lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
Files
5c6c05efbe058f033f3f35def695f64a7c70b9ce
FYS-STK4155/doc/pub/week40/html/._week40-bs010.html
T
mhjensen 15cb17c67d updating week40
2020-09-29 17:02:23 +02:00

363 lines
24 KiB
HTML
Raw Blame History

<!--
Automatically generated HTML file from DocOnce source
(https://github.com/hplgit/doconce/)
-->
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="description" content="Week 40: From Stochastic Gradient Descent to Neural networks">
<title>Week 40: From Stochastic Gradient Descent to Neural networks</title>
<!-- Bootstrap style: bootstrap -->
<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': [('Plan for week 40', 2, None, '___sec0'),
('Overview video for week 40', 2, None, '___sec1'),
('Stochastic Gradient Descent', 2, None, '___sec2'),
('Computation of gradients', 2, None, '___sec3'),
('SGD example', 2, None, '___sec4'),
('The gradient step', 2, None, '___sec5'),
('Simple example code', 2, None, '___sec6'),
('When do we stop?', 2, None, '___sec7'),
('Slightly different approach', 2, None, '___sec8'),
('Program for stochastic gradient', 2, None, '___sec9'),
('Momentum based GD', 2, None, '___sec10'),
('More on momentum based approaches', 2, None, '___sec11'),
('Momentum parameter', 2, None, '___sec12'),
('Second moment of the gradient', 2, None, '___sec13'),
('RMS prop', 2, None, '___sec14'),
('ADAM optimizer', 2, None, '___sec15'),
('Practical tips', 2, None, '___sec16'),
('Automatic differentiation', 2, None, '___sec17'),
('Using autograd', 2, None, '___sec18'),
('Autograd with more complicated functions', 2, None, '___sec19'),
('More complicated functions using the elements of their '
'arguments directly',
2,
None,
'___sec20'),
('Functions using mathematical functions from Numpy',
2,
None,
'___sec21'),
('More autograd', 2, None, '___sec22'),
('And with loops', 2, None, '___sec23'),
('Using recursion', 2, None, '___sec24'),
('Unsupported functions', 2, None, '___sec25'),
('The syntax a.dot(b) when finding the dot product',
2,
None,
'___sec26'),
('Recommended to avoid', 2, None, '___sec27'),
('Neural networks', 2, None, '___sec28'),
('Artificial neurons', 2, None, '___sec29'),
('Neural network types', 2, None, '___sec30'),
('Feed-forward neural networks', 2, None, '___sec31'),
('Convolutional Neural Network', 2, None, '___sec32'),
('Recurrent neural networks', 2, None, '___sec33'),
('Other types of networks', 2, None, '___sec34'),
('Multilayer perceptrons', 2, None, '___sec35'),
('Why multilayer perceptrons?', 2, None, '___sec36'),
('Mathematical model', 2, None, '___sec37'),
('Mathematical model', 2, None, '___sec38'),
('Mathematical model', 2, None, '___sec39'),
('Mathematical model', 2, None, '___sec40'),
('Mathematical model', 2, None, '___sec41'),
('Matrix-vector notation', 3, None, '___sec42'),
('Matrix-vector notation and activation', 3, None, '___sec43'),
('Activation functions', 3, None, '___sec44'),
('Activation functions, Logistic and Hyperbolic ones',
3,
None,
'___sec45'),
('Relevance', 3, None, '___sec46'),
('The multilayer perceptron (MLP)', 2, None, '___sec47'),
('From one to many layers, the universal approximation theorem',
2,
None,
'___sec48'),
('Deriving the back propagation code for a multilayer perceptron '
'model',
2,
None,
'___sec49'),
('Definitions', 2, None, '___sec50'),
('Derivatives and the chain rule', 2, None, '___sec51'),
('Derivative of the cost function', 2, None, '___sec52'),
('Bringing it together, first back propagation equation',
2,
None,
'___sec53'),
('Derivatives in terms of $z_j^L$', 2, None, '___sec54'),
('Bringing it together', 2, None, '___sec55'),
('Final back propagating equation', 2, None, '___sec56'),
('Setting up the Back propagation algorithm',
2,
None,
'___sec57')]}
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="week40-bs.html">Week 40: From Stochastic Gradient Descent to Neural networks</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="._week40-bs001.html#___sec0" style="font-size: 80%;"><b>Plan for week 40</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs002.html#___sec1" style="font-size: 80%;"><b>Overview video for week 40</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs003.html#___sec2" style="font-size: 80%;"><b>Stochastic Gradient Descent</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs004.html#___sec3" style="font-size: 80%;"><b>Computation of gradients</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs005.html#___sec4" style="font-size: 80%;"><b>SGD example</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs006.html#___sec5" style="font-size: 80%;"><b>The gradient step</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs007.html#___sec6" style="font-size: 80%;"><b>Simple example code</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs008.html#___sec7" style="font-size: 80%;"><b>When do we stop?</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs009.html#___sec8" style="font-size: 80%;"><b>Slightly different approach</b></a></li>
