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Morten Hjorth-Jensen
2021-08-08 22:31:23 +02:00
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commit 2699eaf42b
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doc/pub/week34/html/week34-bs.html
+106 -79
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@@ -139,43 +166,43 @@ MathJax.Hub.Config({
<li class="dropdown">
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
<ul class="dropdown-menu">
<!-- navigation toc: --> <li><a href="._week34-bs001.html#___sec0" style="font-size: 80%;"><b>Overview of first week</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs002.html#___sec1" style="font-size: 80%;"><b>Thursday August 20</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs003.html#___sec2" style="font-size: 80%;"><b>Lectures and ComputerLab</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs004.html#___sec3" style="font-size: 80%;"><b>Course Format</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs005.html#___sec4" style="font-size: 80%;"><b>Teachers</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs006.html#___sec5" style="font-size: 80%;"><b>Deadlines for projects (tentative)</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs007.html#___sec6" style="font-size: 80%;"><b>Recommended textbooks</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs008.html#___sec7" style="font-size: 80%;"><b>Prerequisites</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs009.html#___sec8" style="font-size: 80%;"><b>Learning outcomes</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs010.html#___sec9" style="font-size: 80%;"><b>Topics covered in this course: Statistical analysis and optimization of data</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs011.html#___sec10" style="font-size: 80%;"><b>Topics covered in this course: Machine Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs012.html#___sec11" style="font-size: 80%;"><b>Extremely useful tools, strongly recommended</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs013.html#___sec12" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs014.html#___sec13" style="font-size: 80%;"><b>Introduction</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs015.html#___sec14" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs016.html#___sec15" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs017.html#___sec16" style="font-size: 80%;"><b>Software and needed installations</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs018.html#___sec17" style="font-size: 80%;"><b>Python installers</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs019.html#___sec18" style="font-size: 80%;"><b>Useful Python libraries</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs020.html#___sec19" style="font-size: 80%;"><b>Installing R, C++, cython or Julia</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs021.html#___sec20" style="font-size: 80%;"><b>Installing R, C++, cython, Numba etc</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs022.html#___sec21" style="font-size: 80%;"><b>Numpy examples and Important Matrix and vector handling packages</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs023.html#___sec22" style="font-size: 80%;"><b>Basic Matrix Features</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs024.html#___sec23" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Some famous Matrices</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs025.html#___sec24" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;More Basic Matrix Features</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs026.html#___sec25" style="font-size: 80%;"><b>Numpy and arrays</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs027.html#___sec26" style="font-size: 80%;"><b>Matrices in Python</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs028.html#___sec27" style="font-size: 80%;"><b>Meet the Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs029.html#___sec28" style="font-size: 80%;"><b>Friday August 21</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs030.html#___sec29" style="font-size: 80%;"><b>Reading Data and fitting</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs031.html#___sec30" style="font-size: 80%;"><b>Friday August 21</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec31" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Simple linear regression model using <b>scikit-learn</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec32" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec33" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Organizing our data</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec34" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Seeing the wood for the trees</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec35" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;And what about using neural networks?</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#___sec36" style="font-size: 80%;"><b>A first summary</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs001.html#overview-of-first-week" style="font-size: 80%;"><b>Overview of first week</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs002.html#thursday-august-26" style="font-size: 80%;"><b>Thursday August 26</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs003.html#lectures-and-computerlab" style="font-size: 80%;"><b>Lectures and ComputerLab</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs004.html#course-format" style="font-size: 80%;"><b>Course Format</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs005.html#teachers" style="font-size: 80%;"><b>Teachers</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs006.html#deadlines-for-projects-tentative" style="font-size: 80%;"><b>Deadlines for projects (tentative)</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs007.html#recommended-textbooks" style="font-size: 80%;"><b>Recommended textbooks</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs008.html#prerequisites" style="font-size: 80%;"><b>Prerequisites</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs009.html#learning-outcomes" style="font-size: 80%;"><b>Learning outcomes</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs010.html#topics-covered-in-this-course-statistical-analysis-and-optimization-of-data" style="font-size: 80%;"><b>Topics covered in this course: Statistical analysis and optimization of data</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs011.html#topics-covered-in-this-course-machine-learning" style="font-size: 80%;"><b>Topics covered in this course: Machine Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs012.html#extremely-useful-tools-strongly-recommended" style="font-size: 80%;"><b>Extremely useful tools, strongly recommended</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs013.html#other-courses-on-data-science-and-machine-learning-at-uio" style="font-size: 80%;"><b>Other courses on Data science and Machine Learning at UiO</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs014.html#introduction" style="font-size: 80%;"><b>Introduction</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs015.html#what-is-machine-learning" style="font-size: 80%;"><b>What is Machine Learning?</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs016.html#types-of-machine-learning" style="font-size: 80%;"><b>Types of Machine Learning</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs017.html#software-and-needed-installations" style="font-size: 80%;"><b>Software and needed installations</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs018.html#python-installers" style="font-size: 80%;"><b>Python installers</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs019.html#useful-python-libraries" style="font-size: 80%;"><b>Useful Python libraries</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs020.html#installing-r-c-cython-or-julia" style="font-size: 80%;"><b>Installing R, C++, cython or Julia</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs021.html#installing-r-c-cython-numba-etc" style="font-size: 80%;"><b>Installing R, C++, cython, Numba etc</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs022.html#numpy-examples-and-important-matrix-and-vector-handling-packages" style="font-size: 80%;"><b>Numpy examples and Important Matrix and vector handling packages</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs023.html#basic-matrix-features" style="font-size: 80%;"><b>Basic Matrix Features</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs024.html#some-famous-matrices" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Some famous Matrices</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs025.html#more-basic-matrix-features" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;More