tmvow3OK5XpZZ6innWt3jd9B1Wri4VvnTXFw/nPi7Zh7xOn8tg6pJtvJLxCdMsn+CnpBKh1+OOjPH84OjCpSubwvs0xWJSCe/TFAX35BkSojSR4EOIYhTs58n6l7uwcEQHBrerw9SBLQDYYTSkZ8YEZtu7APCoaQm/W16huXLwil9LuuuLXn77uHRVt7HcOpp7tHU4DIUp9n7ckxHOEePi6iRVgQl3hrlWLDlXyVya9RQyezymP9BSltmKCkOGXYQoZpdmq+zZrAav9jzP+CX7OIcXr9ofZ7l+IxPNX1BfjeVny1i+ctzOZPvdnKfgwURlTzO6YeDQDblzvgJ5LWHObR+XKiQRbv6WvtoGAA7rQYy2PeFKJPdOvzC8PUxU9bbSvHZlvCxZP2Z7hAXTrUmQLJkWFZoEH8Llm2++YdSoUSQkJLi7KuVa7+Y1+OLPKHw9TLSqW4XV+6x0P9eAceZv6KdtYKjpN+7Q/uYN20Os0lsW6JoJ520M+upvydR7BXKbz+FsxwMnz11S0qCPuoE3zN8RqCThMBS+dPTiI/vdpGNBUcAw4PpalQkL8cv3NSXPkKjoZNilhB0/fpxHH32UGjVqYLFYqFOnDs888wxnzpxxlencuTOjRo3K8xqrV6+mS5cu+Pv74+XlRcOGDRkyZAh2u/2yr79mzRoURcnx57XXXqN///78+++/rrLvvvsuLVsW7MtPFFywnyd/vdyFP57vxKR7rmfzmK7MGN6NUbaRPJzxItFGIDWV03xteZ9p5slUp+B5H2Tpbd6rUnKT13wOZzv+8c9/ADRSjjPX8jafWD4lUElin16LOzPe5F37ANKx8GjHUJqF+FHV20qAt6VYfz4hyoMK3fOxKzqBCb/v45XbG3NdzcrF/nqHDx+mXbt2NGrUiDlz5hAaGsqePXt48cUXWbJkCZs2bcLfP/+Z7nv27KFnz548/fTTTJkyBU9PTw4cOMBPP/2ErusFrsv+/fuz5N739vbG09MTT0/ZSbMkXDoUoygKFi3z8Rq9Bd3Sr+UZ0y88pv3O7dpmblZ3Mc3el/85epJO5hebqkBu36kGFTtTZn69GNl7g/Kbz+E8dig6ltdMP/OQtgyTonPesDDV3o8vHL1cCcOCfK28evu1qApkOHTZFE6IAqjQPR+/bI9h4+Ez/LI9pkReb8SIEVgsFpYvX06nTp2oXbs2PXv2ZOXKlcTExDBmzJjLXmPFihUEBwczadIkwsLCqF+/Pj169OCrr77CYin4HVe1atUICgpy/fH29uabb76hcuXKQOYQzMSJE9m5c6erd+Sbb765wp9cXI5zVUxoYCXO48G79oH0zniH7XoDvJU0RpvnsdLyIneomwAj18DD6UoyZRamt6C0ulwvxqW9QQ7d4Ju/ovJMja7h4H5tFX9YXuAx0xJMis5Sx43cmv4enzr6ZclUGt6nKZqqyG60QhRChev5OJGYxtFkA01VWbzzBACLd57gnhtqYhhQpZKZmlW8ivx14+PjWbZsGe+8806O3oWgoCAGDRrEvHnzmDZtWr7XCQoKIjY2lnXr1nHzzTcXeT2d+vfvz44dO1i9ejUrV64EwM8v/3FsceWcq2I0ReGmSauJTUzjH6MOd2eE00fdwMvmudRST/Gp5RMe0hsx3jaIHUbDfK9Z0KW3hektKK0u14txaW/Qir1x+ezJYtBN3cZo0zwaqpk3JVF6dcLtD7FWvz5LSVXJnFxaVtpIiNKkwgUft0/f5vq3s0M6PiWDXlPWu44fefeOIn/dAwcOYBgG116bezKpa6+9lrNnz3Lq1Kl8r3PvvfeybNkyOnXqRFBQEG3btqVr1648+OCDl93C+FI1a9bM8vjo0aNZHnt6elKpUiVMJhNBQQXLzCiujvOueWzvJjw5azsABioL9Y4sT2/FE9pvDDX9yo3qv8y3jmWVozkf2u8h0qiX6/UKsvTW2VuQ/Uvb2VtQVpZ/5rYq5VLO3qCpqw4yeeW/uQYprZR9vGSey41q5ryneMObKfY7+d5xKxlkbjs+4MaatK0fmOdKFiFEwVS4YZd3ejfEdGEc3PkB5PzbpCpM7t/cHdXCMDJroSj5j9FrmsaMGTOIjo5m0qRJ1KhRg3feeYemTZsSG1vwSYZ//vknERERrj9VqlS5qvqLotMjLDjLBnUA5/HgY8fddEn/gHn2ztgNlVu0CH61vsbn5g9prBzLco3KXmY+/uNfdkUn5Pk6BZnzUBRp2y8d0imuTdMK2ssz46+obD+vQTt1D3PMb/OT9U1uVP8lzTDzqb0PndInM8PR0xV4AMzZEo3VpNK+QaAEHkJchQr3v+eOptVoVrsqfT7dkOPcghEdLrtE7ko1aNAARVHYu3cv/fr1y3F+3759VKlShcDAwAJdLyQkhMGDBzN48GDefvttGjVqxGeffca4ceMK9PzQ0FDX/A5R+gxoU4e+LUKIOJbAqXPpVPW2YjGp3PPZRl6yP8F0R2+eNs2nn/oXt2lbuU3byh+OFnxh78XfRmMSUm1sOhzPL9tjcp1Mfbk5D1A0aduzD+lYNYNJrWHlP//R87qal3l2wRU0wVrCeduFfxl0UnfxlGk+rS70dGQYGj85buYT+13EkffPW1En8wpRlCpc8HEp57p859/FKSAggG7dujFt2jSeffbZLPM+4uLi+P7773nwwQcv2/ORmypVqhAcHExKSkpRVhmz2YzD4bh8QVEsnBvUOUXGJAKZ79cjRjDP2YYzTenDKNPP3K5upqu2g67aDnbq9Zip9GVB+g2u+Uz/xiUz6++jhPdpyomE8/nMecgpv16FvJJzQd5DOgDPzotAUbUiG9JpHepPsJ8HcYlp+e4V7EE6d2rreUhbxjVqNADphpm5js58bu/NCS4f/Ms+OkJcvQoZfDhXFgRX9qD/jbWYt+U4sQlpxb4+f+rUqbRv357bbruNt99+O8tS25CQEN555x1X2VOnThEREZHl+UFBQSxcuJCIiAjuvPNO6tevT1paGt9++y179uxhypQpRVrf2rVrExUVRUREBDVr1sTHxwer1VqkryEKLvv7dsZfRzh4siYjbc8QqsTymPY792jruF49zId8xPPWAOaldeHRKXH8R+YS7o9W/Mua/afy/YLO7sB/59h46EyOLJz5TVTt1iQozyEdp6LsQdBUhbG9mzBs1nYUyPG6IZxisGkl92urqKxkBukphpU5jlv43N6LUxRu2FH20RHi6lTI4MO5ssCiqSiKwsDWtUtkfX7Dhg3ZunUr4eHh9O/fnzNnzhAUFES/fv0YO3Zslhwfs2fPZvbs2VmeP3bsWPr27cv69et58sknOXHiBN7e3jRt2pQFCxbQqVOnIq1vnz59WLp0KV26dCEhIYEZM2bw0EMPFelriILL/r69LsSP3lP/QlEgyghmjP1RPrTfw4Om5QzWVhCinOE58088bfqFVXoLZjtuYf2/12FQuPf51NUHmbr6YJYVMJebqDrq1oYFGtL5aMW/dGgQeFXpxS/N1zP9gZaugMiDdHqoW7hXW0sHbY+r/DG9KjMdt/GDozPJZF3Z5mVRSc24fL4c2UdHiKtTIYMPyJnkqaTW59epU4cZM2bkW2bNmjX5nv/uu++u+PU7d+7smtya3UMPPZQluLBarfz444+oaoWbl1xqXfo+DfSxZukJ+WLdYY6egY/s9zLN3pee6mYGmFbRRt1Hd20b3bVtnDZ8+d3RhsWOdmw1GmEUYs65M7D4dGAL3vrtn3wnqn7x5+ECXTO3wCY/uSUGdObr+XbDUYa0DWFWl/NELP0f3Y2N+CjnXc9d72jKTMdt/KG3RM/j537/nut589e9su29EMWswgYfQpR1l/aE6AZM+eOA61w6FhboHVmQ0ZEGSjQDtVX01f4iUEniQdMKHjSt4IThzzLHjazSW/C3fm2WVR25cebLeG1hJPEptnzLpqQXbq5QXkt7swcbWQKN9gqKAssijtBV3Ubb3Z9Ra882Kisp1Cezssf0qvzk6MQv+k1EG1XzfH1nzo7br6uBqioMcy11vki2vRei6EjwUc707NmTP//8M9dzr776Kq+++moJ10gUJ2dPyObDZ/K8Wz9o1ORN+4O8Yx9EBzWSPtpGuqtbqKHE87BpGQ+zjBTDygY9jDX69WzSr+WQUYOLX7cXGXDZwCM/ea3adR5+es4O5g31oEXtKjh0g09XH2Lj4TNM+H0fL/dszOKdJ1DQ+WfHn/y6czod1EhWq/vwsFys02nDl+WOG1jo6Mhm45p8e3dGdmlA+/oBWXJ2OLe9zz6fJaiMJV4TojST4KOc+eqrrzh//nyu5y63b4wouwoyAdKBxjr9etbp12PlEW5Wd9FV3U4XLYLqSgLdtG100zKT8J0xfNimN2KLfg0RegP2GbVzzI+4EpdLGZLhMJi84gDtGwTw5Z+HOX0ug8okYzmykz8++5JJ6iFaWA/gr5zL8jxnL84SR2u2GtfkOaySXcPq3llWFDnJtvdCFC8JPsqZkJAQd1dBuEFhJ0CmY2GF3ooVeiuwGzRVjtJZjeBmbRfXK4cIUJJd80Scoo1A/tFrs9+oxVGjOtFGVWKMQGKNgCx7neTHYcCWU+DINqfTkzSqKQnUUM5Q6/AJzFGxfKCcoL71BDWV0zmuk2x4skm/lr/0MNbrYRw0Qsitp+Zy8ms32fZeiOIjwYcQ5UBB81zkTmGPUZc9jrp86uiHGTvNlMO0Uvdzo/ovTdQjhChnqKmcpqZ2mm5sz/Js3VA4gy+JRiUSqUSC4U0ilbAZJhwoONBwoKJi4KWk43k0ja6mdLyUdAJJpKqSgK+Se2+d0yE9mJ1GfXbp9dip12e3EYo9n48vk6rgZdFISrPn8RPLxFEh3EmCDyHKgcvlucjLyC4NCPbzYMyCSFeyPTsmthuN2O5oxBcX5o36co7GynEaq8dopERnBiLKKWoqp/BQbFQlkapK4lX9DKmGlTijClFGMIeMGhw2gjmk12C/UZMkvAt1Lbtu8GjHeny08t8c52TiqBDuJ8GHEOVEXhMlc+O883+2WyNOJqdRdWXWpHuHTp4jJePiipUkvNlsXMtmR/aNEQ0CSaKqkoCfkoIf5y78nYIZOxo6mqKjomOgcN6wkoqV81hJNTyIx4eTRmVOGlVIxpMrGTrJS91ALz6TiaNClEoSfAhRjlw6UXLF3ji+/utIjp6Q7Hf+uSXdOxafyt3TN+LrYaJV3SpsPXKW+JQMEs7bsm1HoHAGP04bfijG5XtcSmIrA6dqPh60qx8gE0eFKIUk+BCinHFOlGxXP4DWof4FuvPPnnSvTkAl/rokIDEMg2PxqdwzfaOrh+S7jUfZ/18yjYN8eKBtHeZtOc7hU5k9JtkDjJDKngzvUp+5m49x+L9ErBYLlb0stKpbhU2HznA84TyNg3wY2LoOb/66B5vjyiOU7PM5ZOKoEKWPBB+liKIozJ8/P9ddbwGOHDlCaGgoO3bsoHnz5iVat9zUrVuXUaNGMWrUKHdXReThapaM5haQZO8hOZdux9tqyrJNgUM3suzG26SGL36eZhRF4d4WwSz+bQm39ehEJQ+LK7BJPG9j74kkTp1LZ0TnBkz+40Ch5q646nnhb5nPIUTpJsFHCXnooYeYOXMmAJqmUaNGDe644w7Gjx9PlSqZm1rFxsa6/l1a3HLLLaxduzbHcZvNxpYtW6hUqZLr2OWCJ+EeRXnnnz0g8fEwZ3nsPJ9b7gxnGZMKVpPq2sF52Z64HL0zlb0yr5uQWriEZjKfQ4iyQYKPEtSjRw9mzJiB3W5n7969PPLIIyQkJDBnzhwgc9fa0ujxxx/nzTffzHLMZDJRtWre6aqFKIi8NqhLTLVhAM90bcDMDUdJOJ93EOJfyczrvZoS5CvzOYQoK2THsBJktVoJCgqiZs2adO/enf79+7N8+XLXeUVRWLBggevx5s2badGiBR4eHrRq1YodO3bkuOaiRYto2LAhnp6edOnShZkzZ6IoCgkJCa4yGzZs4Oabb8bT05NatWrx9NNPk5KSUuB6e3l5ERQUlOUPZA67TJ482fVvgDvvvBNFUVyPhciLQzcYt3hvnhvUKcAPW6MZf2czFHKug3EeG39nM+5sEUK7+gESeAhRRpT94MMwICOl4H9sqYUrn9+fq5i2f/jwYZYuXYrZnPtmXikpKfTq1YtrrrmGbdu2ER4ezgsvvJClzJEjR7jnnnvo168fERERDB06lDFjxmQps3v3bm677Tbuuusudu3axbx581i/fj0jR4684rrnZsuWLQDMmDGD2NhY12NRvjh0g42HzrAwIoaNh87guFy+9HxsjorPd0mwAcQmplGlkoXpD7QkyC9rNtIgP48cG9EJIcqGYht2mTZtGu+99x6xsbE0bdqUyZMnc9NNNxX9C9lSYXyNAhVVgcpF+dqvngBLpcuXu+DXX3/F29sbh8NBWlrmh+6HH36Ya9nvv/8eh8PB119/jZeXF02bNiU6Opphw4a5ynz22Wdcc801vPfeewBcc801REZG8s4777jKvPfeewwcONA1KbRhw4Z88skndOrUienTp+Phcfm03NOmTeOrr75yPR46dCgffPBBljLOIZjKlSuX2uEjcXWWRsbmmJsRfBVzLAqyH42zXN/mIbJkVohypFiCj3nz5jFq1CimTZtGhw4d+Pzzz+nZsyd79+6ldu3axfGSZUKXLl2YPn06qampfPXVV/z777889dRTuZb9559/uP766/HyuriZV7t27bKU2b9/PzfeeGOWY61bt87yeNu2bRw8eJDvv//edcwwDHRdJyoqimuvzZ40KqdBgwZl6VGpXLnyZZ8jype85mbEJaYxbNb2K+qBKOh+NM5ysmRWiPKjWIKPDz/8kEcffZTHHnsMgMmTJ7Ns2TKmT5/OhAkTivbFzF6ZPRAFoOs6ScnJ+Pr4oKpFMOJkLtwun5UqVaJBgwYAfPLJJ3Tp0oVx48bx1ltv5ShrFGBIxzAM14qBvJ6n6zpDhw7l6aefzvH8ggaCfn5+rnqLiqcgczPGLd5LtyZBheqJuNx+NLL/ihDlV5EHHxkZGWzbto2XX345y/Hu3buzYcOGHOXT09NJT093PU5KSgIyl3LabFlnuNtsNtddu65fsi2mybNAdTMMA8wODLMXulIE3bWGUeB5H4ZhuOru9Prrr3PHHXcwdOhQatTIHDpy/myNGzfmu+++IyUlBU/PzJ/P2X7OMtdccw1LlizJck3nXAtnmRYtWrBnzx7q1auXa72ytGO2+uZV7+zlnOfMZjM2my3Pspe+pmEY2Gw2NE3Lt2xZ4HyfZn+/lhebo+KJP3ceaz6/qvhz59l08ORlA4VL28oMvHHHNTw7LwLIPQvrG3dcg+6wozuokMr7e6soSVsVXHG1VWGuV+TBx+nTp3E4HFSvXj3L8erVqxMXF5ej/IQJExg3blyO48uXL88y5ACZyzuDgoI4d+4cGRkZV1zH5OTkK37ulbLZbNjtdldwBdCyZUsaN27MuHHjXPM2zp8/T1JSEr169eK1115jyJAhvPDCCxw7doz3338fyJyMmpSUxMCBA/noo4949tlnGTx4MLt372bGjBmun1FVVYYPH0737t154oknGDJkCF5eXuzfv581a9YwadKky9bb4XCQkZGRpd5Ouq6TlpbmOle7dm2WLl3Kddddh9VqzXN4JiMjg/Pnz7Nu3Trs9tx3HS2LVqxY4e4qFJtJrS9f5vQ/m/j9n4Jd79K2mpjPtTOitvF7VMGuWZ6V5/dWUZO2KriibqvU1NQCly22Cae5DQdkPwbwyiuv8Nxzz7keJyUlUatWLbp3746vr2+WsmlpaRw/fhxvb+8CTZTMzjAMkpOT8fHxybUuxclsNmMymXL8TM8//zyPPvoor732GgCenp74+vri6+vLokWLGD58OJ06daJJkyZMnDiRe++9l0qVKuHr60uzZs344YcfePHFF/n8889p164dY8aMYcSIEVStWhUPDw/at2/P6tWree2117j99tsxDIP69etz33335ajLpZxtpWkaFosl17KqquLh4eE698EHH/DCCy/w7bffEhISwuHDh3O9dlpaGp6entx8881X9HssbWw2GytWrKBbt255rl4qyzZHxfPIzMuvXvp6yI0F6vnIra0cusG2o2c5fS6dQG8rN9SpIpNJKf/vraIkbVVwxdVWud2k5qXIg4/AwEA0TcvRy3Hy5MkcvSGQmfvCarXmOG42m3M0isPhQFEUVFW9ojkbzuEA5zVKkjO7aXYPPPAADzzwAJBzvkb79u2JiIjIcix7mX79+mXJKPrOO+9Qs2bNLL1Gbdq0KXSE62yr1atX59lWR44cyfK4b9++9O3b97LXVtXM7Ja5/Y7LsvL28zi1bVANf2/Py87NaNugWoEDhuxtZQY6NMr5+SAyldf3VnGQtiq4om6rwlyryL+BLRYLN9xwQ44vuxUrVtC+ffuifrkKb9q0aWzZsoXDhw/z3Xff8d577zFkyBB3V0uUI5qqMLZ3EyD3RF8ge6kIIQqnWIZdnnvuOQYPHkyrVq1o164dX3zxBceOHePJJ58sjper0A4cOMDbb79NfHw8tWvX5vnnn+eVV14p0HP//PNPevbsmef56OjooqqmKON6hAUz/YGWBdohVwghLqdYgo/+/ftz5swZ3nzzTWJjYwkLC+P333+nTp06xfFyFdpHH33ERx99dEXPbdWqVY5hHafLrVgRFc/V7JArhBCXKrYJp8OHD2f48OHFdXlRBDw9PfPM36HreqEmD4mKQRJ9CSGKQtnf20UIIYQQZUqZDD5kSKBsk9+fEEJUbMU27FIcLBYLqqpy4sQJqlatisViKVS+Dl3XycjIIC0trcSX2pY1xdFWhmGQkZHBqVOnUFUVi8VSJNcVQghRtpSp4ENVVUJDQ4mNjeXEiYLt53IpwzA4f/48np6eJZ5krKwpzrby8vKidu3aEgAKIUQFVaaCD8js/ahduzZ2ux2Ho3AbPthsNtatW8fNN98sSWguo7jaStM0TCaTBH9CCFGBlbngA7ji7JiapmG32/Hw8JDg4zKkrYQQQhQX6fcWQgghRImS4EMIIYQQJUqCDyGEEEKUqFI358O5a2txZNe02WykpqaSlJQk8xguQ9qq4KStCk7aqnCkvQpO2qrgiqutnN/b2Xdfz02pCz6Sk5MBqFWrlptrIoQQQojCSk5Oxs/PL98yilGQEKUE6brOiRMn8PHxKfLlmElJSdSqVYvjx4/j6+tbpNcub6StCk7aquCkrQpH2qvgpK0KrrjayjAMkpOTqVGjxmXzOJW6ng9VValZs2axvoavr6+8OQtI2qrgpK0KTtqqcKS9Ck7aquCKo60u1+PhJBNOhRBCCFGiJPgQQgghRImqUMGH1Wpl7NixWK1Wd1el1JO2Kjhpq4KTtiocaa+Ck7YquNLQVqVuwqkQQgghyrcK1fMhhBBCCPeT4EMIIYQQJUqCDyGEEEKUKAk+hBBCCFGiKmzw0adPH2rXro2HhwfBwcEMHjyYEydOuLtapc6RI0d49NFHCQ0NxdPTk/r16zN27FgyMjLcXbVS65133qF9+/Z4eXlRuXJld1enVJk2bRqhoaF4eHhwww038Oeff7q7SqXSunXr6N27NzVq1EBRFBYsWODuKpVKEyZM4MYbb8THx4dq1arRr18/9u/f7+5qlVrTp0/nuuuucyUXa9euHUuWLHFLXSps8NGlSxd++OEH9u/fz88//8yhQ4e455573F2tUmffvn3ous7nn3/Onj17+Oijj/jss8949dVX3V21UisjI4N7772XYcOGubsqpcq8efMYNWoUY8aMYceOHdx000307NmTY8eOubtqpU5KSgrXX389U6dOdXdVSrW1a9cyYsQINm3axIoVK7Db7XTv3p2UlBR3V61UqlmzJu+++y5bt25l69at3HLLLfTt25c9e/aUfGUMYRiGYSxcuNBQFMXIyMhwd1VKvUmTJhmhoaHurkapN2PGDMPPz8/d1Sg1WrdubTz55JNZjjVu3Nh4+eWX3VSjsgEw5s+f7+5qlAknT540AGPt2rXurkqZUaVKFeOrr74q8detsD0fl4qPj+f777+nffv2shVzASQmJuLv7+/uaogyJCMjg23bttG9e/csx7t3786GDRvcVCtR3iQmJgLI51MBOBwO5s6dS0pKCu3atSvx16/QwcdLL71EpUqVCAgI4NixYyxcuNDdVSr1Dh06xJQpU3jyySfdXRVRhpw+fRqHw0H16tWzHK9evTpxcXFuqpUoTwzD4LnnnqNjx46EhYW5uzql1u7du/H29sZqtfLkk08yf/58mjRpUuL1KFfBR3h4OIqi5Ptn69atrvIvvvgiO3bsYPny5WiaxoMPPohRQRK+FratAE6cOEGPHj249957eeyxx9xUc/e4kvYSOSmKkuWxYRg5jglxJUaOHMmuXbuYM2eOu6tSql1zzTVERESwadMmhg0bxpAhQ9i7d2+J18NU4q9YjEaOHMn999+fb5m6deu6/h0YGEhgYCCNGjXi2muvpVatWmzatMktXVAlrbBtdeLECbp06UK7du344osvirl2pU9h20tkFRgYiKZpOXo5Tp48maM3RIjCeuqpp1i0aBHr1q2jZs2a7q5OqWaxWGjQoAEArVq1YsuWLXz88cd8/vnnJVqPchV8OIOJK+Hs8UhPTy/KKpVahWmrmJgYunTpwg033MCMGTNQ1XLVYVYgV/PeEpkfeDfccAMrVqzgzjvvdB1fsWIFffv2dWPNRFlmGAZPPfUU8+fPZ82aNYSGhrq7SmWOYRhu+d4rV8FHQW3evJnNmzfTsWNHqlSpwuHDh3njjTeoX79+hej1KIwTJ07QuXNnateuzfvvv8+pU6dc54KCgtxYs9Lr2LFjxMfHc+zYMRwOBxEREQA0aNAAb29v91bOjZ577jkGDx5Mq1atXD1ox44dk/lDuTh37hwHDx50PY6KiiIiIgJ/f39q167txpqVLiNGjGD27NksXLgQHx8fV8+an58fnp6ebq5d6fPqq6/Ss2dPatWqRXJyMnPnzmXNmjUsXbq05CtT4utrSoFdu3YZXbp0Mfz9/Q2r1WrUrVvXePLJJ43o6Gh3V63UmTFjhgHk+kfkbsiQIbm21+rVq91dNbf79NNPjTp16hgWi8Vo2bKlLInMw+rVq3N9Dw0ZMsTdVStV8vpsmjFjhrurVio98sgjrv9/VatWNbp27WosX77cLXVRDKOCzLAUQgghRKlQ8QbvhRBCCOFWEnwIIYQQokRJ8CGEEEKIEiXBhxBCCCFKlAQfQgghhChREnwIIYQQokRJ8CGEEEKIEiXBhxBCCCFKlAQfQgghhChREnwIIYQQokRJ8CGEEEKIEiXBhxBCCCFK1P8BtqD5pxfNaEwAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_176_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -3786,38 +3399,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "[0.47179152 5.01549939]\n",
-      "[0.47176783 5.01542292]\n",
-      "1.7993408651198877\n",
-      "1.7995707762668065\n",
-      "  \n",
-      "test MSE of OLS:\n",
-      "1.1394311129039245\n",
-      "  \n",
-      "test MSE of Ridge\n",
-      "1.1395084586525954\n"
-     ]
-    },
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week37_208_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\n",
     "np.random.seed(2018)\n",
@@ -3903,19 +3485,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'RegRidge' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [11]\u001b[0m, in \u001b[0;36m<cell line: 34>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     32\u001b[0m ypredictOLS \u001b[38;5;241m=\u001b[39m OLS\u001b[38;5;241m.\u001b[39mpredict(X_test_scaled)\n\u001b[1;32m     33\u001b[0m linear_model\u001b[38;5;241m.\u001b[39mRidge(Lambda)\n\u001b[0;32m---> 34\u001b[0m \u001b[43mRegRidge\u001b[49m\u001b[38;5;241m.\u001b[39mfit(X_train_scaled,y_train_scaled)\n\u001b[1;32m     35\u001b[0m ypredictRidge \u001b[38;5;241m=\u001b[39m RegRidge\u001b[38;5;241m.\u001b[39mpredict(X_test_scaled)\n\u001b[1;32m     36\u001b[0m betaOLS \u001b[38;5;241m=\u001b[39m OLS\u001b[38;5;241m.\u001b[39mcoef_\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'RegRidge' is not defined"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "from sklearn import linear_model\n",
     "np.random.seed(2018)\n",
@@ -3990,7 +3560,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
index 502d4850c..edb418296 100644
--- a/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/week38.ipynb
@@ -197,18 +197,20 @@
    },
    "outputs": [
     {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_10_0.png"
-      }
-     },
-     "output_type": "display_data"
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
     }
    ],
    "source": [
@@ -518,152 +520,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
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-       "    .dataframe tbody tr th:only-of-type {\n",
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-       "\n",
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-       "      <td>1</td>\n",
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-       "      <th>...</th>\n",
-       "      <td>...</td>\n",
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-       "      <th>95</th>\n",
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-       "      <td>1</td>\n",
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-       "      <td>1</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>97</th>\n",
-       "      <td>98</td>\n",
-       "      <td>65</td>\n",
-       "      <td>8</td>\n",
-       "      <td>1</td>\n",
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-       "      <th>98</th>\n",
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-       "      <td>64</td>\n",
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-       "</table>\n",
-       "<p>100 rows × 4 columns</p>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "     ID  Age  Agegroup  CHD\n",
-       "0     1   21         1    0\n",
-       "1     2   23         1    0\n",
-       "2     3   25         1    1\n",
-       "3     4   29         1    0\n",
-       "4     5   21         1    0\n",
-       "..  ...  ...       ...  ...\n",
-       "95   96   61         8    1\n",
-       "96   97   69         8    1\n",
-       "97   98   65         8    1\n",
-       "98   99   64         8    1\n",
-       "99  100   63         8    0\n",
-       "\n",
-       "[100 rows x 4 columns]"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_22_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "# Common imports\n",
     "import os\n",
@@ -741,22 +598,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_24_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "agegroupmean = np.array([0.1, 0.133, 0.250, 0.333, 0.462, 0.625, 0.765, 0.800])\n",
     "group = np.array([1, 2, 3, 4, 5, 6, 7, 8])\n",
@@ -874,50 +716,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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ggw/K4/Ho//7v/yRJt912m5YuXaqvv/5a5557rjZs2KDCwkI9+eSTbf3UAAAAQc3r86muwaMah0s19S7VOFyqdbhU2+BWbX1Tqaytdx377Jaj0d0uBfI7dlvYsY9wRdrCFGULU2REmCKPLY+MCFekzdq07NhHXLRNQzOTWv2cLS6fLpdLM2fOVE1NjSTp17/+tbp166annnpKkuR0OuXxePzrp6en64UXXtDjjz+uiIgIuVwuLVy4UOnp6a0ODQAAEEzcHp+q65yqqnWqpt4ll086WF6rqhqnjjpcOlrX9Lmu3q226pKRtjDF2MMVHRmuaHuE/+uo7z4f+/j3r6Mim4qm3dZUMK0mnE9jMYz27NNtp7y81uwIARceblViYoyqqlq/aRsdB+MdWhjv0MJ4d2wer0/VtU4dqWlUZY1TlbWNOlLjVGVNo6pqmwpnXYO71Y9vkRQTFaG46AjFRUUoLtqm2OgIxUZ9/xFjP/Y5Klwx9ghF28MVHoRn06emxp12nXY/5hMAACCY+QxD1bVOlVc3qLy6URVHG1RxtFEV1Q0qP9qo6lpni7dWWixSXLRNCTHHPmJtSoiJVHyMTfExEYqPtjV9HW1TbFRESJ1UTfkEAACdnmEYqqp16mBlvQ5X1qusqkGHqxp0uLrps6cFZ6WHh1mVFB+ppLhIJcbZlRgXqcS4SHWJbfqc0sWu3j0TVVvTwJbuE6B8AgCATsPj9amssl6lFQ4dOlKvg5X1OnSkXocq6+V0e8/oMSJtYUpNsCslIUopCXalJNiVnGBXUrxdyfF2xUVHnHLu8fBwa1DuEg8WlE8AANDh+AxDFdUNKj5cp9Jyh0orHDpQ4dChynp5z2BqxoQYm7omRqlrl6imz4nR6prYVDZjo05dLnF2KJ8AACCouT1elZQ7VHy4TvvLarX/cJ1KDtep0XXqLZkR4VZ1S4pW9+RodUuKVrfkaHVPilHXxChFRVKBzMJvHgAABA2P16cDFQ4VHazR3kO1KjpYo9Jyxym3ZoaHWdUjOVrpqTHqkRKj9NRYpafEKDnBbspUQjg1yicAADBNVa1ThaVHVXjgqHaXHtX+sjr/ZRxPJCHWpl5d49QrLVYZXZs+0hKjQ+ps8Y6O8gkAAALCZxgqLXdoZ3G1dpVUq7C0RkdqGk+6flJ8pPp0i1efbnHq0z1OvbrGKT7GFsDEaA+UTwAA0C58PkPFh+u0Y3+VdhRXa2dxtRyNnhOuGxUZrqwe8crsEa++3ePVp3u8EiianRLlEwAAtAnDMHS4qkFb91Zqa1Gltu+vVoPzxGWzW1K0+qUnKCs9Xv3SE9Q9JYbjM0ME5RMAALSao9GtrUWVKthbqa1FVSfdjd4zNUYDMxI1sFcXDcjowu7zEEb5BAAAZ8wwDB2ocCiv8Ig2767Q7tIa+Yzjz0TvnhytIX2SNLh3ogZkdFFsVIQJaRGMKJ8AAOCUPF6fduyv1sZd5dq8+8gJt27GR0doSJ+kYx+JSoq3m5AUHQHlEwAAHMfl9mrr3kp9s6Ncm3ZVqP4Hx25aJPXtEa/crGQNy0pRRlosx2zijFA+AQCAJMnp9mrz7gpt2FGu/MIjx10LPSoyTNl9kzUsK1k5mckct4lWoXwCABDCPF6ftu2r0hdby/TtrnI5f3DJytioCI0YkKIRA7pqSJ9EhYdZTUqKzoLyCQBAiDEMQ4UHavTF1kP6evth1da7m92eGBepEQNS9aMBqeqfkaAwK4UTbYfyCQBAiKiuc2rdlkP6LO+gDlXWN7stxh6ucwd11aghaeqf0YXjN9FuKJ8AAHRiHq9Pm3cf0Wd5B5S/p7LZtEi2CKtG9E/VqCFpyu6bxC51BATlEwCATqjiaIM+3nhAn+YdOG63+oCeCRqX20MjB6XKbqMKILD4FwcAQCfhMwwVFFVq9bel2lxYoX+f+71LrE0/zumucTndlZYUbV5IhDzKJwAAHVx9o0ef5R3Q6o2lOlzV4F9usUjDslJ04Tk9lN03iROHEBQonwAAdFAVRxv04YYSrd18oNkUSXHREbpgWA+NH95DKQlRJiYEjkf5BACgg9l7qEb/+qpYX2873OwEoqwe8Zo4oqdGDuqqiHC2ciI4UT4BAOgADMPQ1qJKrfxin7bvr/Yvt1ikkQO76rLzeimzR7x5AYEzRPkEACCIGYahzYVH9O7nRSo6WOtfHhkRpvNzu+uSczOU2oVd6+g4KJ8AAAQhn2Fo484KvbuuSPvL6vzL42NsumRkT40fnq7YqAgTEwKtQ/kEACCIGIahb3aUa8XnRSopd/iXd4m16fLRvTV+WA/ZIsJMTAicHconAABBYuveSi37uFB7D32/ez0pPlJXju6tcbndFRFO6UTHR/kEAMBkRQdrtPTjQm3bV+Vflhxv11Vje+vHOd257CU6FconAAAmOXjEobc+2aNvdpT7l8VHR+jqH/fVBcN6MF0SOiXKJwAAAVbX4NY7nxVpzbel/nk67bYwTRrVS5eem8H11tGp8a8bAIAA8fp8+uibEi3/dI8cjR5JUniYVRNHpOvKMb0VF20zOSHQ/iifAAAEwLc7DmvhW3kqrfj+DPZzB3XV9ROyuAQmQgrlEwCAdnS4ukFvfLRLG3dV+Jf1TovTTRf314CMLuYFA0xC+QQAoB14vD69/+V+vbtur9wen6SmCeKnXZCpH+d0l9VqMTkhYA7KJwAAbWxncbVe+dcOHTi2iz3MatE1F2TpsnN7KoJpkxDiKJ8AALSRuga33lyzW5/mHfQv69czQTOuGKycgWmqqnLIc2wrKBCqKJ8AAJwlwzD0ZUGZ/vbhLtU1uCVJMfZwXT+hn8bldudymMC/oXwCAHAWjjpceuX97c1OKBqT3U3TJ/ZTfAxTJwE/RPkEAKAVDMPQl9vK9OoHO/1zdqZ2setnkwZpcJ8kk9MBwYvyCQBACx11uLTkXzv0zc7vL4t50Yieuu7CLEXa2MUOnArlEwCAFtiw/bBe+dcO/7GdKQl2zbhisAb1TjQ5GdAxUD4BADgDjS6P/rZqlz7L//5M9okj0nXdhVlcix1oAV4tAACcRtHBGi1csVVlVQ2SpKT4SM28YjDHdgKtQPkEAOAkfIahf325X299skdenyGp6Xrst00aqBh7hMnpgI6J8gkAwAlU1Tr10j8KtG1flSQpMiJMP7mkv8bldJfFwqUxgdaifAIA8ANbiyr1woqt/pOK+nSL0+zJ2UpLijY5GdDxUT4BADjGZxj6x+d79c5nRTIkWSRNGt1L156fqXCuyQ60CconAACSautdevHdAm0pqpTUdHnMWZOzlZOZbHIyoHOhfAIAQt6eAzVasDxfR2qckqS+3eN195ShSk6wm5wM6HwonwCAkGUYhtZsLNVrH+7yn80+cUS6pk/sr4hwdrMD7YHyCQAISW6PT0s+2KFP85omjbdFWPWzSYM0OrubycmAzo3yCQAIOTUOl555O1+7S45KkrolResXU3OUnhJjcjKg86N8AgBCyv6yWj29LM9/fGduVrJmXZ2taDt/EoFA4JUGAAgZG7Yf1kvvFcjl9kmSLh/VS9PGZ8lqZdJ4IFAonwCATs9nGFrxWZFWfL5XkhQeZtXPLh+osUO7mxsMCEGUTwBAp+b2+PTyym36sqBMkpQQa9M9U3OU1SPB5GRAaKJ8AgA6LUejW88sy9eO4mpJUu9ucfrltFwlxkWaGwwIYa0qn6tWrdKCBQtkt9tltVr18MMPq3///idc1zAMLViwQO+//77i4+NVX1+v6dOna/r06WcVHACAU6k42qD5f9+sg0fqJUnD+6Vo9uRsRdrCTE4GhLYWl8+8vDzNnTtXy5YtU2ZmppYvX66ZM2dq5cqVio2NPW79pUuXatGiRVq5cqXS0tJ08OBBXXXVVUpLS9OFF17YFj8DAADN7D1Uoz+9maejDpekponjf3LxAE4sAoJAiy/f8OKLL2r8+PHKzMyUJE2ePFler1fLly8/4frbt29XZmam0tLSJEndu3dX37599dlnn7U+NQAAJ5FXWKHHXt3oL543TOinmy+heALBosXlc/369crJyfn+AaxWZWdna926dSdc/6KLLlJhYaF27NghqamM7tq1SykpKa2MDADAiX2y+YCeWpovp9ur8DCL7rwmW5NG9ZLFQvEEgkWLdrtXVVWptrb2uOKYkpKi/Pz8E95n7Nix+sMf/qCf/vSnSkpKUlFRkUaOHKmf/OQnLQpqtVpC7n+tYWHWZp/RuTHeoYXxbnvvrd+rNz7aLUmKsYfrP28YpoG9Ek1O1YTxDi2M96m1qHw2NjZKkmw2W7PlNpvNf9sPrVmzRr/5zW+0aNEiDR06VMXFxfrnP/8pu93eoqBJSTEh+z/X+PgosyMggBjv0MJ4nz3DMPTKym1aurqpeKYk2PXI7LHKSIszOdnxGO/QwnifWIvK53eF0eVyNVvucrlOWibnz5+vSy65REOHDpUkZWRkaO/evfrtb3+r3/72t2f83JWVjpDc8hkfH6WamgZ5vT6z46CdMd6hhfFuGz6fob++v11rvi2VJKUlReuBn5yjWJtVVVUOk9N9j/EOLaE83omJMaddp0XlMzExUXFxcaqoqGi2vKKiQhkZGSe8z759+3T55Zc3W9azZ0/95S9/aVH59PkM+XxGS+J2Gl6vTx5PaP3jDWWMd2hhvFvP4/XppX8U6KtthyVJvbrG6lfThyshxha0v1PGO7Qw3ifW4oMRRo8erS1btvi/NwxDBQUFGjt27AnXT0tLU3l5ebNl5eXlioxkgl8AQOs43V49vSzfXzz790zQ3J+MUEKM7TT3BGC2FpfPWbNmae3atSoqKpIkrVixQlarVVOmTJEkPfjgg7r//vv960+bNk0rV67UgQMHJEmlpaVauXLlcVtDAQA4Ew1Oj+a/sUn5e45IknIyk/Xr6cMVbeeifUBH0OJXam5urh577DHNmTPHf4WjRYsW+SeYdzqd8ng8/vVnzpwpi8WiX/ziF7Lb7aqrq9ONN96ou+++u+1+CgBASGhwejT/75u1u/SoJOm8wV11x1VDFM5ZxUCHYTEMo0McSFleXmt2hIALD7cqMTFGVVUOjhkJAYx3aGG8W66+0aM//n2T9hyokST9OKebbr98cIc4GZXxDi2hPN6pqaefZYJ9FACAoOdodOuPb2xS0cGmDREXDOuu2yYNkjVEp+ADOjLKJwAgqNU1uDXv9U3aV9ZUPC8c3kO3XDaQ4gl0UJRPAEDQqmtw64nXNmr/4TpJ0sQR6br5kgEhe9ERoDOgfAIAglJdg1uP/22jSsqbiufFP+qpmy7uT/EEOjjKJwAg6NQ3evTHNzb5i+el52Zo+sR+FE+gE2BuCgBAUGl0efTkm5u191DTMZ4Xj+xJ8QQ6EconACBouNxePbU0zz+P5/jhPXTTRexqBzoTyicAICi4PT4983a+tu+vliSNye6mWy8bSPEEOhnKJwDAdB6vTy+s2KoteyolSSMHddWMK5nHE+iMKJ8AAFP5fIYWvbdN3+4slyQN75eiWVcPUZiVP1FAZ8QrGwBgGsMwtOSDHfqyoEySlN0nUXdNyeZa7UAnxqsbAGCadz4r0sebDkiS+vdM0D3TchURHmZyKgDtifIJADDFR9+UaMXneyVJPVNjde91uYqMoHgCnR3lEwAQcF8WlOlvq3ZKklIS7Pr19GGKtkeYnApAIFA+AQABtaXoiF76R4EMSfHREZpz43B1iY00OxaAAKF8AgACpvDAUT371hZ5fYbstjD96obhSkuMNjsWgACifAIAAuLgEYf+9GaenG6vwsMs+uW0XPXuFmd2LAABRvkEALS7ow6X5v99s+oa3LJYpNmTh2pQ70SzYwEwAeUTANCunC6v/vTmZlUcbZQk3XrpQP1oYKrJqQCYhfIJAGg3Pp+hF1Zs1d5DtZKkK8f01oXnpJucCoCZKJ8AgHZhGIZe/XCnNu2ukCSNGpKmay/INDkVALNRPgEA7eJfXxVrzbelkqSBGV0044rBslosJqcCYDbKJwCgzX21rUx/X7NbktQ9OVr3TMtRRDh/cgBQPgEAbWxXSbVe+sc2SVJ8jE3/ef0wxXD1IgDHUD4BAG3mcHWDnl6WL4/XJ1uEVfdel6vULlFmxwIQRCifAIA20eD06KmleU1zeUqaPTlbfbvHmx0LQJChfAIAzprX59Pz72zVgQqHJOn6Cf10Tn/m8gRwPMonAOCs/X11ofL3HJEkjcvprsvOyzA5EYBgRfkEAJyVjzeVatWGYknSgIwuum3SQFmYUgnASVA+AQCttm1flV79YKckKbWLXb+4dqjCw/jTAuDkeIcAALRKWWW9nns7X16foajIMP3yumGKi7aZHQtAkKN8AgBarL7Roz8tzZOj0SOLRbrzmqFKT4kxOxaADoDyCQBoEZ9h6MV3t+pQZb0k6caL+isnM9nkVAA6CsonAKBF3vm0SJsLj53ZnttdF/+op8mJAHQklE8AwBn7ZsdhvbturyQps0e8br2UM9sBtAzlEwBwRkrK6/zXbE+IsekX1+YoIpw/IwBahncNAMBp1TW49fSyPDndXoVZLfrF1BwlxkWaHQtAB0T5BACcktfn0wvvbFF5daMk6dbLBqpfeoLJqQB0VJRPAMApLVu7R1v3VkmSJoxI1wXDepicCEBHRvkEAJzUV9vK9P6X+yVJA3om6KaL+pucCEBHR/kEAJzQgQqH/rxyuyQpMS5Sd12bw6UzAZw13kUAAMdpcHr0zFv5/hOM7p4yVAkxXDoTwNmjfAIAmjEMQy+v3Oa/gtFNF/dXFicYAWgjlE8AQDP/+qpY3+wolySNye6mCeekm5wIQGdC+QQA+G3fV6WlHxdKknqmxuq2SVzBCEDbonwCACRJVbVOPf/OFvkMQ1GR4frF1KGKjAgzOxaATobyCQCQx+vTguVbVFPvliT9/KohSkuMNjkVgM6I8gkA0NKPC7W79Kgk6aqxvTW8f4rJiQB0VpRPAAhx3+wo1wdfF0uSBvdO1JRxmSYnAtCZUT4BIIQdrm7Qyyu3SZISYm2aPTlbVisnGAFoP5RPAAhRbo9XC97eoganR1aLRXdOzlY8E8kDaGeUTwAIUa+v3q19ZbWSpGsv6KuBvRJNTgQgFFA+ASAEfVlQpjXflkqScrOSdfno3iYnAhAqKJ8AEGIOHnHoL+9vlyQlxUfqjquGyMpE8gAChPIJACHE5fZqwfItcrq8CrNadNc1QxUbFWF2LAAhhPIJACHkbx/uUkm5Q5J0/YR+ykpPMDkRgFBD+QSAEPFlQZk+2XxAkjRiQKouGdnT5EQAQhHlEwBCQFlVvf567DjP5Hi7br9ikCwc5wnABOGtudOqVau0YMEC2e12Wa1WPfzww+rfv/9J16+srNS8efO0f/9+ORwOuVwu3X333briiitaHRwAcGbcHp+ef2erGl1eWS0Wzb4mWzF2jvMEYI4Wb/nMy8vT3Llz9cQTT+hvf/ubrrvuOs2cOVN1dXUnXN/lcun222/Xueeeq8WLF+utt97S+eefr/z8/LMODwA4vaUfF2rfoab5PKeOz1Q/jvMEYKIWl88XX3xR48ePV2Zm07V/J0+eLK/Xq+XLl59w/TfffFORkZGaMmWKf9nPf/5zXXfdda0KDAA4cxt3lWvVhqbrtg/tm6RJo3qZnAhAqGtx+Vy/fr1ycnK+fwCrVdnZ2Vq3bt0J1//ggw907rnnNluWlJSkrKyslj41AKAFKmsa9fJ7x67bHmNjPk8AQaFFx3xWVVWptrZWKSkpzZanpKScdDf6zp07NXLkSD388MPasWOHIiIidMUVV+jGG2/kYHcAaCden0/Pr9gqR6NHFkk/v3oI120HEBRaVD4bGxslSTZb8zcwm83mv+2Hampq9MILL+jZZ5/V//7v/2rv3r26+eabVVtbq1mzZp3xc1utFlmtoVVWw8KszT6jc2O8Q0t7j/fyj4u0u+SoJOnqcX2V2y/lNPdAe+L1HVoY71NrUfm02+2Smk4i+ncul8t/2w9ZLBbl5uZq/PjxkqQ+ffpo2rRp+utf/9qi8pmUFBOyW0rj46PMjoAAYrxDS3uMd/7uCr37eZEkKTszWTMmD+WPYJDg9R1aGO8Ta1H5TExMVFxcnCoqKpotr6ioUEZGxgnv0717d3Xr1q3Zsh49eqiiokKNjY0nLa0/VFnpCMktn/HxUaqpaZDX6zM7DtoZ4x1a2mu8a+td+r8lG2QYUow9XHdcOVg1NQ1t9vhoHV7foSWUxzsxMea067R4ns/Ro0dry5Yt/u8Nw1BBQYHuvPPOE64/cuRIlZSUNFtWUVGhxMTEMy6ekuTzGfL5jJbG7RS8Xp88ntD6xxvKGO/Q0pbjbRiGXnq3QFW1TknSzy4fpIQYG/+eggiv79DCeJ9Yi/fDzJo1S2vXrlVRUdMunRUrVshqtfqnUnrwwQd1//33+9f/6U9/qry8POXl5UmSqqur9c477+jWW29tg/gAgO98vLFUG3c17Zm68Jx0/WhgV5MTAcDxWrzlMzc3V4899pjmzJnjv8LRokWLFBsbK0lyOp3yeDz+9QcNGqRnnnlGjzzyiMLDw+X1enXDDTdoxowZbfdTAECIKymv0+urd0uSeqTEaPrEfiYnAoATsxiG0SH2ZZeX15odIeDCw61KTIxRVZWDzfYhgPEOLW053i63V7/96waVVjgUHmbVb346Uj27xrZRUrQFXt+hJZTHOzU17rTrcPojAHRwb6zerdIKhyRp+sR+FE8AQY3yCQAd2Lc7y7VmY6kkaXi/FE0ckW5yIgA4NconAHRQVbVO/Xll0+Uzu8TadPsVg0J2PmQAHQflEwA6IJ9h6KV/FPzb5TOzFRfN5TMBBD/KJwB0QP/6ar+27auSJE0a3UuDeyeanAgAzgzlEwA6mH2HavXW2j2SpN7d4nTt+ZkmJwKAM0f5BIAOxOny6vkVW+X1GbJFWDV7crbCuW47gA6EdywA6EBe+2iXyirrJUk/uXiAuiVFm5wIAFqG8gkAHcQ3O8r1yeYDkqQfDUjV+bndTU4EAC1H+QSADqCq1qm//LNpWqXEuEj99HKmVQLQMVE+ASDI/XBapTuuGqLYqAizYwFAq1A+ASDIffBV8ffTKo1iWiUAHRvlEwCC2P6yWr31SaEkqXdanK69gGmVAHRslE8ACFIut1cL3y2Qx2vIFm7VrMlDmFYJQIfHuxgABKk3Py7UgQqHJGn6xH7qnhxjciIAOHuUTwAIQvl7juijb0okScOyknXhOekmJwKAtkH5BIAgU1Pv0qL3mqZVio+O0O1XDGZaJQCdBuUTAIKIYRj6y8rtqnG4JEkzrhys+BibyakAoO1QPgEgiKzdfECbdldIkiaOSFduVorJiQCgbVE+ASBIHKqs1+sf7ZIkdU+O1g0T+pmcCADaHuUTAIKAx+vTi+9ulcvtU5jVollXZ8sWEWZ2LABoc5RPAAgCKz7fq6KDtZKkqeMz1btbnMmJAKB9UD4BwGS7Sqr13vq9kqRBvbrosnN7mRsIANoR5RMATNTg9OjFdwtkGFJUZLhmXjlEVivTKgHovCifAGCiJf/aoYqjjZKkWy8boOQEu8mJAKB9UT4BwCSfbz6gT/MOSpJGD0nT6CHdTE4EAO2P8gkAJqisadSzSzdJkpLiI3XLpQPMDQQAAUL5BIAA8xmGXnq3QLX1blkk3XHlEEXbI8yOBQABQfkEgAD7aEOJthRVSpKuGNNbg3onmpwIAAKH8gkAAVRSXqc3Py6UJPXtEa+p47NMTgQAgUX5BIAAcXt8WriiQB6vTxHhVt13848UEc7bMIDQwrseAATIW58UqqS8TpI0/aJ+6tUt3uREABB4lE8ACICCvZX611fFkqShfZN08cgMkxMBgDkonwDQzhyNbi16b5skKTYqQrdfMVhWC1cxAhCaKJ8A0I4Mw9Ar7+9QVa1TkvTTSQOVGBdpcioAMA/lEwDa0Rdby/T19sOSpHG53fWjgV1NTgQA5qJ8AkA7qahu0JJVOyRJqV3suumi/iYnAgDzUT4BoB34fIZe+keBGpxeWSzSz6/OVlRkuNmxAMB0lE8AaAcrv9innSVHJUlXjemjfukJJicCgOBA+QSANlZ0sEbvfFYkSerbPV5X/7iPuYEAIIhQPgGgDTldXi18t0Ben6HIiDDNmjxE4WG81QLAd3hHBIA29MbqXSqrrJck3XRxf6UlRpucCACCC+UTANrIxl3l+njTAUnSiAGpOj+3u8mJACD4UD4BoA0crXPqzyu3S5ISYm362eWDZOEqRgBwHMonAJwlwzC0aOU21TW4JUl3XDlEsVERJqcCgOBE+QSAs7T621Jt2VMpSbpkZIay+yaZnAgAghflEwDOQml5nf6+ZrckqWdqjK67MNPkRAAQ3CifANBKbo9XL6wokNvjU3iYVbOuzlZEeJjZsQAgqFE+AaCVln68RyXldZKk6ydkqWfXWJMTAUDwo3wCQCvk7zmiVRuKJUk5mcm6+Ec9TU4EAB0D5RMAWqjG4dKi97ZJkuKjIzTjysFMqwQAZ4jyCQAtYBiG/rxym2ocLknSjCsHKyHGZnIqAOg4KJ8A0AJrNpZqc+ERSdJFI3oqNyvF5EQA0LFQPgHgDJWW1+mN1U3TKqWnxuj6CVkmJwKAjofyCQBn4IfTKs2+Olu2CKZVAoCWonwCwBl4c03h99MqXci0SgDQWpRPADiNTbsr9OE3JZKk3KxkXTySaZUAoLUonwBwCtV1Tr383bRKMTbNuIJplQDgbFA+AeAkfIahF98tUF2DW5L086uGKJ5plQDgrLSqfK5atUpTp07VT37yE91yyy3atWvXGd1vzZo1GjhwoN56663WPC0ABNT7X+7Xtn1VkqRJo3opu2+SyYkAoOMLb+kd8vLyNHfuXC1btkyZmZlavny5Zs6cqZUrVyo29uQH4NfX1+vJJ588m6wAEDB7DtTo7U/2SJL6dIvT1AsyTU4EAJ1Di7d8vvjiixo/frwyM5veiCdPniyv16vly5ef8n5PPfWUbrrpplaFBIBAanB69MKKLfL6DEXawjT7mmyFh3GUEgC0hRa/m65fv145OTnfP4DVquzsbK1bt+6k9ykoKFBeXp6mT5/eupQAEECLP9ih8upGSdKtlw5QWmK0yYkAoPNo0W73qqoq1dbWKiWl+eXkUlJSlJ+ff8L7+Hw+PfLII/qf//mfszpD1Gq1yGoNrTNMw45taQlji0tIYLyDw6ebD+iLrWWSpLFDu+mC4ent8jyMd2hhvEML431qLSqfjY1NWwJstuZne9psNv9tP7RkyRKNGDFCgwYNamXEJklJMSE7vUl8fJTZERBAjLd5istq9cq/dkiSuiVH696bRijaHtGuz8l4hxbGO7Qw3ifWovJpt9slSS6Xq9lyl8vlv+3flZWV6c0339Qbb7xxFhGbVFY6QnLLZ3x8lGpqGuT1+syOg3bGeJvL5fbqD3/5Wk6XV2FWi+68ZqicDS45G1ynv3MrMN6hhfEOLaE83omJMaddp0XlMzExUXFxcaqoqGi2vKKiQhkZGcet/9lnn0mSZs+e3Wz5woUL9fbbb+vee+/VyJEjz+i5fT5DPp/Rkridhtfrk8cTWv94QxnjbY5XP9ip4sPHLp85oZ96dY0NyDgw3qGF8Q4tjPeJtXiqpdGjR2vLli3+7w3DUEFBge68887j1p02bZqmTZvWbNnAgQM1a9YsTZ06tRVxAaDtfb39sNZsLJUkDe+Xoku4fCYAtJsWHwk7a9YsrV27VkVFRZKkFStWyGq1asqUKZKkBx98UPfff3+bhgSA9lJe3aC//LPp8pmJcZGacSWXzwSA9tTiLZ+5ubl67LHHNGfOHNntdlmtVi1atMg/wbzT6ZTH4znufgsXLtSnn37q//rtt9/W4sWLzzI+ALSex+vT8+9sVYPTK4tFmj05W7FR7XuCEQCEOothGB3iQMry8lqzIwRceLhViYkxqqpycMxICGC8A+/vq3fr/a/2S5KuvSBTV4/tE7DnZrxDC+MdWkJ5vFNT4067DhNQAQhJeYUV/uI5uHeirhzd2+REABAaKJ8AQs6Ro4168d0CSVJ8dIRmXT0k5KZyAwCzUD4BhJSm4zy3yNHokUXSzydnKyE20uxYABAyKJ8AQsrSjwtVeKBGkjR5XF9l90kyOREAhBbKJ4CQ8c2Ocn3wdbEkaUifxICeYAQAaEL5BBASDlc36OWVTfN5JsTaNOvqbI7zBAATUD4BdHpuj1cL3t6iBqdHVotFd07OVnyMzexYABCSKJ8AOr3XV+/WvrKmuYKnjs/UwF6JJicCgNBF+QTQqX1ZUKY13zZdtz03K1mTRvUyOREAhDbKJ4BOq7S8Tn/553ZJUnJ8pO64aoisXLcdAExF+QTQKTU4PXrm7S1yur0KD7PozilDuW47AAQByieATscwDL383jaVVdZLkm66eICyeiSYnAoAIFE+AXRC73+1X9/sLJck/XhoN104vIfJiQAA36F8AuhUtu2r0tKPCyVJvbrG6tbLBsrCcZ4AEDQonwA6japap154Z4sMQ4qODNfdU3NkiwgzOxYA4N9QPgF0Ch6vT88tz1dNvVuS9POrh6hrlyiTUwEAfojyCaBTeP2jXSosrZEkXT22j4b1SzE5EQDgRCifADq8T/MOaPWxieSH9k3SNeP6mpwIAHAylE8AHVrhgaNa/K8dkqSUBLtmTc6W1coJRgAQrCifADqs6jqnnn0rXx6vIVuEVb+clstE8gAQ5CifADokt8enZ9/OV3WdS5J0x5VD1LNrrMmpAACnQ/kE0OEYhqFXV+3wn2B05ZjeGjmoq8mpAABngvIJoMP5eGOpPtl8UJKUm5Wsa8/PNDkRAOBMUT4BdCg79lfpbx/ukiSlJUVr1tVDOMEIADoQyieADqPiaIOeW75FXp8huy1M/zE1R9F2TjACgI6E8gmgQ2hwevSnpXmqrXfLoqYrGPVIiTE7FgCghSifAIKez2do4YqtKi13SJKmXZilc/qnmpwKANAalE8AQW/px4XaXHhEkjR2aDddPqqXyYkAAK1F+QQQ1D7ZfEDvf7VfktSvZ4J+OmmQLBZOMAKAjoryCSBo7dhf1ezSmfdMzVFEOG9bANCR8S4OICgdrqrXM2/l+89s/+V1uYqPtpkdCwBwliifAIJOfaNbf1qaJ0ejRxaLdOc12eqZyqUzAaAzoHwCCCoer0/PvJWvg0fqJUnTJ/RTblaKyakAAG2F8gkgaBiGoT+v3Kbt+6slSRcO76FLzs0wNxQAoE1RPgEEjbc/LdL6rWWSmq7ZfvOlAzizHQA6GcongKDwyeYD+se6vZKk3mlxuvOabIVZeYsCgM6Gd3YAptuy54heeb9pSqXk+Ejde32u7LZwk1MBANoD5ROAqfaX1erZ5VvkMwxFRYbrP28Yri6xkWbHAgC0E8onANNU1jTqyTc3y+nyKsxq0T1Tc5SeEmN2LABAO6J8AjBFXYNb897YpOo6lyRpxpWDNbh3osmpAADtjfIJIOAaXR7N//tm/1ye08Znakx2N5NTAQACgfIJIKA8Xp+efXuLig7WSJIuPTdDV4zubXIqAECgUD4BBIzPMPTSPwq0tahSkjQmO003TOzHXJ4AEEIonwACwjAMvbZql77adlhS0yTyt18xWFaKJwCEFMongIB4d91effRtiSSpX3qC7poyVOFhvAUBQKjhnR9Au1vzbYmWf1okSUpPidEvr8tVZESYyakAAGagfAJoV5/nH9TiD3ZKarp60a+nD1dsVITJqQAAZqF8Amg3X20r08srt0mSEmJsmnPjOUqM4+pFABDKKJ8A2sW3O8u1cEWBDEOKjYrQfTcOV7ekaLNjAQBMRvkE0Oby9xzR8+98f732OdOHKz011uxYAIAgQPkE0Ka276vSM2/ly+M1FGkL069vGKbe3eLMjgUACBKUTwBtZnfpUf1paZ7cHp9s4Vb953W5ykpPMDsWACCIhJsdAEDnsLvkqP74901yur0KD7PoP6blamCvRLNjAQCCDOUTwFnbWVyt+W9ultPlVZjVorun5Ci7b5LZsQAAQYjyCeCsbN9XpSeXbpbL7VN4mEV3X5uj4f1SzI4FAAhSlE8ArVawt1JPLc2Ty+NTeJhV90zNUW5WstmxAABBjPIJoFW2FB3R08vy5fb4FBFu1X9My9HQvhRPAMCpUT4BtFj+nqbi6fE2ndX+y+tyNaQPx3gCAE6vVeVz1apVWrBggex2u6xWqx5++GH179//hOuuW7dOr7zyiurr6+V0OhUTE6P77rtPQ4YMOavgAMzxzY7DemHFVnm8hmwRVv3ndcM0qDdntQMAzkyL5/nMy8vT3Llz9cQTT+hvf/ubrrvuOs2cOVN1dXUnXP/hhx/WxIkT9corr+iNN97QsGHDdPvtt+vIkSNnHR5AYH26+YCeW77FP4H8r66neAIAWqbF5fPFF1/U+PHjlZmZKUmaPHmyvF6vli9ffsL1hw4dquuuu87//a233qrq6mqtW7eudYkBmOJfX+3Xn/+53X+t9rk3ncM8ngCAFmtx+Vy/fr1ycnK+fwCrVdnZ2Sctk/Pnz5fV+v3TREZGSpLcbndLnxqACQzD0FufFOqN1bslSYlxkXrg5hHq2z3e5GQAgI6oReWzqqpKtbW1SklpPodfSkqKiouLz+gxNm3aJLvdrgsvvLAlTw3ABD7D0JJVO/WPdfskSV0To/TgzSOUnhJjcjIAQEfVohOOGhsbJUk2m63ZcpvN5r/tVAzD0IIFC3TvvfcqKallZ8ZarRZZrZYW3aejCwuzNvuMzi3Yxtvj9WnRu9u0fushSVJG11jd/5Nz1CU20uRknUOwjTfaF+MdWhjvU2tR+bTb7ZIkl8vVbLnL5fLfdipPP/200tLSNGPGjJY8rSQpKSlGFktolc/vxMdHmR0BARQM4+1ocGveX7/S5l0VkqTBfZL0mztGKzYqwuRknU8wjDcCh/EOLYz3ibWofCYmJiouLk4VFRXNlldUVCgjI+OU93399deVn5+vZ599tuUpJVVWOkJyy2d8fJRqahrk9frMjoN2FizjfeRoo+a9vlEl5Q5JUm5Wsv5jWq7cjS5VNbpOc2+cqWAZbwQG4x1aQnm8ExNPf1hWi+f5HD16tLZs2eL/3jAMFRQU6M477zzpff7xj39o5cqVWrhwoWw2m4qLi1VcXKyxY8ee8fP6fIZ8PqOlcTsFr9cnjye0/vGGMjPHe39ZrZ58c7Oq65pK5gXDuuvWywYqzGrh32A74fUdWhjv0MJ4n1iLD0aYNWuW1q5dq6KiIknSihUrZLVaNWXKFEnSgw8+qPvvv9+//po1azRv3jzdfffd2rVrl/Lz8/X555/rm2++aZufAECb2FJ0RP/v1W/9xXPqBZn66aRBCrNyzBIAoO20eMtnbm6uHnvsMc2ZM8d/haNFixYpNjZWkuR0OuXxePzrP/jgg6qqqtJPf/rTZo9zzz33nGV0AG3l07wDeuX9HfL6DIVZLZpxxWCNGdrN7FgAgE7IYhhGh9iXXV5ea3aEgAsPtyoxMUZVVQ4224cAM8bbZxh6+5M9em9901RKUZHhumdqjgZz1aJ2x+s7tDDeoSWUxzs1Ne6067Tq2u4AOr4Gp0cvvlugTbubTiBMio/Uf14/TD1TY01OBgDozCifQAg6XN2gp5fmqbSi6Yz2rB7xumdqjhKYwxMA0M4on0CI2bavSs+9nS9HY9Ox2T8e2k23TRqoiPAwk5MBAEIB5RMIIau/LdHfVu2SzzBksUg3TOinS8/NCNkLOAAAAo/yCYQAt8erV1ft1CebD0pqOrHozmuylZOZbHIyAECooXwCndzh6gY993a+9pfVSZLSEqP0y+ty1T359FehAACgrVE+gU5s064KvfSPAtU7m47vHN4vRXdcNVjRdq7RDgAwB+UT6IS8Pp/e/qRIK79omr/TYpGmjc/SpFG9ZOX4TgCAiSifQCdz1OHSC+9s0fb91ZKk+Bib7pycrUFMHA8ACAKUT6ATyd9zRIve26YaR9P12Qf0TNCdU4aqC/N3AgCCBOUT6ATcHp+WrS3UB18X+5dddl6Gpo3PUniY1cRkAAA0R/kEOrgDFQ69sGKrig83nc0eFx2hmVcOVm5WisnJAAA4HuUT6KAMw9DaTQf0+ke75PL4JElD+yZp5pWDuUwmACBoUT6BDuiow6VX3t+ujbsqJEnhYRZdd2E/XTyyJ2ezAwCCGuUT6EAMw9BX2w7r1VU7VdfgliR1T47W7MnZ6pUWZ3I6AABOj/IJdBA1DpcW/2uHvtlZ7l82cUS6rp/QT5ERYSYmAwDgzFE+gQ7gq21lWvLB91s7UxLsuv2KwRrM3J0AgA6G8gkEseo6p/62aqc27Ph+a+eEEem6/sIs2W28fAEAHQ9/vYAg5PMZWrOxVG99UqgGp1fSsa2dlw/S4D5JJqcDAKD1KJ9AkNl7qEZ/fm+7ig7WSJIski4cka7rxmcpKpKXLACgY+MvGRAkGl0evfTOFq34tFCG0bQso2usbps0UFk9EswNBwBAG6F8AiYzDENfbz+sv6/ercpapyQpMiJM14zrq0vO7akwK5fHBAB0HpRPwER7D9XotQ93aVfJUf+yEQNSddNF/ZWcYDcxGQAA7YPyCZjgaJ1Ty9bu0ef5B3VsD7tSu0Rp1rU5GpgeL8+xy2UCANDZUD6BAHJ7vFq1oUTvrtsrp6vpLPZIW5iuGtNbl4/prbTUeFVVOUxOCQBA+6F8AgHg8xlat+WQ3vlsj47UNB3XaZH045zumjo+U11iIxUezrGdAIDOj/IJtCPDMLRxV4Xe+mSPDlR8v0WzX88E/eTi/urTLd7EdAAABB7lE2gnO/ZXaenHhSo8UONf1j05WtPGZ+mc/imyWCwmpgMAwByUT6CN7Syu1rufF2nr3ir/sqT4SE0Zl6mxQ7vJaqV0AgBCF+UTaAOGYWj7/qbSuX1/tX95bFSErhrTWxNGpCsiPMy8gAAABAnKJ3AWDMNQwd4qrfi8qNlcnTH2cF0yMkOXnJvBJTEBAPg3/FUEWsHr8+nbnRV6/8v9/muwS01bOi87L0MTR/SkdAIAcAL8dQRaoNHl0Wd5B/XB18WqONroXx4fHaHLRvXShHPSZbfxsgIA4GT4Kwmcgeo6pz76pkQfbyyVo9HjX54cb9el52boguE9FBnBMZ0AAJwO5RM4CcMwtKvkqFZ/W6JvdpTL6zP8t/XpFqdJo3rpRwNTFWZlcngAAM4U5RP4gUaXR19sLdPqb0tVUl7X7Lbh/VJ02XkZGpDRhXk6AQBoBconcEzJ4Tqt3XxA67YcVIPT618eFRmmHw/trgkj0tU9OcbEhAAAdHyUT4S0+ka3viwo06d5B7X3UG2z23qmxmjiiJ4anZ3GSUQAALQR/qIi5PgMQ9v3VemzvIP6Zme53B6f/7bwMItGDEjVxBE91b9nArvWAQBoY5RPhATDMLSvrFZfbC3T19sPq6rW2ez2jK6xOj+3u0Znd1NsVIRJKQEA6Pwon+jUDlXW68uCMn1RUKayyvpmt8XYwzV6SDeNy+2u3t3iTEoIAEBooXyiUzEMQweO1OubHYf17Y5y7T/c/Gz18DCLhmWlaNSQNA3rl8z11gEACDDKJzq873apf7OjXN/sKNehH2zhtFikwb0TNWpImn40IFXRdnarAwBgFsonOiSn26tt+6qUV3hEeYUVqqxpfgynxSINzOiiEQNSNXJQV3WJjTQpKQAA+HeUT3QYFdUNyttzRHmFR7RtX1Wzs9QlKcxq0ZA+SfrRwFQN75ei+BibSUkBAMDJUD4RtOob3dq2r1oFeyu1dW+lDlc1HLdOdGS4hmYmaVi/FA3LSmaXOgAAQY7yiaDhdHtVWHpU2/dXa9veSu05WCPDOH699JQY5fZL1rCsFGWlx3NtdQAAOhDKJ0zT4PSosPSodhRXa8f+ahUdrJHXd3zbjLGHa3CfJA3pk6ihfZKU0iXKhLQAAKAtUD4REIZhqOJoowpLj2p36VEVltao+HCdfCfYtBkeZlW/9Hhl903SkD5J6p0WJ6uVKw0BANAZUD7RLuob3dp7qFZ7D9Vqz4EaFZYe1VGH64Tr2sKtykpP0MBeXTQwo4sye8Qz/yYAAJ0U5RNnrb7RreLDdf6yufdgjcpOcHLQd+KiI5TVI0FZ6fEamJGoPt3jFB7GcZsAAIQCyifOmO/YrvOSw3XaX1ar4sN12l9WpyM1jSe9j9ViUXpqjLLSE9QvPV790hOU2iVKFgu70QEACEWUTxzHMAxV1TpVWuFQablDpRV1Ki136MARh1xu30nvZ5HULTlafbvHq0+3OPXtHq+MrrGyRbALHQAANKF8hrBGl0eHqxp0qLJeB4/UH/vsUFllg5xu7ynvGxFuVc/UGGV0jVOvtFj16hqn9NQYRUXyTwoAAJwcTaETMwxDtQ1uHTnaqPLqBpVVNehwVb0OVzXocFXDSU8A+ncWi9Q1MVo9U2LUIyVG6akxSk+NVbekKObXBAAALUb57MB8hqEah0tHahpVWeNUZU2jKo42qqK6QRU1jaqobjztFszv2MKtSkuKVvfkaHVLavrokRKj7snRnHkOAADaDOUzSLk9PlU7XCo76tS+A9WqqG5Uda1TVXVOVdU2Fc2qWucJJ2U/mfAwi1K7RCktMVpdE6P8H92SopUUb5eVk4AAAEA7o3wGkNvjU229S7X1btXUu1TjOPa1w6Vqh1NH61w66nDpaJ1TjkZPix/fYpG6xEYqNcGulC5RSkmwKyUhSqldmj4nxkUyWTsAADAV5bMVDMOQy+2To9Gtuga3HI0eORrcqmt0y9HglqPB01QyG5pur613qa7BrQbnme0CPxGLpLgYmxJjI5UY1/SRFB+p5Hi7kuLtSo63q0ucjeMwAQBAUGtV+Vy1apUWLFggu90uq9Wqhx9+WP379z/p+hs2bNDjjz8um80ml8uluXPnauTIka0OfTYMw5Db41Ojy6sGl0eNTq8anB41uDxNn51e1Tu/+7rpo77RI0ejR/VOj+ob3apv9LRod/ephFktio2OUEKMTV1iIxUfY1OXWJsSYiKVGB+p3j26KEyGYu3hTMQOAAA6vBaXz7y8PM2dO1fLli1TZmamli9frpkzZ2rlypWKjY09bv3S0lLNnj1bzz33nEaNGqWvvvpKs2fP1ooVK5Senn7Gz7u/rFYuj08ut1cut08uj1fOY1873V41urxyuZuWOd1eOV1Nyxpd3mO3e/zL2qo4nkh4mFUxUeGKi7IpLjpCcdERio2KUFy0TbFREYqPsSk+uulzXLRN0fbwkx5rGR5uVWJijKqqHPJ4Tj6/JgAAQEfR4vL54osvavz48crMzJQkTZ48Wf/3f/+n5cuX65Zbbjlu/cWLFyszM1OjRo2SJJ133nnq27evlixZogceeOCMn/d//vx1S6O2mi3cqqjIcP9HjD1c0fZwRdsjmr6ObPo+xh6hmKimZbFRTV/bwq1cvQcAAOAkWlw+169fr7vuusv/vdVqVXZ2ttatW3fC8rlu3brjdrHn5ORo3bp1rYh7YuFhVkVGWBVpC1NkxPcfdluYIm1hstvCm76OCJM9MkxRx763R4Yr6tjtUZFh/rLJ7m0AAID20aLyWVVVpdraWqWkpDRbnpKSovz8/BPep7i4WJMmTTpu/eLi4hYFfeAn58geGa7IiDDZIqyyHSuYtghrpz3JJuxYCQ6jDIcExju0MN6hhfEOLYz3qbWofDY2NkqSbDZbs+U2m81/24nu05L1T+bHIzJCdnd2fHyU2REQQIx3aGG8QwvjHVoY7xNrUfm02+2SJJer+WUZXS6X/7YT3acl659MZaUj5OaoDAuzKj4+SjU1DfJ6OeGos2O8QwvjHVoY79ASyuOdmBhz2nVaVD4TExMVFxenioqKZssrKiqUkZFxwvtkZGS0aP2T8fkM+drxLPVg5vX6ONs9hDDeoYXxDi2Md2hhvE+sxQcjjB49Wlu2bPF/bxiGCgoKNHbs2BOuP2bMmGbrS9KWLVtOuj4AAAA6rxaXz1mzZmnt2rUqKiqSJK1YsUJWq1VTpkyRJD344IO6//77/evfdtttKiws1NdfN02VtGHDBhUWFp7wzHgAAAB0bi2eaik3N1ePPfaY5syZ47/C0aJFi/wTzDudTnk831+XPD09XS+88IIef/xxRUREyOVyaeHChS2aYB4AAACdg8UwjA5xIGV5ea3ZEQKOKxyFFsY7tDDeoYXxDi2hPN6pqXGnXYcJqAAAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwlE8AAAAEDOUTAAAAAUP5BAAAQMBQPgEAABAwFsMwDLNDAAAAIDSw5RMAAAABQ/kEAABAwFA+AQAAEDCUTwAAAAQM5RMAAAABQ/kEAABAwFA+AQAAEDCUTwAAAAQM5RMAAAABE252ALSMz+fTDTfcoMrKSq1evdrsOGgH1dXVWrx4sdatW6fw8HDV1NTosssu06xZsxQezku2M1i1apUWLFggu90uq9Wqhx9+WP379zc7FtrBypUrtXTpUnm9XtXV1alHjx6aO3euMjIyzI6GdrZ48WI9+uijeuWVVzRq1Ciz4wQV/pJ1MK+++qr27dunuLg4s6Ognaxdu1bvv/++Xn/9dcXFxamsrExTp06V2+3Wvffea3Y8nKW8vDzNnTtXy5YtU2ZmppYvX66ZM2dq5cqVio2NNTse2tjcuXP1/PPPa9y4cfL5fHrooYd0xx13aMWKFYqMjDQ7HtpJWVmZXn75ZbNjBC12u3cgZWVlWrp0qW644Qazo6AddenSRbfffrv/PxhpaWm67LLLtHLlSpOToS28+OKLGj9+vDIzMyVJkydPltfr1fLly80NhnYxceJEjRs3TpJktVp18803a+/evdq6davJydCeHn30Uc2aNcvsGEGL8tmBPProo/r1r38tu91udhS0o/Hjx+u6665rtiwyMlJut9ukRGhL69evV05Ojv97q9Wq7OxsrVu3zsRUaC9PPfVUs++/29rJ67nzWr16tcLDw3X++eebHSVoUT47iNWrVyssLEzjx483OwpMsHHjRl122WVmx8BZqqqqUm1trVJSUpotT0lJUXFxsUmpEEibNm1S165dNWLECLOjoB3U19dr/vz5evDBB82OEtQonx2Aw+HQ/Pnz9dBDD5kdBSZYv369Dh48qLvvvtvsKDhLjY2NkiSbzdZsuc1m89+GzsvlcmnRokX67//+b0VERJgdB+3gT3/6k2688UZ17drV7ChBjROOTPT000/rmWeeOeU6S5cu1bvvvss/5k7gTMf733fJlpWV6X/+53/03HPPcZJZJ/DdITMul6vZcpfLxeE0IeA3v/mNLrvsMvZidFIFBQXavHmzHnjgAbOjBD2LYRiG2SFClcPhUH19/SnXSUxM1NSpUxUXFyertWlDdWlpqcrLyzV8+HD16tVLv/vd7wIRF2fpTMf7u+mUqqurNWPGDN13330aO3ZsICIiAEaOHKm77rpLM2fO9C/7bhqt5557zsRkaE9PPPGEqqqq9Oijj8pisZgdB+3g2Wef1YcffuiftcLpdGrz5s0aNGiQ4uPj9eijj6p3794mpwwOlM8O6Omnn9bbb7/NPJ+dWF1dne644w7dcccduvjiiyVJb7zxhqZPn25yMpyte+65RxEREZo/f74kyTAMnX/++brzzjt1yy23mJwO7WHhwoXatm2b5s2bJ6vVqi1btkiShg4danIytKeSkhJddNFFzPN5AhzzCQQZp9Opu+66S8OHD1daWpry8/OVn5+vN954w+xoaAOzZs3S2rVrVVRUJElasWKFrFarpkyZYm4wtIvXXntNK1as0G233aatW7cqPz9fa9as0c6dO82OBpiGLZ8dSHl5uX7961832+1+7bXXaurUqWZHQxt69dVX9cgjj5zwth07dgQ4DdoDVzgKDXV1dTr33HPl8/mOu+0Pf/gD792d2O9+9ztt3rzZv9s9MzPTv7cDlE8AAAAEELvdAQAAEDCUTwAAAAQM5RMAAAABQ/kEAABAwFA+AQAAEDCUTwAAAAQM5RMAAAABQ/kEAABAwFA+AQAAEDCUTwAAAARMuNkBACBUlJSUaPr06crMzPQvO3DggEpKSrRgwQJNnDjRxHQAEBiUTwAIoPPPP1//7//9P0nS0aNHde211+riiy+meAIIGRbDMAyzQwBAKHC73aqqqlLXrl1lGIbuuusu7dq1S2+//bbi4+PNjgcAAcGWTwAIkIiICHXt2lWStGjRIn322Wd67bXXKJ4AQgonHAFAgH3zzTeaP3++/uu//ks5OTlmxwGAgGK3OwAEUGVlpa699loNGzZMTz31lCSptrZWtbW16tGjh8npAKD9seUTAALEMAzNnTtXNptNv//97/3LCwoKtGzZMhOTAUDgcMwnAATIBx98oE8//VQ9evTQjBkz/Mvr6up0+eWXm5gMAAKH3e4AAAAIGHa7AwAAIGAonwAAAAgYyicAAAAChvIJAACAgKF8AgAAIGAonwAAAAgYyicAAAAChvIJAACAgKF8AgAAIGAonwAAAAgYyicAAAAChvIJAACAgPn/0sJT0hXVi6AAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_32_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_32_1.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_32_2.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "\"\"\"The sigmoid function (or the logistic curve) is a\n",
     "function that takes any real number, z, and outputs a number (0,1).\n",
@@ -1474,22 +1273,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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KysJisdCr1xM0bXobAHPmvM+6dWs4cSKaWrVq889OKCUlmVtuqeW8eca/5fT43323mpMnTxARUdtl//j4OFq3fvCSm1Fc7o52kya965xH/OqrY9i58zciImrh7x/Atm3Zq4c0b34Ho0e/QmZmJtOnv8OPP26gQoVwIiJqExX1O6dPn6JVqwcYOPBJlzHh4ZVo2LARW7dupnHjpvTp08+ZZcmShXzzzdcEBRXHbDbTu3dfmjS5+kWWCxZ8xKpVK5x3tBsw4Enq1av//zVNYfr0d9i58zdCQ0tRvHggTz75LGXLViA1NZVZs6aze/fvFCtWjNTUVFq0aEmvXo87jz1u3MscOXIIHx9fXnzx1at+UnA5pUoFXnsQaopviJFNMWTP/fnh+Dpe3zSWwwmH2NpzF6WLlS6wTJ5AP6yMobobQ3U3hupuDE+se0pKMl5e3i7L0nbv3pG+fQfQqtUDBZLBiLrntCkuvPMF5JpMJhMtK97P+q4/sarTepeG+MSFaPqu7sWBuP1XOYKIiIh4ilWrvmHhwo+cj7du3cyFCwk0a5a71bfclVuuPuFpzCYzt5SMcNn25pbxfHPoa1Yd/obetZ5gZOMXCfULvcIRRERExN1FRNRm5szpDBnS7//vmufF5MnTCAoqbnS0QkFNsRtyOByU9S+H1WzFZrcxL+oDPt//Kc/eOpyBdYfg6+VrdEQREREpYLfcUov//e99o2MUWpo+4YZMJhMv3zaWyB6/0rF6ZyB7pYoJm1+j+aKGfLH/U+wOz5g/JSIiIpITaordWMWgSsy8/0NWdVpP07LZV8RGJx1nyLr+9Pi2s8HpRERERAoPNcUeoGGZxixvv5oPWy+kSvGqALQMv8/gVCIiIiKFh5piD2EymWh7Uzt+6r6VyXdP5fHa/V2eX/THAmLTzhuUTkRERMRYaoo9jNVipVfE41gtf69RuPnUJp774SmaftKAWbvew5ZlMzChiIiISMFTUyz8FL0BgIT0eF75ZQwtljZj7ZFV6L4uIiIi4inUFAsjG4/hmw7f0aD0rQAcjP+Lniu70XVFe/bF/mFwOhEREZH8p6ZYAGhStimrOn3Pe/fOpqx/OQA2Rv/A3UtvY9TG50nKSDI4oYiIiEj+UVMsTmaTmS43dyeyx68Mb/QCvhZf7A47m09F4mvRDT9ERETEfakplkv4e/vzQpOX/v/mH10Y1/xNvMx/3/wwLi1W841FRETEreg2z3JFFQLDmXn/XJdtWfYsOnzdllC/Uoy//U0iStYyKJ2IiIhI3tGZYsmVz/YvYe/5KH6M/oGWn97OyI3PE5MaY3QsERERkRuiplhy5eGb2jOi0Wj8vPywO+x8vGcuTT+pz4yd07S+sYiIiBRZaoolV/y9/RnV5EUiH/2VTtW7AnDBlsjYyJe4c0kTVh3+VvONRUREpMhRUyzXpXxgBd6//wNWdlxHwzKNADiccIg+qx7l93M7jQ0nIiIikktqiuWGNAprwsqO63n/vg8o51+eB6s8TL3SDYyOJSIiIpIrWn1CbpjJZKJTja48UKXtJTf5WPzHQuLS4+hfZxBWi9WghCIiIiJXpzPFkmeKeRejdLHSzsfxaXGM2/QyYyNf4u6lt/H9se8MTCciIiJyZWqKJd/EpcdRpXhVAP6KP0D3bzrRa2U3DiUcNDiZiIiIiCs1xZJvqhSvyrcd1zG15fuULlYGgDVHVnHX4qZM2DT2kqkWIiIiIkZRUyz5ymwy073mY2zq8StP1X8Wb7M3NruNqTumcNsnt/LLiZ+MjigiIiKiplgKRqA1iNeav86P3TdzX8VWACSkxxMeWNHgZCIiIiJafUIK2E0lqrOo7eesO7qGYxeOUTGokvO5hPR4bFkZlCpWysCEIiIi4ol0plgMcV+l1vStPcBl28Qtr3PboluZtes9MrIyDEomIiIinkhNsRQKp5JOMn/vPBJtCbzyyxju+bQ5G45/b3QsERER8RBqiqVQKBtQjuXtV1O/VPbd8PbH/UnXFe3pv6YPJ5NOGJxORERE3J2aYik0GoU1YXXnH3j3nvcI9cueV7z84Fc0X9SIGTunaUqFiIiI5Bs1xVKomE1metzSi009fqVfnYGYTWZSMpMZG/kSc3bPNDqeiIiIuCk1xVIoFfcpwcQ732Zt5w3cWroh4YEVebxWP6NjiYiIiJvSkmxSqNUtVZ+VndYTfeE4xbyLObf/GbuPTSd/oVfE41jMFgMTioiIiDvQmWIp9Mwms8t6xg6Hgxd+HMaoH5/nwS/vZdfZHQamExEREXegpliKnPNp54lPjwdgx9nfaPX53bz88wskZSQZG0xERESKLDXFUuSE+oWyrsuPvH77RPy9A3DgYPbv73PX4qasP7rW6HgiIiJSBKkpliLJy+zFoHpPEfnodtpUeQiA6KTjPPptZ4Z815+Y1BiDE4qIiEhRoqZYirSyAeX4uM0i5rZeQOliZQD44sCnbDi+3uBkIiIiUpQY3hTbbDYmT55MREQE0dHR1xxvt9uZN28edevWZcuWLdd1zNGjR9O1a1d69erl/O/VV1+94fcixjCZTDx80yP83H0rvSIep2XF++hUvavRsURERKQIMXRJtujoaIYPH07lypXJysq65viEhASeeeYZKlasSHp6+g0dc8qUKVSoUOG6s0vhU8I3mMl3TyUjKwOTyeTc/sOx9RxKOMgTtftjNhn+e6CIiIgUQoZ2CCkpKUyaNImOHTvmaHxqaiojRoxg0KBBeXZMcT/eFm/nn+PT4njuh6cY89MIuqxoT/SF4wYmExERkcLK0Ka4Ro0aVKpU6doD/19YWBh16tTJ02OKe4tNj6WETzAAP0VvoMXS21j8x0IcDofByURERKQw8dg72s2ePZvDhw+TmZlJzZo1eeqppwgNDc3VMcxmE2az6doD84DFYnb5KjlTo2R1vu/+I5O2TuR/v07hgi2RZ394kpWHV/DOvdMI8w+76v6quzFUd2Oo7sZQ3Y2huhujMNfdI5viypUrU65cOcaOHUtmZibjxo2ja9eurFixAn9//xwfJyTE32XuakEICvIr0NdzD/5Meei/dK3XiT7L+rD//H7WHFnF7Z80ZsZDM+heu/s1j6C6G0N1N4bqbgzV3RiquzEKY909sikePHiw889Wq5UxY8bQuHFjvv32W7p2zfmqBbGxyQV6pjgoyI/ExFSysuwF8pru5mb/Onzf9WcmbBrHzJ3vEZcWR48velDZrzo3h9S87D6quzFUd2Oo7sZQ3Y2huhvDiLoHB+fshKdHNsX/FhAQQEhICMeOHcvVfna7A7u9YOemZmXZyczUP97rZTX5Mr75RNpUeohnvh9C5xpduSmoxjVrqrobQ3U3hupuDNXdGKq7MQpj3QvfhI4CMGHCBJfHNpuN+Ph4ypYta1AiKWjNy9/B911/ZkTjMS7bd53dQZb92ssDioiIiHsp1E3xmDFjGDlyZJ4fd8mSJezevdv5eMaMGQQEBNCmTZs8fy0pvIJ8iuNl/vvDkj/O76XtV63osuIRTiWdNDCZiIiIFDRDp0/YbDb69etHYmIiAMOGDSMsLIypU6cCkJ6eTmZmpss+Q4cO5ezZswC8+eabBAUF8dFHH2GxWHJ0TIAXXniBiRMnYrFYSEtLIzg4mPnz51OyZMl8f89SeL2383+kZ6Xz84kfufezO3j/vrncW+Veo2OJiIhIATA5tGDrdTt37kKBvZaXl5ngYH/i4pIL3Rwcd5GRlcFbW99g6o4pAJgwMbrZS0xoNY6E+FTVvQDp+90YqrsxVHdjqO7GMKLupUoF5mhcoZ4+IVKQvC3evHzbWBY/9DnBPsE4cDBx8wQeWvQQsannjY4nIiIi+UhNsci/3FupFeu6/kSD0rcCsPqv1dy95A5+O7Pd4GQiIiKSX9QUi1xGeGBFlndYQ/+6AwGIvnCcA3H7DU4lIiIi+UXrFItcgY/Fh0l3T6Fltbv56VAk3Wr2MDqSiIiI5BM1xSLX8GidR2lToZ3LBQG7zu6gYlAlgn1DDEwmIiIieUXTJ0Ry6WjiEbp904E2X7Rkf+yfRscRERGRPKCmWCSXlh9cRmxaLIcTDtHmi5asO7rG6EgiIiJyg9QUi+TS0w2eY9Jd7+Bl9iIp4wI9V3ZjXtQHRscSERGRG6CmWOQ6PF67H589/DXBPsHYHXZe+HEYEzaNxe7QAvAiIiJFkZpiket0e/k7+bbjOioGVQZg6o4pPLluAOlZ6cYGExERkVxTUyxyA6oFV2dlx3XUL9UAgC8PfManfy42OJWIiIjklpZkE7lBpYuV5qv2Kxm09gkCrIE8dktvoyOJiIhILqkpFskD/t7+fPTAIuwOO2aTPoAREREpavTTWySPeJm9sFqszsfnU8/TbUUH/oo7YGAqERERyQk1xSL5ICMrg0e/6cgPx9fTbllrdp/bZXQkERERuQo1xSL5wNviTc+IxzFhIiY1hg5ft2XHmV+NjiUiIiJXoKZYJJ/0rvUEM++fi5fZi0RbAl1WtGfn2d+MjiUiIiKXoaZYJB91qN6ZWffPczbGnZc/osZYRESkEFJTLJLPHr7pETXGIiIihZyaYpEC8O/G+D9bJxgdSURERP5B6xSLFJCHb3oEmMec399n9v3zjI4jIiIi/6CmWKQAPXzTIzxU9WHd4ENERKSQ0U9mkQL2z4Y4057JG5vHcSb5tIGJRERERE2xiEGy7Fn0X9OH//02ma4rOhCXFmt0JBEREY+lpljEIBazhVtKRgDwR+weenzbhZSMFINTiYiIeCY1xSIGGtX4RfrXGQTAr2e2MXhdP7LsWQanEhER8TxqikUMZDKZmHDHW3So1gmA1Ye/5ZVfRuNwOAxOJiIi4lnUFIsYzGwyM/XemdxW7nYAPtg9i1m/v2dwKhEREc+iplikEPCx+PBRm0+oVqI6AK/98hIrDn5tcCoRERHPoaZYpJAI9g1hcdsvCPUrRVn/ctxUoprRkURERDyGbt4hUohUCqrM0rZfZjfGAeWMjiMiIuIx1BSLFDJ1StW7ZJvD4cBkMhmQRkRExDNo+oRIIeZwOJi2412GrOuvFSlERETykc4UixRi8/Z8wOubXgXglpAInm043OBEIiIi7klnikUKsW4396BWyToAvLllPGuOrDI4kYiIiHtSUyxSiPl7+zP/wcWE+oXiwMGQ7/pzMP6A0bFERETcjppikUIuPLAiH7ZeiJfZi6SMC/Rd3ZuUjBSjY4mIiLgVNcUiRUCzcs159bbxAPwRu4cxP40wOJGIiIh7UVMsUkQMqvsUD1VtB8DifQtZ9McCgxOJiIi4D8ObYpvNxuTJk4mIiCA6Ovqa4+12O/PmzaNu3bps2bLluo+5ZMkSOnToQPfu3Rk4cCBnzpy5ofchkt9MJhP/u+c9KgdVoYRPCUr5lTI6koiIiNswtCmOjo6mV69enD17lqysrGuOT0hI4IknnuDQoUOkp6df9zHXrl3LtGnT+OCDD1iyZAl169Zl0KBB2O32G3o/IvktyKc4Hz+wmHVdfuL+ym2MjiMiIuI2DG2KU1JSmDRpEh07dszR+NTUVEaMGMGgQYNu6JgzZ86kffv2lCxZEoA+ffpw4MABNm7cmLs3IGKAW0pGUDGoktExRERE3IqhTXGNGjWoVCnnP9zDwsKoU6fODR0zISGBPXv2uBwnMDCQypUrExkZmeMsIoXF8r++4ssDnxkdQ0REpEjzuDvaHT9+HIDQ0FCX7aGhoc7ncspsNmE2m/Is29VYLGaXr1IwCnvdJ26ewH+3/gd/b38alW1E1RI3GR0pTxT2ursr1d0YqrsxVHdjFOa6e1xTnJaWBoDVanXZbrVanc/lVEiIPyZTwTTFFwUF+RXo60m2wlr3LnU78s72t0nOSGbIuv780vcXvC3eRsfKM4W17u5OdTeG6m4M1d0YhbHuHtcU+/r6AtkrVPyTzWbDzy93f0GxsckFeqY4KMiPxMRUsrJ0QWBBKex1r1YsgjFNX+b1TWPZdnIbo1e/yMvNxxod64YV9rq7K9XdGKq7MVR3YxhR9+Bg/xyN87imODw8HICYmBiX7TExMTRv3jxXx7LbHdjtjjzLlhNZWXYyM/WPt6AV5ro/We9Z1h9dR+TJn3ln+2TuKt+S5uXvMDpWnijMdXdnqrsxVHdjqO7GKIx1L3wTOvJZ8eLFiYiIICoqyrktKSmJI0eO5LopFikMLGYL7907mxI+JXDg4Ml1A0hIjzc6loiISJFSqJviMWPGMHLkyDw/7pAhQ1i2bBmxsbEAzJ8/n+rVq9OiRYs8fy2RglA+sAKT754KwMnkE7zyyxiDE4mIiBQthk6fsNls9OvXj8TERACGDRtGWFgYU6dm/3BPT08nMzPTZZ+hQ4dy9uxZAN58802CgoL46KOPsFgsOTomQKtWrTh//jz9+vXDx8eHoKAgZs6cidlcqH9HELmqh29qT6fqXfniwKd8sf9ThjUcReXiVYyOJSIiUiSYHA5HwU6KdSPnzl0osNfy8jITHOxPXFxyoZuD486KWt3j0mJ5ct0AXm42jlqhtY2Oc92KWt3dhepuDNXdGKq7MYyoe6lSgTka53EX2om4s2DfEBa3/cLoGCIiIkWO5guIuLnUzFSjI4iIiBR6aopF3JQty8Z/tk7g9kWNiEuLNTqOiIhIoaamWMRNbT4VyZTtk4hOOs7LP482Oo6IiEihpqZYxE3dVeFuutd8DIDP9i9h4/EfDE4kIiJSeKkpFnFj45q/QahfKAAjNz6n+cUiIiJXoKZYxI0F+4Yw/vaJABxJPMw72/9rcCIREZHCSU2xiJvrVL0rd4e3BGD6znf54/xegxOJiIgUPmqKRdycyWTirbum4GvxJdOeyYiNz2J3aKF6ERGRf1JTLOIBqhSvyojG2StQHE44xJHEwwYnEhERKVx0RzsRDzGk3tOkZaYxsO4QSvgGGx1HRESkUFFTLOIhvC3ejGryotExRERECiVNnxDxYBdsiUZHEBERKRTUFIt4oKOJR+i96lEeWfYgWfYso+OIiIgYTk2xiAdaf+w7Vh/+lqiY35m/d57RcURERAynpljEA/WJ6Evt0LoATNwynvOp5w1OJCIiYiw1xSIeyGK28Oad2Xe3i0+P580t4w1OJCIiYiw1xSIeqlnZ2+hcoxsAC/d+xK6zOwxOJCIiYhw1xSIe7LXbXsffOwAHDsb8NBKHw2F0JBEREUOoKRbxYGX8wxje6AUAtp/ZyoqDy4wNJCIiYhA1xSIebkDdwVQMqgzA5wc+NTaMiIiIQXRHOxEP52PxYeIdkziXeo5uN/cwOo6IiIgh1BSLCPdXbmN0BBEREUNp+oSIXEIX3ImIiKdRUywiLr4/9h33fnYnB+L2Gx1FRESkwKgpFhGnMyln6LOqB1ExvzN+0ytGxxERESkwaopFxKlMsTIMrPskAGuOrOLnEz8anEhERKRgqCkWERfP3jqMEN8QAN7YPFbzi0VExCOoKRYRF0E+xXmu4QgAfj2znVWHvzU4kYiISP5TUywil3i8Vn/KB1QA4M0t48iyZxmcSEREJH+pKRaRS/h6+TKq8YsA7I/7k8/2LzE4kYiISP5SUywil9Xl5u7UCL4ZgElb3yQjK8PgRCIiIvlHTbGIXJaX2YsXm75GozJNeO++2XhbvI2OJCIikm90m2cRuaIHqjzEA1UewmQyGR1FREQkX6kpFpErUjMsIiKeQtMnRCRHbFk25u+ZR2zaeaOjiIiI5DmdKRaRa0pIj6flp3dw/MIxoi8c58VmrxodSUREJE/pTLGIXFNxnxLcEhIBwJzdMzmfqrPFIiLiXtQUi0iOjGqSvW5xckYSM3ZONTiNiIhI3jK8KbbZbEyePJmIiAiio6OvOd5utzNv3jzq1q3Lli1bLjvmu+++o2PHjvTo0YOePXty4MABl+dHjx5N165d6dWrl/O/V1/Vx8EiV1O3VH3aVHkIgLm7Z3Eu5ZzBiURERPKOoXOKo6OjGT58OJUrVyYr69q3kU1ISOCZZ56hYsWKpKenX3bM77//zqhRo/jiiy+oWrUqy5Yto1+/fqxcuZKAgADnuClTplChQoU8ey8inmBk4zGsPvwtKZkpTN/xLuNuf8PoSCIiInnC0DPFKSkpTJo0iY4dO+ZofGpqKiNGjGDQoEFXHDNnzhxatGhB1apVAWjXrh1ZWVksW7YsLyKLeLQ6oXV5qGo7AD7a8wFnUs4YnEhERCRvGNoU16hRg0qVKuV4fFhYGHXq1LnqmE2bNrmMMZvN1KpVi8jIyOvOKSJ/G9l4DACpmalM/+0dg9OIiIjkDbdaki0uLo4LFy4QGhrqsj00NJTdu3e7bJs9ezaHDx8mMzOTmjVr8tRTT12y37WYzSbM5oK5uYHFYnb5KgVDdb9U3TJ1aF+9I18f+IoLmRewWEx5fpMP1d0YqrsxVHdjqO7GKMx1d6umOC0tDQCr1eqy3Wq1Op8DqFy5MuXKlWPs2LFkZmYybtw4unbtyooVK/D398/x64WE+Bf4Hb+CgvwK9PUkm+ruavID/2XCfeOpVbpWvr6O6m4M1d0YqrsxVHdjFMa6u1VT7OvrC2SvaPFPNpvN+RzA4MGDnX+2Wq2MGTOGxo0b8+2339K1a9ccv15sbHKBnikOCvIjMTGVrCx7gbymqO5XEkwZgr0hLi45X46vuhtDdTeG6m4M1d0YRtQ9ODhnJzzdqikODg4mMDCQmJgYl+0xMTGEh4dfcb+AgABCQkI4duxYrl7PbndgtzuuK+v1ysqyk5mpf7wFTXW/uix7FhazJe+Pq7obQnU3hupuDNXdGIWx7oVvQscNatasGVFRUc7HDoeDvXv30rx5c+e2CRMmuOxjs9mIj4+nbNmyBZZTxB3EpcXy1tY3aPpJfRLS442OIyIict0KdVM8ZswYRo4cmat9Bg4cyMaNGzl8+DAAy5cvx2w20759e+eYJUuWuFx4N2PGDAICAmjTpk2e5BbxFH/FH2Dy9rc4duEoH+6eY3QcERGR62bo9AmbzUa/fv1ITEwEYNiwYYSFhTF1avYtZNPT08nMzHTZZ+jQoZw9exaAN998k6CgID766CMsluyPbuvWrctbb73F8OHD8fX1xWw2M3fuXJcbd7zwwgtMnDgRi8VCWloawcHBzJ8/n5IlSxbE2xZxG43DmnJn+Rb8dGIjs35/jwH1hhDgHXDtHUVERAoZk8PhKNhJsW7k3LkLBfZaXl5mgoP9iYtLLnRzcNyZ6n5tP5/4kY5ftwVgXPM3GVJ/6A0fU3U3hupuDNXdGKq7MYyoe6lSgTkaV6inT4hI4Xd7uTtpVKYJADN2TiUtM+0ae4iIiBQ+aopF5IaYTCaGNcqe+38m5TSL9y00OJGIiEjuqSkWkRt2b8VW1AmtB8D0He+SkZVhcCIREZHcUVMsIjfMZDLxXMPhABy/cIwvDnxqcCIREZHccaubd4iIcR6q2o76pRrQtFxzWlS4x+g4IiIiuaKmWETyhNlkZnXnHzCb9AGUiIgUPfrpJSJ5Rg2xiIgUVfoJJiL54mTSCQ7F/2V0DBERkRxRUywiee6ln0bRaGEdxka+bHQUERGRHFFTLCJ5rpi3P5n2TFYfWcn+2D+NjiMiInJNaopFJM/1rzsYq9kKZN/lTkREpLBTUywiea5MsTJ0vflRAD7fv5TTyacMTiQiInJ1aopFJF88Wf8ZTJiw2W3M+X2m0XFERESuSk2xiOSLasHVaVPlIQA+3vMhF2yJBicSERG5MjXFIpJvnqr/LACJtgQW7P3Y4DQiIiJXpqZYRPJNk7JNaRLWDICl+xbhcDgMTiQiInJ5us2ziOSrkY3H8GfsH/SI6I3JZDI6joiIyGWpKRaRfNUi/B5ahN9jdAwREZGr0vQJEREREfF4aopFpMDsOPMr7+3QzTxERKTwyXFT3LJlS+699162b99+2edXrlxJy5YtqVevXp6FExH38WHUHFp/cQ/jNr3Mofi/jI4jIiLiIsdNcfny5Vm/fj2NGjVi2bJlLv8BPPjgg3z//ffUrFkzv7KKSBH2QOWH8DJnX8Yw+/f3DU4jIiLiKsdN8T+vGo+OjiY6Oppp06YRHR19xXEiIheVDSjHIzd1BGDJvk+IT4szOJGIiMjfrmtO8dChQxk6dCjlypVj6NCheZ1JRNzU4HpPAZCSmcLCP+YbnEZERORvOW6KL7fovs4Ki0hu1CvdgKZlbwNg7u5ZZNozDU4kIiKS7bqmT4iIXK9BdbPPFp9Iiuabg18bnEZERCRbjm/esXPnTu69916XbTExMZdsO3fuXN4kExG39ECVh6gYVJljiUeY9fsM2lfvZHQkERGRnDfFQUFBNGnS5KpjHA4HP/744w2HEhH3ZTFbGFBnEK/8Moa4tFhi084T4lvS6FgiIuLhctwUV6lShYkTJ15zXLdu3W4okIi4vx639KJy8arcX6k1ZpPuISQiIsbLcVP8wQcf5Gjc/Pm6olxEri7QGkTryg8YHUNERMQpx6dofHx88nSciIiIiEhhkeOmeN++fcyfP58vv/zSuS0rK4tx48bRtGlTmjVrxltvvXXZpdtERC4n057J1399SdcV7UnKSDI6joiIeLAcN8WLFi1izpw5xMfHO7fNnTuXxYsXU69ePR555BG+/fZbPvzww/zIKSJu6Ncz2xmw9nE2HP+epfsWGR1HREQ8WI6b4qioKBYuXEjfvn2B7JUmFi9eTIMGDZg9ezZjxozho48+4ptvvsm3sCLiXpqENaVuqfoAfLh7tj5pEhERw+S4Kfb396dSpUrOx1FRUZw6dYpOnf5eY7Rq1aqYzbqSXERyxmQy0b/OIAAOxO/nx+gNxgYSERGPdd13tNu4cSNms5l77rnHZbu/v3/eJBMRj/BItY6E+IYA2bd+FhERMUKOm+KUlBTS09MBsNvtLF++nHr16lGy5N+L7tvtdlJSUvI+pYi4LT8vP3re8jgAa46s4mjiEUPziIiIZ8pxU9y8eXMGDRrEokWLGDp0KMePH+fRRx91Pu9wOHjvvfcIDQ3Nl6Ai4r4er90Ps8mMAwcfRc01Oo6IiHigHDfFAwYMIDMzk/Hjx7NhwwZ69OhBu3btADhz5gz169fnvffe4/bbb8+3sCLinioEhtOm8kMAfPLHx6Rk6BMnEREpWDm+o11gYCALFy4kNjaWgIAArFar87kyZcqwa9eu6wpgs9mYNm0ac+fOZe3atVSoUOGq4+12Ox9//DHvvPMOc+bMoWnTppeM+e6773j//ffx9fXFbDbz2muvUb16dZcxS5YsYenSpfj4+BAUFMTrr79OmTJlrus9iMiN6193ECsPr6BOaD1iUs9RnlJGRxIREQ+S4zPFI0eOBCAkJMSlIf631157LccvHh0dTa9evTh79ixZWVnXHJ+QkMATTzzBoUOHnPOb/+33339n1KhRvP322yxatIjOnTvTr18/kpL+vjHA2rVrmTZtGh988AFLliyhbt26DBo0CLvdnuPsIpK3bi93J5GP/soXj6ygYlCla+8gIiKSh3J8pjgqKoply5Zdc9y2bdty/OIpKSlMmjSJ06dP5+jYqampjBgxguDgYD799NPLjpkzZw4tWrSgatWqALRr147//ve/LFu2jJ49ewIwc+ZM2rdv77xIsE+fPrz//vts3LjxktU0RKRgmEwmqgVXv/ZAERGRfJDjpvjw4cOMGTMG4KoL7P976barqVGjBgCnT5/O0fiwsDDCwsKIjo6+4phNmzYxZMgQ52Oz2UytWrWIjIykZ8+eJCQksGfPHgYOHOgcExgYSOXKlYmMjFRTLFJI6EYeIiJSkHLcFL/00kt8/PHH3HHHHfTs2RM/P79LxjgcDoYPH56nAXMjLi6OCxcuXLICRmhoKLt37wbg+PHjzm3/HnPxuZwym02YzTn/JeBGWCxml69SMFT3gpeQHs/Hv89jwZ6P+Kbzasr4lTU6ksfQ97sxVHdjqO7GKMx1z3FT3KtXL7p168bSpUsZMWIEDz74IL169bqkOW7fvn1eZ8yxtLQ0gEvmPFutVudzORmTUyEh/rk6M54XgoIu/WVE8p/qXnBiY08z7udXceDgk30f83rL142O5HH0/W4M1d0YqrsxCmPdc9wUQ3bjeLE5XrJkCV27duXhhx+mZ8+eFCtWDMBl7eKC5uvrC2SvaPFPNpvN+dzVxlzu7PfVxMYmF+iZ4qAgPxITU8nK0gWBBUV1L3ghpjBaVWnNmsOrmfXrbJ6q8zw+Xj5Gx/II+n43hupuDNXdGEbUPTg4Z3dbzlVTfJHVaqV37950796dxYsX061bt0uaYyMEBwcTGBhITEyMy/aYmBjCw8MBnF8vN6Z58+a5ej273YHdXrDzHrOy7GRm6h9vQVPdC1b/uoNZc3g151LO8sWfn9P1ZuN+2fZE+n43hupuDNXdGIWx7jc0ocNqtdKgQQNKlizJO++8w4oVK/Iq13Vr1qwZUVFRzscOh4O9e/c6G97ixYsTERHhMiYpKYkjR47kuikWkfxxT8WWVA/JXoniw92zDU4jIiKe4Lqb4t27dzNo0CC6devGH3/8wTPPPEPbtm3zMhtjxoxxro+cUwMHDmTjxo0cPnwYgOXLl2M2m13mOg8ZMoRly5YRGxsLwPz586levTotWrTIs+wicv3MJjNDmwwF4Lezv/Lbme0GJxIREXeX6+kTUVFRTJ8+nY0bNxIUFMSzzz5Lr1698PfP2XyNf7LZbPTr14/ExEQAhg0bRlhYGFOnTgUgPT2dzMxMl32GDh3K2bNnAXjzzTcJCgrio48+wmKxAFC3bl3eeusthg8f7ryj3dy5cwkICHAeo1WrVpw/f55+/fo572g3c+ZMzObCdyWkiKd6vP7jvLT+JZIykvhg9yxmlGlkdCQREXFjJkcOFwPds2cP06ZNY+PGjRQvXpwnnniCnj17XtIML1myhO7du+dL2MLm3LkLBfZaXl5mgoP9iYtLLnRzcNyZ6m6Mi3Xv/+VA5u6eg7fZmx29/6B0sdJGR3Nr+n43hupuDNXdGEbUvVSpwByNy/GZ4k6dOmG1WunatSu9evWiWLFiJCQkkJCQ4BzjcDhYtmyZxzTFIpK/+tcbxOI/PqFD9c5k2jOMjiMiIm4sx01xYGAgNWvW5NChQ4wfP/6Kd5s6dOhQnoUTEc92c0hNoh4/QIA1Z7/li4iIXK8cN8U1a9ZkwYIF1xzXq1evGwokIvJPaohFRKQg5PjKspdeeilH4yZOnHjdYUREriY5I9noCCIi4qZy3BTXrFkzR+MqVKhw3WFERC7ndPIpRmx4jlrzqrEv9g+j44iIiBvSGmQiUuhZTF4s2beQlMxk5kXNMTqOiIi4ITXFIlLolSpWinbVOgDw6Z9LuGBLNDiRiIi4GzXFIlIk9KszEIDkjCQ+/XOxwWlERMTdqCkWkSLh1tKNqFeqAQAf7p5zxWUhRUREroeaYhEpEkwmE31rDwDgQPx+fjqx0eBEIiLiTtQUi0iR0b56J4J9ggGYu3u2wWlERMSdqCkWkSLDz8uPHrf0BmDNkZVEXzhucCIREXEXaopFpEh5vHY/KgSEM6rxi/h7+xsdR0RE3ESOb/MsIlIYVAqqzPZeuzGb9Du9iIjkHf1UEZEiRw2xiIjkNf1kEZEi7fiFY0ZHEBERN6CmWESKpMMJh+i6oj0NF9Rm19kdRscREZEiTk2xiBRJIb4hbD21GYAPo+YYnEZERIo6NcUiUiQV9ylBpxrdAPjqwOfEpp03OJGIiBRlaopFpMi6eIe7tKw0Fv2x0OA0IiJSlKkpFpEiq1ZobZqVbQ7AR1EfkGXPMjiRiIgUVWqKRaRIu3i2+NiFo6w/ttbgNCIiUlSpKRaRIu3Bqg9TplgYAHN3zzY4jYiIFFVqikWkSLNarPSKeByAH46v51D8X8YGEhGRIkm3eRaRIq93rSf46cRG+tTqS/nAcKPjiIhIEaSmWESKvDD/sqzosMboGCIiUoRp+oSIiIiIeDw1xSLiVuwOO5tPRuJwOIyOIiIiRYiaYhFxG3+c38vtixvRblkbtpzaZHQcEREpQtQUi4jbqBhUiXMp5wD4MErLs4mISM6pKRYRt+Hv7c+jNR8D4JtDyzmTfNrgRCIiUlSoKRYRt/JE7f4AZNozmb93nsFpRESkqFBTLCJupWqJatwd3hKA+XvmkZGVYXAiEREpCtQUi4jb6VdnEABnUk6z8vAKg9OIiEhRoKZYRNzOfRVbER5YEYC5u3XBnYiIXJuaYhFxOxazhcf/f27x5lOR7I/90+BEIiJS2Ok2zyLilh67pRf7zu/l8dr9qB5cw+g4IiJSyKkpFhG3FOJbkvfu09QJERHJGU2fEBERERGPZ/iZYpvNxrRp05g7dy5r166lQoUKVx2/fft2Jk2ahNVqxWazMWrUKBo1auR8PiMjgzlz5rBhwwZMJhMOh4ORI0fSuHFj55jRo0dz6NAhfHx8nNuqVKnC+PHj8/4NiojhkjOS+fbQcjrX6IbZpHMBIiJyKUOb4ujoaIYPH07lypXJysq65vgTJ04waNAgZsyYQdOmTdm6dSuDBg1i+fLllC9fHoB33nmHjRs3smTJEgIDA/nxxx8ZMGAAy5cvp2LFis5jTZky5ZoNuIgUfbvO7qDT8nYk2hIo5Veaeyrea3QkEREphAw9ZZKSksKkSZPo2LFjjsYvWLCAqlWr0rRpUwCaNGlClSpVWLhwIQB2u51FixbRuXNnAgMDAbjrrrsoX7488+fPz583ISKFWs2SEVgt3gB8GKU5xiIicnmGNsU1atSgUqVKOR4fGRlJnTp1XLbVqVOHyMhIAOLi4khNTaVkyZIuY0qXLs327dtvPLCIFDk+Fh963vI4AGuPrOZo4hFD84iISOFk+Jzi3Dh+/Dht2rRx2RYaGsrx48cBCAkJoVixYpw6dcplzOnTp4mLi3PZNnv2bA4fPkxmZiY1a9bkqaeeIjQ0NFd5zGYTZrPpOt5J7lksZpevUjBUd2Pkdd371uvH1B1TsDvsLPhjHmNvfz1Pjutu9P1uDNXdGKq7MQpz3YtUU5yWlobVanXZZrVaSUtLA8BkMtGzZ0+WLl1Ku3btKFu2LMuXL+f48eMUK1bMuU/lypUpV64cY8eOJTMzk3HjxtG1a1dWrFiBv79/jvOEhPhjMhVMU3xRUJBfgb6eZFPdjZFXdQ8Orkm7m9uxbN8yFu79mP+0fgM/b/2dXom+342huhtDdTdGYax7kWqKfX19sdlsLttsNhu+vr7Ox8899xzBwcEMHz4cgHr16tG9e3c2bNjgHDN48GDnn61WK2PGjKFx48Z8++23dO3aNcd5YmOTC/RMcVCQH4mJqWRl2QvkNUV1N0p+1L3PLf1Ytm8ZsamxfLh1Pj0ieubJcd2Jvt+NobobQ3U3hhF1Dw7O2QnPItUUh4eHExMT47ItJiaG8PBw52OLxULfvn3p27evc9vo0aOpUePKd7QKCAggJCSEY8eO5SqP3e7Abnfkap8blZVlJzNT/3gLmupujLyse/Owu6heogYH4vczZ9csulR/tMA/6Skq9P1uDNXdGKq7MQpj3QvfhI6ruO2224iKinLZFhUVRfPmzZ2P9+3bR3x8vPOxw+Fg+/bttG7d2rltwoQJLsew2WzEx8dTtmzZ/AkuIoYzmUz0rTMAgN0xuziU8JfBiUREpDAp1E3xmDFjGDlypPNx7969OXjwINu2bQOyb+Rx8OBBevb8+2PQTz/9lAULFjgfL1iwgJIlS9K2bVvntiVLlrB7927n4xkzZhAQEHDJRXwi4l663vwowxqOZHvP3dxUorrRcUREpBAxdPqEzWajX79+JCYmAjBs2DDCwsKYOnUqAOnp6WRmZjrHly9fnlmzZjFp0iS8vb2x2WzMnj3beeMOgLp16zJr1iw2btyI1WqlWrVqzJkzB4vF4hzzwgsvMHHiRCwWC2lpaQQHBzN//vxLlnITEfcSaA1idNNXjI4hIiKFkMnhcBTspFg3cu7chQJ7LS8vM8HB/sTFJRe6OTjuTHU3hupuDNXdGKq7MVR3YxhR91KlAnM0rlBPnxARyS/HLxxjyvZJZNozrz1YRETcXpFafUJEJC9sPbWFdstaY3fYqRkSwYNV2157JxERcWs6UywiHufWMg0pUywMgLlRsw1OIyIihYGaYhHxOF5mL/rUyl7L/KfoDeyP/dPgRCIiYjQ1xSLikXpGPI632RuAeXvmGJxGRESMpqZYRDxS6WKlefim9gAs3beYJFvBrSYjIiKFj5piEfFY/eoMBCAp4wKf7l9icBoRETGSmmIR8ViNyjShTmg9AObtnoOWbRcR8VxqikXEY5lMJufZ4tMppzmaeMTYQCIiYhitUywiHq1D9c44HA46VO9MMe9iRscRERGDqCkWEY/m5+XHYxG9jY4hIiIG0/QJEREREfF4aopFRACHw8HmU5sY9sPTpGelGx1HREQKmKZPiIgAkSd/psPXDwFwW7nb6XJzd4MTiYhIQdKZYhERshvhKsWrAjDr9xlank1ExMOoKRYRAcwmMwPrPgnA7+d2sunkLwYnEhGRgqSmWETk/3Wv+RglfEoAMHPXdGPDiIhIgVJTLCLy//y9/elTqx8Aa46s4mD8AYMTiYhIQVFTLCLyD/3qDMTb7I0DB7N2zTA6joiIFBA1xSIi/xDmX5b21ToBsPTPRcSmnTc4kYiIFAQ1xSIi/zK4/lAAwgMrcuJCtMFpRESkIGidYhGRf6kTWpeVHdfRsExjTCaT0XFERKQAqCkWEbmMRmFNjI4gIiIFSNMnRESuweFw6GYeIiJuTk2xiMgVZGRl8MX+T2n1+d38dGKj0XFERCQfqSkWEbmCTEcmL/08il3ndjBzp27mISLiztQUi4hcgZ+XH4/X7g/AumNr+eP8XoMTiYhIflFTLCJyFX1rD8TH4gPA9B3vGhtGRETyjZpiEZGrKF2sNI/W7AnAV399TvSF4wYnEhGR/KCmWETkGp6s/wxmk5lMeyYzd2lusYiIO1JTLCJyDZWLV+GRmzoAsHDvx7r1s4iIG1JTLCKSA0MbPAdASmYKc3fPNjaMiIjkOd3RTkQkB+qUqsc94fdiNpm5q8I9RscREZE8pqZYRCSH5j+4xLkShYiIuBc1xSIiOaSGWKRoszvsJGckccF2gSwyOO/wIy4+iYzMLKqVqI7JZAL+/9buODCbNMvUk6gpFhG5DmmZaZxMiqZqiWpGRxERIDUzlb/iD3Ag7k8eqtrO+UtsckYyty9qRKItkaSMC1fc/8Sg83hbvAGIT4/j5g8r4+8dQEm/UEJ9S1LSLzT7z36lKB9QnvDAitxfqY2zkZaiT02xiEguLdn3CRM2jyXEN4QN3TbpbJJIAbtgS+TXM9vZfnoru87t4M/YfRxNPIIDBwCbH9tB1eI3AVDMqxjx6fGkZCZf9ZgX94XsBhsgOSOJ5IwkjiUeuWR8iG8I+/r+vf1U0kne2DKOGsE1qRF8MzVCbqZSYGUsZssNvlspKGqKRURyKcuexdmUM5xNOcN3R9fQuvIDRkcS8RiPftOJ74+tc2li/+1U0klnU2wymXi+4QgyHZkEegcSaA0iwBqAn7cvQYHFSE624bA78DL/3RIFWgN54463SEhP4HxaDOdTYzifep6Y1BjOpZ4lJvUc4YGVXF5zz/ndfPrnYpdtPhYfbipRnZoht1C3VH2ahDWlUViTPKyG5CU1xSIiudT55m68te0NTief4t1f36aVPkIVyXOH4v/i28Pf0CSsGU3LNnNuD7QGOhtiq9lKnVJ1uSWkFjVCbqZGcE1uDq5J2YByLsd6tuHwS47v5WUmONifuLhkMjPtLs8FWoMYUHfIFbOlZqaSkB7vsi3TnsXNwTU5mPAXmfZMANKz0tl7Poq956P48sBnPFjlYT564BPnPvti/+B08inqlapPsG9Izgoj+cbwpthmszFt2jTmzp3L2rVrqVChwlXHb9++nUmTJmG1WrHZbIwaNYpGjRo5n8/IyGDOnDls2LABk8mEw+Fg5MiRNG7c2OU4S5YsYenSpfj4+BAUFMTrr79OmTJl8uU9ioh78bH4MKTe07wW+SK/ntnGj9EbaBGuZdpEbtSppJMs++tLvjrwGTvP7QCgd0Rfl6a4682P0qB0IxqFNaZuqfqGXADr5+WHn5efy7Y2VR6kTZUHycjK4HDCIfbH/cn+uH38GfsHe8/v4UD8fuqWqueyzyd/zGfWrvcAuKlENRqVaUKjsCY0KtOEmiG3aOpFATO0KY6Ojmb48OFUrlyZrKysa44/ceIEgwYNYsaMGTRt2pStW7cyaNAgli9fTvny5QF455132LhxI0uWLCEwMJAff/yRAQMGsHz5cipWrAjA2rVrmTZtGsuXL6dkyZJMnz6dQYMG8eWXX2I2a26giFxb71pPMPW3yZxPO8+UXyepKRa5TrYsGysPrWD+3nn8cuInl2kRJkycT4txGX9fpdbcV6l1QcfMMW+Ld/ZZ65CbgXbO7ckZyWTaM1zGRp373fnng/F/cTD+L5b+uQgAf+8Abi3dkFFNXnL5pUDyj6EdYEpKCpMmTaJjx445Gr9gwQKqVq1K06ZNAWjSpAlVqlRh4cKFANjtdhYtWkTnzp0JDAwE4K677qJ8+fLMnz/feZyZM2fSvn17SpYsCUCfPn04cOAAGzduzMu3JyJuzN/bnyH1nwFg08lfiDzxs8GJRIqeQ/F/ceuCWgz87gl+PvGjsyG+tXRDXr99Irv67GNem4UGp8wb/t7+FPcp4bJtUdvPWdVpPW/c8RYdq3em4j/mKSdnJPHTiY2Y/zU1a9LWN1mw9yP2xf6B3eE67UNujKFnimvUqAHA6dOnczQ+MjLSZaoEQJ06dYiMjAQgLi6O1NRUZ7N7UenSpdm+fTsACQkJ7Nmzh4EDBzqfDwwMpHLlykRGRnLPPTrbIyI507d2f97b8S5x6XFM/nUSzcvfYXQkkSKlUlAV5/SHioGV6HFLLzpU70yV4lUNTlYw/Lz8aFimMQ3LNGYA2XOYz6ScYfvprfx6Zhs7zvxK3VL1neOTM5J559f/kuXI/nQ9yFqcRmGNaRzWlMZhTbm1dEMCrIFGvBW3YPic4tw4fvw4bdq0cdkWGhrK8ePHAQgJCaFYsWKcOnXKZczp06eJi4tzHuPiflc6johITgRYAxlU7yn+s3UCkSd+4lDCQecV7yLiauupLfzvt7fpW3sA91ZqBYDFbGFs8wn4WnxpWfF+zaEFyhQrw0NVH+ahqg9f8tzJpBOUD6jAsQtHAUi0JfD9sXV8f2wdAGaTmYZlGvNNh7W6+Pc6FKmmOC0tDavV6rLNarWSlpYGZC+70rNnT5YuXUq7du0oW7Ysy5cv5/jx4xQrVsx5jIv7Xek4OWU2mzCbC+abzmIxu3yVgqG6G6Mo1X1wgyGcTT3Nkw2epmqJot0QF6W6uxN3r/vWU1uYEDmWn0/8BMCFjERa3/T3Ca4ON+dsCmVeK4p1v6VUTXY+sYdTSafYdnoLW09l/7fr7A4y7BnYHXasFm+8vf/+5WLzyUhm7JhG47LZq3jUK1UfHy/j7s5ZmOtepJpiX19fbDabyzabzYavr6/z8XPPPUdwcDDDh2cvv1KvXj26d+/Ohg0bnMe4uN+/j+Pn53ol6bWEhPgX+G9iQUG5yyh5Q3U3RlGoezD+zO04x+gYeaoo1N0duVvd95/fz5j1Y/jyjy+d24r7FOe+m+4lsLiPy7rARiqKdQ8OrkZEeDX68BiQfYfNX0/+SuTxSMoFliM42N85dtvvm/jm4Aq+ObgCAKvFSqNyjWheoTnNw5tzW/hthAWEFfh7KIx1LxzfkTkUHh5OTIzrVagxMTGEh4c7H1ssFvr27Uvfvn2d20aPHu2cv3xx7OWO07x581zliY1NLtAzxUFBfiQmppKVpYn1BUV1N4bqbgzV3RjuVvezKWeYtGUiH0fNc5n7+kzD5+hfdyBBPsW5kJAOpBua093qHhFYn4iI+gDExf199z4/RwC1Q+uwJyYKBw5sWTYij0cSeTwSNmWPGX/Hmwy99ZkCyWlE3f/5S8LVFKmm+LbbbmPHjh0u26Kiolya2X379hEWFkaJEiUAcDgcbN++naeffhqA4sWLExERQVRUlHN+clJSEkeOHGHEiBG5ymO3O7Dbr3xHnfyQlWW/ZJFxyX+quzGKWt3PpZxj5q7pPFKtg8vFMUVNUau7u3CXuj+2ohu/nsm+uN1qttK3zkCeazicEN/si+AL23t0l7pfyeO1BvB4rQFcsCXy25lf2XZ6C9tOb2H7mW1csCUCUKNETZca9F71KMm2JOqVbkDd0HrULV2fKkFV8/TT8cJY90LdFI8ZM4bMzEz++9//AtC7d28+//xztm3bRuPGjdm+fTsHDx7k3Xffde7z6aefEhwc7GyCFyxYQMmSJWnbtq1zzJAhQxg/fjx9+/YlJCSE+fPnU716dVq0aFGg709E3Ed6Vjp3L72Nc6ln2Re7l08e+szoSCKGGNP0Vbosf4SO1bswpukrVAyqdO2dJN8FWoNoEX6Pc031LHsW++P+ZNvpLTQq8/cNzjLtmfx4fAMpmcn8dOLvpWqDrMWpW6oedUvVp16p+rSp8tAlNzAp6gxtim02G/369SMxMfs3lWHDhhEWFsbUqVMBSE9PJzMz0zm+fPnyzJo1i0mTJuHt7Y3NZmP27NnOG3cA1K1bl1mzZrFx40asVivVqlVjzpw5WCx/Tzpv1aoV58+fp1+/fs472s2cOVM37hCR6+Zj8aFnRG/e+fVtvju6hm2nt9A4rKnRsUTyVUJ6PB/unsMztw5zrhxxV4W72dTjV6qWqGZwOrkai9nCLSUjuKVkhMv2tMxU+tUZyG9ntvN7zC7n2eREWwI/n/iRn0/8iMVk4dCAk859kjKS+OrA59QMuYVbQiKK7LJwJofDUbCf/7uRc+cuFNhrXe0e7ZJ/VHdjFNW6x6fF0WhhXRJtCdxZ4W6+aLfc6Ei5UlTrXtQV1bqvP7qWYRue4VTySd66awpP1O5vdKRcKap1L0h2h50jCYf4/dwudp3bye/ndvJ7zC7K+ZdnY/dNznHbTm/hoS/vdz6uGFiJW0pGUDMku+m+JaQWN5WohtViNaTupUrlrEkv1NMnRESKkhK+wTxZ/2n+s3UCP0Vv4OcTP3JH+buMjiWSpxLTE3j1lxdZtG+Bc9sf5/cYmEjyi9lkpmqJalQtUY321TsB2ddqxaXHuow7GP+Xy+NjF45y7MJR1hxZ5dzWsuJ9LGn7JYWZmmIRkTw0sO4QZv8+g9i0WP6zZQIrOqzRIvriNjYc/57nvn+Kk8knAChdrAxvt/gfbao8aHAyKSgmk8l50eRF3Ws+xv2V2rAvdi/7Yvey93z21z/O7yUpI/tT9WolqhsRN1fUFIuI5KEAayBPNxjGuE0vs/X0Zn44vo6WFe+/9o4ihZgty8abW8YzY+dU57aO1bvw5p2TLmmQxDOV9CvJ7eXv5Pbydzq3ORwOopOOs+/8XsICyhmYLmd0ZZmISB57onZ/ShcrA8DELRPQpRtS1L388wvOhrikb0nmtfmEmffPVUMsV2UymQgPrMj9ldtQJ7Su0XGuSU2xiEgeK+ZdjOcbjsDfO4B7K96HzW679k4ihdjTtz5PcZ8S3FnhbjZ028RDVR82OpJIntP0CRGRfNAz4nEeqdaJUL9Qo6OI5Fp6VjomTFgtVgDCAyuysuM6bipRDbNJ59PEPek7W0QkH/hYfNQQS5F04kI0j3zVhpd/fsFle/XgGmqIxa3pu1tEpADsPb+HlIwUo2OIXNXPJ37k/s/v4rezv/LRnrl8f2yd0ZFECoyaYhGRfJSWmcaz3z/JPUubM/v3GUbHEbksh8PBjJ3T6LL8EWJSYzBhYlTjF7k7vKXR0UQKjJpiEZF85GPx4VjiURw4mPrbO8SkxhgdScRFSkYKg757grGRL5HlyKK4TwkWPriUEY1Ha7qEeBR9t4uI5COTycSrt40HICnjAlO2v2VwIpG/nUk5Q4evH2TZX9l3GrslpBZrO2/g/sptDE4mUvDUFIuI5LMGZRrSoVr2LVI/2jOXQwkHDU4kkj1lov+a3uw4+xsAD9/UnpWd1lGleFWDk4kYQ02xiEgBGNP0VbzN3mTaM3lz83ij44hgMpn4z52T8fcO4PmGI5jT6iP8vf2NjiViGDXFIiIFoHLxKjxRuz8Ayw9+xbbTWwxOJJ7I4XC43GGxVmhtNvX4lTFNX9X8YfF4+hcgIlJAnm84iiBrcQBe+mkUdofd4ETiSbLsWYz5aQTTdrzjsj3Mv6xBiUQKFzXFIiIFpKRfSUY1HgNAXHocJ5NOGJxIPEVaZhr91/bhw6g5TNg8lrVHVhkdSaTQ0W2eRUQK0BO1B+Bl8aZHzV74evkaHUc8QEJ6PL1XPcqmk78A0Kxsc5qENTM4lUjho6ZYRKQAeVu86Vt7gNExxEOcTDrBo9904o/YvQA8WOVh3r//A/y8/AxOJlL4aPqEiIiBHA4HiekJRscQN/Rn7D4e/OI+Z0P8eK1+zG09Xw2xyBWoKRYRMciuszto+1UrBn/Xz+go4ma2nNrMw1+14mRy9rz1MU1e4a27pmAxWwxOJlJ4afqEiIhBVhz82rk023dHVusuYpJnUjKSScpIwmKy8HaL//FYRG+jI4kUejpTLCJikOcaDqdMsTAAXvr5BVIzUw1OJO7inor3Mq3lTD5+YJEaYpEcUlMsImKQAGsgY5tPAOBI4mHe/fW/BieSouxU0kmXx51qdKVV5QcMSiNS9KgpFhExUMfqXWhR4R4Apu/4H/ti/zA4kRRFs3a9R9NP6vPziR+NjiJSZKkpFhExkMlkYlKLd/C1+JJhz2Dkxud0pzvJMYfDwdvb/sMrv4whLSuNFzYOI9OeaXQskSJJTbGIiMGqFK/KsEajANhyahOL/lhgcCIpChwOB+M2vcKkbW8CUCmoMovafo6XWdfQi1wPNcUiIoXAk/Wf4ebgmgBsPhVpcBop7LLsWYzc+Dwzdk4F4ObgmqzosIZKQZWNDSZShOnXSRGRQsBqsTLlnmmcTTnLg1XaGh1HCrGMrAye/n4wXx74DIC6peqztO1XlPQraXAykaJNTbGISCHROKyp0RGkkMuyZ9F/bR9WHf4GgCZhzVj00GcE+RQ3OJlI0afpEyIihVRMaoxuAS0uLGYLdUvVA+Du8JYsffgrNcQieURnikVECqEVB7/mhR+fp1WlB3i35XtGx5FCZFjDUVQICKd99U74WHyMjiPiNnSmWESkEPr20HJiUmNYtG8B64+uNTqOGCgmNYZDCQedj00mE91q9lBDLJLH1BSLiBRCb945iVJ+pQEYtuEZEtLjjQ0khjiVdJJHvmpDp68f5viFY0bHEXFraopFRAqhEN+SvH33/wA4lXySF38aZXAiKWhHEg7z8LI2HIjfz4mkaJb/tczoSCJuTU2xiEgh9UCVh+hSozsAn+1fwlcHPjc4kRSU/bF/0m5ZG44lHgFgdJOXebL+08aGEnFzaopFRAqxiXf+l/DAigCM3Pg80ReOG5xI8tvuc7t4ZFkbTiefAmDC7f9hWKNRmEwmg5OJuDc1xSIihViQT3Heu28OZpOZRFsCT60fSJY9y+hYkk+2ntpCh6/bcj7tPCZMvHvPewys96TRsUQ8gppiEZFCrlnZ23iu4Qi8zF7cW/F+o+NIPok6t5uuKx4h0ZaAl9mLWfd/SI9behkdS8RjaJ1iEZEiYHjDF2h3UwciStYyOorkk5tDanJX+D38cGwdH7ZewP2V2xgdScSjGN4U22w2pk2bxty5c1m7di0VKlS46vjt27czadIkrFYrNpuNUaNG0ahRI5fjvf3222zZsoXAwEDS09MZOHAg99//99mV0aNHc+jQIXx8/l7jsUqVKowfPz7v36CISB7wtnirIXZz3hZvZt8/j32xe6lf+laj44h4HEOb4ujoaIYPH07lypXJyrr2HLkTJ04waNAgZsyYQdOmTdm6dSuDBg1i+fLllC9fHoAZM2awfv16vv76awICAti7dy9du3bl888/p2bNms5jTZky5ZoNuIhIYfXbme3M3zOPyXdPxWK2GB1HrtOKg19zX5X7CMYfAF8vXzXEIgYxdE5xSkoKkyZNomPHjjkav2DBAqpWrUrTpk0BaNKkCVWqVGHhwoXOMfv27aNOnToEBAQAEBERQWBgIJs3b877NyAiYoBNJ3/h4a9as2jfAqb8OsnoOHKd3t85nX5revHYiq6kZqQaHUfE4xnaFNeoUYNKlSrleHxkZCR16tRx2VanTh0iIyOdj1u1asX27ds5ffo0AD/99BOxsbGULFkyb0KLiBisYZnG1C1VH4C3t/2H74+tMzaQ5IrD4WDCprG8FvkiAIcSDnE66bTBqUTE8DnFuXH8+HHatHG98CA0NJTjx/9et7Njx46kpKTQtm1bSpUqxeHDh2nduvUl+82ePZvDhw+TmZlJzZo1eeqppwgNDS2Q9yEiciOsFitzWn3EvZ/eQVx6HIO+68uaTt9TtUQ1o6PJNWTaMxmx4VkW7VsAQJXiVfmqwwqqBFchLi7Z4HQinq1INcVpaWlYrVaXbVarlbS0NOfjJUuW8MEHH/Dll19SsWJF9u3bx+bNm/Hy+vutVq5cmXLlyjF27FgyMzMZN24cXbt2ZcWKFfj7++c4j9lswmwumMXULRazy1cpGKq7MVT3a6scXIm5D8yny9ftSUiPp9eq7nzX9QeCfIpf9zFV9/yVmplK/zWPs+rwtwDUK1WfTx/5krDAMEB1L2j6fjdGYa57kWqKfX19sdlsLttsNhu+vr5A9kdSkydPpm/fvlSsmH0HqJo1azJx4kTS0tIYPHgwgPMrZDfVY8aMoXHjxnz77bd07do1x3lCQvwL/A5DQUF+Bfp6kk11N4bqfnUdgtsyJW0Kz65+lgNx+3nq+4F83f3rG77wTnXPe3GpcXRb0oGfj/0MwL1V7uXLbl8S5BPkHKO6G0N1N0ZhrHuRaorDw8OJiYlx2RYTE0N4eDgAsbGxJCYmOleiuKhChQqsWbPGpRn+p4CAAEJCQjh27Fiu8sTGJhfomeKgID8SE1PJyrIXyGuK6m4U1T3nelbvy9Zjv/LJ3vl8e+Bbhq0cydjbX7+uY6nu+efJtUOdDXH76h15//45ZKVYiEtJVt0Norobw4i6BwfnbBZAkWqKb7vtNnbs2OGyLSoqiubNmwMQHByM1Wrl3LlzLmPOnTvnsibxhAkTePnll52PbTYb8fHxlC1bNld57HYHdrsjt2/jhmRl2cnM1D/egqa6G0N1z5n/3DmZ/bF/su30FnzNfmRkZN3Qp1iqe9579bYJbD21hbvDW/LGHZOwYLmkxqq7MVR3YxTGuhe+CR3/MGbMGEaOHOl83Lt3bw4ePMi2bduA7Bt5HDx4kJ49ewJgNpvp0KEDn332GQkJCQDs2bOHyMhIHnjgAedxlixZwu7du52PZ8yYQUBAwCUX44mIFAU+Fh/mtfmEmffPZUTj0QU+rUuuLdQvlNWdvmfinW9rXWmRQsrQM8U2m41+/fqRmJgIwLBhwwgLC2Pq1KkApKenk5mZ6Rxfvnx5Zs2axaRJk/D29sZmszF79myX6RJjxoxh2rRpPP744/j6+pKcnMzw4cPp3bu3c8wLL7zAxIkTsVgspKWlERwczPz587Vsm4gUWaWLlaZj9S4u2xwOhxpkg3z25xI2HP+eaffOxGzKPv9UwjfY4FQicjUmh8NRsJ//u5Fz5y4U2Gt5eZkJDvYnLi650H3c4M5Ud2Oo7jduf+yfDF0/kOn3zqZGyM052kd1v3EOh4P/bpvI29v/A8CIRqMZ1eTFq+6juhtDdTeGEXUvVSowR+MK9fQJERHJvYT0eB5Z1oad53bQeUU7DiccMjqSR0jPSuep9QOdDXFZ/3I8WPVhg1OJSE6pKRYRcTPFfUrwUrOxAJxOPkXn5e04cSHa2FBu7nzqebosf4TP9y8FoE5oPVZ3+p7aoXWusaeIFBZqikVE3FDPiD68ccdbABy/cIxOyx/mTMoZg1O5p6iY3bT+/G42n4oEoFWlNnzdYRVlA8oZnExEckNNsYiImxpQdwgv//8Z40MJB2m/7AFOJp0wNpSbWX90LQ99eR/HLhwFYGDdIXz8wGICvAMMTiYiuaWmWETEjT1z6zCGN3oBgIPxf9HuqzYcSThscCr3cXPILfh7++Nj8WFqy/eZcMdbWnJNpIhSUywi4uZeaPISLzV9DYBjF47y8Z4PDU7kPioEhvNh64Usb7+a7jUfMzqOiNyAInVHOxERuT7PNhxOMe9i/Hpmm3NKheTezyd+ZN3RtYxtPsG5rVm55gYmEpG8oqZYRMRDDKg7hP6OwS439EjPSsfH4mNgqqIhy57FlF8nMXn7W9gddmqG3KIzwyJuRtMnREQ8yD8b4oT0eO7/7C6m7/gfuo/TlZ1KOkmXFY/w320TsTvslPApQbBviNGxRCSPqSkWEfFQIzc+x77YPxi/6RWeWj+QlIwUoyMVKg6Hg8/3L+Wupc34+cSPADQs05j1XX+mdeUHDE4nInlNTbGIiId6udk4bg6uCcDn+5fS+rOWHIw9aHCqwuFcyjn6runFk+sGkJAejwkTQxs8x/L2qwkPrGh0PBHJB2qKRUQ8VMWgSqzstI62VR8BYE9MFA1nN+TbgysMTma8Z78fwreHlgNQKagyX7dfxau3jcfb4m1wMhHJL2qKRUQ8WKA1iLmt5/PabRMwm8wkpCfQ69tHef6HoSTZLhgdzzCvNZ+Ar8WXx2v144dukVphQsQDqCkWEfFwJpOJpxo8w7IO31AuMPvWxJ/8MZ8Poz4wOFnBSMtMY8bOaSRnJDu33RxSk82P7WBSi3d0dzoRD6El2UREBIA7KtzF7iG76ffVAA7FH2JwvaeMjpSvHA4Ha46s4rXIFzmccIjY1PO8fNtY5/PlAsobF05ECpyaYhERcQrxC2Fum4+JS4nHarE6t/92ZjsH4/+ic41uLsu6FVVbT21h/KZX2Hp6s3PbrnM7sDvsmE36EFXEE+lfvoiIuDCZTAT5FHc+zrRnMnzDszy1fiAPfNHSuTxZUfTbme30WtmNtl/d72yIy/mX5717Z/Ppw8vUEIt4MJ0pFhGRqzqZdILUzOw1jH87+ysdv27L3eEtGd3kZW4t08jgdDnXd3Uvvjn0tfNxcZ8SPHPrMPrXGYSfl5+ByUSkMNCvxCIiclUVgyqxsftmJtz+H0r6lgRgw/HvafNFSx5Z9gBrjqzC7rAbnPLaqhSvCkCAdyBPN3ierY/t5OkGz6khFhFAZ4pFRCQHfCw+DKz3JD1u6cX7u6b//2oNSWw6+QubTv7C4HpDGX/7m0bHxO6ws/lkJF8c+AxbVjrT7p3pfG5Qvaco5l2MfrUHUsI32MCUIlIYqSkWEZEcC7AGMrLxGAbWHcL8vR8x5/f3OZ18ilaV27iM+/7YOm4JiaBsQLl8z5Selc6mk7+w/uhalh9cxqnkkwCYTWZeaPISFQLDAShdrDTDG72Q73lEpGhSUywiIrlW3KcETzd4jkF1n2TloRU0L3eH87m0zDT6ru5JSmYKtUPrcnd4SxqWaUyjMo0p4x+WZxk+iprLuqNr+PnET6RkJrs85+8dwINV2pJhz8iz1xMR96amWERErpvVYqV99U4u27af2UrK/1+YFxXzO1ExvzufK+dfnpuCq9O4TGNGN33FuT0+LY4TSSdw/P//suyZxKXFEZcey/nUGI4lHuWeivfSsuL9zn3WH1vL2qOrnY+LeRWjRXhLOlXvwv2V22iusIjkippiERHJU3eUv4vNj+1g3ZE1fHd0DdvPbCM5IwmAk8knOJl8Ase/Lsxbdfhbnv3hyase12yyuDTFTcrexomkE9xR/i7urXg/zco1x8fik/dvSEQ8gppiERHJc1WL38TAek8ysN6TZNmz2B/3J7+e2cbumF0cTjjEraUbuoyPT4+/6vFK+ZXG2+ztsu3pBs/xdIPn8ji5iHgqNcUiIpKvLGYLt5SM4JaSEVcc8/BNj1A7tA5mkxkTJsxmCyV8ShDiW5Jgn2C8Ld5X3FdEJC+oKRYREcNVCAx3rhIhImIE3bxDRERERDyemmIRERER8XhqikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE46kpFhERERGPZ3I4HA6jQ4iIiIiIGElnikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE43kZHUCun91up2vXrsTGxvL9998bHcet2Ww2Zs6cydatW/Hy8iI+Pp7y5cszevRowsPDjY7ntuLj41mwYAGRkZF4eXmRmJhI69atGThwIF5e+r+v/HbkyBFGjx6Nt7c3CxYsMDqOW/ruu+94//338fX1xWw289prr1G9enWjY7k9m83GtGnTmDt3LmvXrqVChQpGR3J7K1eu5PPPPycrK4ukpCTKlSvHqFGjCtXPUP1UKcI++eQTjh49SmBgoNFR3F5CQgKffvopy5YtIzQ0FLvdzvPPP89zzz3HF198YXQ8t7Vx40ZWr17NkiVLCAwM5MyZM3Ts2JGMjAyeffZZo+O5tWXLlrF48WLMZn2gmF9+//13Ro0axRdffEHVqlVZtmwZ/fr1Y+XKlQQEBBgdz21FR0czfPhwKleuTFZWltFxPMaoUaOYOXMmd9xxB3a7nRdffJH+/fuzfPlyfHx8jI4HaPpEkXXmzBk+//xzunbtanQUj1C8eHFmz55NaGgoAGazmUaNGnHkyBFjg7m5EiVK8MQTTzh/8StTpgytW7dm5cqVBidzf8HBwSxYsIBKlSoZHcVtzZkzhxYtWlC1alUA2rVrR1ZWFsuWLTM2mJtLSUlh0qRJdOzY0egoHqVly5bccccdQPbP0Mcee4wjR46wZ88eg5P9TU1xETVhwgSGDRuGr6+v0VE8gtVqJSIiwvn4zJkzfPXVV/Tu3dvAVO6vRYsWdO7c2WWbj48PGRkZBiXyHC1atMBqtRodw61t2rSJOnXqOB+bzWZq1apFZGSkgancX40aNfTLngGmTp3q8vji2eHC9P/naoqLoO+//x6LxUKLFi2MjuJxLn58f99993HnnXfqI3wD7Nixg9atWxsdQ+SGxMXFceHCBeenTxeFhoZy/Phxg1KJFJydO3dSunRpbr31VqOjOGlOcRGTnJzMO++8w9y5c42O4pHKlCnDl19+yZkzZ3jyySc5f/48EyZMMDqWx9i0aROnTp1izpw5RkcRuSFpaWkAl5yNt1qtzudE3JXNZmPu3Lm8/PLLeHt7Gx3HSU1xITFt2jSmT59+1TGff/45K1asoHv37pQuXbqAkrm3nNb9nx9xQnZzPHz4cJ544gn69Omjq8Vz6XrqfubMGcaOHcuMGTN0cel1ut7vd8l7F6e+2Ww2l+02m03T4sTtvfrqq7Ru3brQfeqnpriQ6Nu3L927d7/qmODgYF566SX27NnD6tWrAThx4gTnzp2jV69eVKxYkTfeeKMg4rqNnNb94hXKFovFub1KlSoA/PXXX2qKcymndb8oPj6eIUOG8Nprr1GrVq38jue2clt3yT/BwcEEBgYSExPjsj0mJqZQLVElktfefvttLBYLzz//vNFRLqGmuJDw9/fH39//muOWL1/u8njatGl89dVXWkP0OuW07l9++SVxcXH069fPue3cuXMAOmt/HXJad4CkpCQGDx7Mk08+SfPmzQFYunQp3bp1y8+Ibik3dZf816xZM6KiopyPHQ4He/fuZfDgwQamEsk/s2fP5sSJE0yePBmTyeT8/q9du7bBybLpQjuRHPriiy+IjY0FID09nRkzZlCjRg191JyP0tPTGTJkCPXr16dMmTLs3r2b3bt3s3TpUqOjidywgQMHsnHjRg4fPgxkn/Qwm820b9/e2GAi+WDx4sUsX76c3r17s2fPHnbv3s0PP/zA/v37jY7mZHI4HA6jQ0junTt3jmHDhjmnT9SvX58OHTpo3cV8curUKT744AN+++03ihUrRkpKCtWqVWPYsGGULVvW6Hhu65NPPmH8+PGXfe7PP/8s4DSeZf369Xz00UccOnSI9PR0brnlFtq1a0eXLl2MjuZWdEe7gmez2ejXrx+JiYns27ePevXqERYWdsmSYZJ3kpKSaNy4MXa7/ZLnJk6cWGh6FzXFIiIiIuLxNH1CRERERDyemmIRERER8XhqikVERETE46kpFhERERGPp6ZYRERERDyemmIRERER8XhqikVERETE46kpFhHxAImJiSQmJhodo8BER0cbHUFEihg1xSIiubBw4UIeeeQRbr755nxrvDIyMpg9ezb16tXjyy+/vOK4Dz74gPbt2/PYY4/RpUsXfvnll8uOi4yMZMiQIWRlZbF9+3Z69erFzTfffNVj56VBgwZx++2306tXr1ztt2PHjuvOunnzZp599lnS09NztZ+IeC41xSIiudCzZ09efPHFfDv+oUOHePTRRzl16hRpaWlXHDdz5kwWLFjA3Llz+eSTTxg+fDiDBw9m165dLuMOHz7MCy+8wJQpUwgODqZRo0YsWLAg3/JfzqxZs7jzzjtzvV+DBg2uO2vnzp0pX748r7/++nXtLyKeR02xiEghkpKSwuTJk+nXr98VxyQlJTFz5kx69OhByZIlAWjWrBkNGjTg3XffdRk7ceJEHnnkEcqUKZOfsQulQYMGsWLFCn7//Xejo4hIEeBldAARkaIuIyOD6dOns379eooVK0ZqaiqdO3emT58+LmMmTZrEd999R7ly5ShdujTVq1dn6tSpNGnShGeffZZGjRpRu3Zt4OpzYrdt20ZqaioNGjRw2d6gQQPmzJlDamoqfn5+xMbG8ssvv9C/f/9rvoedO3fy/vvvk5CQgJeXFzabjf79+9OqVSsAjh49yssvv8zOnTvp06cP6enp7N27l7Nnz/L888/TuHFjJk+ezP79+zGZTEyaNImbbrrpkteZN28eP//8M8eOHSMsLIyxY8e6jFu3bh1TpkzBx8eH0NBQnnjiiVxnvah48eLUrVuXFStWULdu3WvWQEQ8m5piEZEbNGbMGHbv3s3ixYsJCQnh6NGjdO3alcTERJ5++mkA3nnnHVauXMlnn31GuXLlOHPmDN27dwfI9RSBI0eOAFC6dGmX7WXKlCErK4vjx49To0YNfvvtNzIzM6lcufI1jxkZGUmFChWYNWsWAPv27ePRRx+lTJky1KtXj0qVKrFgwQJatmzJypUrWbx4MWXKlGHBggWMGTOG3r17M378eKxWK0OHDuWNN97gww8/dHmNqKgoOnTowNy5c7Hb7YwYMYL+/fuzevVqfHx8+PPPP3nmmWd47bXX6NatG3a7nTfeeCPXWf+pSpUqbN++PaelFREPpukTIiI34OjRo6xYsYLHHnuMkJAQACpVqkS7du344IMPSElJITU1lQULFtCuXTvKlSsHZDewDz/88HW9ZkpKCgBWq9Vl+8XHF58/d+4cACVKlLjmMbt27crzzz/vfFyzZk2qV6/O999/f8nYpk2bOqdjNGvWjLS0NG666Sbn6zdr1ozdu3dfsl9gYCAdOnQAwGw2M3DgQE6ePMk333wDwNy5cylRogRdunRxjunZs+cNZS1evLizDiIiV6MzxSIiN2DPnj0Al5yNrVKlCmlpafz1119YrVZsNhuVKlVyGVOhQoXrek1/f38AbDaby/aLj4sVKwbgXILN29s7R8edPn06u3btwmw2YzabOXTo0GWnQPxzfrKfn98l24oVK3bZ5d/KlSuHyWRyPq5SpQoABw4ccH4NDw/HbP77fM2VapTTrF5eXsTHx1/tbYuIAGqKRUTyxD+bvStxOBx58loXm+uzZ8+6NONnzpzBYrEQHh4OZJ8lhez5zP8+q/xvAwcOJCsri3nz5jnPePfq1euymS0WyyXb/tnI3oic1Cg3WTMzM3N0plxERNMnRERuQJ06dYDspdT+6dChQ/j6+lK9enUqVaqEj48PR48edRlzvescN2nSBD8/P3bs2OGyfceOHTRt2tR59vbinOO4uLirHi8+Pp49e/bQokULZ5MJl56JvlEnTpxwaVwPHz4MQPXq1QGoUaMGx48fx263O8f8u0a5zRoXF3fJ3GsRkctRUywicgPCw8Pp0KEDixYtIjY2Fvh7nnH//v3x8/PDz8+PXr16sWLFCk6dOgVkn9Vds2bNdb2mv78/gwcPZtGiRZw/fx6ALVu2sGPHDp577jnnuIYNG+Lt7X1Jw/5vxYsXp2zZsmzevNl5s4sDBw7wxx9/XFe+K4mNjXXehMNutzN79mzKlStH27ZtAejbty8JCQl89tlnQPZZ439frJfbrIcOHaJZs2Z5+j5ExD2ZHHn1eZ6IiAdYuHAhn332Gfv27aNevXoMGDCAu+++m/fee4/vvvsOf39/UlNT6dSpE48//rhzP5vNxn//+1/Wrl1LhQoVqFChAtWrV+edd95xzksGSE5OZvDgwaSnp7Nr1y6qVKlCqVKlnEu2XeRwOJg7dy4rVqwgICAAm83Gs88+yx133OGSd+jQoZQvX54xY8YAsH37dv73v/+xdetWqlSpwoMPPsgzzzzD3r17eeONNzhz5gzVqlWjTJky7Ny5k5iYGG6//XZGjx7Ns88+y86dOylVqhTt27fnzjvvZOLEiezatYuaNWsydOhQzp07x/z58zl8+DBNmjTh5ZdfZsqUKURFRVG1alWaNGnCb7/9RnR0NGFhYbz22mtUq1bNmXf9+vVMnjwZq9VKSEgIjz76KEOHDqVKlSq0bt2a559//ppZJ02aBGQ34S1atOCzzz6jZs2a+fHtICJuRE2xiEgBuHDhAlarFR8fH+e2GTNmsGLFClatWpVvr3vixAl69OjBggULqFixYr69TmE0btw4vL298/UOhCLiPjR9QkSkACxYsICpU6c6H58/f56vvvqKbt265evrli9fnnfffZeXXnrJOdXCE3zyySdkZGQwcuRIo6OISBGhM8UiIgVg27ZtvPfee6SmpuLt7U16ejoPP/wwPXv2zLOVG64mNTWVrKwsAgIC8v21CoOYmBhCQ0ONjiEiRYiaYhERERHxeJo+ISIiIiIeT02xiIiIiHg8NcUiIiIi4vHUFIuIiIiIx1NTLCIiIiIeT02xiIiIiHg8NcUiIiIi4vHUFIuIiIiIx1NTLCIiIiIe7/8Ag9LVassvPrgAAAAASUVORK5CYII=\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_72_0.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "import pandas as pd\n",
