diff --git a/doc/pub/week39/html/week39-bs.html b/doc/pub/week39/html/week39-bs.html index 63c281832..2c358574c 100644 --- a/doc/pub/week39/html/week39-bs.html +++ b/doc/pub/week39/html/week39-bs.html @@ -267,7 +267,8 @@ doconce format html week39.do.txt --html_style=bootstrap --pygments_html_style=d 2, None, 'introducing-jax-https-jax-readthedocs-io-en-latest'), - ('Weekend challenge', 2, None, 'weekend-challenge')]} + ('Weekend challenge', 2, None, 'weekend-challenge'), + ('algorithms', 2, None, 'algorithms')]} end of tocinfo --> @@ -389,6 +390,7 @@ MathJax.Hub.Config({
  • And Logistic Regression
  • Introducing "JAX":"https://jax.readthedocs.io/en/latest/"
  • Weekend challenge
  • +
  • algorithms
  • @@ -443,7 +445,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
  • -
  • 88
  • +
  • 89
  • »
  • diff --git a/doc/pub/week39/html/week39-reveal.html b/doc/pub/week39/html/week39-reveal.html index 24943ab03..5eaf31872 100644 --- a/doc/pub/week39/html/week39-reveal.html +++ b/doc/pub/week39/html/week39-reveal.html @@ -3781,6 +3781,30 @@ derivative_fn = grad(sum_logistic) +
    +

    algorithms

    + +

    \begin{algorithm} +\caption{An algorithm with caption} +\KwData{\( n \geq 0 \)} +\KwResult{\( y = x^n \)} +$y \gets 1$\; +$X \gets x$\; +$N \gets n$\; +\While{\( N \neq 0 \)}{ + \eIf{\( N \) is even}{ + $X \gets X \times X$\; + \( N \gets \frac{N}{2} \) \Comment*[r]{This is a comment} + }{\If{\( N \) is odd}{ + $y \gets y \times X$\; + $N \gets N - 1$\; + } + } +} +\end{algorithm} +

    +
    + diff --git a/doc/pub/week39/html/week39-solarized.html b/doc/pub/week39/html/week39-solarized.html index 29b59d761..3ff32528d 100644 --- a/doc/pub/week39/html/week39-solarized.html +++ b/doc/pub/week39/html/week39-solarized.html @@ -294,7 +294,8 @@ div.toc p,a { 2, None, 'introducing-jax-https-jax-readthedocs-io-en-latest'), - ('Weekend challenge', 2, None, 'weekend-challenge')]} + ('Weekend challenge', 2, None, 'weekend-challenge'), + ('algorithms', 2, None, 'algorithms')]} end of tocinfo --> @@ -3712,6 +3713,29 @@ derivative_fn = grad(sum_logistic)
  • Add a more complicated function and study the rate of convergence for the derivatives as function of the different methods
  • Extend from linear regression to logistic regression.
  • +









    +

    algorithms

    + +

    \begin{algorithm} +\caption{An algorithm with caption} +\KwData{\( n \geq 0 \)} +\KwResult{\( y = x^n \)} +$y \gets 1$\; +$X \gets x$\; +$N \gets n$\; +\While{\( N \neq 0 \)}{ + \eIf{\( N \) is even}{ + $X \gets X \times X$\; + \( N \gets \frac{N}{2} \) \Comment*[r]{This is a comment} + }{\If{\( N \) is odd}{ + $y \gets y \times X$\; + $N \gets N - 1$\; + } + } +} +\end{algorithm} +

    +
    © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license diff --git a/doc/pub/week39/html/week39.html b/doc/pub/week39/html/week39.html index 14b139823..a3c5eb61e 100644 --- a/doc/pub/week39/html/week39.html +++ b/doc/pub/week39/html/week39.html @@ -371,7 +371,8 @@ div.toc p,a { 2, None, 'introducing-jax-https-jax-readthedocs-io-en-latest'), - ('Weekend challenge', 2, None, 'weekend-challenge')]} + ('Weekend challenge', 2, None, 'weekend-challenge'), + ('algorithms', 2, None, 'algorithms')]} end of tocinfo --> @@ -3789,6 +3790,29 @@ derivative_fn = grad(sum_logistic)
  • Add a more complicated function and study the rate of convergence for the derivatives as function of the different methods
  • Extend from linear regression to logistic regression.
  • +









    +

    algorithms

    + +

    \begin{algorithm} +\caption{An algorithm with caption} +\KwData{\( n \geq 0 \)} +\KwResult{\( y = x^n \)} +$y \gets 1$\; +$X \gets x$\; +$N \gets n$\; +\While{\( N \neq 0 \)}{ + \eIf{\( N \) is even}{ + $X \gets X \times X$\; + \( N \gets \frac{N}{2} \) \Comment*[r]{This is a comment} + }{\If{\( N \) is odd}{ + $y \gets y \times X$\; + $N \gets N - 1$\; + } + } +} +\end{algorithm} +

    +
    © 1999-2022, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license diff --git a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz index ca1ac9bc3..ae275ac59 100644 Binary files a/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz and b/doc/pub/week39/ipynb/ipynb-week39-src.tar.gz differ diff --git a/doc/pub/week39/ipynb/week39.ipynb b/doc/pub/week39/ipynb/week39.ipynb index cb39753a3..399e7971b 100644 --- a/doc/pub/week39/ipynb/week39.ipynb +++ b/doc/pub/week39/ipynb/week39.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0d859933", + "id": "8533e353", "metadata": { "editable": true }, @@ -14,7 +14,7 @@ }, { "cell_type": "markdown", - "id": "aa268840", + "id": "3b97d908", "metadata": { "editable": true }, @@ -29,7 +29,7 @@ }, { "cell_type": "markdown", - "id": "4df2434d", + "id": "a0cb6347", "metadata": { "editable": true }, @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "7e5e2f0b", + "id": "74dd4c1d", "metadata": { "editable": true }, @@ -78,7 +78,7 @@ }, { "cell_type": "markdown", - "id": "a82104f2", + "id": "52b8c93d", "metadata": { "editable": true }, @@ -95,7 +95,7 @@ }, { "cell_type": "markdown", - "id": "8bad6687", + "id": "d8732a0f", "metadata": { "editable": true }, @@ -110,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "8b49e49b", + "id": "1d591429", "metadata": { "editable": true }, @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "b400d96b", + "id": "3d811f8b", "metadata": { "editable": true }, @@ -136,7 +136,7 @@ }, { "cell_type": "markdown", - "id": "9999fb11", + "id": "377529c8", "metadata": { "editable": true }, @@ -148,7 +148,7 @@ }, { "cell_type": "markdown", - "id": "5921a1ed", + "id": "7a1bfe70", "metadata": { "editable": true }, @@ -159,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "ffe526e9", + "id": "b63de896", "metadata": { "editable": true }, @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "a6607e45", + "id": "18e19ab5", "metadata": { "editable": true }, @@ -181,7 +181,7 @@ }, { "cell_type": "markdown", - "id": "e55e59f8", + "id": "d6926502", "metadata": { "editable": true }, @@ -195,7 +195,7 @@ }, { "cell_type": "markdown", - "id": "cf2da679", + "id": "61c3adb1", "metadata": { "editable": true }, @@ -207,7 +207,7 @@ }, { "cell_type": "markdown", - "id": "365c2c53", + "id": "983a05f3", "metadata": { "editable": true }, @@ -217,7 +217,7 @@ }, { "cell_type": "markdown", - "id": "f0e428e7", + "id": "ae045eb0", "metadata": { "editable": true }, @@ -229,7 +229,7 @@ }, { "cell_type": "markdown", - "id": "3be57abc", + "id": "d9475100", "metadata": { "editable": true }, @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "39dc09f0", + "id": "cf2bf428", "metadata": { "editable": true }, @@ -261,7 +261,7 @@ }, { "cell_type": "markdown", - "id": "164d01d9", + "id": "c854aff4", "metadata": { "editable": true }, @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "5b227b84", + "id": "a70b9978", "metadata": { "editable": true }, @@ -293,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "a1c4dae1", + "id": "9f5e3609", "metadata": { "editable": true }, @@ -304,7 +304,7 @@ }, { "cell_type": "markdown", - "id": "6cad87b7", + "id": "86de0473", "metadata": { "editable": true }, @@ -316,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "53785baf", + "id": "db9ec962", "metadata": { "editable": true }, @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "bb159c2d", + "id": "71375230", "metadata": { "editable": true }, @@ -338,7 +338,7 @@ }, { "cell_type": "markdown", - "id": "770c992b", + "id": "d1be8353", "metadata": { "editable": true }, @@ -348,7 +348,7 @@ }, { "cell_type": "markdown", - "id": "96be42f4", + "id": "f90f299d", "metadata": { "editable": true }, @@ -360,7 +360,7 @@ }, { "cell_type": "markdown", - "id": "c0c30def", + "id": "ffeb698c", "metadata": { "editable": true }, @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "c113542b", + "id": "25a7b632", "metadata": { "editable": true }, @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "84e9893b", + "id": "9584787f", "metadata": { "editable": true }, @@ -408,7 +408,7 @@ }, { "cell_type": "markdown", - "id": "ce630143", + "id": "16305b7c", "metadata": { "editable": true }, @@ -418,7 +418,7 @@ }, { "cell_type": "markdown", - "id": "5ed26c39", + "id": "46fb81f5", "metadata": { "editable": true }, @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "1e461033", + "id": "39458051", "metadata": { "editable": true }, @@ -446,7 +446,7 @@ }, { "cell_type": "markdown", - "id": "4e5abd41", + "id": "5d6beb18", "metadata": { "editable": true }, @@ -461,7 +461,7 @@ }, { "cell_type": "markdown", - "id": "6dc12326", + "id": "a1f072ab", "metadata": { "editable": true }, @@ -471,7 +471,7 @@ }, { "cell_type": "markdown", - "id": "5d6638aa", + "id": "3926639e", "metadata": { "editable": true }, @@ -485,7 +485,7 @@ }, { "cell_type": "markdown", - "id": "c3ffe861", + "id": "7d8826ad", "metadata": { "editable": true }, @@ -495,7 +495,7 @@ }, { "cell_type": "markdown", - "id": "84178eb0", + "id": "fb76b46e", "metadata": { "editable": true }, @@ -509,7 +509,7 @@ }, { "cell_type": "markdown", - "id": "be84a70d", + "id": "924ad08e", "metadata": { "editable": true }, @@ -524,7 +524,7 @@ }, { "cell_type": "markdown", - "id": "8a5c98b0", + "id": "90ce7ba0", "metadata": { "editable": true }, @@ -541,7 +541,7 @@ }, { "cell_type": "markdown", - "id": "619106a3", + "id": "ec6b3ca5", "metadata": { "editable": true }, @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "bd096718", + "id": "27d689d4", "metadata": { "editable": true }, @@ -567,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "12fdf66c", + "id": "53a410f6", "metadata": { "editable": true }, @@ -582,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "aecfd024", + "id": "94effaa2", "metadata": { "editable": true }, @@ -594,7 +594,7 @@ }, { "cell_type": "markdown", - "id": "8b0f8d9b", + "id": "89abbfa1", "metadata": { "editable": true }, @@ -605,7 +605,7 @@ }, { "cell_type": "markdown", - "id": "86d0d93a", + "id": "bd31acde", "metadata": { "editable": true }, @@ -633,7 +633,7 @@ }, { "cell_type": "markdown", - "id": "89c736e2", + "id": "546e7d7d", "metadata": { "editable": true }, @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "e0f78c77", + "id": "a3d9aa57", "metadata": { "editable": true }, @@ -677,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "f5d2f3ab", + "id": "770b4101", "metadata": { "editable": true }, @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "752a667e", + "id": "6186be42", "metadata": { "editable": true }, @@ -726,7 +726,7 @@ }, { "cell_type": "markdown", - "id": "5bb030de", + "id": "ae5508fd", "metadata": { "editable": true }, @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "69a3b6d7", + "id": "a4cd8292", "metadata": { "editable": true }, @@ -784,7 +784,7 @@ }, { "cell_type": "markdown", - "id": "d3decfcd", + "id": "a7ba1f4e", "metadata": { "editable": true }, @@ -804,7 +804,7 @@ }, { "cell_type": "markdown", - "id": "56adc284", + "id": "922e83d6", "metadata": { "editable": true }, @@ -816,7 +816,7 @@ }, { "cell_type": "markdown", - "id": "b2273219", + "id": "055039cf", "metadata": { "editable": true }, @@ -826,7 +826,7 @@ }, { "cell_type": "markdown", - "id": "64a244fd", + "id": "1876007b", "metadata": { "editable": true }, @@ -838,7 +838,7 @@ }, { "cell_type": "markdown", - "id": "529d8b30", + "id": "7742cb67", "metadata": { "editable": true }, @@ -850,7 +850,7 @@ }, { "cell_type": "markdown", - "id": "c24a02a0", + "id": "01ebfcdc", "metadata": { "editable": true }, @@ -862,7 +862,7 @@ }, { "cell_type": "markdown", - "id": "39614ba7", + "id": "f222fc32", "metadata": { "editable": true }, @@ -874,7 +874,7 @@ }, { "cell_type": "markdown", - "id": "48fdf7d1", + "id": "ded79cd8", "metadata": { "editable": true }, @@ -885,7 +885,7 @@ }, { "cell_type": "markdown", - "id": "f5a90738", + "id": "ec238c51", "metadata": { "editable": true }, @@ -898,7 +898,7 @@ }, { "cell_type": "markdown", - "id": "99e20aec", + "id": "ac7217a2", "metadata": { "editable": true }, @@ -910,7 +910,7 @@ }, { "cell_type": "markdown", - "id": "082b9fa8", + "id": "52d17e54", "metadata": { "editable": true }, @@ -920,7 +920,7 @@ }, { "cell_type": "markdown", - "id": "9238a951", + "id": "62fd8e0d", "metadata": { "editable": true }, @@ -932,7 +932,7 @@ }, { "cell_type": "markdown", - "id": "11625e87", + "id": "b5aeee6b", "metadata": { "editable": true }, @@ -942,7 +942,7 @@ }, { "cell_type": "markdown", - "id": "7b2185eb", + "id": "236b71cd", "metadata": { "editable": true }, @@ -953,7 +953,7 @@ }, { "cell_type": "markdown", - "id": "220e7591", + "id": "fcb93654", "metadata": { "editable": true }, @@ -965,7 +965,7 @@ }, { "cell_type": "markdown", - "id": "68501c2b", + "id": "8200ddc6", "metadata": { "editable": true }, @@ -977,7 +977,7 @@ }, { "cell_type": "markdown", - "id": "7f28173b", + "id": "c3804e8c", "metadata": { "editable": true }, @@ -989,7 +989,7 @@ }, { "cell_type": "markdown", - "id": "8e0ef1b7", + "id": "e17ed519", "metadata": { "editable": true }, @@ -1000,7 +1000,7 @@ }, { "cell_type": "markdown", - "id": "cdbfc572", + "id": "50a9f2cc", "metadata": { "editable": true }, @@ -1011,7 +1011,7 @@ }, { "cell_type": "markdown", - "id": "61a36617", + "id": "3b41b141", "metadata": { "editable": true }, @@ -1023,7 +1023,7 @@ }, { "cell_type": "markdown", - "id": "9d9f56ed", + "id": "cf5ea400", "metadata": { "editable": true }, @@ -1033,7 +1033,7 @@ }, { "cell_type": "markdown", - "id": "5165013a", + "id": "6e1e55cc", "metadata": { "editable": true }, @@ -1045,7 +1045,7 @@ }, { "cell_type": "markdown", - "id": "c8fdd875", + "id": "ab1125a1", "metadata": { "editable": true }, @@ -1055,7 +1055,7 @@ }, { "cell_type": "markdown", - "id": "c4da7bec", + "id": "d6a213fb", "metadata": { "editable": true }, @@ -1067,7 +1067,7 @@ }, { "cell_type": "markdown", - "id": "4ba2e429", + "id": "f7021f88", "metadata": { "editable": true }, @@ -1077,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "72b9d7af", + "id": "c5dddabe", "metadata": { "editable": true }, @@ -1089,7 +1089,7 @@ }, { "cell_type": "markdown", - "id": "3df4b6ac", + "id": "79cac872", "metadata": { "editable": true }, @@ -1099,7 +1099,7 @@ }, { "cell_type": "markdown", - "id": "aa5ab727", + "id": "5e98371d", "metadata": { "editable": true }, @@ -1111,7 +1111,7 @@ }, { "cell_type": "markdown", - "id": "6884e4ca", + "id": "66ac0c03", "metadata": { "editable": true }, @@ -1122,7 +1122,7 @@ { "cell_type": "code", "execution_count": 1, - "id": "53108ecb", + "id": "cf4269cf", "metadata": { "collapsed": false, "editable": true @@ -1155,7 +1155,7 @@ }, { "cell_type": "markdown", - "id": "5cf4960b", + "id": "5adbb25d", "metadata": { "editable": true }, @@ -1166,7 +1166,7 @@ { "cell_type": "code", "execution_count": 2, - "id": "6acb0608", + "id": "ca2c38c3", "metadata": { "collapsed": false, "editable": true @@ -1180,7 +1180,7 @@ }, { "cell_type": "markdown", - "id": "ce5ac787", + "id": "8fcecb47", "metadata": { "editable": true }, @@ -1191,7 +1191,7 @@ { "cell_type": "code", "execution_count": 3, - "id": "a5efd293", + "id": "b8ad1d5e", "metadata": { "collapsed": false, "editable": true @@ -1204,7 +1204,7 @@ }, { "cell_type": "markdown", - "id": "c5933d92", + "id": "b4c03a01", "metadata": { "editable": true }, @@ -1215,7 +1215,7 @@ { "cell_type": "code", "execution_count": 4, - "id": "cd82ffad", + "id": "a45928cc", "metadata": { "collapsed": false, "editable": true @@ -1233,7 +1233,7 @@ }, { "cell_type": "markdown", - "id": "3b2a906c", + "id": "3ba586e3", "metadata": { "editable": true }, @@ -1244,7 +1244,7 @@ { "cell_type": "code", "execution_count": 5, - "id": "1119203b", + "id": "454d6e51", "metadata": { "collapsed": false, "editable": true @@ -1259,7 +1259,7 @@ }, { "cell_type": "markdown", - "id": "84cfc9f8", + "id": "0c9f1ef8", "metadata": { "editable": true }, @@ -1269,7 +1269,7 @@ }, { "cell_type": "markdown", - "id": "9ff1bce5", + "id": "bb1fe9ad", "metadata": { "editable": true }, @@ -1283,7 +1283,7 @@ }, { "cell_type": "markdown", - "id": "98a7bb2d", + "id": "06ac534f", "metadata": { "editable": true }, @@ -1295,7 +1295,7 @@ }, { "cell_type": "markdown", - "id": "36ca430a", + "id": "b9ccebc1", "metadata": { "editable": true }, @@ -1306,7 +1306,7 @@ }, { "cell_type": "markdown", - "id": "4c8ed175", + "id": "cde9da1b", "metadata": { "editable": true }, @@ -1318,7 +1318,7 @@ }, { "cell_type": "markdown", - "id": "4d3f4029", + "id": "b878fbc7", "metadata": { "editable": true }, @@ -1329,7 +1329,7 @@ }, { "cell_type": "markdown", - "id": "d5d682e0", + "id": "9efa227e", "metadata": { "editable": true }, @@ -1340,7 +1340,7 @@ }, { "cell_type": "markdown", - "id": "19fc76dc", + "id": "a0781d34", "metadata": { "editable": true }, @@ -1352,7 +1352,7 @@ }, { "cell_type": "markdown", - "id": "ea733d39", + "id": "d40cf1ab", "metadata": { "editable": true }, @@ -1362,7 +1362,7 @@ }, { "cell_type": "markdown", - "id": "45afd454", + "id": "26e10b52", "metadata": { "editable": true }, @@ -1374,7 +1374,7 @@ }, { "cell_type": "markdown", - "id": "5fea2b9e", + "id": "5c15b595", "metadata": { "editable": true }, @@ -1386,7 +1386,7 @@ }, { "cell_type": "markdown", - "id": "76542173", + "id": "0cde0c5a", "metadata": { "editable": true }, @@ -1398,7 +1398,7 @@ }, { "cell_type": "markdown", - "id": "52a864c4", + "id": "9660e880", "metadata": { "editable": true }, @@ -1410,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "fbfec9af", + "id": "93c5522f", "metadata": { "editable": true }, @@ -1421,7 +1421,7 @@ }, { "cell_type": "markdown", - "id": "00016a46", + "id": "4e6adde5", "metadata": { "editable": true }, @@ -1433,7 +1433,7 @@ }, { "cell_type": "markdown", - "id": "88c83bdb", + "id": "1974d411", "metadata": { "editable": true }, @@ -1443,7 +1443,7 @@ }, { "cell_type": "markdown", - "id": "fed94240", + "id": "d143b416", "metadata": { "editable": true }, @@ -1455,7 +1455,7 @@ }, { "cell_type": "markdown", - "id": "aa81232d", + "id": "b3b07be1", "metadata": { "editable": true }, @@ -1465,7 +1465,7 @@ }, { "cell_type": "markdown", - "id": "500bf48a", + "id": "f2fd4fa4", "metadata": { "editable": true }, @@ -1477,7 +1477,7 @@ }, { "cell_type": "markdown", - "id": "dfbf44b1", + "id": "1f87c2f8", "metadata": { "editable": true }, @@ -1497,7 +1497,7 @@ }, { "cell_type": "markdown", - "id": "069b850b", + "id": "5d0ded80", "metadata": { "editable": true }, @@ -1509,7 +1509,7 @@ }, { "cell_type": "markdown", - "id": "4567d3dd", + "id": "e372c9b0", "metadata": { "editable": true }, @@ -1519,7 +1519,7 @@ }, { "cell_type": "markdown", - "id": "9aea676c", + "id": "a71622b1", "metadata": { "editable": true }, @@ -1531,7 +1531,7 @@ }, { "cell_type": "markdown", - "id": "f69e09d0", + "id": "2ff17b9f", "metadata": { "editable": true }, @@ -1541,7 +1541,7 @@ }, { "cell_type": "markdown", - "id": "8afcb217", + "id": "7426a823", "metadata": { "editable": true }, @@ -1552,7 +1552,7 @@ }, { "cell_type": "markdown", - "id": "673af0e4", + "id": "7cf01d2f", "metadata": { "editable": true }, @@ -1564,7 +1564,7 @@ }, { "cell_type": "markdown", - "id": "4fd20310", + "id": "a40c574c", "metadata": { "editable": true }, @@ -1576,7 +1576,7 @@ }, { "cell_type": "markdown", - "id": "45379d2c", + "id": "f6e862f9", "metadata": { "editable": true }, @@ -1588,7 +1588,7 @@ }, { "cell_type": "markdown", - "id": "a4536674", + "id": "53f71689", "metadata": { "editable": true }, @@ -1601,7 +1601,7 @@ }, { "cell_type": "markdown", - "id": "d9260eb6", + "id": "a018eae8", "metadata": { "editable": true }, @@ -1612,7 +1612,7 @@ }, { "cell_type": "markdown", - "id": "ea8b0492", + "id": "1264aa6a", "metadata": { "editable": true }, @@ -1624,7 +1624,7 @@ }, { "cell_type": "markdown", - "id": "4a4bb6a1", + "id": "9d2cd202", "metadata": { "editable": true }, @@ -1640,7 +1640,7 @@ }, { "cell_type": "markdown", - "id": "da82788f", + "id": "6cf2dd8e", "metadata": { "editable": true }, @@ -1652,7 +1652,7 @@ }, { "cell_type": "markdown", - "id": "28297e74", + "id": "66638271", "metadata": { "editable": true }, @@ -1663,7 +1663,7 @@ }, { "cell_type": "markdown", - "id": "0e09460e", + "id": "22f431c4", "metadata": { "editable": true }, @@ -1675,7 +1675,7 @@ }, { "cell_type": "markdown", - "id": "7ef6c522", + "id": "495bd5ed", "metadata": { "editable": true }, @@ -1685,7 +1685,7 @@ }, { "cell_type": "markdown", - "id": "450192c2", + "id": "56277e52", "metadata": { "editable": true }, @@ -1697,7 +1697,7 @@ }, { "cell_type": "markdown", - "id": "937b867a", + "id": "942d5e70", "metadata": { "editable": true }, @@ -1707,7 +1707,7 @@ }, { "cell_type": "markdown", - "id": "3958a356", + "id": "6383d0cd", "metadata": { "editable": true }, @@ -1719,7 +1719,7 @@ }, { "cell_type": "markdown", - "id": "3a1d707d", + "id": "ab1aaabb", "metadata": { "editable": true }, @@ -1729,7 +1729,7 @@ }, { "cell_type": "markdown", - "id": "fbc6ee13", + "id": "a5c6ff60", "metadata": { "editable": true }, @@ -1741,7 +1741,7 @@ }, { "cell_type": "markdown", - "id": "51ebb055", + "id": "2b06185a", "metadata": { "editable": true }, @@ -1765,7 +1765,7 @@ { "cell_type": "code", "execution_count": 6, - "id": "15ecab56", + "id": "5d32ef01", "metadata": { "collapsed": false, "editable": true @@ -1778,7 +1778,7 @@ }, { "cell_type": "markdown", - "id": "a60329a8", + "id": "8ff5d0b6", "metadata": { "editable": true }, @@ -1789,7 +1789,7 @@ }, { "cell_type": "markdown", - "id": "4863a35b", + "id": "1b0ca7a1", "metadata": { "editable": true }, @@ -1801,7 +1801,7 @@ }, { "cell_type": "markdown", - "id": "3e11211b", + "id": "17d5ec37", "metadata": { "editable": true }, @@ -1811,7 +1811,7 @@ }, { "cell_type": "markdown", - "id": "c9a054b6", + "id": "445e9846", "metadata": { "editable": true }, @@ -1823,7 +1823,7 @@ }, { "cell_type": "markdown", - "id": "3da7d0b3", + "id": "bd15f560", "metadata": { "editable": true }, @@ -1837,7 +1837,7 @@ }, { "cell_type": "markdown", - "id": "65f33820", + "id": "e627d886", "metadata": { "editable": true }, @@ -1853,7 +1853,7 @@ }, { "cell_type": "markdown", - "id": "8231c088", + "id": "aa37943d", "metadata": { "editable": true }, @@ -1863,7 +1863,7 @@ }, { "cell_type": "markdown", - "id": "fb50e4c9", + "id": "41146fe8", "metadata": { "editable": true }, @@ -1875,7 +1875,7 @@ }, { "cell_type": "markdown", - "id": "dd8ba495", + "id": "e2a67762", "metadata": { "editable": true }, @@ -1885,7 +1885,7 @@ }, { "cell_type": "markdown", - "id": "72c59d05", + "id": "6a827d24", "metadata": { "editable": true }, @@ -1897,7 +1897,7 @@ }, { "cell_type": "markdown", - "id": "f8dad31f", + "id": "0174e317", "metadata": { "editable": true }, @@ -1911,7 +1911,7 @@ }, { "cell_type": "markdown", - "id": "788d725a", + "id": "fda78b68", "metadata": { "editable": true }, @@ -1921,7 +1921,7 @@ }, { "cell_type": "markdown", - "id": "ed745c32", + "id": "1a8e1f73", "metadata": { "editable": true }, @@ -1932,7 +1932,7 @@ }, { "cell_type": "markdown", - "id": "cd6c152d", + "id": "02d6f83f", "metadata": { "editable": true }, @@ -1947,7 +1947,7 @@ }, { "cell_type": "markdown", - "id": "76f53e55", + "id": "1a233b58", "metadata": { "editable": true }, @@ -1957,7 +1957,7 @@ }, { "cell_type": "markdown", - "id": "1da3e91b", + "id": "c96e5fc2", "metadata": { "editable": true }, @@ -1969,7 +1969,7 @@ }, { "cell_type": "markdown", - "id": "c238d1a1", + "id": "fa785c18", "metadata": { "editable": true }, @@ -1981,7 +1981,7 @@ }, { "cell_type": "markdown", - "id": "96f20edf", + "id": "6b3ac8ce", "metadata": { "editable": true }, @@ -1996,7 +1996,7 @@ }, { "cell_type": "markdown", - "id": "5891f2d5", + "id": "4c89ca10", "metadata": { "editable": true }, @@ -2009,7 +2009,7 @@ { "cell_type": "code", "execution_count": 