Basic Matrix Features</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs026.html#numpy-and-arrays" style="font-size: 80%;"><b>Numpy and arrays</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs027.html#matrices-in-python" style="font-size: 80%;"><b>Matrices in Python</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs028.html#meet-the-pandas" style="font-size: 80%;"><b>Meet the Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs031.html#friday-august-21" style="font-size: 80%;"><b>Friday August 21</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs030.html#reading-data-and-fitting" style="font-size: 80%;"><b>Reading Data and fitting</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs031.html#friday-august-21" style="font-size: 80%;"><b>Friday August 21</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#simple-linear-regression-model-using-_scikit-learn_" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Simple linear regression model using <b>scikit-learn</b></a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;To our real data: nuclear binding energies. Brief reminder on masses and binding energies</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#organizing-our-data" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Organizing our data</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#seeing-the-wood-for-the-trees" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Seeing the wood for the trees</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#and-what-about-using-neural-networks" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;And what about using neural networks?</a></li>
<!-- navigation toc: --> <li><a href="._week34-bs032.html#a-first-summary" style="font-size: 80%;"><b>A first summary</b></a></li>
</ul>
</li>
@@ -210,7 +237,7 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>
<center><h4>Sep 16, 2020</h4></center> <!-- date -->
<center><h4>Aug 8, 2021</h4></center> <!-- date -->
<br>
<p>
@@ -246,13 +273,13 @@ MathJax.Hub.Config({
<!-- Bootstrap footer
<footer>
<a href="http://..."><img width="250" align=right src="http://..."></a>
<a href="https://..."><img width="250" align=right src="https://..."></a>
</footer>
-->
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
<!-- copyright --> &copy; 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
</center>
doc/pub/week34/html/week34-reveal.html
+136 -139
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="description" content="Week 34: Introduction to the course, Logistics and Practicalities">
@@ -13,7 +13,7 @@
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.reveal .alert-block p+p {margin-top:5px}
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@@ -148,38 +148,38 @@ MathJax.Hub.Config({
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
<br>
<p>&nbsp;<br>
<center><h4>Sep 16, 2020</h4></center> <!-- date -->
<center><h4>Aug 8, 2021</h4></center> <!-- date -->
<br>
<p>
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
<!-- copyright --> &copy; 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
</center>
</section>
<section>
<h2 id="___sec0">Overview of first week </h2>
<h2 id="overview-of-first-week">Overview of first week </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<ul>
<p><li> Thursday August 20: First lecture: Presentation of the course, aims and content</li>
<p><li> Thursday August 26: First lecture: Presentation of the course, aims and content</li>
<p><li> Thursday: Second Lecture: Start with simple linear regression and repetition of linear algebra and elements of statistics</li>
<p><li> Friday August 21: Linear regression</li>
<p><li> Friday August 27: Linear regression</li>
<p><li> Computer lab: Wednesdays, 8am-6pm. First time: Wednesday August 26.</li>
<p><li> Computer lab: Wednesdays, 8am-6pm. First time: Wednesday August 25.</li>
</ul>
</div>
</section>
<section>
<h2 id="___sec1">Thursday August 20 </h2>
<h2 id="thursday-august-26">Thursday August 26 </h2>
<p>
<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/zoom_0.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a>.
@@ -187,14 +187,14 @@ MathJax.Hub.Config({
<section>
<h2 id="___sec2">Lectures and ComputerLab </h2>
<h2 id="lectures-and-computerlab">Lectures and ComputerLab </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<ul>
<p><li> Lectures: Thursday (12.15pm-2pm and Friday (12.15pm-2pm). Due to the present COVID-19 situation all lectures will be online. They will be recorded and posted online at the official UiO <a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/index.html" target="_blank">website</a>.</li>
<p><li> Lectures: Thursday (12.15pm-2pm and Friday (12.15pm-2pm).</li>
<p><li> Weekly reading assignments and videos needed to solve projects and exercises.</li>
@@ -211,7 +211,7 @@ MathJax.Hub.Config({
<section>
<h2 id="___sec3">Course Format </h2>
<h2 id="course-format">Course Format </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
@@ -239,7 +239,7 @@ MathJax.Hub.Config({
<section>
<h2 id="___sec4">Teachers </h2>
<h2 id="teachers">Teachers </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
@@ -264,17 +264,14 @@ MathJax.Hub.Config({
<p><li> <b>Office</b>: Department of Physics, University of Oslo, Eastern wing, room F&#216;452</li>
</ul>
<p><li> Michael Bitney, m.s.bitney@fys.uio.no</li>
<p><li> Kristian Wold, kriswold@student.matnat.uio.no</li>
<p><li> Nicolai Haug, nicoha@student.matnat.uio.no</li>
<p><li> Per-Dimitri S&#248;nsteland, perdimitri.bs@gmail.com</li>
<p>
</ul>
</div>
</section>
<section>
<h2 id="___sec5">Deadlines for projects (tentative) </h2>
<h2 id="deadlines-for-projects-tentative">Deadlines for projects (tentative) </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
@@ -294,7 +291,7 @@ Projects are handed in using <b>Canvas</b>. We use Github as repository for code
<section>
<h2 id="___sec6">Recommended textbooks </h2>
<h2 id="recommended-textbooks">Recommended textbooks </h2>
<ul>
<p><li> <a href="https://www.springer.com/gp/book/9780387848570" target="_blank">Trevor Hastie, Robert Tibshirani, Jerome H. Friedman, The Elements of Statistical Learning, Springer</a></li>
@@ -304,7 +301,7 @@ Projects are handed in using <b>Canvas</b>. We use Github as repository for code
<section>
<h2 id="___sec7">Prerequisites </h2>
<h2 id="prerequisites">Prerequisites </h2>
<p>
Basic knowledge in programming and mathematics, with an emphasis on
@@ -320,7 +317,7 @@ Python is the recurring programming language.
<section>
<h2 id="___sec8">Learning outcomes </h2>
<h2 id="learning-outcomes">Learning outcomes </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
@@ -345,7 +342,7 @@ This course aims at giving you insights and knowledge about many of the central
<section>
<h2 id="___sec9">Topics covered in this course: Statistical analysis and optimization of data </h2>
<h2 id="topics-covered-in-this-course-statistical-analysis-and-optimization-of-data">Topics covered in this course: Statistical analysis and optimization of data </h2>
<p>
The course has two central parts
@@ -360,7 +357,7 @@ These topics will be scattered thorughout the course and may not necessarily be
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b>Statistical analysis and optimization of data.</b>
<b>Statistical analysis and optimization of data</b>
<p>
The following topics will be covered
@@ -378,7 +375,7 @@ The following topics will be covered
<section>
<h2 id="___sec10">Topics covered in this course: Machine Learning </h2>
<h2 id="topics-covered-in-this-course-machine-learning">Topics covered in this course: Machine Learning </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
@@ -405,11 +402,11 @@ Hands-on demonstrations, exercises and projects aim at deepening your understand
<section>
<h2 id="___sec11">Extremely useful tools, strongly recommended </h2>
<h2 id="extremely-useful-tools-strongly-recommended">Extremely useful tools, strongly recommended </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b>and discussed at the lab sessions.</b>
<b>and discussed at the lab sessions</b>
<ul>
<p><li> GIT for version control, and GitHub or GitLab as repositories, highly recommended. This will be discussed during the first exercise session</li>
@@ -421,7 +418,7 @@ Hands-on demonstrations, exercises and projects aim at deepening your understand
<section>
<h2 id="___sec12">Other courses on Data science and Machine Learning at UiO </h2>
<h2 id="other-courses-on-data-science-and-machine-learning-at-uio">Other courses on Data science and Machine Learning at UiO </h2>
<p>
The link here <a href="https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/" target="_blank"><tt>https://www.mn.uio.no/english/research/about/centre-focus/innovation/data-science/studies/</tt></a> gives an excellent overview of courses on Machine learning at UiO.