<!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;"><b>Program for stochastic gradient</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs011.html#___sec10" style="font-size: 80%;"><b>Momentum based GD</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs012.html#___sec11" style="font-size: 80%;"><b>More on momentum based approaches</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs013.html#___sec12" style="font-size: 80%;"><b>Momentum parameter</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs014.html#___sec13" style="font-size: 80%;"><b>Second moment of the gradient</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs015.html#___sec14" style="font-size: 80%;"><b>RMS prop</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs016.html#___sec15" style="font-size: 80%;"><b>ADAM optimizer</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs017.html#___sec16" style="font-size: 80%;"><b>Practical tips</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs018.html#___sec17" style="font-size: 80%;"><b>Automatic differentiation</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs019.html#___sec18" style="font-size: 80%;"><b>Using autograd</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs020.html#___sec19" style="font-size: 80%;"><b>Autograd with more complicated functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs021.html#___sec20" style="font-size: 80%;"><b>More complicated functions using the elements of their arguments directly</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs022.html#___sec21" style="font-size: 80%;"><b>Functions using mathematical functions from Numpy</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs023.html#___sec22" style="font-size: 80%;"><b>More autograd</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs024.html#___sec23" style="font-size: 80%;"><b>And with loops</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs025.html#___sec24" style="font-size: 80%;"><b>Using recursion</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs026.html#___sec25" style="font-size: 80%;"><b>Unsupported functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs027.html#___sec26" style="font-size: 80%;"><b>The syntax a.dot(b) when finding the dot product</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs028.html#___sec27" style="font-size: 80%;"><b>Recommended to avoid</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs029.html#___sec28" style="font-size: 80%;"><b>Neural networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs030.html#___sec29" style="font-size: 80%;"><b>Artificial neurons</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs031.html#___sec30" style="font-size: 80%;"><b>Neural network types</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs032.html#___sec31" style="font-size: 80%;"><b>Feed-forward neural networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs033.html#___sec32" style="font-size: 80%;"><b>Convolutional Neural Network</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs034.html#___sec33" style="font-size: 80%;"><b>Recurrent neural networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs035.html#___sec34" style="font-size: 80%;"><b>Other types of networks</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs036.html#___sec35" style="font-size: 80%;"><b>Multilayer perceptrons</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs037.html#___sec36" style="font-size: 80%;"><b>Why multilayer perceptrons?</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs038.html#___sec37" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs039.html#___sec38" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs040.html#___sec39" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs041.html#___sec40" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs042.html#___sec41" style="font-size: 80%;"><b>Mathematical model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs043.html#___sec42" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs044.html#___sec43" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Matrix-vector notation and activation</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs045.html#___sec44" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Activation functions</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs046.html#___sec45" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Activation functions, Logistic and Hyperbolic ones</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs047.html#___sec46" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Relevance</a></li>
