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Morten Hjorth-Jensen
2023-09-03 14:23:01 +02:00
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doc/LectureNotes/_build/html/_sources/week36.ipynb
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@@ -1005,20 +1005,30 @@ values and the column vectors of <span class="math notranslate nohighlight">\(\b
<div class="section" id="code-for-svd-and-inversion-of-matrices">
<h2>Code for SVD and Inversion of Matrices<a class="headerlink" href="#code-for-svd-and-inversion-of-matrices" title="Permalink to this headline"></a></h2>
<p>How do we use the SVD to invert a matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}^\boldsymbol{X}\)</span> which is singular or near singular?
The simple answer is to use the linear algebra function for pseudoinvers, that is</p>
The simple answer is to use the linear algebra function for the computation of the pseudoinverse of a given matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span>, that is</p>
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<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">Ainv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linlag</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span> <span class="p">[</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],[</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]])</span>
<span class="n">Xinv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linlag</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
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<div class="output traceback highlight-ipythontb notranslate"><div class="highlight"><pre><span></span><span class="gt">---------------------------------------------------------------------------</span>
<span class="ne">NameError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 1&gt;</span><span class="nt">()</span>
<span class="ne">----&gt; </span><span class="mi">1</span> <span class="n">Ainv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linlag</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
<span class="ne">AttributeError</span><span class="g g-Whitespace"> </span>Traceback (most recent call last)
<span class="nn">Input In [1],</span> in <span class="ni">&lt;cell line: 3&gt;</span><span class="nt">()</span>
<span class="g g-Whitespace"> </span><span class="mi">1</span> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="g g-Whitespace"> </span><span class="mi">2</span> <span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span> <span class="p">[</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">],[</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">],[</span><span class="mi">3</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">]])</span>
<span class="ne">----&gt; </span><span class="mi">3</span> <span class="n">Xinv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linlag</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="ne">NameError</span>: name &#39;np&#39; is not defined
<span class="nn">File ~/miniforge3/envs/myenv/lib/python3.9/site-packages/numpy/__init__.py:313,</span> in <span class="ni">__getattr__</span><span class="nt">(attr)</span>
<span class="g g-Whitespace"> </span><span class="mi">310</span> <span class="kn">from</span> <span class="nn">.testing</span> <span class="kn">import</span> <span class="n">Tester</span>
<span class="g g-Whitespace"> </span><span class="mi">311</span> <span class="k">return</span> <span class="n">Tester</span>
<span class="ne">--&gt; </span><span class="mi">313</span> <span class="k">raise</span> <span class="ne">AttributeError</span><span class="p">(</span><span class="s2">&quot;module </span><span class="si">{!r}</span><span class="s2"> has no attribute &quot;</span>
<span class="g g-Whitespace"> </span><span class="mi">314</span> <span class="s2">&quot;</span><span class="si">{!r}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="vm">__name__</span><span class="p">,</span> <span class="n">attr</span><span class="p">))</span>
<span class="ne">AttributeError</span>: module &#39;numpy&#39; has no attribute &#39;linlag&#39;
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