@@ -443,7 +440,7 @@ The link here <a href="https://www.mn.uio.no/english/research/about/centre-focus
<section>
<h2 id="___sec13">Introduction </h2>
<h2 id="introduction">Introduction </h2>
<p>
Our emphasis throughout this series of lectures
@@ -485,7 +482,7 @@ get started with programming.
<section>
<h2 id="___sec14">What is Machine Learning? </h2>
<h2 id="what-is-machine-learning">What is Machine Learning? </h2>
<p>
Statistics, data science and machine learning form important fields of
@@ -558,7 +555,7 @@ of algorithms and methods we will discuss.
<section>
<h2 id="___sec15">Types of Machine Learning </h2>
<h2 id="types-of-machine-learning">Types of Machine Learning </h2>
<p>
The approaches to machine learning are many, but are often split into
@@ -600,7 +597,7 @@ At the heart of basically all ML algorithms there are so-called minimization alg
<section>
<h2 id="___sec16">Software and needed installations </h2>
<h2 id="software-and-needed-installations">Software and needed installations </h2>
<p>
We will make extensive use of Python as programming language and its
@@ -646,7 +643,7 @@ etc etc.
<section>
<h2 id="___sec17">Python installers </h2>
<h2 id="python-installers">Python installers </h2>
<p>
If you don't want to perform these operations separately and venture
@@ -682,7 +679,7 @@ no setup and runs entirely in the cloud. Try it out!
<section>
<h2 id="___sec18">Useful Python libraries </h2>
<h2 id="useful-python-libraries">Useful Python libraries </h2>
Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)
<ul>
@@ -702,7 +699,7 @@ Here we list several useful Python libraries we strongly recommend (if you use a
<section>
<h2 id="___sec19">Installing R, C++, cython or Julia </h2>
<h2 id="installing-r-c-cython-or-julia">Installing R, C++, cython or Julia </h2>
<p>
You will also find it convenient to utilize <b>R</b>. We will mainly
@@ -723,7 +720,7 @@ To install <b>R</b> with Jupyter notebook
<section>
<h2 id="___sec20">Installing R, C++, cython, Numba etc </h2>
<h2 id="installing-r-c-cython-numba-etc">Installing R, C++, cython, Numba etc </h2>
<p>
For the C++ aficionados, Jupyter/IPython notebook allows you also to
@@ -747,7 +744,7 @@ further processing. For example, convert to latex as
<p>
<!-- code=text typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>pycod jupyter nbconvert filename.ipynb --to latex
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>pycod jupyter nbconvert filename.ipynb --to latex
</pre></div>
<p>
And to add more versatility, the Python package <a href="http://www.sympy.org/en/index.html" target="_blank">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.
@@ -760,7 +757,7 @@ formats, ipython notebooks, latex files, pdf files etc with minimal edits. These
<section>
<h2 id="___sec21">Numpy examples and Important Matrix and vector handling packages </h2>
<h2 id="numpy-examples-and-important-matrix-and-vector-handling-packages">Numpy examples and Important Matrix and vector handling packages </h2>
<p>
There are several central software libraries for linear algebra and eigenvalue problems. Several of the more
@@ -780,11 +777,11 @@ developed in the 1970s, namely EISPACK and LINPACK. We describe them shortly he
<section>
<h2 id="___sec22">Basic Matrix Features </h2>
<h2 id="basic-matrix-features">Basic Matrix Features </h2>
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b>Matrix properties reminder.</b>
<b>Matrix properties reminder</b>
<p>&nbsp;<br>
$$
\mathbf{A} =
@@ -831,7 +828,7 @@ $$
<section>
<h3 id="___sec23">Some famous Matrices </h3>
<h3 id="some-famous-matrices">Some famous Matrices </h3>
<ul>
@@ -858,11 +855,11 @@ $$
<section>
<h3 id="___sec24">More Basic Matrix Features </h3>
<h3 id="more-basic-matrix-features">More Basic Matrix Features </h3>
<p>
<div class="alert alert-block alert-block alert-text-normal">
<b>Some Equivalent Statements.</b>
<b>Some Equivalent Statements</b>
<p>
For an \( N\times N \) matrix \( \mathbf{A} \) the following properties are all equivalent
@@ -885,22 +882,22 @@ For an \( N\times N \) matrix \( \mathbf{A} \) the following properties are all
<section>
<h2 id="___sec25">Numpy and arrays </h2>
<h2 id="numpy-and-arrays">Numpy and arrays </h2>
<a href="http://www.numpy.org/" target="_blank">Numpy</a> provides an easy way to handle arrays in Python. The standard way to import this library is as
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
</pre></div>
<p>
Here follows a simple example where we set up an array of ten elements, all determined by random numbers drawn according to the normal distribution,
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>n = <span style="color: #B452CD">10</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>n = <span style="color: #B452CD">10</span>
x = np.random.normal(size=n)
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
We defined a vector \( x \) with \( n=10 \) elements with its values given by the Normal distribution \( N(0,1) \).