@@ -1571,21 +1355,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "GridSearchCV(estimator=Ridge(),\n",
-      "             param_grid={'alpha': array([1.00000000e-04, 4.64158883e-04, 2.15443469e-03, 1.00000000e-02,\n",
-      "       4.64158883e-02, 2.15443469e-01, 1.00000000e+00, 4.64158883e+00,\n",
-      "       2.15443469e+01, 1.00000000e+02])})\n",
-      "Best estimated lambda-value: 100.0\n",
-      "MSE score: 1.0892144853354966\n",
-      "R2 score: -0.0038332550504751595\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "from sklearn.model_selection import train_test_split\n",
@@ -1673,19 +1443,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "RandomizedSearchCV(estimator=Ridge(), n_iter=100,\n",
-      "                   param_distributions={'alpha': <scipy.stats._distn_infrastructure.rv_frozen object at 0x1309f4ca0>})\n",
-      "Best estimated lambda-value: 0.9849967686928113\n",
-      "MSE score: 1.0853136633465326\n",
-      "R2 score: -0.0002382102844775691\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np\n",
     "from sklearn.model_selection import train_test_split\n",
@@ -1754,31 +1512,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(426, 30)\n",
-      "(143, 30)\n",
-      "Test set accuracy with Logistic Regression: 0.94\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1819,36 +1553,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<Figure size 1000x2000 with 30 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_82_0.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 1500x800 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_82_1.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -1977,155 +1682,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "(426, 30)\n",
-      "(143, 30)\n",
-      "[1.         0.86666667 1.         0.92857143 1.         0.85714286\n",
-      " 1.         0.92857143 0.92857143 1.        ]\n",
-      "Test set accuracy with Logistic Regression: 0.94\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n",
-      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
-      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
-      "\n",
-      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
-      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
-      "Please also refer to the documentation for alternative solver options:\n",
-      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
-      "  n_iter_i = _check_optimize_result(\n"
-     ]
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_89_2.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_89_3.png"
-      }
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
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\n",
-      "text/plain": [
-       "<Figure size 800x550 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "filenames": {
-       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/week38_89_4.png"
-      }
-     },
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
@@ -2919,19 +2476,7 @@
     "collapsed": false,
     "editable": true
    },
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'm' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "Input \u001b[0;32mIn [13]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m2\u001b[39m\u001b[38;5;241m*\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrand(\u001b[43mm\u001b[49m,\u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m      2\u001b[0m y \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m4\u001b[39m\u001b[38;5;241m+\u001b[39m\u001b[38;5;241m3\u001b[39m\u001b[38;5;241m*\u001b[39mx\u001b[38;5;241m+\u001b[39mnp\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mrandn(m,\u001b[38;5;241m1\u001b[39m)\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'm' is not defined"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "x = 2*np.random.rand(m,1)\n",
     "y = 4+3*x+np.random.randn(m,1)"
@@ -3491,7 +3036,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.9.10"
+   "version": "3.9.18"
   }
  },
  "nbformat": 4,
diff --git a/doc/LectureNotes/_build/jupyter_execute/week39.ipynb b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb
new file mode 100644
index 000000000..8cea423cf
--- /dev/null
+++ b/doc/LectureNotes/_build/jupyter_execute/week39.ipynb
@@ -0,0 +1,4904 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "97c9bb6c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)\n",
+    "doconce format html week39.do.txt --no_mako -->\n",
+    "<!-- dom:TITLE: Week 39: Optimization and  Gradient Methods -->"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ade8d870",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "# Week 39: Optimization and  Gradient Methods\n",
+    "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University\n",
+    "\n",
+    "Date: **Week 39**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87cd74c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Plan for week 39\n",
+    "\n",
+    "**Material for the active learning sessions on Tuesday and Wednesday.**\n",
+    "\n",
+    "  * Discussions on how to structure your report for the first project\n",
+    "\n",
+    "  * Exercise for week 39 on how to write the abstract and the introduction of the report and how to include references. \n",
+    "\n",
+    "  * Work on project 1, in particular resampling methods like cross-validation and bootstrap. **For more discussions of project 1, chapter 5 of Goodfellow et al is a good read, in particular sections 5.1-5.5 and 5.7-5.11**.\n",
+    "\n",
+    "These sections summarize neatly what we have done till now and point to what is coming with respect to deep learning. \n",
+    "  * A general guideline can be found at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md>.\n",
+    "\n",
+    "  \n",
+    "\n",
+    "**Material for the lecture on Thursday September 28.**\n",
+    "\n",
+    "  * Repetition of Logistic regression equations and classification problems and discussion of Gradient methods. Examples on how to implement Logistic Regression and discussion of stochastic gradient descent \n",
+    "\n",
+    "  * Stochastic Gradient descent with examples and automatic differentiation\n",
+    "\n",
+    "  * [Video of lecture](https://youtu.be/)\n",
+    "\n",
+    "  * Whiteboard notes TBA at <https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/2023/NotesSep28.pdf>\n",
+    "\n",
+    "  * Readings and Videos:\n",
+    "\n",
+    "    * These lecture notes\n",
+    "\n",
+    "    * For a good discussion on gradient methods, we would like to recommend Goodfellow et al section 4.3-4.5 and sections 8.3-8.6. We will come back to the latter chapter in our discussion of Neural networks as well. \n",
+    "\n",
+    "    * [Video on gradient descent](https://www.youtube.com/watch?v=sDv4f4s2SB8)\n",
+    "\n",
+    "    * [Video on stochastic gradient descent](https://www.youtube.com/watch?v=vMh0zPT0tLI)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "529184e5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Optimization, the central part of any Machine Learning algortithm\n",
+    "\n",
+    "The first few slides here are a repetition from last week. \n",
+    "\n",
+    "Almost every problem in machine learning and data science starts with\n",
+    "a dataset $X$, a model $g(\\beta)$, which is a function of the\n",
+    "parameters $\\beta$ and a cost function $C(X, g(\\beta))$ that allows\n",
+    "us to judge how well the model $g(\\beta)$ explains the observations\n",
+    "$X$. The model is fit by finding the values of $\\beta$ that minimize\n",
+    "the cost function. Ideally we would be able to solve for $\\beta$\n",
+    "analytically, however this is not possible in general and we must use\n",
+    "some approximative/numerical method to compute the minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1a65465a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Revisiting our Logistic Regression case\n",
+    "\n",
+    "In our discussion on Logistic Regression we studied the \n",
+    "case of\n",
+    "two classes, with $y_i$ either\n",
+    "$0$ or $1$. Furthermore we assumed also that we have only two\n",
+    "parameters $\\beta$ in our fitting, that is we\n",
+    "defined probabilities"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b67231b3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{align*}\n",
+    "p(y_i=1|x_i,\\boldsymbol{\\beta}) &= \\frac{\\exp{(\\beta_0+\\beta_1x_i)}}{1+\\exp{(\\beta_0+\\beta_1x_i)}},\\nonumber\\\\\n",
+    "p(y_i=0|x_i,\\boldsymbol{\\beta}) &= 1 - p(y_i=1|x_i,\\boldsymbol{\\beta}),\n",
+    "\\end{align*}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3f5e03db",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e83141ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The equations to solve\n",
+    "\n",
+    "Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n",
+    "elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n",
+    "$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n",
+    "$p(y_i\\vert x_i,\\boldsymbol{\\beta})$. We rewrote in a more compact form\n",
+    "the first derivative of the cost function as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cef5864b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2f59bbb1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n",
+    "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3869b3c6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4656e92",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This defines what is called  the Hessian matrix."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b73ae554",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Solving using Newton-Raphson's method\n",
+    "\n",
+    "If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the  matrices that define the first and second derivatives. \n",
+    "\n",
+    "Our iterative scheme is then given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "70a2df05",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e36f976",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or in matrix form as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c4959c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c553379e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The right-hand side is computed with the old values of $\\beta$. \n",
+    "\n",
+    "If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "145f9699",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Brief reminder on Newton-Raphson's method\n",
+    "\n",
+    "Let us quickly remind ourselves how we derive the above method.\n",
+    "\n",
+    "Perhaps the most celebrated of all one-dimensional root-finding\n",
+    "routines is Newton's method, also called the Newton-Raphson\n",
+    "method. This method  requires the evaluation of both the\n",
+    "function $f$ and its derivative $f'$ at arbitrary points. \n",
+    "If you can only calculate the derivative\n",
+    "numerically and/or your function is not of the smooth type, we\n",
+    "normally discourage the use of this method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9a68f686",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The equations\n",
+    "\n",
+    "The Newton-Raphson formula consists geometrically of extending the\n",
+    "tangent line at a current point until it crosses zero, then setting\n",
+    "the next guess to the abscissa of that zero-crossing.  The mathematics\n",
+    "behind this method is rather simple. Employing a Taylor expansion for\n",
+    "$x$ sufficiently close to the solution $s$, we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d523ab61",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"eq:taylornr\"></div>\n",
+    "\n",
+    "$$\n",
+    "f(s)=0=f(x)+(s-x)f'(x)+\\frac{(s-x)^2}{2}f''(x) +\\dots.\n",
+    "    \\label{eq:taylornr} \\tag{1}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8205fd3a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "For small enough values of the function and for well-behaved\n",
+    "functions, the terms beyond linear are unimportant, hence we obtain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "98d52e46",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(x)+(s-x)f'(x)\\approx 0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "203f65e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "yielding"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd40195b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "s\\approx x-\\frac{f(x)}{f'(x)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e13a7340",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Having in mind an iterative procedure, it is natural to start iterating with"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "30c258c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84f880c9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple geometric interpretation\n",
+    "\n",
+    "The above is Newton-Raphson's method. It has a simple geometric\n",
+    "interpretation, namely $x_{n+1}$ is the point where the tangent from\n",
+    "$(x_n,f(x_n))$ crosses the $x$-axis.  Close to the solution,\n",
+    "Newton-Raphson converges fast to the desired result. However, if we\n",
+    "are far from a root, where the higher-order terms in the series are\n",
+    "important, the Newton-Raphson formula can give grossly inaccurate\n",
+    "results. For instance, the initial guess for the root might be so far\n",
+    "from the true root as to let the search interval include a local\n",
+    "maximum or minimum of the function.  If an iteration places a trial\n",
+    "guess near such a local extremum, so that the first derivative nearly\n",
+    "vanishes, then Newton-Raphson may fail totally"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b237f214",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Extending to more than one variable\n",
+    "\n",
+    "Newton's method can be generalized to systems of several non-linear equations\n",
+    "and variables. Consider the case with two equations"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b4ea1db2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n",
+    "                     f_2(x_1,x_2) &=0,\\end{array}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8b2b6606",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which we Taylor expand to obtain"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9d217a4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n",
+    "                     \\partial f_1/\\partial x_1+h_2\n",
+    "                     \\partial f_1/\\partial x_2+\\dots\\\\\n",
+    "                     0=f_2(x_1+h_1,x_2+h_2)=&f_2(x_1,x_2)+h_1\n",
+    "                     \\partial f_2/\\partial x_1+h_2\n",
+    "                     \\partial f_2/\\partial x_2+\\dots\n",
+    "                       \\end{array}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "54f87f7c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Defining the Jacobian matrix ${\\bf \\boldsymbol{J}}$ we have"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2711fc8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "{\\bf \\boldsymbol{J}}=\\left( \\begin{array}{cc}\n",
+    "                         \\partial f_1/\\partial x_1  & \\partial f_1/\\partial x_2 \\\\\n",
+    "                          \\partial f_2/\\partial x_1     &\\partial f_2/\\partial x_2\n",
+    "             \\end{array} \\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e0409f1c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "we can rephrase Newton's method as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53651890",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n",
+    "\\left(\\begin{array}{c} x_1^{n} \\\\ x_2^{n} \\end{array} \\right)+\n",
+    "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e70e7ac",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9336db1d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n",
+    "   -{\\bf \\boldsymbol{J}}^{-1}\n",
+    "   \\left(\\begin{array}{c} f_1(x_1^{n},x_2^{n}) \\\\ f_2(x_1^{n},x_2^{n}) \\end{array} \\right).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c2ae028",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We need thus to compute the inverse of the Jacobian matrix and it\n",
+    "is to understand that difficulties  may\n",
+    "arise in case ${\\bf \\boldsymbol{J}}$ is nearly singular.\n",
+    "\n",
+    "It is rather straightforward to extend the above scheme to systems of\n",
+    "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cdf99885",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent\n",
+    "\n",
+    "The basic idea of gradient descent is\n",
+    "that a function $F(\\mathbf{x})$, \n",
+    "$\\mathbf{x} \\equiv (x_1,\\cdots,x_n)$, decreases fastest if one goes from $\\bf {x}$ in the\n",
+    "direction of the negative gradient $-\\nabla F(\\mathbf{x})$.\n",
+    "\n",
+    "It can be shown that if"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "11bb1b41",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5d957768",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $\\gamma_k > 0$.\n",
+    "\n",
+    "For $\\gamma_k$ small enough, then $F(\\mathbf{x}_{k+1}) \\leq\n",
+    "F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n",
+    "we are always moving towards smaller function values, i.e a minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "455b420a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on Steepest descent\n",
+    "\n",
+    "The previous observation is the basis of the method of steepest\n",
+    "descent, which is also referred to as just gradient descent (GD). One\n",
+    "starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n",
+    "computes new approximations according to"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "aacb8b05",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2bb3385b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The parameter $\\gamma_k$ is often referred to as the step length or\n",
+    "the learning rate within the context of Machine Learning."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21326ef0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The ideal\n",
+    "\n",
+    "Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n",
+    "minimum of the function $F$. In general we do not know if we are in a\n",
+    "global or local minimum. In the special case when $F$ is a convex\n",
+    "function, all local minima are also global minima, so in this case\n",
+    "gradient descent can converge to the global solution. The advantage of\n",
+    "this scheme is that it is conceptually simple and straightforward to\n",
+    "implement. However the method in this form has some severe\n",
+    "limitations:\n",
+    "\n",
+    "In machine learing we are often faced with non-convex high dimensional\n",
+    "cost functions with many local minima. Since GD is deterministic we\n",
+    "will get stuck in a local minimum, if the method converges, unless we\n",
+    "have a very good intial guess. This also implies that the scheme is\n",
+    "sensitive to the chosen initial condition.\n",
+    "\n",
+    "Note that the gradient is a function of $\\mathbf{x} =\n",
+    "(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a41b3cc6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The sensitiveness of the gradient descent\n",
+    "\n",
+    "The gradient descent method \n",
+    "is sensitive to the choice of learning rate $\\gamma_k$. This is due\n",
+    "to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n",
+    "F(\\mathbf{x}_k)$ for sufficiently small $\\gamma_k$. The problem is to\n",
+    "determine an optimal learning rate. If the learning rate is chosen too\n",
+    "small the method will take a long time to converge and if it is too\n",
+    "large we can experience erratic behavior.\n",
+    "\n",
+    "Many of these shortcomings can be alleviated by introducing\n",
+    "randomness. One such method is that of Stochastic Gradient Descent\n",
+    "(SGD), see below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a01f11a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Convex functions\n",
+    "\n",
+    "Ideally we want our cost/loss function to be convex(concave).\n",
+    "\n",
