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mhjensen 15cb17c67d updating week40
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<!-- navigation toc: --> <li><a href="._week40-bs001.html#___sec0" style="font-size: 80%;"><b>Plan for week 40</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs003.html#___sec2" style="font-size: 80%;"><b>Stochastic Gradient Descent</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs011.html#___sec10" style="font-size: 80%;"><b>Momentum based GD</b></a></li>
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<!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;"><b>More complicated functions using the elements of their arguments directly</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs026.html#___sec25" style="font-size: 80%;"><b>Unsupported functions</b></a></li>
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<!-- 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>
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<!-- navigation toc: --> <li><a href="._week40-bs031.html#___sec30" style="font-size: 80%;"><b>Neural network types</b></a></li>
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<!-- navigation toc: --> <li><a href="._week40-bs041.html#___sec40" style="font-size: 80%;"><b>Mathematical model</b></a></li>
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<h2 id="___sec20" class="anchor">More complicated functions using the elements of their arguments directly </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: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">autograd.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">from</span> <span style="color: #0000FF; font-weight: bold">autograd</span> <span style="color: #008000; font-weight: bold">import</span> grad
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">f3</span>(x): <span style="color: #408080; font-style: italic"># Assumes x is an array of length 5 or higher</span>
<span style="color: #008000; font-weight: bold">return</span> <span style="color: #666666">2*</span>x[<span style="color: #666666">0</span>] <span style="color: #666666">+</span> <span style="color: #666666">3*</span>x[<span style="color: #666666">1</span>] <span style="color: #666666">+</span> <span style="color: #666666">5*</span>x[<span style="color: #666666">2</span>] <span style="color: #666666">+</span> <span style="color: #666666">7*</span>x[<span style="color: #666666">3</span>] <span style="color: #666666">+</span> <span style="color: #666666">11*</span>x[<span style="color: #666666">4</span>]<span style="color: #666666">**2</span>
f3_grad <span style="color: #666666">=</span> grad(f3)
x <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>,<span style="color: #666666">4</span>,<span style="color: #666666">5</span>)
<span style="color: #408080; font-style: italic"># Print the computed gradient:</span>
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;The computed gradient of f3 is: &quot;</span>, f3_grad(x))
<span style="color: #408080; font-style: italic"># The analytical gradient is: (2, 3, 5, 7, 22*x[4])</span>
f3_grad_analytical <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">2</span>, <span style="color: #666666">3</span>, <span style="color: #666666">5</span>, <span style="color: #666666">7</span>, <span style="color: #666666">22*</span>x[<span style="color: #666666">4</span>]])
<span style="color: #408080; font-style: italic"># Print the analytical gradient:</span>
<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;The analytical gradient of f3 is: &quot;</span>, f3_grad_analytical)
</pre></div>
<p>
Note that in this case, when sending an array as input argument, the
output from Autograd is another array. This is the true gradient of
the function, as opposed to the function in the previous example. By
using arrays to represent the variables, the output from Autograd
might be easier to work with, as the output is closer to what one
could expect form a gradient-evaluting function.
<p>
<p>
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