@@ -908,9 +905,9 @@ Another alternative is to declare a vector as follows
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
x = np.array([<span style="color: #B452CD">1</span>, <span style="color: #B452CD">2</span>, <span style="color: #B452CD">3</span>])
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
Here we have defined a vector with three elements, with \( x_0=1 \), \( x_1=2 \) and \( x_2=3 \). Note that both Python and C++
@@ -918,9 +915,9 @@ start numbering array elements from \( 0 \) and on. This means that a vector wit
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
x = np.log(np.array([<span style="color: #B452CD">4</span>, <span style="color: #B452CD">7</span>, <span style="color: #B452CD">8</span>]))
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
In the last example we used Numpy's unary function \( np.log \). This function is
@@ -934,12 +931,12 @@ logarithms of a vector would be to write
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">math</span> <span style="color: #8B008B; font-weight: bold">import</span> log
x = np.array([<span style="color: #B452CD">4</span>, <span style="color: #B452CD">7</span>, <span style="color: #B452CD">8</span>])
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #B452CD">0</span>, <span style="color: #658b00">len</span>(x)):
x[i] = log(x[i])
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
We note that our code is much longer already and we need to import the <b>log</b> function from the <b>math</b> module.
@@ -947,33 +944,33 @@ The attentive reader will also notice that the output is \( [1, 1, 2] \). Python
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
x = np.log(np.array([<span style="color: #B452CD">4</span>, <span style="color: #B452CD">7</span>, <span style="color: #B452CD">8</span>], dtype = np.float64))
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
or simply write them as double precision numbers (Python uses 64 bits as default for floating point type variables), that is
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
x = np.log(np.array([<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">7.0</span>, <span style="color: #B452CD">8.0</span>])
<span style="color: #8B008B; font-weight: bold">print</span>(x)
<span style="color: #658b00">print</span>(x)
</pre></div>
<p>
To check the number of bytes (remember that one byte contains eight bits for double precision variables), you can use simple use the <b>itemsize</b> functionality (the array \( x \) is actually an object which inherits the functionalities defined in Numpy) as
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
x = np.log(np.array([<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">7.0</span>, <span style="color: #B452CD">8.0</span>])
<span style="color: #8B008B; font-weight: bold">print</span>(x.itemsize)
<span style="color: #658b00">print</span>(x.itemsize)
</pre></div>
</section>
<section>
<h2 id="___sec26">Matrices in Python </h2>
<h2 id="matrices-in-python">Matrices in Python </h2>
<p>
Having defined vectors, we are now ready to try out matrices. We can
@@ -983,62 +980,62 @@ lowercase letters for vectors and uppercase letters for matrices)
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
A = np.log(np.array([ [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">7.0</span>, <span style="color: #B452CD">8.0</span>], [<span style="color: #B452CD">3.0</span>, <span style="color: #B452CD">10.0</span>, <span style="color: #B452CD">11.0</span>], [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">5.0</span>, <span style="color: #B452CD">7.0</span>] ]))
<span style="color: #8B008B; font-weight: bold">print</span>(A)
<span style="color: #658b00">print</span>(A)
</pre></div>
<p>
If we use the <b>shape</b> function we would get \( (3, 3) \) as output, that is verifying that our matrix is a \( 3\times 3 \) matrix. We can slice the matrix and print for example the first column (Python organized matrix elements in a row-major order, see below) as
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
A = np.log(np.array([ [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">7.0</span>, <span style="color: #B452CD">8.0</span>], [<span style="color: #B452CD">3.0</span>, <span style="color: #B452CD">10.0</span>, <span style="color: #B452CD">11.0</span>], [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">5.0</span>, <span style="color: #B452CD">7.0</span>] ]))
<span style="color: #228B22"># print the first column, row-major order and elements start with 0</span>
<span style="color: #8B008B; font-weight: bold">print</span>(A[:,<span style="color: #B452CD">0</span>])
<span style="color: #658b00">print</span>(A[:,<span style="color: #B452CD">0</span>])
</pre></div>
<p>
We can continue this was by printing out other columns or rows. The example here prints out the second column
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
A = np.log(np.array([ [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">7.0</span>, <span style="color: #B452CD">8.0</span>], [<span style="color: #B452CD">3.0</span>, <span style="color: #B452CD">10.0</span>, <span style="color: #B452CD">11.0</span>], [<span style="color: #B452CD">4.0</span>, <span style="color: #B452CD">5.0</span>, <span style="color: #B452CD">7.0</span>] ]))
<span style="color: #228B22"># print the first column, row-major order and elements start with 0</span>
<span style="color: #8B008B; font-weight: bold">print</span>(A[<span style="color: #B452CD">1</span>,:])
<span style="color: #658b00">print</span>(A[<span style="color: #B452CD">1</span>,:])
</pre></div>
<p>
Numpy contains many other functionalities that allow us to slice, subdivide etc etc arrays. We strongly recommend that you look up the <a href="http://www.numpy.org/" target="_blank">Numpy website for more details</a>. Useful functions when defining a matrix are the <b>np.zeros</b> function which declares a matrix of a given dimension and sets all elements to zero
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
n = <span style="color: #B452CD">10</span>
<span style="color: #228B22"># define a matrix of dimension 10 x 10 and set all elements to zero</span>
A = np.zeros( (n, n) )
<span style="color: #8B008B; font-weight: bold">print</span>(A)
<span style="color: #658b00">print</span>(A)
</pre></div>
<p>
or initializing all elements to
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
n = <span style="color: #B452CD">10</span>
<span style="color: #228B22"># define a matrix of dimension 10 x 10 and set all elements to one</span>
A = np.ones( (n, n) )
<span style="color: #8B008B; font-weight: bold">print</span>(A)
<span style="color: #658b00">print</span>(A)
</pre></div>
<p>
or as unitarily distributed random numbers (see the material on random number generators in the statistics part)
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
n = <span style="color: #B452CD">10</span>
<span style="color: #228B22"># define a matrix of dimension 10 x 10 and set all elements to random numbers with x \in [0, 1]</span>
A = np.random.rand(n, n)
<span style="color: #8B008B; font-weight: bold">print</span>(A)
<span style="color: #658b00">print</span>(A)
</pre></div>
<p>
As we will see throughout these lectures, there are several extremely useful functionalities in Numpy.