+    "First we give the definition of a convex set: A set $C$ in\n",
+    "$\\mathbb{R}^n$ is said to be convex if, for all $x$ and $y$ in $C$ and\n",
+    "all $t \\in (0,1)$ , the point $(1 − t)x + ty$ also belongs to\n",
+    "C. Geometrically this means that every point on the line segment\n",
+    "connecting $x$ and $y$ is in $C$ as discussed below.\n",
+    "\n",
+    "The convex subsets of $\\mathbb{R}$ are the intervals of\n",
+    "$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n",
+    "regular polygons (triangles, rectangles, pentagons, etc...)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "076a32fa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Convex function\n",
+    "\n",
+    "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "73adde3c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conditions on convex functions\n",
+    "\n",
+    "In the following we state first and second-order conditions which\n",
+    "ensures convexity of a function $f$. We write $D_f$ to denote the\n",
+    "domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n",
+    "details and proofs we refer to: [S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press](http://stanford.edu/boyd/cvxbook/, 2004).\n",
+    "\n",
+    "**First order condition.**\n",
+    "\n",
+    "Suppose $f$ is differentiable (i.e $\\nabla f(x)$ is well defined for\n",
+    "all $x$ in the domain of $f$). Then $f$ is convex if and only if $D_f$\n",
+    "is a convex set and $$f(y) \\geq f(x) + \\nabla f(x)^T (y-x) $$ holds\n",
+    "for all $x,y \\in D_f$. This condition means that for a convex function\n",
+    "the first order Taylor expansion (right hand side above) at any point\n",
+    "a global under estimator of the function. To convince yourself you can\n",
+    "make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n",
+    "note that it is always below the graph.\n",
+    "\n",
+    "**Second order condition.**\n",
+    "\n",
+    "Assume that $f$ is twice\n",
+    "differentiable, i.e the Hessian matrix exists at each point in\n",
+    "$D_f$. Then $f$ is convex if and only if $D_f$ is a convex set and its\n",
+    "Hessian is positive semi-definite for all $x\\in D_f$. For a\n",
+    "single-variable function this reduces to $f''(x) \\geq 0$. Geometrically this means that $f$ has nonnegative curvature\n",
+    "everywhere.\n",
+    "\n",
+    "This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9f9ab5ff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on convex functions\n",
+    "\n",
+    "The next result is of great importance to us and the reason why we are\n",
+    "going on about convex functions. In machine learning we frequently\n",
+    "have to minimize a loss/cost function in order to find the best\n",
+    "parameters for the model we are considering. \n",
+    "\n",
+    "Ideally we want the\n",
+    "global minimum (for high-dimensional models it is hard to know\n",
+    "if we have local or global minimum). However, if the cost/loss function\n",
+    "is convex the following result provides invaluable information:\n",
+    "\n",
+    "**Any minimum is global for convex functions.**\n",
+    "\n",
+    "Consider the problem of finding $x \\in \\mathbb{R}^n$ such that $f(x)$\n",
+    "is minimal, where $f$ is convex and differentiable. Then, any point\n",
+    "$x^*$ that satisfies $\\nabla f(x^*) = 0$ is a global minimum.\n",
+    "\n",
+    "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b2a482b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Some simple problems\n",
+    "\n",
+    "1. Show that $f(x)=x^2$ is convex for $x \\in \\mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \\in D_f$ and any $\\lambda \\in [0,1]$ $\\lambda f(x)+(1-\\lambda)f(y)-f(\\lambda x + (1-\\lambda) y ) \\geq 0$.\n",
+    "\n",
+    "2. Using the second order condition show that the following functions are convex on the specified domain.\n",
+    "\n",
+    " * $f(x) = e^x$ is convex for $x \\in \\mathbb{R}$.\n",
+    "\n",
+    " * $g(x) = -\\ln(x)$ is convex for $x \\in (0,\\infty)$.\n",
+    "\n",
+    "3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \\in \\mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex.\n",
+    "\n",
+    "4. A norm is any function that satisfy the following properties\n",
+    "\n",
+    " * $f(\\alpha x) = |\\alpha| f(x)$ for all $\\alpha \\in \\mathbb{R}$.\n",
+    "\n",
+    " * $f(x+y) \\leq f(x) + f(y)$\n",
+    "\n",
+    " * $f(x) \\leq 0$ for all $x \\in \\mathbb{R}^n$ with equality if and only if $x = 0$\n",
+    "\n",
+    "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6566ee55",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Standard steepest descent\n",
+    "\n",
+    "Before we proceed, we would like to discuss the approach called the\n",
+    "**standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able\n",
+    "to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).\n",
+    "\n",
+    "[The success of the CG method](https://www.cs.cmu.edu/~quake-papers/painless-conjugate-gradient.pdf)\n",
+    "for finding solutions of non-linear problems is based on the theory\n",
+    "of conjugate gradients for linear systems of equations. It belongs to\n",
+    "the class of iterative methods for solving problems from linear\n",
+    "algebra of the type"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2e30cc1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5012b398",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In the iterative process we end up with a problem like"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca65d9a9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ec9323dd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n",
+    "\n",
+    "When we have found the exact solution, $\\boldsymbol{r}=0$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5caf0f7f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient method\n",
+    "\n",
+    "The residual is zero when we reach the minimum of the quadratic equation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "07734ce6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "468dcb52",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n",
+    "symmetric.  This defines also the Hessian and we want it to be  positive definite."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b63a89ae",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent  method\n",
+    "\n",
+    "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
+    "We can assume without loss of generality that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "56a122a3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_0=0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3256eb29",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or consider the system"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b6bab858",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7ff39e96",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "instead."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6678fce9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent  method\n",
+    "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "853eb11f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c229917",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n",
+    "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c8f310a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8a8c317",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and \n",
+    "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "49b64ed0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Final expressions\n",
+    "We can compute the residual iteratively as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "857ee939",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e5611fa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "384d5aa2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0ce677be",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e97f9044",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d7fbeb68",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "293c09b1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "af88e065",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "leading to the iterative scheme"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2757e302",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_{k},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "87aab66b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Steepest descent example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "a0e20ff7",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [
+    {
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'matplotlib'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mget_ipython\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_line_magic\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mmatplotlib\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43minline\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mlinalg\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mla\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:2432\u001b[0m, in \u001b[0;36mInteractiveShell.run_line_magic\u001b[0;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[1;32m   2430\u001b[0m     kwargs[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mlocal_ns\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_local_scope(stack_depth)\n\u001b[1;32m   2431\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mbuiltin_trap:\n\u001b[0;32m-> 2432\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mfn\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   2434\u001b[0m \u001b[38;5;66;03m# The code below prevents the output from being displayed\u001b[39;00m\n\u001b[1;32m   2435\u001b[0m \u001b[38;5;66;03m# when using magics with decorator @output_can_be_silenced\u001b[39;00m\n\u001b[1;32m   2436\u001b[0m \u001b[38;5;66;03m# when the last Python token in the expression is a ';'.\u001b[39;00m\n\u001b[1;32m   2437\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(fn, magic\u001b[38;5;241m.\u001b[39mMAGIC_OUTPUT_CAN_BE_SILENCED, \u001b[38;5;28;01mFalse\u001b[39;00m):\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/magics/pylab.py:99\u001b[0m, in \u001b[0;36mPylabMagics.matplotlib\u001b[0;34m(self, line)\u001b[0m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28mprint\u001b[39m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mAvailable matplotlib backends: \u001b[39m\u001b[38;5;132;01m%s\u001b[39;00m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;241m%\u001b[39m backends_list)\n\u001b[1;32m     98\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m---> 99\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mshell\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43menable_matplotlib\u001b[49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mlower\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mstr\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgui\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    100\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_show_matplotlib_backend(args\u001b[38;5;241m.\u001b[39mgui, backend)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/IPython/core/interactiveshell.py:3606\u001b[0m, in \u001b[0;36mInteractiveShell.enable_matplotlib\u001b[0;34m(self, gui)\u001b[0m\n\u001b[1;32m   3585\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21menable_matplotlib\u001b[39m(\u001b[38;5;28mself\u001b[39m, gui\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m   3586\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Enable interactive matplotlib and inline figure support.\u001b[39;00m\n\u001b[1;32m   3587\u001b[0m \n\u001b[1;32m   3588\u001b[0m \u001b[38;5;124;03m    This takes the following steps:\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m   3604\u001b[0m \u001b[38;5;124;03m        display figures inline.\u001b[39;00m\n\u001b[1;32m   3605\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m-> 3606\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib_inline\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackend_inline\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m configure_inline_support\n\u001b[1;32m   3608\u001b[0m     \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mIPython\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mcore\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m pylabtools \u001b[38;5;28;01mas\u001b[39;00m pt\n\u001b[1;32m   3609\u001b[0m     gui, backend \u001b[38;5;241m=\u001b[39m pt\u001b[38;5;241m.\u001b[39mfind_gui_and_backend(gui, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpylab_gui_select)\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/__init__.py:1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01m.\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_inline, config  \u001b[38;5;66;03m# noqa\u001b[39;00m\n\u001b[1;32m      2\u001b[0m __version__ \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m0.1.6\u001b[39m\u001b[38;5;124m\"\u001b[39m  \u001b[38;5;66;03m# noqa\u001b[39;00m\n",
+      "File \u001b[0;32m~/miniforge3/lib/python3.9/site-packages/matplotlib_inline/backend_inline.py:6\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;124;03m\"\"\"A matplotlib backend for publishing figures via display_data\"\"\"\u001b[39;00m\n\u001b[1;32m      3\u001b[0m \u001b[38;5;66;03m# Copyright (c) IPython Development Team.\u001b[39;00m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;66;03m# Distributed under the terms of the BSD 3-Clause License.\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\n\u001b[1;32m      7\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m colors\n\u001b[1;32m      8\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mbackends\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m backend_agg\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'matplotlib'"
+     ]
+    }
+   ],
+   "source": [
+    "%matplotlib inline\n",
+    "\n",
+    "import numpy as np\n",
+    "import numpy.linalg as la\n",
+    "\n",
+    "import scipy.optimize as sopt\n",
+    "\n",
+    "import matplotlib.pyplot as pt\n",
+    "from mpl_toolkits.mplot3d import axes3d\n",
+    "\n",
+    "def f(x):\n",
+    "    return x[0]**2 + 3.0*x[1]**2\n",
+    "\n",
+    "def df(x):\n",
+    "    return np.array([2*x[0], 6*x[1]])\n",
+    "\n",
+    "fig = pt.figure()\n",
+    "ax = fig.gca(projection=\"3d\")\n",
+    "\n",
+    "xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]\n",
+    "fmesh = f(np.array([xmesh, ymesh]))\n",
+    "ax.plot_surface(xmesh, ymesh, fmesh)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c01b471a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "And then as countor plot"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "5b835c85",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "pt.axis(\"equal\")\n",
+    "pt.contour(xmesh, ymesh, fmesh)\n",
+    "guesses = [np.array([2, 2./5])]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d6a3c121",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Find guesses"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "19e1d73c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "x = guesses[-1]\n",
+    "s = -df(x)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9f7b2dfc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Run it!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7d8247e6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "def f1d(alpha):\n",
+    "    return f(x + alpha*s)\n",
+    "\n",
+    "alpha_opt = sopt.golden(f1d)\n",
+    "next_guess = x + alpha_opt * s\n",
+    "guesses.append(next_guess)\n",
+    "print(next_guess)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c44006da",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "What happened?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "bb8a0fd8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "pt.axis(\"equal\")\n",
+    "pt.contour(xmesh, ymesh, fmesh, 50)\n",
+    "it_array = np.array(guesses)\n",
+    "pt.plot(it_array.T[0], it_array.T[1], \"x-\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3d3c98f0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that we did only one iteration here. We can easily add more using our previous guesses."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "29e5e792",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "In the CG method we define so-called conjugate directions and two vectors \n",
+    "$\\boldsymbol{s}$ and $\\boldsymbol{t}$\n",
+    "are said to be\n",
+    "conjugate if"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b0e0db3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "401dd643",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The philosophy of the CG method is to perform searches in various conjugate directions\n",
+    "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bc29d596",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1b7adb4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Two vectors are conjugate if they are orthogonal with respect to \n",
+    "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18924232",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "An example is given by the eigenvectors of the matrix"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1764ac31",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "379d5862",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which is zero unless $i=j$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9587d8bf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "Assume now that we have a symmetric positive-definite matrix $\\boldsymbol{A}$ of size\n",
+    "$n\\times n$. At each iteration $i+1$ we obtain the conjugate direction of a vector"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c3d0bfb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4079ca1a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n",
+    "Then the $\\boldsymbol{p}_{i}$  form a basis of $R^n$ and we can expand the solution \n",
+    "$  \\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}$ in this basis, namely"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e5b487a5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}  = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b623d7f7",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "The coefficients are given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8520c560",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "52575016",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Multiplying with $\\boldsymbol{p}_k^T$  from the left gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b8a85bd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e53b0f45",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and we can define the coefficients $\\alpha_k$ as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2238e15f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f00e8864",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method and iterations\n",
+    "\n",
+    "If we choose the conjugate vectors $\\boldsymbol{p}_k$ carefully, \n",
+    "then we may not need all of them to obtain a good approximation to the solution \n",
+    "$\\boldsymbol{x}$. \n",
+    "We want to regard the conjugate gradient method as an iterative method. \n",
+    "This will us to solve systems where $n$ is so large that the direct \n",
+    "method would take too much time.\n",
+    "\n",
+    "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n",
+    "We can assume without loss of generality that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7a17895d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{x}_0=0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d4bafcb3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or consider the system"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78a7d2c3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3192cbf",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "instead."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0d99ed55",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9653ede",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "78441105",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n",
+    "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n",
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "317355d2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9bb15157",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and \n",
+    "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n",
+    "The other vectors in the basis will be conjugate to the gradient, \n",
+    "hence the name conjugate gradient method."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ac584971",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "Let  $\\boldsymbol{r}_k$ be the residual at the $k$-th step:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "911f1dfa",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d1472568",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n",
+    "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n",
+    "so the gradient descent method would be to move in the direction $\\boldsymbol{r}_k$. \n",
+    "Here, we insist that the directions $\\boldsymbol{p}_k$ are conjugate to each other, \n",
+    "so we take the direction closest to the gradient $\\boldsymbol{r}_k$  \n",
+    "under the conjugacy constraint. \n",
+    "This gives the following expression"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c79708e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "535d3e73",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Conjugate gradient method\n",
+    "We can also  compute the residual iteratively as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad718f62",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0a90fa5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which equals"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "860e9217",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6d8a72c8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "or"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "746e6fc0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f76c0e69",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which gives"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9aee35ca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce9ce258",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Revisiting our first homework\n",
+    "\n",
+    "We will use linear regression as a case study for the gradient descent\n",
+    "methods. Linear regression is a great test case for the gradient\n",
+    "descent methods discussed in the lectures since it has several\n",
+    "desirable properties such as:\n",
+    "\n",
+    "1. An analytical solution (recall homework set 1).\n",
+    "\n",
+    "2. The gradient can be computed analytically.\n",
+    "\n",