<!-- navigation toc: --> <li><a href="._week40-bs048.html#___sec47" style="font-size: 80%;"><b>The multilayer perceptron (MLP)</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs049.html#___sec48" style="font-size: 80%;"><b>From one to many layers, the universal approximation theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs050.html#___sec49" style="font-size: 80%;"><b>Deriving the back propagation code for a multilayer perceptron model</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs051.html#___sec50" style="font-size: 80%;"><b>Definitions</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs052.html#___sec51" style="font-size: 80%;"><b>Derivatives and the chain rule</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs053.html#___sec52" style="font-size: 80%;"><b>Derivative of the cost function</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs054.html#___sec53" style="font-size: 80%;"><b>Bringing it together, first back propagation equation</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs055.html#___sec54" style="font-size: 80%;"><b>Derivatives in terms of \( z_j^L \)</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs056.html#___sec55" style="font-size: 80%;"><b>Bringing it together</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs057.html#___sec56" style="font-size: 80%;"><b>Final back propagating equation</b></a></li>
<!-- navigation toc: --> <li><a href="._week40-bs058.html#___sec57" style="font-size: 80%;"><b>Setting up the Back propagation algorithm</b></a></li>
</ul>
</li>
</ul>
</div>
</div>
</div> <!-- end of navigation bar -->
<div class="container">
<p>&nbsp;</p><p>&nbsp;</p><p>&nbsp;</p> <!-- add vertical space -->
<a name="part0010"></a>
<!-- !split -->
<h2 id="___sec9" class="anchor">Program for stochastic gradient </h2>
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Importing various packages</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">math</span> <span style="color: #008000; font-weight: bold">import</span> exp, sqrt
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">random</span> <span style="color: #008000; font-weight: bold">import</span> random, seed
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> SGDRegressor
m <span style="color: #666666">=</span> <span style="color: #666666">100</span>
x <span style="color: #666666">=</span> <span style="color: #666666">2*</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>rand(m,<span style="color: #666666">1</span>)
y <span style="color: #666666">=</span> <span style="color: #666666">4+3*</span>x<span style="color: #666666">+</span>np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(m,<span style="color: #666666">1</span>)
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((m,<span style="color: #666666">1</span>)), x]
theta_linreg <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>inv(X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> X) <span style="color: #666666">@</span> (X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> y)
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Own inversion&quot;</span>)
<span style="color: #008000">print</span>(theta_linreg)
sgdreg <span style="color: #666666">=</span> SGDRegressor(max_iter <span style="color: #666666">=</span> <span style="color: #666666">50</span>, penalty<span style="color: #666666">=</span><span style="color: #008000; font-weight: bold">None</span>, eta0<span style="color: #666666">=0.1</span>)
sgdreg<span style="color: #666666">.</span>fit(x,y<span style="color: #666666">.</span>ravel())
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;sgdreg from scikit&quot;</span>)
<span style="color: #008000">print</span>(sgdreg<span style="color: #666666">.</span>intercept_, sgdreg<span style="color: #666666">.</span>coef_)
theta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
eta <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>
Niterations <span style="color: #666666">=</span> <span style="color: #666666">1000</span>
<span style="color: #008000; font-weight: bold">for</span> <span style="color: #008000">iter</span> <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(Niterations):
gradients <span style="color: #666666">=</span> <span style="color: #666666">2.0/</span>m<span style="color: #666666">*</span>X<span style="color: #666666">.</span>T <span style="color: #666666">@</span> ((X <span style="color: #666666">@</span> theta)<span style="color: #666666">-</span>y)
theta <span style="color: #666666">-=</span> eta<span style="color: #666666">*</span>gradients