7, - "id": "456818f1", + "id": "546b381f", "metadata": { "collapsed": false, "editable": true @@ -2066,7 +2066,7 @@ }, { "cell_type": "markdown", - "id": "a69c64cd", + "id": "4febc02b", "metadata": { "editable": true }, @@ -2077,7 +2077,7 @@ { "cell_type": "code", "execution_count": 8, - "id": "b6637a97", + "id": "75212a59", "metadata": { "collapsed": false, "editable": true @@ -2104,7 +2104,7 @@ }, { "cell_type": "markdown", - "id": "2e56d9a7", + "id": "346dab39", "metadata": { "editable": true }, @@ -2116,7 +2116,7 @@ }, { "cell_type": "markdown", - "id": "abe087fd", + "id": "c07596fd", "metadata": { "editable": true }, @@ -2128,7 +2128,7 @@ }, { "cell_type": "markdown", - "id": "5addb291", + "id": "dac22a2b", "metadata": { "editable": true }, @@ -2138,7 +2138,7 @@ }, { "cell_type": "markdown", - "id": "1713a164", + "id": "46c0a906", "metadata": { "editable": true }, @@ -2152,7 +2152,7 @@ }, { "cell_type": "markdown", - "id": "1690ca2e", + "id": "f4eaf502", "metadata": { "editable": true }, @@ -2162,7 +2162,7 @@ }, { "cell_type": "markdown", - "id": "609d0d1a", + "id": "80cc98b0", "metadata": { "editable": true }, @@ -2174,7 +2174,7 @@ }, { "cell_type": "markdown", - "id": "9dfdc0ef", + "id": "1673c144", "metadata": { "editable": true }, @@ -2185,7 +2185,7 @@ }, { "cell_type": "markdown", - "id": "f73fb45c", + "id": "6f98a936", "metadata": { "editable": true }, @@ -2200,7 +2200,7 @@ }, { "cell_type": "markdown", - "id": "5fa7d252", + "id": "30c65791", "metadata": { "editable": true }, @@ -2214,7 +2214,7 @@ }, { "cell_type": "markdown", - "id": "857862a9", + "id": "8b4462ec", "metadata": { "editable": true }, @@ -2225,7 +2225,7 @@ { "cell_type": "code", "execution_count": 9, - "id": "e79ad5eb", + "id": "98081021", "metadata": { "collapsed": false, "editable": true @@ -2286,7 +2286,7 @@ }, { "cell_type": "markdown", - "id": "a02fe4bb", + "id": "6df1ff19", "metadata": { "editable": true }, @@ -2308,7 +2308,7 @@ }, { "cell_type": "markdown", - "id": "93683051", + "id": "c1dc355b", "metadata": { "editable": true }, @@ -2321,7 +2321,7 @@ { "cell_type": "code", "execution_count": 10, - "id": "b2ce272c", + "id": "feb5d806", "metadata": { "collapsed": false, "editable": true @@ -2387,7 +2387,7 @@ }, { "cell_type": "markdown", - "id": "a966523d", + "id": "5a42c36d", "metadata": { "editable": true }, @@ -2398,7 +2398,7 @@ { "cell_type": "code", "execution_count": 11, - "id": "9217824f", + "id": "07f2a9d5", "metadata": { "collapsed": false, "editable": true @@ -2472,7 +2472,7 @@ }, { "cell_type": "markdown", - "id": "b6351079", + "id": "af03be04", "metadata": { "editable": true }, @@ -2484,7 +2484,7 @@ }, { "cell_type": "markdown", - "id": "c0eb5dde", + "id": "2bc5382f", "metadata": { "editable": true }, @@ -2505,7 +2505,7 @@ }, { "cell_type": "markdown", - "id": "4fd85cdd", + "id": "a2cc24e0", "metadata": { "editable": true }, @@ -2537,7 +2537,7 @@ }, { "cell_type": "markdown", - "id": "91588609", + "id": "8c6adb6f", "metadata": { "editable": true }, @@ -2554,7 +2554,7 @@ }, { "cell_type": "markdown", - "id": "7ec42a60", + "id": "88a52811", "metadata": { "editable": true }, @@ -2567,7 +2567,7 @@ }, { "cell_type": "markdown", - "id": "a2e9073e", + "id": "7679a1a9", "metadata": { "editable": true }, @@ -2580,7 +2580,7 @@ }, { "cell_type": "markdown", - "id": "98404b6f", + "id": "8a19cfcc", "metadata": { "editable": true }, @@ -2593,7 +2593,7 @@ }, { "cell_type": "markdown", - "id": "2c9563a1", + "id": "eba84a66", "metadata": { "editable": true }, @@ -2607,7 +2607,7 @@ }, { "cell_type": "markdown", - "id": "9416f11d", + "id": "f5755090", "metadata": { "editable": true }, @@ -2629,7 +2629,7 @@ }, { "cell_type": "markdown", - "id": "8da26655", + "id": "89d04a88", "metadata": { "editable": true }, @@ -2644,7 +2644,7 @@ }, { "cell_type": "markdown", - "id": "bc10af13", + "id": "d64176d4", "metadata": { "editable": true }, @@ -2656,7 +2656,7 @@ }, { "cell_type": "markdown", - "id": "3d6b10ba", + "id": "f0f0af10", "metadata": { "editable": true }, @@ -2669,7 +2669,7 @@ }, { "cell_type": "markdown", - "id": "aecc765e", + "id": "f720494b", "metadata": { "editable": true }, @@ -2683,7 +2683,7 @@ }, { "cell_type": "markdown", - "id": "1ff38661", + "id": "6b10a625", "metadata": { "editable": true }, @@ -2694,7 +2694,7 @@ { "cell_type": "code", "execution_count": 12, - "id": "0bfd88f4", + "id": "99d07a9e", "metadata": { "collapsed": false, "editable": true @@ -2719,7 +2719,7 @@ }, { "cell_type": "markdown", - "id": "897b03c6", + "id": "52efa202", "metadata": { "editable": true }, @@ -2735,7 +2735,7 @@ }, { "cell_type": "markdown", - "id": "3aff1545", + "id": "568802bc", "metadata": { "editable": true }, @@ -2756,7 +2756,7 @@ }, { "cell_type": "markdown", - "id": "ccc9a60d", + "id": "f4499506", "metadata": { "editable": true }, @@ -2776,7 +2776,7 @@ }, { "cell_type": "markdown", - "id": "70cf7621", + "id": "8fe9438b", "metadata": { "editable": true }, @@ -2795,7 +2795,7 @@ { "cell_type": "code", "execution_count": 13, - "id": "0276e5cc", + "id": "7ae0653e", "metadata": { "collapsed": false, "editable": true @@ -2830,7 +2830,7 @@ }, { "cell_type": "markdown", - "id": "e6923a4b", + "id": "27e4dae0", "metadata": { "editable": true }, @@ -2843,7 +2843,7 @@ { "cell_type": "code", "execution_count": 14, - "id": "91a543b0", + "id": "9e8761de", "metadata": { "collapsed": false, "editable": true @@ -2920,7 +2920,7 @@ }, { "cell_type": "markdown", - "id": "4c4d7160", + "id": "cee17d5b", "metadata": { "editable": true }, @@ -2935,7 +2935,7 @@ }, { "cell_type": "markdown", - "id": "47ad1177", + "id": "35347efd", "metadata": { "editable": true }, @@ -2950,7 +2950,7 @@ }, { "cell_type": "markdown", - "id": "55139c9d", + "id": "9821a818", "metadata": { "editable": true }, @@ -2962,7 +2962,7 @@ }, { "cell_type": "markdown", - "id": "ba5d79f7", + "id": "b4b9e68d", "metadata": { "editable": true }, @@ -2980,7 +2980,7 @@ }, { "cell_type": "markdown", - "id": "f3dbddf8", + "id": "8ebaf5b0", "metadata": { "editable": true }, @@ -2999,7 +2999,7 @@ }, { "cell_type": "markdown", - "id": "2663e3d9", + "id": "9fb573ac", "metadata": { "editable": true }, @@ -3011,7 +3011,7 @@ }, { "cell_type": "markdown", - "id": "47252196", + "id": "95c18b0f", "metadata": { "editable": true }, @@ -3021,7 +3021,7 @@ }, { "cell_type": "markdown", - "id": "906972a3", + "id": "27e35618", "metadata": { "editable": true }, @@ -3037,7 +3037,7 @@ }, { "cell_type": "markdown", - "id": "9b30fb4f", + "id": "f9a5d451", "metadata": { "editable": true }, @@ -3049,7 +3049,7 @@ }, { "cell_type": "markdown", - "id": "bf337271", + "id": "dcdb5059", "metadata": { "editable": true }, @@ -3059,7 +3059,7 @@ }, { "cell_type": "markdown", - "id": "22b6483f", + "id": "2fa88353", "metadata": { "editable": true }, @@ -3071,7 +3071,7 @@ }, { "cell_type": "markdown", - "id": "6a1f145e", + "id": "f900e21e", "metadata": { "editable": true }, @@ -3081,7 +3081,7 @@ }, { "cell_type": "markdown", - "id": "8cd3eb09", + "id": "257e6504", "metadata": { "editable": true }, @@ -3093,7 +3093,7 @@ }, { "cell_type": "markdown", - "id": "d0d2fe73", + "id": "c70b04b3", "metadata": { "editable": true }, @@ -3109,7 +3109,7 @@ }, { "cell_type": "markdown", - "id": "0adccd47", + "id": "a90c8352", "metadata": { "editable": true }, @@ -3121,7 +3121,7 @@ }, { "cell_type": "markdown", - "id": "9f2b327e", + "id": "fba8ec5d", "metadata": { "editable": true }, @@ -3154,7 +3154,7 @@ }, { "cell_type": "markdown", - "id": "44fbe404", + "id": "43b417d7", "metadata": { "editable": true }, @@ -3166,7 +3166,7 @@ }, { "cell_type": "markdown", - "id": "e313eeff", + "id": "68b90133", "metadata": { "editable": true }, @@ -3184,7 +3184,7 @@ }, { "cell_type": "markdown", - "id": "7708a12c", + "id": "a76ab8e2", "metadata": { "editable": true }, @@ -3194,7 +3194,7 @@ }, { "cell_type": "markdown", - "id": "dd075d28", + "id": "af9fb961", "metadata": { "editable": true }, @@ -3225,7 +3225,7 @@ }, { "cell_type": "markdown", - "id": "a401e710", + "id": "ddeed265", "metadata": { "editable": true }, @@ -3240,7 +3240,7 @@ }, { "cell_type": "markdown", - "id": "03c130fa", + "id": "291adb82", "metadata": { "editable": true }, @@ -3258,7 +3258,7 @@ }, { "cell_type": "markdown", - "id": "e641e929", + "id": "42e4df6d", "metadata": { "editable": true }, @@ -3270,7 +3270,7 @@ }, { "cell_type": "markdown", - "id": "18c8aa8d", + "id": "b43031f3", "metadata": { "editable": true }, @@ -3282,7 +3282,7 @@ }, { "cell_type": "markdown", - "id": "46597677", + "id": "7baa4c51", "metadata": { "editable": true }, @@ -3300,7 +3300,7 @@ }, { "cell_type": "markdown", - "id": "db604c08", + "id": "8d5d64e1", "metadata": { "editable": true }, @@ -3329,7 +3329,7 @@ }, { "cell_type": "markdown", - "id": "5f21aceb", + "id": "8e03c514", "metadata": { "editable": true }, @@ -3347,7 +3347,7 @@ }, { "cell_type": "markdown", - "id": "e9b5219a", + "id": "7b2628ed", "metadata": { "editable": true }, @@ -3359,7 +3359,7 @@ }, { "cell_type": "markdown", - "id": "223344a1", + "id": "4ed84706", "metadata": { "editable": true }, @@ -3371,7 +3371,7 @@ }, { "cell_type": "markdown", - "id": "19f5fd77", + "id": "4776feba", "metadata": { "editable": true }, @@ -3383,7 +3383,7 @@ }, { "cell_type": "markdown", - "id": "c8bc527e", + "id": "0c990dc1", "metadata": { "editable": true }, @@ -3395,7 +3395,7 @@ }, { "cell_type": "markdown", - "id": "df59808d", + "id": "6ef9b119", "metadata": { "editable": true }, @@ -3407,7 +3407,7 @@ }, { "cell_type": "markdown", - "id": "aaffa7f8", + "id": "899d64fb", "metadata": { "editable": true }, @@ -3424,7 +3424,7 @@ }, { "cell_type": "markdown", - "id": "70305113", + "id": "9c93975f", "metadata": { "editable": true }, @@ -3443,7 +3443,7 @@ }, { "cell_type": "markdown", - "id": "8446ccef", + "id": "de8c7158", "metadata": { "editable": true }, @@ -3455,7 +3455,7 @@ }, { "cell_type": "markdown", - "id": "d6f482ec", + "id": "c32850ec", "metadata": { "editable": true }, @@ -3469,7 +3469,7 @@ }, { "cell_type": "markdown", - "id": "516a9609", + "id": "9f274cf8", "metadata": { "editable": true }, @@ -3489,7 +3489,7 @@ }, { "cell_type": "markdown", - "id": "012b9de9", + "id": "a17d68d5", "metadata": { "editable": true }, @@ -3527,7 +3527,7 @@ }, { "cell_type": "markdown", - "id": "2c3f4cd1", + "id": "231b1e7c", "metadata": { "editable": true }, @@ -3539,7 +3539,7 @@ }, { "cell_type": "markdown", - "id": "0612ac57", + "id": "a17063fb", "metadata": { "editable": true }, @@ -3549,7 +3549,7 @@ }, { "cell_type": "markdown", - "id": "a09764b1", + "id": "286438d2", "metadata": { "editable": true }, @@ -3561,7 +3561,7 @@ }, { "cell_type": "markdown", - "id": "a971d493", + "id": "46e032ff", "metadata": { "editable": true }, @@ -3572,7 +3572,7 @@ { "cell_type": "code", "execution_count": 15, - "id": "592f8078", + "id": "9e9cf074", "metadata": { "collapsed": false, "editable": true @@ -3617,7 +3617,7 @@ }, { "cell_type": "markdown", - "id": "3ad717cf", + "id": "3f1c32e8", "metadata": { "editable": true }, @@ -3634,7 +3634,7 @@ { "cell_type": "code", "execution_count": 16, - "id": "a5d9ff13", + "id": "82582292", "metadata": { "collapsed": false, "editable": true @@ -3662,7 +3662,7 @@ }, { "cell_type": "markdown", - "id": "e91a824d", + "id": "dfec99fc", "metadata": { "editable": true }, @@ -3677,7 +3677,7 @@ { "cell_type": "code", "execution_count": 17, - "id": "4ce4d756", + "id": "d0b87f74", "metadata": { "collapsed": false, "editable": true @@ -3721,7 +3721,7 @@ }, { "cell_type": "markdown", - "id": "a12460ab", + "id": "7fada558", "metadata": { "editable": true }, @@ -3731,7 +3731,7 @@ }, { "cell_type": "markdown", - "id": "a99b746f", + "id": "0f886cfb", "metadata": { "editable": true }, @@ -3742,7 +3742,7 @@ { "cell_type": "code", "execution_count": 18, - "id": "888c7eff", + "id": "9c9c4df9", "metadata": { "collapsed": false, "editable": true @@ -3770,7 +3770,7 @@ }, { "cell_type": "markdown", - "id": "30c2c76e", + "id": "6ec0147f", "metadata": { "editable": true }, @@ -3785,7 +3785,7 @@ }, { "cell_type": "markdown", - "id": "bb93a532", + "id": "5446ffe8", "metadata": { "editable": true }, @@ -3796,7 +3796,7 @@ { "cell_type": "code", "execution_count": 19, - "id": "4c771981", + "id": "ca1ab7d2", "metadata": { "collapsed": false, "editable": true @@ -3824,7 +3824,7 @@ }, { "cell_type": "markdown", - "id": "0b0ed151", + "id": "4d4eba85", "metadata": { "editable": true }, @@ -3835,7 +3835,7 @@ { "cell_type": "code", "execution_count": 20, - "id": "dde0202d", + "id": "6c7b4c12", "metadata": { "collapsed": false, "editable": true @@ -3860,7 +3860,7 @@ }, { "cell_type": "markdown", - "id": "126b10f8", + "id": "9dddde59", "metadata": { "editable": true }, @@ -3871,7 +3871,7 @@ { "cell_type": "code", "execution_count": 21, - "id": "2394cae9", + "id": "be215e26", "metadata": { "collapsed": false, "editable": true @@ -3907,7 +3907,7 @@ { "cell_type": "code", "execution_count": 22, - "id": "b38afc90", + "id": "7c62a516", "metadata": { "collapsed": false, "editable": true @@ -3927,7 +3927,7 @@ }, { "cell_type": "markdown", - "id": "1af76d42", + "id": "ea928f66", "metadata": { "editable": true }, @@ -3938,7 +3938,7 @@ { "cell_type": "code", "execution_count": 23, - "id": "2a026b87", + "id": "918b74cc", "metadata": { "collapsed": false, "editable": true @@ -3976,7 +3976,7 @@ }, { "cell_type": "markdown", - "id": "d00daeeb", + "id": "f19cbc65", "metadata": { "editable": true }, @@ -3986,7 +3986,7 @@ }, { "cell_type": "markdown", - "id": "baa84f41", + "id": "6b2c5881", "metadata": { "editable": true }, @@ -4000,7 +4000,7 @@ { "cell_type": "code", "execution_count": 24, - "id": "0308cfd8", + "id": "9b68aec1", "metadata": { "collapsed": false, "editable": true @@ -4022,7 +4022,7 @@ }, { "cell_type": "markdown", - "id": "d827fb20", + "id": "723d762d", "metadata": { "editable": true }, @@ -4032,7 +4032,7 @@ }, { "cell_type": "markdown", - "id": "7fc41308", + "id": "6d7d989e", "metadata": { "editable": true }, @@ -4043,7 +4043,7 @@ { "cell_type": "code", "execution_count": 25, - "id": "30989d6c", + "id": "3559c2cb", "metadata": { "collapsed": false, "editable": true @@ -4065,7 +4065,7 @@ }, { "cell_type": "markdown", - "id": "73ccedf5", + "id": "51c3fee4", "metadata": { "editable": true }, @@ -4078,7 +4078,7 @@ { "cell_type": "code", "execution_count": 26, - "id": "ffd95824", + "id": "9ca02fad", "metadata": { "collapsed": false, "editable": true @@ -4103,7 +4103,7 @@ }, { "cell_type": "markdown", - "id": "f45616e1", + "id": "fadb03a2", "metadata": { "editable": true }, @@ -4115,7 +4115,7 @@ { "cell_type": "code", "execution_count": 27, - "id": "5d8293bc", + "id": "a267c85f", "metadata": { "collapsed": false, "editable": true @@ -4130,7 +4130,7 @@ }, { "cell_type": "markdown", - "id": "b0bf29ea", + "id": "e5f0be99", "metadata": { "editable": true }, @@ -4145,7 +4145,7 @@ { "cell_type": "code", "execution_count": 28, - "id": "8ff9539c", + "id": "134f3682", "metadata": { "collapsed": false, "editable": true @@ -4205,7 +4205,7 @@ }, { "cell_type": "markdown", - "id": "18b6a498", + "id": "bfcb5de2", "metadata": { "editable": true }, @@ -4216,7 +4216,7 @@ { "cell_type": "code", "execution_count": 29, - "id": "1414904c", + "id": "23a94b70", "metadata": { "collapsed": false, "editable": true @@ -4280,7 +4280,7 @@ }, { "cell_type": "markdown", - "id": "6749a917", + "id": "27e037a3", "metadata": { "editable": true }, @@ -4291,7 +4291,7 @@ { "cell_type": "code", "execution_count": 30, - "id": "cb359ac1", + "id": "d05b20bf", "metadata": { "collapsed": false, "editable": true @@ -4340,7 +4340,7 @@ }, { "cell_type": "markdown", - "id": "4a053c61", + "id": "d13c8737", "metadata": { "editable": true }, @@ -4352,7 +4352,7 @@ { "cell_type": "code", "execution_count": 31, - "id": "237e8e34", + "id": "091d1190", "metadata": { "collapsed": false, "editable": true @@ -4436,7 +4436,7 @@ }, { "cell_type": "markdown", - "id": "25351a67", + "id": "07923dc6", "metadata": { "editable": true }, @@ -4447,7 +4447,7 @@ { "cell_type": "code", "execution_count": 32, - "id": "ed9dfd38", + "id": "3d64b1c0", "metadata": { "collapsed": false, "editable": true @@ -4525,7 +4525,7 @@ }, { "cell_type": "markdown", - "id": "8d34c4fc", + "id": "402c1916", "metadata": { "editable": true }, @@ -4536,7 +4536,7 @@ { "cell_type": "code", "execution_count": 33, - "id": "0970ff25", + "id": "46c3b509", "metadata": { "collapsed": false, "editable": true @@ -4600,7 +4600,7 @@ }, { "cell_type": "markdown", - "id": "cd606f46", + "id": "a9332be2", "metadata": { "editable": true }, @@ -4610,7 +4610,7 @@ }, { "cell_type": "markdown", - "id": "2e53d090", + "id": "779b4b26", "metadata": { "editable": true }, @@ -4621,7 +4621,7 @@ { "cell_type": "code", "execution_count": 34, - "id": "ed042f25", + "id": "024961b7", "metadata": { "collapsed": false, "editable": true @@ -4690,7 +4690,7 @@ }, { "cell_type": "markdown", - "id": "13ea32ca", + "id": "26e4c513", "metadata": { "editable": true }, @@ -4701,7 +4701,7 @@ { "cell_type": "code", "execution_count": 35, - "id": "6953bd9c", + "id": "4ea50168", "metadata": { "collapsed": false, "editable": true @@ -4745,7 +4745,7 @@ }, { "cell_type": "markdown", - "id": "dae45584", + "id": "ec11c5ee", "metadata": { "editable": true }, @@ -4764,7 +4764,7 @@ { "cell_type": "code", "execution_count": 36, - "id": "0131f40c", + "id": "e0243ea4", "metadata": { "collapsed": false, "editable": true @@ -4784,7 +4784,7 @@ }, { "cell_type": "markdown", - "id": "e1b80b40", + "id": "ecb14805", "metadata": { "editable": true }, @@ -4797,6 +4797,35 @@ "\n", "* Extend from linear regression to logistic regression." ] + }, + { + "cell_type": "markdown", + "id": "ce9501d7", + "metadata": { + "editable": true + }, + "source": [ + "## algorithms\n", + "\n", + "\\begin{algorithm}\n", + "\\*Figure: An algorithm with caption*\n", + "\\KwData{$n \\geq 0$}\n", + "\\KwResult{$y = x^n$}\n", + "$y \\gets 1$\\;\n", + "$X \\gets x$\\;\n", + "$N \\gets n$\\;\n", + "\\While{$N \\neq 0$}{\n", + " \\eIf{$N$ is even}{\n", + " $X \\gets X \\times X$\\;\n", + " $N \\gets \\frac{N}{2}$ \\Comment*[r]{This is a comment}\n", + " }{\\If{$N$ is odd}{\n", + " $y \\gets y \\times X$\\;\n", + " $N \\gets N - 1$\\;\n", + " }\n", + " }\n", + "}\n", + "\\end{algorithm}" + ] } ], "metadata": {}, diff --git a/doc/src/week39/week39.do.txt b/doc/src/week39/week39.do.txt index a63e6e7ad..1c0c3fe7e 100644 --- a/doc/src/week39/week39.do.txt +++ b/doc/src/week39/week39.do.txt @@ -2638,40 +2638,27 @@ print(derivative_fn(x_small)) * Extend from linear regression to logistic regression. +!split +===== algorithms ===== -AdaGrad (for adaptive gradient algorithm) is a modified stochastic gradient descent algorithm with per-parameter learning rate, first published in 2011.[24] Informally, this increases the learning rate for sparser parameters and decreases the learning rate for ones that are less sparse. This strategy often improves convergence performance over standard stochastic gradient descent in settings where data is sparse and sparse parameters are more informative. Examples of such applications include natural language processing and image recognition.[24] It still has a base learning rate η, but this is multiplied with the elements of a vector {Gj,j} which is the diagonal of the outer product matrix +\begin{algorithm} +\caption{An algorithm with caption} +\KwData{$n \geq 0$} +\KwResult{$y = x^n$} +$y \gets 1$\; +$X \gets x$\; +$N \gets n$\; +\While{$N \neq 0$}{ + \eIf{$N$ is even}{ + $X \gets X \times X$\; + $N \gets \frac{N}{2}$ \Comment*[r]{This is a comment} + }{\If{$N$ is odd}{ + $y \gets y \times X$\; + $N \gets N - 1$\; + } + } +} +\end{algorithm} -{\displaystyle G=\sum _{\tau =1}^{t}g_{\tau }g_{\tau }^{\mathsf {T}}}G=\sum _{\tau =1}^{t}g_{\tau }g_{\tau }^{\mathsf {T}} -where {\displaystyle g_{\tau }=\nabla Q_{i}(w)}g_{\tau }=\nabla Q_{i}(w), the gradient, at iteration τ. The diagonal is given by -{\displaystyle G_{j,j}=\sum _{\tau =1}^{t}g_{\tau ,j}^{2}}G_{j,j}=\sum _{\tau =1}^{t}g_{\tau ,j}^{2}. -This vector is updated after every iteration. The formula for an update is now -{\displaystyle w:=w-\eta \,\mathrm {diag} (G)^{-{\frac {1}{2}}}\odot g}{\displaystyle w:=w-\eta \,\mathrm {diag} (G)^{-{\frac {1}{2}}}\odot g}[a] -or, written as per-parameter updates, - -{\displaystyle w_{j}:=w_{j}-{\frac {\eta }{\sqrt {G_{j,j}}}}g_{j}.}w_{j}:=w_{j}-{\frac {\eta }{\sqrt {G_{j,j}}}}g_{j}. -Each {G(i,i)} gives rise to a scaling factor for the learning rate that applies to a single parameter wi. Since the denominator in this factor, {\displaystyle {\sqrt {G_{i}}}={\sqrt {\sum _{\tau =1}^{t}g_{\tau }^{2}}}}{\sqrt {G_{i}}}={\sqrt {\sum _{\tau =1}^{t}g_{\tau }^{2}}} is the ℓ2 norm of previous derivatives, extreme parameter updates get dampened, while parameters that get few or small updates receive higher learning rates.[21] - -While designed for convex problems, AdaGrad has been successfully applied to non-convex optimization.[25] - -RMSProp -RMSProp (for Root Mean Square Propagation) is also a method in which the learning rate is adapted for each of the parameters. The idea is to divide the learning rate for a weight by a running average of the magnitudes of recent gradients for that weight.[26] So, first the running average is calculated in terms of means square, - -{\displaystyle v(w,t):=\gamma v(w,t-1)+(1-\gamma )(\nabla Q_{i}(w))^{2}}{\displaystyle v(w,t):=\gamma v(w,t-1)+(1-\gamma )(\nabla Q_{i}(w))^{2}} -where, {\displaystyle \gamma }\gamma is the forgetting factor. - -And the parameters are updated as, - -{\displaystyle w:=w-{\frac {\eta }{\sqrt {v(w,t)}}}\nabla Q_{i}(w)}{\displaystyle w:=w-{\frac {\eta }{\sqrt {v(w,t)}}}\nabla Q_{i}(w)} -RMSProp has shown good adaptation of learning rate in different applications. RMSProp can be seen as a generalization of Rprop and is capable to work with mini-batches as well opposed to only full-batches.[27] - -Adam -Adam[28] (short for Adaptive Moment Estimation) is an update to the RMSProp optimizer. In this optimization algorithm, running averages of both the gradients and the second moments of the gradients are used. Given parameters {\displaystyle w^{(t)}}{\displaystyle w^{(t)}} and a loss function {\displaystyle L^{(t)}}{\displaystyle L^{(t)}}, where {\displaystyle t}t indexes the current training iteration (indexed at {\displaystyle 0}{\displaystyle 0 }), Adam's parameter update is given by: - -{\displaystyle m_{w}^{(t+1)}\leftarrow \beta _{1}m_{w}^{(t)}+(1-\beta _{1})\nabla _{w}L^{(t)}}{\displaystyle m_{w}^{(t+1)}\leftarrow \beta _{1}m_{w}^{(t)}+(1-\beta _{1})\nabla _{w}L^{(t)}} -{\displaystyle v_{w}^{(t+1)}\leftarrow \beta _{2}v_{w}^{(t)}+(1-\beta _{2})(\nabla _{w}L^{(t)})^{2}}{\displaystyle v_{w}^{(t+1)}\leftarrow \beta _{2}v_{w}^{(t)}+(1-\beta _{2})(\nabla _{w}L^{(t)})^{2}} -{\displaystyle {\hat {m}}_{w}={\frac {m_{w}^{(t+1)}}{1-\beta _{1}^{t}}}}{\displaystyle {\hat {m}}_{w}={\frac {m_{w}^{(t+1)}}{1-\beta _{1}^{t}}}} -{\displaystyle {\hat {v}}_{w}={\frac {v_{w}^{(t+1)}}{1-\beta _{2}^{t}}}}{\displaystyle {\hat {v}}_{w}={\frac {v_{w}^{(t+1)}}{1-\beta _{2}^{t}}}} -{\displaystyle w^{(t+1)}\leftarrow w^{(t)}-\eta {\frac {{\hat {m}}_{w}}{{\sqrt {{\hat {v}}_{w}}}+\epsilon }}}{\displaystyle w^{(t+1)}\leftarrow w^{(t)}-\eta {\frac {{\hat {m}}_{w}}{{\sqrt {{\hat {v}}_{w}}}+\epsilon }}} -where {\displaystyle \epsilon }\epsilon is a small scalar (e.g. {\displaystyle 10^{-8}}10^{{-8}}) used to prevent division by 0, and {\displaystyle \beta _{1}}\beta _{1} (e.g. 0.9) and {\displaystyle \beta _{2}}\beta _{2} (e.g. 0.999) are the forgetting factors for gradients and second moments of gradients, respectively. Squaring and square-rooting is done element-wise.