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paciorek committed Oct 31, 2024
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2 changes: 1 addition & 1 deletion .nojekyll
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Expand Up @@ -836,7 +836,7 @@ <h4 class="anchored">Week 11</h4>

<th scope="row" rowspan="1">Mon Nov 4:</th>

<td><strong class="label label-Problem_Set">Problem_Set 6</strong> <a href="ps/ps6.html" target="_blank">Problem Set 6</a></td>
<td><strong class="label label-Activity">Activity 7</strong> <a href="units/unit10-linalg.html#1-preliminaries" target="_blank">Read Section 1 of Unit 10</a></td>

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<th scope="row" rowspan="1">Wed Nov 6:</th>

<td><strong class="label label-Activity">Activity 7</strong> <a href="units/unit10-linalg.html#1-preliminaries" target="_blank">Read Section 1 of Unit 10</a></td>
<td><strong class="label label-Problem_Set">Problem_Set 6</strong> <a href="ps/ps6.html" target="_blank">Problem Set 6</a></td>

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</head>

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Expand Up @@ -542,9 +542,9 @@ <h1 class="title">Numerical linear algebra</h1>
</header>


<p><a href="./unit10-linalg.pdf" class="btn btn-primary">PDF</a></p>
<section id="overview" class="level1">
<h1>Overview</h1>
<p><a href="./unit10-linalg.pdf" class="btn btn-primary">PDF</a></p>
<p>References:</p>
<ul>
<li>Gentle: Numerical Linear Algebra for Applications in Statistics (available via UC Library Search) (my notes here are based primarily on this source) [Gentle-NLA]
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<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>y <span class="op">=</span> e[<span class="dv">1</span>] <span class="op">@</span> ((evals <span class="op">**</span> <span class="fl">0.5</span>) <span class="op">*</span> np.random.normal(size <span class="op">=</span> <span class="dv">5</span>))</span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>y.<span class="bu">sum</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>2.220446049250313e-16</code></pre>
<pre><code>-5.551115123125783e-17</code></pre>
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<p>In the second order case, we have two non-identifiabilities: for the sum and for the linear component of the variation in <span class="math inline">\(y\)</span> (linear in the indices of <span class="math inline">\(y\)</span>).</p>
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</div>
<div class="sourceCode cell-code" id="cb25"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb25-1"><a href="#cb25-1" aria-hidden="true" tabindex="-1"></a>sm.OLS(y, X1).fit().params</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<pre><code>array([ 2.50521739e+02, -1.97599638e-01, 1.87455868e-04])</code></pre>
<pre><code>array([-1.48169405e+04, 1.48998050e+01, -3.59439471e-03])</code></pre>
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<div class="sourceCode cell-code" id="cb27"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a>t2 <span class="op">=</span> t1 <span class="op">-</span> <span class="dv">2000</span> <span class="co"># centered</span></span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>X2 <span class="op">=</span> np.column_stack((np.ones(<span class="dv">21</span>), t2, t2 <span class="op">**</span> <span class="dv">2</span>))</span>
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