@@ -1084,32 +1081,32 @@ covariance matrix through the <b>np.linalg.eig()</b> function.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
n = <span style="color: #B452CD">100</span>
x = np.random.normal(size=n)
<span style="color: #8B008B; font-weight: bold">print</span>(np.mean(x))
<span style="color: #658b00">print</span>(np.mean(x))
y = <span style="color: #B452CD">4</span>+<span style="color: #B452CD">3</span>*x+np.random.normal(size=n)
<span style="color: #8B008B; font-weight: bold">print</span>(np.mean(y))
<span style="color: #658b00">print</span>(np.mean(y))
z = x**<span style="color: #B452CD">3</span>+np.random.normal(size=n)
<span style="color: #8B008B; font-weight: bold">print</span>(np.mean(z))
<span style="color: #658b00">print</span>(np.mean(z))
W = np.vstack((x, y, z))
Sigma = np.cov(W)
<span style="color: #8B008B; font-weight: bold">print</span>(Sigma)
<span style="color: #658b00">print</span>(Sigma)
Eigvals, Eigvecs = np.linalg.eig(Sigma)
<span style="color: #8B008B; font-weight: bold">print</span>(Eigvals)
<span style="color: #658b00">print</span>(Eigvals)
</pre></div>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">scipy</span> <span style="color: #8B008B; font-weight: bold">import</span> sparse
eye = np.eye(<span style="color: #B452CD">4</span>)
<span style="color: #8B008B; font-weight: bold">print</span>(eye)
<span style="color: #658b00">print</span>(eye)
sparse_mtx = sparse.csr_matrix(eye)
<span style="color: #8B008B; font-weight: bold">print</span>(sparse_mtx)
<span style="color: #658b00">print</span>(sparse_mtx)
x = np.linspace(-<span style="color: #B452CD">10</span>,<span style="color: #B452CD">10</span>,<span style="color: #B452CD">100</span>)
y = np.sin(x)
plt.plot(x,y,marker=<span style="color: #CD5555">&#39;x&#39;</span>)
@@ -1119,7 +1116,7 @@ plt.show()
<section>
<h2 id="___sec27">Meet the Pandas </h2>
<h2 id="meet-the-pandas">Meet the Pandas </h2>
<p>
<br /><br /><center><p><img src="fig/pandas.jpg" align="bottom" width=600></p></center><br /><br />
@@ -1138,7 +1135,7 @@ The following simple example shows how we can, in an easy way make tables of our
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">IPython.display</span> <span style="color: #8B008B; font-weight: bold">import</span> display
data = {<span style="color: #CD5555">&#39;First Name&#39;</span>: [<span style="color: #CD5555">&quot;Frodo&quot;</span>, <span style="color: #CD5555">&quot;Bilbo&quot;</span>, <span style="color: #CD5555">&quot;Aragorn II&quot;</span>, <span style="color: #CD5555">&quot;Samwise&quot;</span>],
<span style="color: #CD5555">&#39;Last Name&#39;</span>: [<span style="color: #CD5555">&quot;Baggins&quot;</span>, <span style="color: #CD5555">&quot;Baggins&quot;</span>,<span style="color: #CD5555">&quot;Elessar&quot;</span>,<span style="color: #CD5555">&quot;Gamgee&quot;</span>],
@@ -1156,7 +1153,7 @@ Displaying these results, we see that the indices are given by the default numbe
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>data_pandas = pd.DataFrame(data,index=[<span style="color: #CD5555">&#39;Frodo&#39;</span>,<span style="color: #CD5555">&#39;Bilbo&#39;</span>,<span style="color: #CD5555">&#39;Aragorn&#39;</span>,<span style="color: #CD5555">&#39;Sam&#39;</span>])
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>data_pandas = pd.DataFrame(data,index=[<span style="color: #CD5555">&#39;Frodo&#39;</span>,<span style="color: #CD5555">&#39;Bilbo&#39;</span>,<span style="color: #CD5555">&#39;Aragorn&#39;</span>,<span style="color: #CD5555">&#39;Sam&#39;</span>])
display(data_pandas)
</pre></div>
<p>
@@ -1164,14 +1161,14 @@ Thereafter we display the content of the row which begins with the index <b>Arag
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>display(data_pandas.loc[<span style="color: #CD5555">&#39;Aragorn&#39;</span>])
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>display(data_pandas.loc[<span style="color: #CD5555">&#39;Aragorn&#39;</span>])
</pre></div>
<p>
We can easily append data to this, for example
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>new_hobbit = {<span style="color: #CD5555">&#39;First Name&#39;</span>: [<span style="color: #CD5555">&quot;Peregrin&quot;</span>],
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>new_hobbit = {<span style="color: #CD5555">&#39;First Name&#39;</span>: [<span style="color: #CD5555">&quot;Peregrin&quot;</span>],
<span style="color: #CD5555">&#39;Last Name&#39;</span>: [<span style="color: #CD5555">&quot;Took&quot;</span>],
<span style="color: #CD5555">&#39;Place of birth&#39;</span>: [<span style="color: #CD5555">&quot;Shire&quot;</span>],
<span style="color: #CD5555">&#39;Date of Birth T.A.&#39;</span>: [<span style="color: #B452CD">2990</span>]
@@ -1185,7 +1182,7 @@ of dimensionality \( 10\times 5 \) and compute the mean value and standard devia
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">IPython.display</span> <span style="color: #8B008B; font-weight: bold">import</span> display
np.random.seed(<span style="color: #B452CD">100</span>)
@@ -1195,8 +1192,8 @@ cols = <span style="color: #B452CD">5</span>
a = np.random.randn(rows,cols)
df = pd.DataFrame(a)
display(df)
<span style="color: #8B008B; font-weight: bold">print</span>(df.mean())
<span style="color: #8B008B; font-weight: bold">print</span>(df.std())
<span style="color: #658b00">print</span>(df.mean())
<span style="color: #658b00">print</span>(df.std())
display(df**<span style="color: #B452CD">2</span>)
</pre></div>
<p>
@@ -1204,13 +1201,13 @@ Thereafter we can select specific columns only and plot final results
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>df.columns = [<span style="color: #CD5555">&#39;First&#39;</span>, <span style="color: #CD5555">&#39;Second&#39;</span>, <span style="color: #CD5555">&#39;Third&#39;</span>, <span style="color: #CD5555">&#39;Fourth&#39;</span>, <span style="color: #CD5555">&#39;Fifth&#39;</span>]
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>df.columns = [<span style="color: #CD5555">&#39;First&#39;</span>, <span style="color: #CD5555">&#39;Second&#39;</span>, <span style="color: #CD5555">&#39;Third&#39;</span>, <span style="color: #CD5555">&#39;Fourth&#39;</span>, <span style="color: #CD5555">&#39;Fifth&#39;</span>]
df.index = np.arange(<span style="color: #B452CD">10</span>)
display(df)
<span style="color: #8B008B; font-weight: bold">print</span>(df[<span style="color: #CD5555">&#39;Second&#39;</span>].mean() )
<span style="color: #8B008B; font-weight: bold">print</span>(df.info())
<span style="color: #8B008B; font-weight: bold">print</span>(df.describe())
<span style="color: #658b00">print</span>(df[<span style="color: #CD5555">&#39;Second&#39;</span>].mean() )
<span style="color: #658b00">print</span>(df.info())
<span style="color: #658b00">print</span>(df.describe())
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">pylab</span> <span style="color: #8B008B; font-weight: bold">import</span> plt, mpl
plt.style.use(<span style="color: #CD5555">&#39;seaborn&#39;</span>)
@@ -1228,10 +1225,10 @@ We can produce a \( 4\times 4 \) matrix
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>b = np.arange(<span style="color: #B452CD">16</span>).reshape((<span style="color: #B452CD">4</span>,<span style="color: #B452CD">4</span>))
<span style="color: #8B008B; font-weight: bold">print</span>(b)
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>b = np.arange(<span style="color: #B452CD">16</span>).reshape((<span style="color: #B452CD">4</span>,<span style="color: #B452CD">4</span>))
<span style="color: #658b00">print</span>(b)
df1 = pd.DataFrame(b)
<span style="color: #8B008B; font-weight: bold">print</span>(df1)
<span style="color: #658b00">print</span>(df1)
</pre></div>
<p>
and many other operations.
@@ -1247,7 +1244,7 @@ For multidimensional arrays, we recommend strongly <a href="http://xarray.pydata
<section>
<h2 id="___sec28">Friday August 21 </h2>
<h2 id="friday-august-21">Friday August 21 </h2>
<p>
<a href="https://www.uio.no/studier/emner/matnat/fys/FYS-STK3155/h20/forelesningsvideoer/LectureAug21.mp4?vrtx=view-as-webpage" target="_blank">Video of Lecture</a> and <a href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/HandWrittenNotes/NotesAugust21.pdf" target="_blank">Handwritten notes</a>
@@ -1255,7 +1252,7 @@ For multidimensional arrays, we recommend strongly <a href="http://xarray.pydata
<section>
<h2 id="___sec29">Reading Data and fitting </h2>
<h2 id="reading-data-and-fitting">Reading Data and fitting </h2>
<p>
In order to study various Machine Learning algorithms, we need to
@@ -1294,13 +1291,13 @@ But before we really start with nuclear physics data, let's just look at some si
<section>
<h2 id="___sec30">Friday August 21 </h2>
<h2 id="friday-august-21">Friday August 21 </h2>
</section>
<section>
<h3 id="___sec31">Simple linear regression model using <b>scikit-learn</b> </h3>
<h3 id="simple-linear-regression-model-using-_scikit-learn_">Simple linear regression model using <b>scikit-learn</b> </h3>
<p>
We start with perhaps our simplest possible example, using <b>Scikit-Learn</b> to perform linear regression analysis on a data set produced by us.
@@ -1356,7 +1353,7 @@ The Python code follows here.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Importing various packages</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Importing various packages</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
@@ -1458,7 +1455,7 @@ We can modify easily the above Python code and plot the relative error instead
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
@@ -1493,7 +1490,7 @@ example of the functionality of <b>Scikit-Learn</b>.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LinearRegression
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.metrics</span> <span style="color: #8B008B; font-weight: bold">import</span> mean_squared_error, r2_score, mean_squared_log_error, mean_absolute_error
@@ -1503,16 +1500,16 @@ y = <span style="color: #B452CD">2.0</span>+ <span style="color: #B452CD">5</spa
linreg = LinearRegression()
linreg.fit(x,y)
ypredict = linreg.predict(x)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;The intercept alpha: \n&#39;</span>, linreg.intercept_)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Coefficient beta : \n&#39;</span>, linreg.coef_)
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;The intercept alpha: \n&#39;</span>, linreg.intercept_)
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Coefficient beta : \n&#39;</span>, linreg.coef_)
<span style="color: #228B22"># The mean squared error </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Mean squared error: %.2f&quot;</span> % mean_squared_error(y, ypredict))
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&quot;Mean squared error: %.2f&quot;</span> % mean_squared_error(y, ypredict))
<span style="color: #228B22"># Explained variance score: 1 is perfect prediction </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Variance score: %.2f&#39;</span> % r2_score(y, ypredict))
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Variance score: %.2f&#39;</span> % r2_score(y, ypredict))
<span style="color: #228B22"># Mean squared log error </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Mean squared log error: %.2f&#39;</span> % mean_squared_log_error(y, ypredict) )
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Mean squared log error: %.2f&#39;</span> % mean_squared_log_error(y, ypredict) )
<span style="color: #228B22"># Mean absolute error </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Mean absolute error: %.2f&#39;</span> % mean_absolute_error(y, ypredict))
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Mean absolute error: %.2f&#39;</span> % mean_absolute_error(y, ypredict))
plt.plot(x, ypredict, <span style="color: #CD5555">&quot;r-&quot;</span>)
plt.plot(x, y ,<span style="color: #CD5555">&#39;ro&#39;</span>)
plt.axis([<span style="color: #B452CD">0.0</span>,<span style="color: #B452CD">1.0</span>,<span style="color: #B452CD">1.5</span>, <span style="color: #B452CD">7.0</span>])
@@ -1606,7 +1603,7 @@ a linear \( x \)-dependence we study now a cubic polynomial and use the polynomi
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">random</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> Ridge
@@ -1635,10 +1632,10 @@ plt.show()
err=(y-yn)/yn
<span style="color: #8B008B; font-weight: bold">return</span> <span style="color: #658b00">abs</span>(np.sum(err))/<span style="color: #658b00">len</span>(err)
<span style="color: #8B008B; font-weight: bold">print</span> (error(y))
<span style="color: #658b00">print</span> (error(y))
</pre></div>
<h3 id="___sec32">To our real data: nuclear binding energies. Brief reminder on masses and binding energies </h3>
<h3 id="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 </h3>
<p>
Let us now dive into nuclear physics and remind ourselves briefly about some basic features about binding
@@ -1732,7 +1729,7 @@ 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.
<h3 id="___sec33">Organizing our data </h3>
<h3 id="organizing-our-data">Organizing our data </h3>
<p>
Let us start with reading and organizing our data.
@@ -1744,7 +1741,7 @@ We start with preparing folders for storing our calculations and the data file o
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Common imports</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Common imports</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">pandas</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">pd</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
@@ -1774,7 +1771,7 @@ DATA_ID = <span style="color: #CD5555">&quot;DataFiles/&quot;</span>
<span style="color: #8B008B; font-weight: bold">return</span> os.path.join(DATA_ID, dat_id)
<span style="color: #8B008B; font-weight: bold">def</span> <span style="color: #008b45">save_fig</span>(fig_id):
plt.savefig(image_path(fig_id) + <span style="color: #CD5555">&quot;.png&quot;</span>, format=<span style="color: #CD5555">&#39;png&#39;</span>)
plt.savefig(image_path(fig_id) + <span style="color: #CD5555">&quot;.png&quot;</span>, <span style="color: #658b00">format</span>=<span style="color: #CD5555">&#39;png&#39;</span>)
infile = <span style="color: #658b00">open</span>(data_path(<span style="color: #CD5555">&quot;MassEval2016.dat&quot;</span>),<span style="color: #CD5555">&#39;r&#39;</span>)
</pre></div>
@@ -1783,7 +1780,7 @@ Before we proceed, we define also a function for making our plots. You can obvio
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">pylab</span> <span style="color: #8B008B; font-weight: bold">import</span> plt, mpl
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">pylab</span> <span style="color: #8B008B; font-weight: bold">import</span> plt, mpl
plt.style.use(<span style="color: #CD5555">&#39;seaborn&#39;</span>)
mpl.rcParams[<span style="color: #CD5555">&#39;font.family&#39;</span>] = <span style="color: #CD5555">&#39;serif&#39;</span>
@@ -1807,7 +1804,7 @@ In particular, the program that outputs the final nuclear masses is written in F
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #CD5555">&quot;&quot;&quot; </span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #CD5555">&quot;&quot;&quot; </span>
<span style="color: #CD5555">This is taken from the data file of the mass 2016 evaluation. </span>
<span style="color: #CD5555">All files are 3436 lines long with 124 character per line. </span>
<span style="color: #CD5555"> Headers are 39 lines long. </span>
@@ -1827,12 +1824,12 @@ covert them into the <b>pandas</b> DataFrame structure.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Read the experimental data with Pandas</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Read the experimental data with Pandas</span>
Masses = pd.read_fwf(infile, usecols=(<span style="color: #B452CD">2</span>,<span style="color: #B452CD">3</span>,<span style="color: #B452CD">4</span>,<span style="color: #B452CD">6</span>,<span style="color: #B452CD">11</span>),
names=(<span style="color: #CD5555">&#39;N&#39;</span>, <span style="color: #CD5555">&#39;Z&#39;</span>, <span style="color: #CD5555">&#39;A&#39;</span>, <span style="color: #CD5555">&#39;Element&#39;</span>, <span style="color: #CD5555">&#39;Ebinding&#39;</span>),
widths=(<span style="color: #B452CD">1</span>,<span style="color: #B452CD">3</span>,<span style="color: #B452CD">5</span>,<span style="color: #B452CD">5</span>,<span style="color: #B452CD">5</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">3</span>,<span style="color: #B452CD">4</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">13</span>,<span style="color: #B452CD">11</span>,<span style="color: #B452CD">11</span>,<span style="color: #B452CD">9</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">2</span>,<span style="color: #B452CD">11</span>,<span style="color: #B452CD">9</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">3</span>,<span style="color: #B452CD">1</span>,<span style="color: #B452CD">12</span>,<span style="color: #B452CD">11</span>,<span style="color: #B452CD">1</span>),
header=<span style="color: #B452CD">39</span>,
index_col=<span style="color: #658b00">False</span>)
index_col=<span style="color: #8B008B; font-weight: bold">False</span>)
<span style="color: #228B22"># Extrapolated values are indicated by &#39;#&#39; in place of the decimal place, so</span>
<span style="color: #228B22"># the Ebinding column won&#39;t be numeric. Coerce to float and drop these entries.</span>
@@ -1861,12 +1858,12 @@ the number of nucleons \( A \), the number of protons \( Z \) and the number of
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>A = Masses[<span style="color: #CD5555">&#39;A&#39;</span>]
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>A = Masses[<span style="color: #CD5555">&#39;A&#39;</span>]
Z = Masses[<span style="color: #CD5555">&#39;Z&#39;</span>]
N = Masses[<span style="color: #CD5555">&#39;N&#39;</span>]
Element = Masses[<span style="color: #CD5555">&#39;Element&#39;</span>]
Energies = Masses[<span style="color: #CD5555">&#39;Ebinding&#39;</span>]
<span style="color: #8B008B; font-weight: bold">print</span>(Masses)
<span style="color: #658b00">print</span>(Masses)
</pre></div>
<p>
The next step, and we will define this mathematically later, is to set up the so-called <b>design matrix</b>. We will throughout call this matrix \( \boldsymbol{X} \).
@@ -1874,7 +1871,7 @@ It has dimensionality \( p\times n \), where \( n \) is the number of data point
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># Now we set up the design matrix X</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># Now we set up the design matrix X</span>
X = np.zeros((<span style="color: #658b00">len</span>(A),<span style="color: #B452CD">5</span>))
X[:,<span style="color: #B452CD">0</span>] = <span style="color: #B452CD">1</span>
X[:,<span style="color: #B452CD">1</span>] = A
@@ -1887,7 +1884,7 @@ With <b>scikitlearn</b> we are now ready to use linear regression and fit our da
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span>clf = skl.LinearRegression().fit(X, Energies)
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span>clf = skl.LinearRegression().fit(X, Energies)
fity = clf.predict(X)
</pre></div>
<p>
@@ -1896,13 +1893,13 @@ Now we can print measures of how our fit is doing, the coefficients from the fit
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22"># The mean squared error </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Mean squared error: %.2f&quot;</span> % mean_squared_error(Energies, fity))
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22"># The mean squared error </span>
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&quot;Mean squared error: %.2f&quot;</span> % mean_squared_error(Energies, fity))
<span style="color: #228B22"># Explained variance score: 1 is perfect prediction </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Variance score: %.2f&#39;</span> % r2_score(Energies, fity))
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Variance score: %.2f&#39;</span> % r2_score(Energies, fity))
<span style="color: #228B22"># Mean absolute error </span>
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&#39;Mean absolute error: %.2f&#39;</span> % mean_absolute_error(Energies, fity))
<span style="color: #8B008B; font-weight: bold">print</span>(clf.coef_, clf.intercept_)
<span style="color: #658b00">print</span>(<span style="color: #CD5555">&#39;Mean absolute error: %.2f&#39;</span> % mean_absolute_error(Energies, fity))
<span style="color: #658b00">print</span>(clf.coef_, clf.intercept_)
Masses[<span style="color: #CD5555">&#39;Eapprox&#39;</span>] = fity
<span style="color: #228B22"># Generate a plot comparing the experimental with the fitted values values.</span>
@@ -1918,7 +1915,7 @@ save_fig(<span style="color: #CD5555">&quot;Masses2016&quot;</span>)
plt.show()
</pre></div>
<h3 id="___sec34">Seeing the wood for the trees </h3>
<h3 id="seeing-the-wood-for-the-trees">Seeing the wood for the trees </h3>
<p>
As a teaser, let us now see how we can do this with decision trees using <b>scikit-learn</b>. Later we will switch to so-called <b>random forests</b>!
@@ -1926,7 +1923,7 @@ As a teaser, let us now see how we can do this with decision trees using <b>scik
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #228B22">#Decision Tree Regression</span>
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #228B22">#Decision Tree Regression</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.tree</span> <span style="color: #8B008B; font-weight: bold">import</span> DecisionTreeRegressor
regr_1=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">5</span>)
regr_2=DecisionTreeRegressor(max_depth=<span style="color: #B452CD">7</span>)
@@ -1953,18 +1950,18 @@ plt.title(<span style="color: #CD5555">&quot;Decision Tree Regression&quot;</spa
plt.legend()
save_fig(<span style="color: #CD5555">&quot;Masses2016Trees&quot;</span>)
plt.show()
<span style="color: #8B008B; font-weight: bold">print</span>(Masses)
<span style="color: #8B008B; font-weight: bold">print</span>(np.mean( (Energies-y_1)**<span style="color: #B452CD">2</span>))
<span style="color: #658b00">print</span>(Masses)
<span style="color: #658b00">print</span>(np.mean( (Energies-y_1)**<span style="color: #B452CD">2</span>))
</pre></div>
<h3 id="___sec35">And what about using neural networks? </h3>
<h3 id="and-what-about-using-neural-networks">And what about using neural networks? </h3>
The <b>seaborn</b> package allows us to visualize data in an efficient way. Note that we use <b>scikit-learn</b>'s multi-layer perceptron (or feed forward neural network)
functionality.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.neural_network</span> <span style="color: #8B008B; font-weight: bold">import</span> MLPRegressor
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%;"><span></span><span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.neural_network</span> <span style="color: #8B008B; font-weight: bold">import</span> MLPRegressor
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.metrics</span> <span style="color: #8B008B; font-weight: bold">import</span> accuracy_score
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">seaborn</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">sns</span>
@@ -1988,14 +1985,14 @@ sns.set()
train_accuracy[i][j] = dnn.score(X_train, Y_train)
fig, ax = plt.subplots(figsize = (<span style="color: #B452CD">10</span>, <span style="color: #B452CD">10</span>))
sns.heatmap(train_accuracy, annot=<span style="color: #658b00">True</span>, ax=ax, cmap=<span style="color: #CD5555">&quot;viridis&quot;</span>)
sns.heatmap(train_accuracy, annot=<span style="color: #8B008B; font-weight: bold">True</span>, ax=ax, cmap=<span style="color: #CD5555">&quot;viridis&quot;</span>)
ax.set_title(<span style="color: #CD5555">&quot;Training Accuracy&quot;</span>)
ax.set_ylabel(<span style="color: #CD5555">&quot;$\eta$&quot;</span>)
ax.set_xlabel(<span style="color: #CD5555">&quot;$\lambda$&quot;</span>)
plt.show()
</pre></div>
<h2 id="___sec36">A first summary </h2>
<h2 id="a-first-summary">A first summary </h2>
<p>
The aim behind these introductory words was to present to you various
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@@ -8,15 +8,15 @@ DATE: today
===== Overview of first week =====
!bblock
* Thursday August 20: First lecture: Presentation of the course, aims and content
* Thursday August 26: First lecture: Presentation of the course, aims and content
* Thursday: Second Lecture: Start with simple linear regression and repetition of linear algebra and elements of statistics
* Friday August 21: Linear regression
* Computer lab: Wednesdays, 8am-6pm. First time: Wednesday August 26.
* Friday August 27: Linear regression
* Computer lab: Wednesdays, 8am-6pm. First time: Wednesday August 25.
!eblock
!split
===== Thursday August 20 =====
===== Thursday August 26 =====
"Video of Lecture":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/forelesningsvideoer/zoom_0.mp4?vrtx=view-as-webpage".
@@ -25,7 +25,7 @@ DATE: today
===== Lectures and ComputerLab =====
!bblock
* Lectures: Thursday (12.15pm-2pm and Friday (12.15pm-2pm). Due to the present COVID-19 situation all lectures will be online. They will be recorded and posted online at the official UiO "website":"https://www.uio.no/studier/emner/matnat/fys/FYS-STK4155/h20/index.html".
* Lectures: Thursday (12.15pm-2pm and Friday (12.15pm-2pm).
* Weekly reading assignments and videos needed to solve projects and exercises.
* Weekly exercises when not working on projects. You can hand in exercises if you want.
* Detailed lecture notes, exercises, all programs presented, projects etc can be found at the homepage of the course.
@@ -65,10 +65,6 @@ _Teachers :_
* Øyvind Sigmundson Schøyen, oyvinssc@student.matnat.uio.no
* _Office_: Department of Physics, University of Oslo, Eastern wing, room FØ452
* Michael Bitney, m.s.bitney@fys.uio.no
* Kristian Wold, kriswold@student.matnat.uio.no
* Nicolai Haug, nicoha@student.matnat.uio.no
* Per-Dimitri Sønsteland, perdimitri.bs@gmail.com
!eblock