+    "3. The cost function is convex which guarantees that gradient descent converges for small enough learning rates\n",
+    "\n",
+    "We revisit an example similar to what we had in the first homework set. We had a function  of the type"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "f902a0f2",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "x = 2*np.random.rand(m,1)\n",
+    "y = 4+3*x+np.random.randn(m,1)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "36d883b2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n",
+    "The linear regression model is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cde21ef1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f2a021d3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "such that"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea0a91e4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "854f3ebb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient descent example\n",
+    "\n",
+    "Let $\\mathbf{y} = (y_1,\\cdots,y_n)^T$, $\\mathbf{\\boldsymbol{y}} = (\\boldsymbol{y}_1,\\cdots,\\boldsymbol{y}_n)^T$ and $\\beta = (\\beta_0, \\beta_1)^T$\n",
+    "\n",
+    "It is convenient to write $\\mathbf{\\boldsymbol{y}} = X\\beta$ where $X \\in \\mathbb{R}^{100 \\times 2} $ is the design matrix given by (we keep the intercept here)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dd282d2d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "X \\equiv \\begin{bmatrix}\n",
+    "1 & x_1  \\\\\n",
+    "\\vdots & \\vdots  \\\\\n",
+    "1 & x_{100} &  \\\\\n",
+    "\\end{bmatrix}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fd562029",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "The cost/loss/risk function is given by ("
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "25369bc3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a222f3ea",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "and we want to find $\\beta$ such that $C(\\beta)$ is minimized."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1d5fb6f1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The derivative of the cost/loss function\n",
+    "\n",
+    "Computing $\\partial C(\\beta) / \\partial \\beta_0$ and $\\partial C(\\beta) / \\partial \\beta_1$ we can show  that the gradient can be written as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eab2df73",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
+    "\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T(X\\beta - \\mathbf{y}),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "daee1165",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $X$ is the design matrix defined above."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f2c6f5cc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Hessian matrix\n",
+    "The Hessian matrix of $C(\\beta)$ is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ecce0d08",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1}  \\\\\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} &  \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T X.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c4308e5f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4ee64b17",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple program\n",
+    "\n",
+    "We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "57e8db33",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c42e4032",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can use the expression we computed for the gradient and let use a\n",
+    "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n",
+    "when $||\\nabla_\\beta C(\\beta_k) || \\leq \\epsilon = 10^{-8}$. **Note that the code below does not include the latter stop criterion**.\n",
+    "\n",
+    "And finally we can compare our solution for $\\beta$ with the analytic result given by \n",
+    "$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c430cd3",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient Descent Example\n",
+    "\n",
+    "Here our simple example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9ac6096f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "\n",
+    "# Importing various packages\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from mpl_toolkits.mplot3d import Axes3D\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+    "import sys\n",
+    "\n",
+    "# the number of datapoints\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* X.T @ X\n",
+    "# Get the eigenvalues\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y\n",
+    "print(beta_linreg)\n",
+    "beta = np.random.randn(2,1)\n",
+    "\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradient = (2.0/n)*X.T @ (X @ beta-y)\n",
+    "    beta -= eta*gradient\n",
+    "\n",
+    "print(beta)\n",
+    "xnew = np.array([[0],[2]])\n",
+    "xbnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = xbnew.dot(beta)\n",
+    "ypredict2 = xbnew.dot(beta_linreg)\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Gradient descent example')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "df783e1d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And a corresponding example using **scikit-learn**"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "98f08f24",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Importing various packages\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from sklearn.linear_model import SGDRegressor\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "beta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(beta_linreg)\n",
+    "sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n",
+    "sgdreg.fit(x,y.ravel())\n",
+    "print(sgdreg.intercept_, sgdreg.coef_)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50a5ab0d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Gradient descent and Ridge\n",
+    "\n",
+    "We have also discussed Ridge regression where the loss function contains a regularized term given by the $L_2$ norm of $\\beta$,"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b35293d4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fed491ee",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we adjust the gradient as follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a0b4c94e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_\\beta C_{\\text{ridge}}(\\beta)  = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n",
+    "\\sum_{i=1}^{100}\\left( x_i (\\beta_0+\\beta_1x_i)-y_ix_i\\right) \\\\\n",
+    "\\end{bmatrix} + 2\\lambda\\begin{bmatrix} \\beta_0 \\\\ \\beta_1\\end{bmatrix} = 2 (\\frac{1}{n}X^T(X\\beta - \\mathbf{y})+\\lambda \\beta).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4f02dce",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9f297ff",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{\\text{ridge}} = \\left(X^T X + n\\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4e1caf44",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The Hessian matrix for Ridge Regression\n",
+    "The Hessian matrix of Ridge Regression for our simple example  is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a046daea",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0^2} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1}  \\\\\n",
+    "\\frac{\\partial^2 C(\\beta)}{\\partial \\beta_0 \\partial \\beta_1} & \\frac{\\partial^2 C(\\beta)}{\\partial \\beta_1^2} &  \\\\\n",
+    "\\end{bmatrix} = \\frac{2}{n}X^T X+2\\lambda\\boldsymbol{I}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "02f05574",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "This implies that the Hessian matrix  is positive definite, hence the stationary point is a\n",
+    "minimum.\n",
+    "Note that the Ridge cost function is convex being  a sum of two convex\n",
+    "functions. Therefore, the stationary point is a global\n",
+    "minimum of this function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "45484749",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Program example for gradient descent with Ridge Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "9973cd20",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from mpl_toolkits.mplot3d import Axes3D\n",
+    "from matplotlib import cm\n",
+    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
+    "import sys\n",
+    "\n",
+    "# the number of datapoints\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "\n",
+    "#Ridge parameter lambda\n",
+    "lmbda  = 0.001\n",
+    "Id = n*lmbda* np.eye(XT_X.shape[0])\n",
+    "\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X+2*lmbda* np.eye(XT_X.shape[0])\n",
+    "# Get the eigenvalues\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "\n",
+    "beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y\n",
+    "print(beta_linreg)\n",
+    "# Start plain gradient descent\n",
+    "beta = np.random.randn(2,1)\n",
+    "\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ (X @ (beta)-y)+2*lmbda*beta\n",
+    "    beta -= eta*gradients\n",
+    "\n",
+    "print(beta)\n",
+    "ypredict = X @ beta\n",
+    "ypredict2 = X @ beta_linreg\n",
+    "plt.plot(x, ypredict, \"r-\")\n",
+    "plt.plot(x, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Gradient descent example for Ridge')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1836d4ef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using gradient descent methods, limitations\n",
+    "\n",
+    "* **Gradient descent (GD) finds local minima of our function**. Since the GD algorithm is deterministic, if it converges, it will converge to a local minimum of our cost/loss/risk function. Because in ML we are often dealing with extremely rugged landscapes with many local minima, this can lead to poor performance.\n",
+    "\n",
+    "* **GD is sensitive to initial conditions**. One consequence of the local nature of GD is that initial conditions matter. Depending on where one starts, one will end up at a different local minima. Therefore, it is very important to think about how one initializes the training process. This is true for GD as well as more complicated variants of GD.\n",
+    "\n",
+    "* **Gradients are computationally expensive to calculate for large datasets**. In many cases in statistics and ML, the cost/loss/risk function is a sum of terms, with one term for each data point. For example, in linear regression, $E \\propto \\sum_{i=1}^n (y_i - \\mathbf{w}^T\\cdot\\mathbf{x}_i)^2$; for logistic regression, the square error is replaced by the cross entropy. To calculate the gradient we have to sum over *all* $n$ data points. Doing this at every GD step becomes extremely computationally expensive. An ingenious solution to this, is to calculate the gradients using small subsets of the data called \"mini batches\". This has the added benefit of introducing stochasticity into our algorithm.\n",
+    "\n",
+    "* **GD is very sensitive to choices of learning rates**. GD is extremely sensitive to the choice of learning rates. If the learning rate is very small, the training process take an extremely long time. For larger learning rates, GD can diverge and give poor results. Furthermore, depending on what the local landscape looks like, we have to modify the learning rates to ensure convergence. Ideally, we would *adaptively* choose the learning rates to match the landscape.\n",
+    "\n",
+    "* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n",
+    "\n",
+    "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "88975d3d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Improving gradient descent with momentum\n",
+    "\n",
+    "We discuss here some simple examples where we introduce what is called 'memory'about previous steps, or what is normally called momentum gradient descent. The mathematics is explained below in connection with Stochastic gradient descent."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "56f415e0",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from numpy import asarray\n",
+    "from numpy import arange\n",
+    "from numpy.random import rand\n",
+    "from numpy.random import seed\n",
+    "from matplotlib import pyplot\n",
+    " \n",
+    "# objective function\n",
+    "def objective(x):\n",
+    "\treturn x**2.0\n",
+    " \n",
+    "# derivative of objective function\n",
+    "def derivative(x):\n",
+    "\treturn x * 2.0\n",
+    " \n",
+    "# gradient descent algorithm\n",
+    "def gradient_descent(objective, derivative, bounds, n_iter, step_size):\n",
+    "\t# track all solutions\n",
+    "\tsolutions, scores = list(), list()\n",
+    "\t# generate an initial point\n",
+    "\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
+    "\t# run the gradient descent\n",
+    "\tfor i in range(n_iter):\n",
+    "\t\t# calculate gradient\n",
+    "\t\tgradient = derivative(solution)\n",
+    "\t\t# take a step\n",
+    "\t\tsolution = solution - step_size * gradient\n",
+    "\t\t# evaluate candidate point\n",
+    "\t\tsolution_eval = objective(solution)\n",
+    "\t\t# store solution\n",
+    "\t\tsolutions.append(solution)\n",
+    "\t\tscores.append(solution_eval)\n",
+    "\t\t# report progress\n",
+    "\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
+    "\treturn [solutions, scores]\n",
+    " \n",
+    "# seed the pseudo random number generator\n",
+    "seed(4)\n",
+    "# define range for input\n",
+    "bounds = asarray([[-1.0, 1.0]])\n",
+    "# define the total iterations\n",
+    "n_iter = 30\n",
+    "# define the step size\n",
+    "step_size = 0.1\n",
+    "# perform the gradient descent search\n",
+    "solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size)\n",
+    "# sample input range uniformly at 0.1 increments\n",
+    "inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
+    "# compute targets\n",
+    "results = objective(inputs)\n",
+    "# create a line plot of input vs result\n",
+    "pyplot.plot(inputs, results)\n",
+    "# plot the solutions found\n",
+    "pyplot.plot(solutions, scores, '.-', color='red')\n",
+    "# show the plot\n",
+    "pyplot.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3343584",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "ff1e3778",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "from numpy import asarray\n",
+    "from numpy import arange\n",
+    "from numpy.random import rand\n",
+    "from numpy.random import seed\n",
+    "from matplotlib import pyplot\n",
+    " \n",
+    "# objective function\n",
+    "def objective(x):\n",
+    "\treturn x**2.0\n",
+    " \n",
+    "# derivative of objective function\n",
+    "def derivative(x):\n",
+    "\treturn x * 2.0\n",
+    " \n",
+    "# gradient descent algorithm\n",
+    "def gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum):\n",
+    "\t# track all solutions\n",
+    "\tsolutions, scores = list(), list()\n",
+    "\t# generate an initial point\n",
+    "\tsolution = bounds[:, 0] + rand(len(bounds)) * (bounds[:, 1] - bounds[:, 0])\n",
+    "\t# keep track of the change\n",
+    "\tchange = 0.0\n",
+    "\t# run the gradient descent\n",
+    "\tfor i in range(n_iter):\n",
+    "\t\t# calculate gradient\n",
+    "\t\tgradient = derivative(solution)\n",
+    "\t\t# calculate update\n",
+    "\t\tnew_change = step_size * gradient + momentum * change\n",
+    "\t\t# take a step\n",
+    "\t\tsolution = solution - new_change\n",
+    "\t\t# save the change\n",
+    "\t\tchange = new_change\n",
+    "\t\t# evaluate candidate point\n",
+    "\t\tsolution_eval = objective(solution)\n",
+    "\t\t# store solution\n",
+    "\t\tsolutions.append(solution)\n",
+    "\t\tscores.append(solution_eval)\n",
+    "\t\t# report progress\n",
+    "\t\tprint('>%d f(%s) = %.5f' % (i, solution, solution_eval))\n",
+    "\treturn [solutions, scores]\n",
+    " \n",
+    "# seed the pseudo random number generator\n",
+    "seed(4)\n",
+    "# define range for input\n",
+    "bounds = asarray([[-1.0, 1.0]])\n",
+    "# define the total iterations\n",
+    "n_iter = 30\n",
+    "# define the step size\n",
+    "step_size = 0.1\n",
+    "# define momentum\n",
+    "momentum = 0.3\n",
+    "# perform the gradient descent search with momentum\n",
+    "solutions, scores = gradient_descent(objective, derivative, bounds, n_iter, step_size, momentum)\n",
+    "# sample input range uniformly at 0.1 increments\n",
+    "inputs = arange(bounds[0,0], bounds[0,1]+0.1, 0.1)\n",
+    "# compute targets\n",
+    "results = objective(inputs)\n",
+    "# create a line plot of input vs result\n",
+    "pyplot.plot(inputs, results)\n",
+    "# plot the solutions found\n",
+    "pyplot.plot(solutions, scores, '.-', color='red')\n",
+    "# show the plot\n",
+    "pyplot.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c1d70995",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Overview video on Stochastic Gradient Descent\n",
+    "\n",
+    "[What is Stochastic Gradient Descent](https://www.youtube.com/watch?v=vMh0zPT0tLI&ab_channel=StatQuestwithJoshStarmer)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "930a5be8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Batches and mini-batches\n",
+    "\n",
+    "In gradient descent we compute the cost function and its gradient for all data points we have.\n",
+    "\n",
+    "In large-scale applications such as the [ILSVRC challenge](https://www.image-net.org/challenges/LSVRC/), the\n",
+    "training data can have on order of millions of examples. Hence, it\n",
+    "seems wasteful to compute the full cost function over the entire\n",
+    "training set in order to perform only a single parameter update. A\n",
+    "very common approach to addressing this challenge is to compute the\n",
+    "gradient over batches of the training data. For example, a typical batch could contain some thousand  examples from\n",
+    "an  entire training set of several millions. This batch is then used to\n",
+    "perform a parameter update."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0a7fb7ef",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Stochastic Gradient Descent (SGD)\n",
+    "\n",
+    "In stochastic gradient descent, the extreme case is the case where we\n",
+    "have only one batch, that is we include the whole data set.\n",
+    "\n",
+    "This process is called Stochastic Gradient\n",
+    "Descent (SGD) (or also sometimes on-line gradient descent). This is\n",
+    "relatively less common to see because in practice due to vectorized\n",
+    "code optimizations it can be computationally much more efficient to\n",
+    "evaluate the gradient for 100 examples, than the gradient for one\n",
+    "example 100 times. Even though SGD technically refers to using a\n",
+    "single example at a time to evaluate the gradient, you will hear\n",
+    "people use the term SGD even when referring to mini-batch gradient\n",
+    "descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD\n",
+    "for “Batch gradient descent” are rare to see), where it is usually\n",
+    "assumed that mini-batches are used. The size of the mini-batch is a\n",
+    "hyperparameter but it is not very common to cross-validate or bootstrap it. It is\n",
+    "usually based on memory constraints (if any), or set to some value,\n",
+    "e.g. 32, 64 or 128. We use powers of 2 in practice because many\n",
+    "vectorized operation implementations work faster when their inputs are\n",
+    "sized in powers of 2.\n",
+    "\n",
+    "In our notes with  SGD we mean stochastic gradient descent with mini-batches."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dbff87b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Stochastic Gradient Descent\n",
+    "\n",
+    "Stochastic gradient descent (SGD) and variants thereof address some of\n",
+    "the shortcomings of the Gradient descent method discussed above.\n",
+    "\n",
+    "The underlying idea of SGD comes from the observation that the cost\n",
+    "function, which we want to minimize, can almost always be written as a\n",
+    "sum over $n$ data points $\\{\\mathbf{x}_i\\}_{i=1}^n$,"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd292df5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b2ffa4e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Computation of gradients\n",
+    "\n",
+    "This in turn means that the gradient can be\n",
+    "computed as a sum over $i$-gradients"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d0abe4b0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "65c15c60",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Stochasticity/randomness is introduced by only taking the\n",
+    "gradient on a subset of the data called minibatches.  If there are $n$\n",
+    "data points and the size of each minibatch is $M$, there will be $n/M$\n",
+    "minibatches. We denote these minibatches by $B_k$ where\n",
+    "$k=1,\\cdots,n/M$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "460354c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## SGD example\n",
+    "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n",
+    "and we choose to have $M=5$ minibathces,\n",
+    "then each minibatch contains two data points. In particular we have\n",
+    "$B_1 = (\\mathbf{x}_1,\\mathbf{x}_2), \\cdots, B_5 =\n",
+    "(\\mathbf{x}_9,\\mathbf{x}_{10})$. Note that if you choose $M=1$ you\n",
+    "have only a single batch with all data points and on the other extreme,\n",
+    "you may choose $M=n$ resulting in a minibatch for each datapoint, i.e\n",
+    "$B_k = \\mathbf{x}_k$.\n",
+    "\n",
+    "The idea is now to approximate the gradient by replacing the sum over\n",
+    "all data points with a sum over the data points in one the minibatches\n",
+    "picked at random in each gradient descent step"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c2a5dfcd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\nabla_{\\beta}\n",
+    "C(\\mathbf{\\beta}) = \\sum_{i=1}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta}) \\rightarrow \\sum_{i \\in B_k}^n \\nabla_\\beta\n",
+    "c_i(\\mathbf{x}_i, \\mathbf{\\beta}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "eeeb0fe8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The gradient step\n",
+    "\n",
+    "Thus a gradient descent step now looks like"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b49c741",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n",
+    "\\mathbf{\\beta})\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8ba7b9be",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $k$ is picked at random with equal\n",
+    "probability from $[1,n/M]$. An iteration over the number of\n",
+    "minibathces (n/M) is commonly referred to as an epoch. Thus it is\n",
+    "typical to choose a number of epochs and for each epoch iterate over\n",
+    "the number of minibatches, as exemplified in the code below."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "50da33c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Simple example code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "31bd6a24",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "\n",
+    "n = 100 #100 datapoints \n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "n_epochs = 10 #number of epochs\n",
+    "\n",
+    "j = 0\n",
+    "for epoch in range(1,n_epochs+1):\n",
+    "    for i in range(m):\n",
+    "        k = np.random.randint(m) #Pick the k-th minibatch at random\n",
+    "        #Compute the gradient using the data in minibatch Bk\n",
+    "        #Compute new suggestion for \n",
+    "        j += 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0deb8111",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Taking the gradient only on a subset of the data has two important\n",
+    "benefits. First, it introduces randomness which decreases the chance\n",
+    "that our opmization scheme gets stuck in a local minima. Second, if\n",
+    "the size of the minibatches are small relative to the number of\n",
+    "datapoints ($M <  n$), the computation of the gradient is much\n",
+    "cheaper since we sum over the datapoints in the $k-th$ minibatch and not\n",
+    "all $n$ datapoints."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16d54f02",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## When do we stop?\n",
+    "\n",
+    "A natural question is when do we stop the search for a new minimum?\n",
+    "One possibility is to compute the full gradient after a given number\n",
+    "of epochs and check if the norm of the gradient is smaller than some\n",
+    "threshold and stop if true. However, the condition that the gradient\n",
+    "is zero is valid also for local minima, so this would only tell us\n",
+    "that we are close to a local/global minimum. However, we could also\n",
+    "evaluate the cost function at this point, store the result and\n",
+    "continue the search. If the test kicks in at a later stage we can\n",
+    "compare the values of the cost function and keep the $\\beta$ that\n",
+    "gave the lowest value."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b300d06b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Slightly different approach\n",
+    "\n",
+    "Another approach is to let the step length $\\gamma_j$ depend on the\n",
+    "number of epochs in such a way that it becomes very small after a\n",
+    "reasonable time such that we do not move at all. Such approaches are\n",
+    "also called scaling. There are many such ways to [scale the learning\n",
+    "rate](https://towardsdatascience.com/gradient-descent-the-learning-rate-and-the-importance-of-feature-scaling-6c0b416596e1)\n",
+    "and [discussions here](https://www.jmlr.org/papers/volume23/20-1258/20-1258.pdf). See\n",
+    "also\n",
+    "<https://towardsdatascience.com/learning-rate-schedules-and-adaptive-learning-rate-methods-for-deep-learning-2c8f433990d1>\n",
+    "for a discussion of different scaling functions for the learning rate."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bc7778d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Time decay rate\n",
+    "\n",
+    "As an example, let $e = 0,1,2,3,\\cdots$ denote the current epoch and let $t_0, t_1 > 0$ be two fixed numbers. Furthermore, let $t = e \\cdot m + i$ where $m$ is the number of minibatches and $i=0,\\cdots,m-1$. Then the function $$\\gamma_j(t; t_0, t_1) = \\frac{t_0}{t+t_1} $$ goes to zero as the number of epochs gets large. I.e. we start with a step length $\\gamma_j (0; t_0, t_1) = t_0/t_1$ which decays in *time* $t$.\n",
+    "\n",
+    "In this way we can fix the number of epochs, compute $\\beta$ and\n",
+    "evaluate the cost function at the end. Repeating the computation will\n",
+    "give a different result since the scheme is random by design. Then we\n",
+    "pick the final $\\beta$ that gives the lowest value of the cost\n",
+    "function."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "a60fe5bd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "\n",
+    "def step_length(t,t0,t1):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "n = 100 #100 datapoints \n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "n_epochs = 500 #number of epochs\n",
+    "t0 = 1.0\n",
+    "t1 = 10\n",
+    "\n",
+    "gamma_j = t0/t1\n",
+    "j = 0\n",
+    "for epoch in range(1,n_epochs+1):\n",
+    "    for i in range(m):\n",
+    "        k = np.random.randint(m) #Pick the k-th minibatch at random\n",
+    "        #Compute the gradient using the data in minibatch Bk\n",
+    "        #Compute new suggestion for beta\n",
+    "        t = epoch*m+i\n",
+    "        gamma_j = step_length(t,t0,t1)\n",
+    "        j += 1\n",
+    "\n",
+    "print(\"gamma_j after %d epochs: %g\" % (n_epochs,gamma_j))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2192721f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Code with a Number of Minibatches which varies\n",
+    "\n",
+    "In the code here we vary the number of mini-batches."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "e404f2c5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Importing various packages\n",
+    "from math import exp, sqrt\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = 2.0/n*X.T @ ((X @ theta)-y)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fffdbb91",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Replace or not\n",
+    "\n",
+    "In the above code, we have use replacement in setting up the\n",
+    "mini-batches. The discussion\n",
+    "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n",
+    "useful."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cce7a0e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Momentum based GD\n",
+    "\n",
+    "The stochastic gradient descent (SGD) is almost always used with a\n",
+    "*momentum* or inertia term that serves as a memory of the direction we\n",
+    "are moving in parameter space.  This is typically implemented as\n",
+    "follows"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3154c365",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a2a9ceca",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto1\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t},\n",
+    "\\label{_auto1} \\tag{2}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3374c700",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have introduced a momentum parameter $\\gamma$, with\n",
+    "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n",
+    "indicate the gradient is to be taken over a different mini-batch at\n",
+    "each step. We call this algorithm gradient descent with momentum\n",
+    "(GDM). From these equations, it is clear that $\\mathbf{v}_t$ is a\n",
+    "running average of recently encountered gradients and\n",
+    "$(1-\\gamma)^{-1}$ sets the characteristic time scale for the memory\n",
+    "used in the averaging procedure. Consistent with this, when\n",
+    "$\\gamma=0$, this just reduces down to ordinary SGD as discussed\n",
+    "earlier. An equivalent way of writing the updates is"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "893d86fe",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca2449e8",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3cbd4adb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More on momentum based approaches\n",
+    "\n",
+    "Let us try to get more intuition from these equations. It is helpful\n",
+    "to consider a simple physical analogy with a particle of mass $m$\n",
+    "moving in a viscous medium with drag coefficient $\\mu$ and potential\n",
+    "$E(\\mathbf{w})$. If we denote the particle's position by $\\mathbf{w}$,\n",
+    "then its motion is described by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e3f07cbc",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "99f2ac0f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "We can discretize this equation in the usual way to get"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "83336244",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "efd3e708",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Rearranging this equation, we can rewrite this as"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c24d65c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "853d885b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Momentum parameter\n",
+    "\n",
+    "Notice that this equation is identical to previous one if we identify\n",
+    "the position of the particle, $\\mathbf{w}$, with the parameters\n",
+    "$\\boldsymbol{\\theta}$. This allows us to identify the momentum\n",
+    "parameter and learning rate with the mass of the particle and the\n",
+    "viscous drag as:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ab54645",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "90f1503b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Thus, as the name suggests, the momentum parameter is proportional to\n",
+    "the mass of the particle and effectively provides inertia.\n",
+    "Furthermore, in the large viscosity/small learning rate limit, our\n",
+    "memory time scales as $(1-\\gamma)^{-1} \\approx m/(\\mu \\Delta t)$.\n",
+    "\n",
+    "Why is momentum useful? SGD momentum helps the gradient descent\n",
+    "algorithm gain speed in directions with persistent but small gradients\n",
+    "even in the presence of stochasticity, while suppressing oscillations\n",
+    "in high-curvature directions. This becomes especially important in\n",
+    "situations where the landscape is shallow and flat in some directions\n",
+    "and narrow and steep in others. It has been argued that first-order\n",
+    "methods (with appropriate initial conditions) can perform comparable\n",
+    "to more expensive second order methods, especially in the context of\n",
+    "complex deep learning models.\n",
+    "\n",
+    "These beneficial properties of momentum can sometimes become even more\n",
+    "pronounced by using a slight modification of the classical momentum\n",
+    "algorithm called Nesterov Accelerated Gradient (NAG).\n",
+    "\n",
+    "In the NAG algorithm, rather than calculating the gradient at the\n",
+    "current parameters, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t)$, one\n",
+    "calculates the gradient at the expected value of the parameters given\n",
+    "our current momentum, $\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma\n",
+    "\\mathbf{v}_{t-1})$. This yields the NAG update rule"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d496d988",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "258ca1e6",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto2\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\boldsymbol{\\theta}_{t+1}= \\boldsymbol{\\theta}_t -\\mathbf{v}_{t}.\n",
+    "\\label{_auto2} \\tag{3}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84278058",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "feaee2f4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Second moment of the gradient\n",
+    "\n",
+    "In stochastic gradient descent, with and without momentum, we still\n",
+    "have to specify a schedule for tuning the learning rates $\\eta_t$\n",
+    "as a function of time.  As discussed in the context of Newton's\n",
+    "method, this presents a number of dilemmas. The learning rate is\n",
+    "limited by the steepest direction which can change depending on the\n",
+    "current position in the landscape. To circumvent this problem, ideally\n",
+    "our algorithm would keep track of curvature and take large steps in\n",
+    "shallow, flat directions and small steps in steep, narrow directions.\n",
+    "Second-order methods accomplish this by calculating or approximating\n",
+    "the Hessian and normalizing the learning rate by the\n",
+    "curvature. However, this is very computationally expensive for\n",
+    "extremely large models. Ideally, we would like to be able to\n",
+    "adaptively change the step size to match the landscape without paying\n",
+    "the steep computational price of calculating or approximating\n",
+    "Hessians.\n",
+    "\n",
+    "Recently, a number of methods have been introduced that accomplish\n",
+    "this by tracking not only the gradient, but also the second moment of\n",
+    "the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and\n",
+    "[ADAM](https://arxiv.org/abs/1412.6980)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "218edcf1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMS prop\n",
+    "\n",
+    "In RMS prop, in addition to keeping a running average of the first\n",
+    "moment of the gradient, we also keep track of the second moment\n",
+    "denoted by $\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}_t^2]$. The update rule\n",
+    "for RMS prop is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "18dbc91c",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto3\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto3} \\tag{4}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0bfcf74a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5fedd6f0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b210b2a4",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\beta$ controls the averaging time of the second moment and is\n",
+    "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n",
+    "typically chosen to be $10^{-3}$, and $\\epsilon\\sim 10^{-8} $ is a\n",
+    "small regularization constant to prevent divergences. Multiplication\n",
+    "and division by vectors is understood as an element-wise operation. It\n",
+    "is clear from this formula that the learning rate is reduced in\n",
+    "directions where the norm of the gradient is consistently large. This\n",
+    "greatly speeds up the convergence by allowing us to use a larger\n",
+    "learning rate for flat directions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "34ffacbb",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## [ADAM optimizer](https://arxiv.org/abs/1412.6980)\n",
+    "\n",
+    "A related algorithm is the ADAM optimizer. In\n",
+    "[ADAM](https://arxiv.org/abs/1412.6980), we keep a running average of\n",
+    "both the first and second moment of the gradient and use this\n",
+    "information to adaptively change the learning rate for different\n",
+    "parameters.  The method isefficient when working with large\n",
+    "problems involving lots data and/or parameters.  It is a combination of the\n",
+    "gradient descent with momentum algorithm and the RMSprop algorithm\n",
+    "discussed above.\n",
+    "\n",
+    "In addition to keeping a running average of the first and\n",
+    "second moments of the gradient\n",
+    "(i.e. $\\mathbf{m}_t=\\mathbb{E}[\\mathbf{g}_t]$ and\n",
+    "$\\mathbf{s}_t=\\mathbb{E}[\\mathbf{g}^2_t]$, respectively), ADAM\n",
+    "performs an additional bias correction to account for the fact that we\n",
+    "are estimating the first two moments of the gradient using a running\n",
+    "average (denoted by the hats in the update rule below). The update\n",
+    "rule for ADAM is given by (where multiplication and division are once\n",
+    "again understood to be element-wise operations below)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cd03375d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto4\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation}\n",
+    "\\mathbf{g}_t = \\nabla_\\theta E(\\boldsymbol{\\theta}) \n",
+    "\\label{_auto4} \\tag{5}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0db5d6e0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "84c709d9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e4e47496",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "164f27df",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "591f4833",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e2127e8a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "<!-- Equation labels as ordinary links -->\n",
+    "<div id=\"_auto5\"></div>\n",
+    "\n",
+    "$$\n",
+    "\\begin{equation} \n",
+    "\\label{_auto5} \\tag{6}\n",
+    "\\end{equation}\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5cef8b84",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n",
+    "second moment and are typically taken to be $0.9$ and $0.99$\n",
+    "respectively, and $\\eta$ and $\\epsilon$ are identical to RMSprop.\n",
+    "\n",
+    "Like in RMSprop, the effective step size of a parameter depends on the\n",
+    "magnitude of its gradient squared.  To understand this better, let us\n",
+    "rewrite this expression in terms of the variance\n",
+    "$\\boldsymbol{\\sigma}_t^2 = \\boldsymbol{\\mathbf{s}}_t -\n",
+    "(\\boldsymbol{\\mathbf{m}}_t)^2$. Consider a single parameter $\\theta_t$. The\n",
+    "update rule for this parameter is given by"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "505c8905",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 +  m_t^2 }+\\epsilon}.\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ca96ddec",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Algorithms and codes for Adagrad, RMSprop and Adam\n",
+    "\n",
+    "The algorithms we have implemented are well described in the text by [Goodfellow, Bengio and Courville, chapter 8](https://www.deeplearningbook.org/contents/optimization.html).\n",
+    "\n",
+    "The codes which implement these algorithms are discussed after our presentation of automatic differentiation."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fa011176",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Practical tips\n",
+    "\n",
+    "* **Randomize the data when making mini-batches**. It is always important to randomly shuffle the data when forming mini-batches. Otherwise, the gradient descent method can fit spurious correlations resulting from the order in which data is presented.\n",
+    "\n",
+    "* **Transform your inputs**. Learning becomes difficult when our landscape has a mixture of steep and flat directions. One simple trick for minimizing these situations is to standardize the data by subtracting the mean and normalizing the variance of input variables. Whenever possible, also decorrelate the inputs. To understand why this is helpful, consider the case of linear regression. It is easy to show that for the squared error cost function, the Hessian of the cost function is just the correlation matrix between the inputs. Thus, by standardizing the inputs, we are ensuring that the landscape looks homogeneous in all directions in parameter space. Since most deep networks can be viewed as linear transformations followed by a non-linearity at each layer, we expect this intuition to hold beyond the linear case.\n",
+    "\n",
+    "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n",
+    "\n",
+    "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n",
+    "\n",
+    "Geron's text, see chapter 11, has several interesting discussions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b91c4543",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Automatic differentiation\n",
+    "\n",
+    "[Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), \n",
+    "also called algorithmic\n",
+    "differentiation or computational differentiation,is a set of\n",
+    "techniques to numerically evaluate the derivative of a function\n",
+    "specified by a computer program. AD exploits the fact that every\n",
+    "computer program, no matter how complicated, executes a sequence of\n",
+    "elementary arithmetic operations (addition, subtraction,\n",
+    "multiplication, division, etc.) and elementary functions (exp, log,\n",
+    "sin, cos, etc.). By applying the chain rule repeatedly to these\n",
+    "operations, derivatives of arbitrary order can be computed\n",
+    "automatically, accurately to working precision, and using at most a\n",
+    "small constant factor more arithmetic operations than the original\n",
+    "program.\n",
+    "\n",
+    "Automatic differentiation is neither:\n",
+    "\n",
+    "* Symbolic differentiation, nor\n",
+    "\n",
+    "* Numerical differentiation (the method of finite differences).\n",
+    "\n",
+    "Symbolic differentiation can lead to inefficient code and faces the\n",
+    "difficulty of converting a computer program into a single expression,\n",
+    "while numerical differentiation can introduce round-off errors in the\n",
+    "discretization process and cancellation\n",
+    "\n",
+    "Python has tools for so-called **automatic differentiation**.\n",
+    "Consider the following example"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f13065e5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22937f5e",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "which has the following derivative"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e1459fe1",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "$$\n",
+    "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n",
+    "$$"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "441a109a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Using **autograd** we have"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "9043abae",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "\n",
+    "# To do elementwise differentiation:\n",
+    "from autograd import elementwise_grad as egrad \n",
+    "\n",
+    "# To plot:\n",
+    "import matplotlib.pyplot as plt \n",
+    "\n",
+    "\n",
+    "def f(x):\n",
+    "    return np.sin(2*np.pi*x + x**2)\n",
+    "\n",
+    "def f_grad_analytic(x):\n",
+    "    return np.cos(2*np.pi*x + x**2)*(2*np.pi + 2*x)\n",
+    "\n",
+    "# Do the comparison:\n",
+    "x = np.linspace(0,1,1000)\n",
+    "\n",
+    "f_grad = egrad(f)\n",
+    "\n",
+    "computed = f_grad(x)\n",
+    "analytic = f_grad_analytic(x)\n",
+    "\n",
+    "plt.title('Derivative computed from Autograd compared with the analytical derivative')\n",
+    "plt.plot(x,computed,label='autograd')\n",
+    "plt.plot(x,analytic,label='analytic')\n",
+    "\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel('y')\n",
+    "plt.legend()\n",
+    "\n",
+    "plt.show()\n",
+    "\n",
+    "print(\"The max absolute difference is: %g\"%(np.max(np.abs(computed - analytic))))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "787d5d78",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using autograd\n",
+    "\n",
+    "Here we\n",
+    "experiment with what kind of functions Autograd is capable\n",
+    "of finding the gradient of. The following Python functions are just\n",
+    "meant to illustrate what Autograd can do, but please feel free to\n",
+    "experiment with other, possibly more complicated, functions as well."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "6a677479",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def f1(x):\n",
+    "    return x**3 + 1\n",
+    "\n",
+    "f1_grad = grad(f1)\n",
+    "\n",
+    "# Remember to send in float as argument to the computed gradient from Autograd!\n",
+    "a = 1.0\n",
+    "\n",
+    "# See the evaluated gradient at a using autograd:\n",