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;theta from own gd&quot;</span>)
<span style="color: #008000">print</span>(theta)
xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0</span>],[<span style="color: #666666">2</span>]])
Xnew <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[np<span style="color: #666666">.</span>ones((<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)), xnew]
ypredict <span style="color: #666666">=</span> Xnew<span style="color: #666666">.</span>dot(theta)
ypredict2 <span style="color: #666666">=</span> Xnew<span style="color: #666666">.</span>dot(theta_linreg)
n_epochs <span style="color: #666666">=</span> <span style="color: #666666">50</span>
t0, t1 <span style="color: #666666">=</span> <span style="color: #666666">5</span>, <span style="color: #666666">50</span>
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">learning_schedule</span>(t):
<span style="color: #008000; font-weight: bold">return</span> t0<span style="color: #666666">/</span>(t<span style="color: #666666">+</span>t1)
theta <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randn(<span style="color: #666666">2</span>,<span style="color: #666666">1</span>)
<span style="color: #008000; font-weight: bold">for</span> epoch <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(n_epochs):
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(m):
random_index <span style="color: #666666">=</span> np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>randint(m)
xi <span style="color: #666666">=</span> X[random_index:random_index<span style="color: #666666">+1</span>]
yi <span style="color: #666666">=</span> y[random_index:random_index<span style="color: #666666">+1</span>]
gradients <span style="color: #666666">=</span> <span style="color: #666666">2</span> <span style="color: #666666">*</span> xi<span style="color: #666666">.</span>T <span style="color: #666666">@</span> ((xi <span style="color: #666666">@</span> theta)<span style="color: #666666">-</span>yi)
eta <span style="color: #666666">=</span> learning_schedule(epoch<span style="color: #666666">*</span>m<span style="color: #666666">+</span>i)
theta <span style="color: #666666">=</span> theta <span style="color: #666666">-</span> eta<span style="color: #666666">*</span>gradients
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;theta from own sdg&quot;</span>)
<span style="color: #008000">print</span>(theta)
plt<span style="color: #666666">.</span>plot(xnew, ypredict, <span style="color: #BA2121">&quot;r-&quot;</span>)
plt<span style="color: #666666">.</span>plot(xnew, ypredict2, <span style="color: #BA2121">&quot;b-&quot;</span>)
plt<span style="color: #666666">.</span>plot(x, y ,<span style="color: #BA2121">&#39;ro&#39;</span>)
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>,<span style="color: #666666">2.0</span>,<span style="color: #666666">0</span>, <span style="color: #666666">15.0</span>])
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r&#39;$x$&#39;</span>)
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r&#39;$y$&#39;</span>)
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r&#39;Random numbers &#39;</span>)
plt<span style="color: #666666">.</span>show()
</pre></div>
<p>
<b>Challenge</b>: try to write a similar code for a Logistic Regression case.
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
<li><a href="._week40-bs009.html">&laquo;</a></li>
<li><a href="._week40-bs000.html">1</a></li>
<li><a href="">...</a></li>
<li><a href="._week40-bs002.html">3</a></li>
<li><a href="._week40-bs003.html">4</a></li>
<li><a href="._week40-bs004.html">5</a></li>
<li><a href="._week40-bs005.html">6</a></li>
<li><a href="._week40-bs006.html">7</a></li>
<li><a href="._week40-bs007.html">8</a></li>
<li><a href="._week40-bs008.html">9</a></li>
<li><a href="._week40-bs009.html">10</a></li>
<li class="active"><a href="._week40-bs010.html">11</a></li>
<li><a href="._week40-bs011.html">12</a></li>
<li><a href="._week40-bs012.html">13</a></li>
<li><a href="._week40-bs013.html">14</a></li>
<li><a href="._week40-bs014.html">15</a></li>
<li><a href="._week40-bs015.html">16</a></li>
<li><a href="._week40-bs016.html">17</a></li>
<li><a href="._week40-bs017.html">18</a></li>
<li><a href="._week40-bs018.html">19</a></li>
<li><a href="._week40-bs019.html">20</a></li>
<li><a href="">...</a></li>
<li><a href="._week40-bs058.html">59</a></li>
<li><a href="._week40-bs011.html">&raquo;</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="http://..."><img width="250" align=right src="http://..."></a>
</footer>
-->
<center style="font-size:80%">
<!-- copyright only on the titlepage -->
</center>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink