Morten Hjorth-Jensen
398 lines
23 KiB
HTML
398 lines
23 KiB
HTML
<!--
|
|
HTML file automatically generated from DocOnce source
|
|
(https://github.com/doconce/doconce/)
|
|
doconce format html week36.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week36-bs --no_mako
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<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 36: Linear Regression and Gradient descent">
|
|
<title>Week 36: Linear Regression and Gradient descent</title>
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<!-- doconce format html week36.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week36-bs --no_mako -->
|
|
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
|
<!-- not necessary
|
|
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
|
-->
|
|
<style type="text/css">
|
|
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
|
.dropdown-menu {
|
|
height: auto;
|
|
max-height: 400px;
|
|
overflow-x: hidden;
|
|
}
|
|
/* Adds an invisible element before each target to offset for the navigation
|
|
bar */
|
|
.anchor::before {
|
|
content:"";
|
|
display:block;
|
|
height:50px; /* fixed header height for style bootstrap */
|
|
margin:-50px 0 0; /* negative fixed header height */
|
|
}
|
|
</style>
|
|
</head>
|
|
|
|
<!-- tocinfo
|
|
{'highest level': 2,
|
|
'sections': [('Plans for week 36', 2, None, 'plans-for-week-36'),
|
|
('Material for lecture Monday September 2',
|
|
2,
|
|
None,
|
|
'material-for-lecture-monday-september-2'),
|
|
('Mathematical Interpretation of Ordinary Least Squares',
|
|
2,
|
|
None,
|
|
'mathematical-interpretation-of-ordinary-least-squares'),
|
|
('Residual Error', 2, None, 'residual-error'),
|
|
('Simple case', 2, None, 'simple-case'),
|
|
('The singular value decomposition',
|
|
2,
|
|
None,
|
|
'the-singular-value-decomposition'),
|
|
('Linear Regression Problems',
|
|
2,
|
|
None,
|
|
'linear-regression-problems'),
|
|
('Fixing the singularity', 2, None, 'fixing-the-singularity'),
|
|
('Ridge and LASSO Regression',
|
|
2,
|
|
None,
|
|
'ridge-and-lasso-regression'),
|
|
('Deriving the Ridge Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-ridge-regression-equations'),
|
|
('Basic math of the SVD', 2, None, 'basic-math-of-the-svd'),
|
|
('The SVD, a Fantastic Algorithm',
|
|
2,
|
|
None,
|
|
'the-svd-a-fantastic-algorithm'),
|
|
('Economy-size SVD', 2, None, 'economy-size-svd'),
|
|
('Codes for the SVD', 2, None, 'codes-for-the-svd'),
|
|
('Note about SVD Calculations',
|
|
2,
|
|
None,
|
|
'note-about-svd-calculations'),
|
|
('Mathematics of the SVD and implications',
|
|
2,
|
|
None,
|
|
'mathematics-of-the-svd-and-implications'),
|
|
('Example Matrix', 2, None, 'example-matrix'),
|
|
('Setting up the Matrix to be inverted',
|
|
2,
|
|
None,
|
|
'setting-up-the-matrix-to-be-inverted'),
|
|
('Further properties (important for our analyses later)',
|
|
2,
|
|
None,
|
|
'further-properties-important-for-our-analyses-later'),
|
|
('Back to Ridge and LASSO Regression',
|
|
2,
|
|
None,
|
|
'back-to-ridge-and-lasso-regression'),
|
|
('Interpreting the Ridge results',
|
|
2,
|
|
None,
|
|
'interpreting-the-ridge-results'),
|
|
('More interpretations', 2, None, 'more-interpretations'),
|
|
('Deriving the Lasso Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-lasso-regression-equations'),
|
|
('Optimization and gradient descent, the central part of any '
|
|
'Machine Learning algortithm',
|
|
2,
|
|
None,
|
|
'optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm'),
|
|
("Reminder on Newton-Raphson's method",
|
|
2,
|
|
None,
|
|
'reminder-on-newton-raphson-s-method'),
|
|
('The equations', 2, None, 'the-equations'),
|
|
('Simple geometric interpretation',
|
|
2,
|
|
None,
|
|
'simple-geometric-interpretation'),
|
|
('Extending to more than one variable',
|
|
2,
|
|
None,
|
|
'extending-to-more-than-one-variable'),
|
|
('Steepest descent', 2, None, 'steepest-descent'),
|
|
('More on Steepest descent', 2, None, 'more-on-steepest-descent'),
|
|
('The ideal', 2, None, 'the-ideal'),
|
|
('The sensitiveness of the gradient descent',
|
|
2,
|
|
None,
|
|
'the-sensitiveness-of-the-gradient-descent'),
|
|
('Convex functions', 2, None, 'convex-functions'),
|
|
('Convex function', 2, None, 'convex-function'),
|
|
('Conditions on convex functions',
|
|
2,
|
|
None,
|
|
'conditions-on-convex-functions'),
|
|
('More on convex functions', 2, None, 'more-on-convex-functions'),
|
|
('Some simple problems', 2, None, 'some-simple-problems'),
|
|
('Revisiting Ordinary Least Squares',
|
|
2,
|
|
None,
|
|
'revisiting-ordinary-least-squares'),
|
|
('Gradient descent example', 2, None, 'gradient-descent-example'),
|
|
('The derivative of the cost/loss function',
|
|
2,
|
|
None,
|
|
'the-derivative-of-the-cost-loss-function'),
|
|
('The Hessian matrix', 2, None, 'the-hessian-matrix'),
|
|
('Simple program', 2, None, 'simple-program'),
|
|
('Gradient Descent Example', 2, None, 'gradient-descent-example'),
|
|
('Gradient descent and Ridge',
|
|
2,
|
|
None,
|
|
'gradient-descent-and-ridge'),
|
|
('The Hessian matrix for Ridge Regression',
|
|
2,
|
|
None,
|
|
'the-hessian-matrix-for-ridge-regression'),
|
|
('Program example for gradient descent with Ridge Regression',
|
|
2,
|
|
None,
|
|
'program-example-for-gradient-descent-with-ridge-regression'),
|
|
('Using gradient descent methods, limitations',
|
|
2,
|
|
None,
|
|
'using-gradient-descent-methods-limitations'),
|
|
('Material for lab sessions sessions Tuesday and Wednesday',
|
|
2,
|
|
None,
|
|
'material-for-lab-sessions-sessions-tuesday-and-wednesday'),
|
|
('Linear Regression and the SVD',
|
|
2,
|
|
None,
|
|
'linear-regression-and-the-svd'),
|
|
('What does it mean?', 2, None, 'what-does-it-mean'),
|
|
('Ridge and LASSO Regression',
|
|
2,
|
|
None,
|
|
'ridge-and-lasso-regression'),
|
|
('From OLS to Ridge and Lasso',
|
|
2,
|
|
None,
|
|
'from-ols-to-ridge-and-lasso'),
|
|
('Deriving the Ridge Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-ridge-regression-equations'),
|
|
('Note on Scikit-Learn', 2, None, 'note-on-scikit-learn'),
|
|
('Comparison with OLS', 2, None, 'comparison-with-ols'),
|
|
('SVD analysis', 2, None, 'svd-analysis'),
|
|
('Interpreting the Ridge results',
|
|
2,
|
|
None,
|
|
'interpreting-the-ridge-results'),
|
|
('More interpretations', 2, None, 'more-interpretations'),
|
|
('Deriving the Lasso Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-lasso-regression-equations'),
|
|
('Simple example to illustrate Ordinary Least Squares, Ridge and '
|
|
'Lasso Regression',
|
|
2,
|
|
None,
|
|
'simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression'),
|
|
('Ridge Regression', 2, None, 'ridge-regression'),
|
|
('Lasso Regression', 2, None, 'lasso-regression'),
|
|
('Yet another Example', 2, None, 'yet-another-example'),
|
|
('The OLS case', 2, None, 'the-ols-case'),
|
|
('The Ridge case', 2, None, 'the-ridge-case'),
|
|
('Writing the Cost Function',
|
|
2,
|
|
None,
|
|
'writing-the-cost-function'),
|
|
('Lasso case', 2, None, 'lasso-case'),
|
|
('The first Case', 2, None, 'the-first-case'),
|
|
('Simple code for solving the above problem',
|
|
2,
|
|
None,
|
|
'simple-code-for-solving-the-above-problem'),
|
|
('With Lasso Regression', 2, None, 'with-lasso-regression'),
|
|
('Another Example, now with a polynomial fit',
|
|
2,
|
|
None,
|
|
'another-example-now-with-a-polynomial-fit')]}
|
|
end of tocinfo -->
|
|
|
|
<body>
|
|
|
|
|
|
|
|
<script type="text/x-mathjax-config">
|
|
MathJax.Hub.Config({
|
|
TeX: {
|
|
equationNumbers: { autoNumber: "none" },
|
|
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
|
}
|
|
});
|
|
</script>
|
|
<script type="text/javascript" async
|
|
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
|
</script>
|
|
|
|
|
|
<!-- Bootstrap navigation bar -->
|
|
<div class="navbar navbar-default navbar-fixed-top">
|
|
<div class="navbar-header">
|
|
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
<span class="icon-bar"></span>
|
|
</button>
|
|
<a class="navbar-brand" href="week36-bs.html">Week 36: Linear Regression and Gradient descent</a>
|
|
</div>
|
|
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
|
<ul class="nav navbar-nav navbar-right">
|
|
<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="._week36-bs001.html#plans-for-week-36" style="font-size: 80%;">Plans for week 36</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs002.html#material-for-lecture-monday-september-2" style="font-size: 80%;">Material for lecture Monday September 2</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs003.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;">Mathematical Interpretation of Ordinary Least Squares</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs004.html#residual-error" style="font-size: 80%;">Residual Error</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs005.html#simple-case" style="font-size: 80%;">Simple case</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs006.html#the-singular-value-decomposition" style="font-size: 80%;">The singular value decomposition</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs007.html#linear-regression-problems" style="font-size: 80%;">Linear Regression Problems</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs008.html#fixing-the-singularity" style="font-size: 80%;">Fixing the singularity</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs051.html#ridge-and-lasso-regression" style="font-size: 80%;">Ridge and LASSO Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs053.html#deriving-the-ridge-regression-equations" style="font-size: 80%;">Deriving the Ridge Regression Equations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs011.html#basic-math-of-the-svd" style="font-size: 80%;">Basic math of the SVD</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs012.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;">The SVD, a Fantastic Algorithm</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs013.html#economy-size-svd" style="font-size: 80%;">Economy-size SVD</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs014.html#codes-for-the-svd" style="font-size: 80%;">Codes for the SVD</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs015.html#note-about-svd-calculations" style="font-size: 80%;">Note about SVD Calculations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs016.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;">Mathematics of the SVD and implications</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs017.html#example-matrix" style="font-size: 80%;">Example Matrix</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs018.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;">Setting up the Matrix to be inverted</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs019.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;">Further properties (important for our analyses later)</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs020.html#back-to-ridge-and-lasso-regression" style="font-size: 80%;">Back to Ridge and LASSO Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs057.html#interpreting-the-ridge-results" style="font-size: 80%;">Interpreting the Ridge results</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs058.html#more-interpretations" style="font-size: 80%;">More interpretations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs059.html#deriving-the-lasso-regression-equations" style="font-size: 80%;">Deriving the Lasso Regression Equations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs024.html#optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm" style="font-size: 80%;">Optimization and gradient descent, the central part of any Machine Learning algortithm</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs025.html#reminder-on-newton-raphson-s-method" style="font-size: 80%;">Reminder on Newton-Raphson's method</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs026.html#the-equations" style="font-size: 80%;">The equations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs027.html#simple-geometric-interpretation" style="font-size: 80%;">Simple geometric interpretation</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs028.html#extending-to-more-than-one-variable" style="font-size: 80%;">Extending to more than one variable</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs029.html#steepest-descent" style="font-size: 80%;">Steepest descent</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs030.html#more-on-steepest-descent" style="font-size: 80%;">More on Steepest descent</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs031.html#the-ideal" style="font-size: 80%;">The ideal</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs032.html#the-sensitiveness-of-the-gradient-descent" style="font-size: 80%;">The sensitiveness of the gradient descent</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs033.html#convex-functions" style="font-size: 80%;">Convex functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs034.html#convex-function" style="font-size: 80%;">Convex function</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs035.html#conditions-on-convex-functions" style="font-size: 80%;">Conditions on convex functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs036.html#more-on-convex-functions" style="font-size: 80%;">More on convex functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs037.html#some-simple-problems" style="font-size: 80%;">Some simple problems</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs038.html#revisiting-ordinary-least-squares" style="font-size: 80%;">Revisiting Ordinary Least Squares</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs043.html#gradient-descent-example" style="font-size: 80%;">Gradient descent example</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs040.html#the-derivative-of-the-cost-loss-function" style="font-size: 80%;">The derivative of the cost/loss function</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs041.html#the-hessian-matrix" style="font-size: 80%;">The Hessian matrix</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs042.html#simple-program" style="font-size: 80%;">Simple program</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs043.html#gradient-descent-example" style="font-size: 80%;">Gradient Descent Example</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs044.html#gradient-descent-and-ridge" style="font-size: 80%;">Gradient descent and Ridge</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs045.html#the-hessian-matrix-for-ridge-regression" style="font-size: 80%;">The Hessian matrix for Ridge Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs046.html#program-example-for-gradient-descent-with-ridge-regression" style="font-size: 80%;">Program example for gradient descent with Ridge Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs047.html#using-gradient-descent-methods-limitations" style="font-size: 80%;">Using gradient descent methods, limitations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs048.html#material-for-lab-sessions-sessions-tuesday-and-wednesday" style="font-size: 80%;">Material for lab sessions sessions Tuesday and Wednesday</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs049.html#linear-regression-and-the-svd" style="font-size: 80%;">Linear Regression and the SVD</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs050.html#what-does-it-mean" style="font-size: 80%;">What does it mean?</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs051.html#ridge-and-lasso-regression" style="font-size: 80%;">Ridge and LASSO Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs052.html#from-ols-to-ridge-and-lasso" style="font-size: 80%;">From OLS to Ridge and Lasso</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs053.html#deriving-the-ridge-regression-equations" style="font-size: 80%;">Deriving the Ridge Regression Equations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs054.html#note-on-scikit-learn" style="font-size: 80%;">Note on Scikit-Learn</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs055.html#comparison-with-ols" style="font-size: 80%;">Comparison with OLS</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs056.html#svd-analysis" style="font-size: 80%;">SVD analysis</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs057.html#interpreting-the-ridge-results" style="font-size: 80%;">Interpreting the Ridge results</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs058.html#more-interpretations" style="font-size: 80%;">More interpretations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs059.html#deriving-the-lasso-regression-equations" style="font-size: 80%;">Deriving the Lasso Regression Equations</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs060.html#simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression" style="font-size: 80%;">Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs061.html#ridge-regression" style="font-size: 80%;">Ridge Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs062.html#lasso-regression" style="font-size: 80%;">Lasso Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs063.html#yet-another-example" style="font-size: 80%;">Yet another Example</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs064.html#the-ols-case" style="font-size: 80%;">The OLS case</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs065.html#the-ridge-case" style="font-size: 80%;">The Ridge case</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs066.html#writing-the-cost-function" style="font-size: 80%;">Writing the Cost Function</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs067.html#lasso-case" style="font-size: 80%;">Lasso case</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs068.html#the-first-case" style="font-size: 80%;">The first Case</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs069.html#simple-code-for-solving-the-above-problem" style="font-size: 80%;">Simple code for solving the above problem</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs070.html#with-lasso-regression" style="font-size: 80%;">With Lasso Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._week36-bs071.html#another-example-now-with-a-polynomial-fit" style="font-size: 80%;">Another Example, now with a polynomial fit</a></li>
|
|
|
|
</ul>
|
|
</li>
|
|
</ul>
|
|
</div>
|
|
</div>
|
|
</div> <!-- end of navigation bar -->
|
|
<div class="container">
|
|
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
|
<a name="part0000"></a>
|
|
<!-- ------------------- main content ---------------------- -->
|
|
<div class="jumbotron">
|
|
<center>
|
|
<h1>Week 36: Linear Regression and Gradient descent</h1>
|
|
</center> <!-- document title -->
|
|
|
|
<!-- author(s): Morten Hjorth-Jensen -->
|
|
<center>
|
|
<b>Morten Hjorth-Jensen</b>
|
|
</center>
|
|
<!-- institution -->
|
|
<center>
|
|
<b>Department of Physics, University of Oslo, Norway</b>
|
|
</center>
|
|
<br>
|
|
<center>
|
|
<h4>September 1-5, 2025</h4>
|
|
</center> <!-- date -->
|
|
<br>
|
|
|
|
|
|
|
|
<p><a href="._week36-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
|
|
|
|
|
|
</div> <!-- end jumbotron -->
|
|
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li class="active"><a href="._week36-bs000.html">1</a></li>
|
|
<li><a href="._week36-bs001.html">2</a></li>
|
|
<li><a href="._week36-bs002.html">3</a></li>
|
|
<li><a href="._week36-bs003.html">4</a></li>
|
|
<li><a href="._week36-bs004.html">5</a></li>
|
|
<li><a href="._week36-bs005.html">6</a></li>
|
|
<li><a href="._week36-bs006.html">7</a></li>
|
|
<li><a href="._week36-bs007.html">8</a></li>
|
|
<li><a href="._week36-bs008.html">9</a></li>
|
|
<li><a href="._week36-bs009.html">10</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._week36-bs071.html">72</a></li>
|
|
<li><a href="._week36-bs001.html">»</a></li>
|
|
</ul>
|
|
<!-- ------------------- end of main content --------------- -->
|
|
</div> <!-- end container -->
|
|
<!-- include javascript, jQuery *first* -->
|
|
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
|
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
|
<!-- Bootstrap footer
|
|
<footer>
|
|
<a href="https://..."><img width="250" align=right src="https://..."></a>
|
|
</footer>
|
|
-->
|
|
<center style="font-size:80%">
|
|
<!-- copyright --> © 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
|
</center>
|
|
</body>
|
|
</html>
|
|
|