+    "print(\"The gradient of f1 evaluated at a = %g using autograd is: %g\"%(a,f1_grad(a)))\n",
+    "\n",
+    "# Compare with the analytical derivative, that is f1'(x) = 3*x**2 \n",
+    "grad_analytical = 3*a**2\n",
+    "print(\"The gradient of f1 evaluated at a = %g by finding the analytic expression is: %g\"%(a,grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f94a1d32",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Autograd with more complicated functions\n",
+    "\n",
+    "To differentiate with respect to two (or more) arguments of a Python\n",
+    "function, Autograd need to know at which variable the function if\n",
+    "being differentiated with respect to."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "c0eb89fd",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f2(x1,x2):\n",
+    "    return 3*x1**3 + x2*(x1 - 5) + 1\n",
+    "\n",
+    "# By sending the argument 0, Autograd will compute the derivative w.r.t the first variable, in this case x1\n",
+    "f2_grad_x1 = grad(f2,0)\n",
+    "\n",
+    "# ... and differentiate w.r.t x2 by sending 1 as an additional arugment to grad\n",
+    "f2_grad_x2 = grad(f2,1)\n",
+    "\n",
+    "x1 = 1.0\n",
+    "x2 = 3.0 \n",
+    "\n",
+    "print(\"Evaluating at x1 = %g, x2 = %g\"%(x1,x2))\n",
+    "print(\"-\"*30)\n",
+    "\n",
+    "# Compare with the analytical derivatives:\n",
+    "\n",
+    "# Derivative of f2 w.r.t x1 is: 9*x1**2 + x2:\n",
+    "f2_grad_x1_analytical = 9*x1**2 + x2\n",
+    "\n",
+    "# Derivative of f2 w.r.t x2 is: x1 - 5:\n",
+    "f2_grad_x2_analytical = x1 - 5\n",
+    "\n",
+    "# See the evaluated derivations:\n",
+    "print(\"The derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
+    "print(\"The analytical derivative of f2 w.r.t x1: %g\"%( f2_grad_x1(x1,x2) ))\n",
+    "\n",
+    "print()\n",
+    "\n",
+    "print(\"The derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))\n",
+    "print(\"The analytical derivative of f2 w.r.t x2: %g\"%( f2_grad_x2(x1,x2) ))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "05d7497d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24e3ca02",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More complicated functions using the elements of their arguments directly"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "a616e696",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f3(x): # Assumes x is an array of length 5 or higher\n",
+    "    return 2*x[0] + 3*x[1] + 5*x[2] + 7*x[3] + 11*x[4]**2\n",
+    "\n",
+    "f3_grad = grad(f3)\n",
+    "\n",
+    "x = np.linspace(0,4,5)\n",
+    "\n",
+    "# Print the computed gradient:\n",
+    "print(\"The computed gradient of f3 is: \", f3_grad(x))\n",
+    "\n",
+    "# The analytical gradient is: (2, 3, 5, 7, 22*x[4])\n",
+    "f3_grad_analytical = np.array([2, 3, 5, 7, 22*x[4]])\n",
+    "\n",
+    "# Print the analytical gradient:\n",
+    "print(\"The analytical gradient of f3 is: \", f3_grad_analytical)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f695da56",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that in this case, when sending an array as input argument, the\n",
+    "output from Autograd is another array. This is the true gradient of\n",
+    "the function, as opposed to the function in the previous example. By\n",
+    "using arrays to represent the variables, the output from Autograd\n",
+    "might be easier to work with, as the output is closer to what one\n",
+    "could expect form a gradient-evaluting function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5ac073ee",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Functions using mathematical functions from Numpy"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "efc8906e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f4(x):\n",
+    "    return np.sqrt(1+x**2) + np.exp(x) + np.sin(2*np.pi*x)\n",
+    "\n",
+    "f4_grad = grad(f4)\n",
+    "\n",
+    "x = 2.7\n",
+    "\n",
+    "# Print the computed derivative:\n",
+    "print(\"The computed derivative of f4 at x = %g is: %g\"%(x,f4_grad(x)))\n",
+    "\n",
+    "# The analytical derivative is: x/sqrt(1 + x**2) + exp(x) + cos(2*pi*x)*2*pi\n",
+    "f4_grad_analytical = x/np.sqrt(1 + x**2) + np.exp(x) + np.cos(2*np.pi*x)*2*np.pi\n",
+    "\n",
+    "# Print the analytical gradient:\n",
+    "print(\"The analytical gradient of f4 at x = %g is: %g\"%(x,f4_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7c587e8f",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## More autograd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "6428be1f",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f5(x):\n",
+    "    if x >= 0:\n",
+    "        return x**2\n",
+    "    else:\n",
+    "        return -3*x + 1\n",
+    "\n",
+    "f5_grad = grad(f5)\n",
+    "\n",
+    "x = 2.7\n",
+    "\n",
+    "# Print the computed derivative:\n",
+    "print(\"The computed derivative of f5 at x = %g is: %g\"%(x,f5_grad(x)))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8e1de777",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And  with loops"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "770ff6aa",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f6_for(x):\n",
+    "    val = 0\n",
+    "    for i in range(10):\n",
+    "        val = val + x**i\n",
+    "    return val\n",
+    "\n",
+    "def f6_while(x):\n",
+    "    val = 0\n",
+    "    i = 0\n",
+    "    while i < 10:\n",
+    "        val = val + x**i\n",
+    "        i = i + 1\n",
+    "    return val\n",
+    "\n",
+    "f6_for_grad = grad(f6_for)\n",
+    "f6_while_grad = grad(f6_while)\n",
+    "\n",
+    "x = 0.5\n",
+    "\n",
+    "# Print the computed derivaties of f6_for and f6_while\n",
+    "print(\"The computed derivative of f6_for at x = %g is: %g\"%(x,f6_for_grad(x)))\n",
+    "print(\"The computed derivative of f6_while at x = %g is: %g\"%(x,f6_while_grad(x)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "b924cc5d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "# Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9\n",
+    "# The analytical derivative is: sum(i*x**(i-1)) \n",
+    "f6_grad_analytical = 0\n",
+    "for i in range(10):\n",
+    "    f6_grad_analytical += i*x**(i-1)\n",
+    "\n",
+    "print(\"The analytical derivative of f6 at x = %g is: %g\"%(x,f6_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f0b0e1e9",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using recursion"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "1585ab28",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def f7(n): # Assume that n is an integer\n",
+    "    if n == 1 or n == 0:\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return n*f7(n-1)\n",
+    "\n",
+    "f7_grad = grad(f7)\n",
+    "\n",
+    "n = 2.0\n",
+    "\n",
+    "print(\"The computed derivative of f7 at n = %d is: %g\"%(n,f7_grad(n)))\n",
+    "\n",
+    "# The function f7 is an implementation of the factorial of n.\n",
+    "# By using the product rule, one can find that the derivative is:\n",
+    "\n",
+    "f7_grad_analytical = 0\n",
+    "for i in range(int(n)-1):\n",
+    "    tmp = 1\n",
+    "    for k in range(int(n)-1):\n",
+    "        if k != i:\n",
+    "            tmp *= (n - k)\n",
+    "    f7_grad_analytical += tmp\n",
+    "\n",
+    "print(\"The analytical derivative of f7 at n = %d is: %g\"%(n,f7_grad_analytical))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2718df1a",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d8fa5235",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Unsupported functions\n",
+    "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n",
+    "\n",
+    "Assigning a value to the variable being differentiated with respect to"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "196a52d6",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f8(x): # Assume x is an array\n",
+    "    x[2] = 3\n",
+    "    return x*2\n",
+    "\n",
+    "f8_grad = grad(f8)\n",
+    "\n",
+    "x = 8.4\n",
+    "\n",
+    "print(\"The derivative of f8 is:\",f8_grad(x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9127a2c5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b12ed61",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## The syntax a.dot(b) when finding the dot product"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "8ced55c8",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f9(a): # Assume a is an array with 2 elements\n",
+    "    b = np.array([1.0,2.0])\n",
+    "    return a.dot(b)\n",
+    "\n",
+    "f9_grad = grad(f9)\n",
+    "\n",
+    "x = np.array([1.0,0.0])\n",
+    "\n",
+    "print(\"The derivative of f9 is:\",f9_grad(x))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "92ebdc2b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Here we are told that the 'dot' function does not belong to Autograd's\n",
+    "version of a Numpy array.  To overcome this, an alternative syntax\n",
+    "which also computed the dot product can be used:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "276f763e",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "def f9_alternative(x): # Assume a is an array with 2 elements\n",
+    "    b = np.array([1.0,2.0])\n",
+    "    return np.dot(x,b) # The same as x_1*b_1 + x_2*b_2\n",
+    "\n",
+    "f9_alternative_grad = grad(f9_alternative)\n",
+    "\n",
+    "x = np.array([3.0,0.0])\n",
+    "\n",
+    "print(\"The gradient of f9 is:\",f9_alternative_grad(x))\n",
+    "\n",
+    "# The analytical gradient of the dot product of vectors x and b with two elements (x_1,x_2) and (b_1, b_2) respectively\n",
+    "# w.r.t x is (b_1, b_2)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7841ad0b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Recommended to avoid\n",
+    "The documentation recommends to avoid inplace operations such as"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "10107989",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "a += b\n",
+    "a -= b\n",
+    "a*= b\n",
+    "a /=b"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c1139c0",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Using Autograd with OLS\n",
+    "\n",
+    "We conclude the part on optmization by showing how we can make codes\n",
+    "for linear regression and logistic regression using **autograd**. The\n",
+    "first example shows results with ordinary leats squares."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "3022af88",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "04d09021",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "71bf4b6d",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients for OLS\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x#+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 30\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(theta)\n",
+    "    theta -= eta*gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "# Now improve with momentum gradient descent\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "for iter in range(Niterations):\n",
+    "    # calculate gradient\n",
+    "    gradients = training_gradient(theta)\n",
+    "    # calculate update\n",
+    "    new_change = eta*gradients+delta_momentum*change\n",
+    "    # take a step\n",
+    "    theta -= new_change\n",
+    "    # save the change\n",
+    "    change = new_change\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"theta from own gd wth momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ad417bba",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## But noen of these can compete with Newton's method"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "c394bcef",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Newton's method\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "def CostOLS(beta):\n",
+    "    return (1.0/n)*np.sum((y-X @ beta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "beta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(beta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "# Note that here the Hessian does not depend on the parameters beta\n",
+    "invH = np.linalg.pinv(H)\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "beta = np.random.randn(2,1)\n",
+    "Niterations = 5\n",
+    "\n",
+    "# define the gradient\n",
+    "training_gradient = grad(CostOLS)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = training_gradient(beta)\n",
+    "    beta -= invH @ gradients\n",
+    "    print(iter,gradients[0],gradients[1])\n",
+    "print(\"beta from own Newton code\")\n",
+    "print(beta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e4cf4b5",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Including Stochastic Gradient Descent with Autograd\n",
+    "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "47411bcf",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 1000\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "xnew = np.array([[0],[2]])\n",
+    "Xnew = np.c_[np.ones((2,1)), xnew]\n",
+    "ypredict = Xnew.dot(theta)\n",
+    "ypredict2 = Xnew.dot(theta_linreg)\n",
+    "\n",
+    "plt.plot(xnew, ypredict, \"r-\")\n",
+    "plt.plot(xnew, ypredict2, \"b-\")\n",
+    "plt.plot(x, y ,'ro')\n",
+    "plt.axis([0,2.0,0, 15.0])\n",
+    "plt.xlabel(r'$x$')\n",
+    "plt.ylabel(r'$y$')\n",
+    "plt.title(r'Random numbers ')\n",
+    "plt.show()\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "# Can you figure out a better way of setting up the contributions to each batch?\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        theta = theta - eta*gradients\n",
+    "print(\"theta from own sdg\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f8e30af2",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Same code but now with momentum gradient descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "dd594924",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using SGD\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 100\n",
+    "x = 2*np.random.rand(n,1)\n",
+    "y = 4+3*x+np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "# Hessian matrix\n",
+    "H = (2.0/n)* XT_X\n",
+    "EigValues, EigVectors = np.linalg.eig(H)\n",
+    "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "eta = 1.0/np.max(EigValues)\n",
+    "Niterations = 100\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "\n",
+    "for iter in range(Niterations):\n",
+    "    gradients = (1.0/n)*training_gradient(y, X, theta)\n",
+    "    theta -= eta*gradients\n",
+    "print(\"theta from own gd\")\n",
+    "print(theta)\n",
+    "\n",
+    "\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "t0, t1 = 5, 50\n",
+    "def learning_schedule(t):\n",
+    "    return t0/(t+t1)\n",
+    "\n",
+    "theta = np.random.randn(2,1)\n",
+    "\n",
+    "change = 0.0\n",
+    "delta_momentum = 0.3\n",
+    "\n",
+    "for epoch in range(n_epochs):\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        eta = learning_schedule(epoch*m+i)\n",
+    "        # calculate update\n",
+    "        new_change = eta*gradients+delta_momentum*change\n",
+    "        # take a step\n",
+    "        theta -= new_change\n",
+    "        # save the change\n",
+    "        change = new_change\n",
+    "print(\"theta from own sdg with momentum\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "75c4c29d",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Similar (second order function now) problem but now with AdaGrad"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "4dd14fc5",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using AdaGrad and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        Giter += gradients*gradients\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "        theta -= update\n",
+    "print(\"theta from own AdaGrad\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be4ce0cd",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "Running this code we note an almost perfect agreement with the results from matrix inversion."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0b739495",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## RMSprop for adaptive learning rate with Stochastic Gradient Descent"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 34,
+   "id": "ae87789c",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameter rho\n",
+    "rho = 0.99\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-8\n",
+    "for epoch in range(n_epochs):\n",
+    "    Giter = 0.0\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "\t# Accumulated gradient\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        Giter = (rho*Giter+(1-rho)*gradients*gradients)\n",
+    "\t# Taking the diagonal only and inverting\n",
+    "        update = gradients*eta/(delta+np.sqrt(Giter))\n",
+    "\t# Hadamard product\n",
+    "        theta -= update\n",
+    "print(\"theta from own RMSprop\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "76c8872b",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And finally [ADAM](https://arxiv.org/pdf/1412.6980.pdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
+   "id": "e99dbaa4",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "# Using Autograd to calculate gradients using RMSprop  and Stochastic Gradient descent\n",
+    "# OLS example\n",
+    "from random import random, seed\n",
+    "import numpy as np\n",
+    "import autograd.numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "from autograd import grad\n",
+    "\n",
+    "# Note change from previous example\n",
+    "def CostOLS(y,X,theta):\n",
+    "    return np.sum((y-X @ theta)**2)\n",
+    "\n",
+    "n = 1000\n",
+    "x = np.random.rand(n,1)\n",
+    "y = 2.0+3*x +4*x*x# +np.random.randn(n,1)\n",
+    "\n",
+    "X = np.c_[np.ones((n,1)), x, x*x]\n",
+    "XT_X = X.T @ X\n",
+    "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n",
+    "print(\"Own inversion\")\n",
+    "print(theta_linreg)\n",
+    "\n",
+    "\n",
+    "# Note that we request the derivative wrt third argument (theta, 2 here)\n",
+    "training_gradient = grad(CostOLS,2)\n",
+    "# Define parameters for Stochastic Gradient Descent\n",
+    "n_epochs = 50\n",
+    "M = 5   #size of each minibatch\n",
+    "m = int(n/M) #number of minibatches\n",
+    "# Guess for unknown parameters theta\n",
+    "theta = np.random.randn(3,1)\n",
+    "\n",
+    "# Value for learning rate\n",
+    "eta = 0.01\n",
+    "# Value for parameters beta1 and beta2, see https://arxiv.org/abs/1412.6980\n",
+    "beta1 = 0.9\n",
+    "beta2 = 0.999\n",
+    "# Including AdaGrad parameter to avoid possible division by zero\n",
+    "delta  = 1e-7\n",
+    "iter = 0\n",
+    "for epoch in range(n_epochs):\n",
+    "    first_moment = 0.0\n",
+    "    second_moment = 0.0\n",
+    "    iter += 1\n",
+    "    for i in range(m):\n",
+    "        random_index = M*np.random.randint(m)\n",
+    "        xi = X[random_index:random_index+M]\n",
+    "        yi = y[random_index:random_index+M]\n",
+    "        gradients = (1.0/M)*training_gradient(yi, xi, theta)\n",
+    "        # Computing moments first\n",
+    "        first_moment = beta1*first_moment + (1-beta1)*gradients\n",
+    "        second_moment = beta2*second_moment+(1-beta2)*gradients*gradients\n",
+    "        first_term = first_moment/(1.0-beta1**iter)\n",
+    "        second_term = second_moment/(1.0-beta2**iter)\n",
+    "\t# Scaling with rho the new and the previous results\n",
+    "        update = eta*first_term/(np.sqrt(second_term)+delta)\n",
+    "        theta -= update\n",
+    "print(\"theta from own ADAM\")\n",
+    "print(theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "596df570",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## And Logistic Regression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "6693f042",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import autograd.numpy as np\n",
+    "from autograd import grad\n",
+    "\n",
+    "def sigmoid(x):\n",
+    "    return 0.5 * (np.tanh(x / 2.) + 1)\n",
+    "\n",
+    "def logistic_predictions(weights, inputs):\n",
+    "    # Outputs probability of a label being true according to logistic model.\n",
+    "    return sigmoid(np.dot(inputs, weights))\n",
+    "\n",
+    "def training_loss(weights):\n",
+    "    # Training loss is the negative log-likelihood of the training labels.\n",
+    "    preds = logistic_predictions(weights, inputs)\n",
+    "    label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n",
+    "    return -np.sum(np.log(label_probabilities))\n",
+    "\n",
+    "# Build a toy dataset.\n",
+    "inputs = np.array([[0.52, 1.12,  0.77],\n",
+    "                   [0.88, -1.08, 0.15],\n",
+    "                   [0.52, 0.06, -1.30],\n",
+    "                   [0.74, -2.49, 1.39]])\n",
+    "targets = np.array([True, True, False, True])\n",
+    "\n",
+    "# Define a function that returns gradients of training loss using Autograd.\n",
+    "training_gradient_fun = grad(training_loss)\n",
+    "\n",
+    "# Optimize weights using gradient descent.\n",
+    "weights = np.array([0.0, 0.0, 0.0])\n",
+    "print(\"Initial loss:\", training_loss(weights))\n",
+    "for i in range(100):\n",
+    "    weights -= training_gradient_fun(weights) * 0.01\n",
+    "\n",
+    "print(\"Trained loss:\", training_loss(weights))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a40ed853",
+   "metadata": {
+    "editable": true
+   },
+   "source": [
+    "## Introducing [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "Presently, instead of using **autograd**, we recommend using [JAX](https://jax.readthedocs.io/en/latest/)\n",
+    "\n",
+    "**JAX** is Autograd and [XLA (Accelerated Linear Algebra))](https://www.tensorflow.org/xla),\n",
+    "brought together for high-performance numerical computing and machine learning research.\n",
+    "It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.\n",
+    "\n",
+    "Here's a simple example on how you can use **JAX** to compute the derivate of the logistic function."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "02f88360",
+   "metadata": {
+    "collapsed": false,
+    "editable": true
+   },
+   "outputs": [],
+   "source": [
+    "import jax.numpy as jnp\n",
+    "from jax import grad, jit, vmap\n",
+    "\n",
+    "def sum_logistic(x):\n",
+    "  return jnp.sum(1.0 / (1.0 + jnp.exp(-x)))\n",
+    "\n",
+    "x_small = jnp.arange(3.)\n",
+    "derivative_fn = grad(sum_logistic)\n",
+    "print(derivative_fn(x_small))"
+   ]
+  }
+ ],
+ "metadata": {
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.18"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
\ No newline at end of file
diff --git a/doc/LectureNotes/_toc.yml b/doc/LectureNotes/_toc.yml
index 802377ef9..5172dc12e 100644
--- a/doc/LectureNotes/_toc.yml
+++ b/doc/LectureNotes/_toc.yml
@@ -51,6 +51,8 @@ parts:
     - file: week37.ipynb
     - file: exercisesweek38.ipynb
     - file: week38.ipynb
+    - file: exercisesweek39.ipynb
+    - file: week39.ipynb
   - caption: Projects
     numbered: false
     chapters: