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doc/LectureNotes/_build/html/week36.html

@@ -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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doc/LectureNotes/_build/jupyter_execute/week36.py

@@ -142,12 +142,14 @@
 # ## Code for SVD and Inversion of Matrices
 # 
 # How do we use the SVD to invert a matrix $\boldsymbol{X}^\boldsymbol{X}$ which is singular or near singular?
-# The simple answer is to use the linear algebra function for pseudoinvers, that is
+# The simple answer is to use the linear algebra function for the computation of the pseudoinverse of a given matrix $\boldsymbol{X}$, that is
 
 # In[1]:
 
 
-Ainv = np.linlag.pinv(A)
+import numpy as np
+X = np.array( [ [1,2,3],[2,4,5],[3,5,6]])
+Xinv = np.linlag.pinv(X)
 
 
 # Let us first look at a matrix which does not causes problems and write our own function where we just use the SVD.