Documentation updated

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fjosw 2023-11-17 17:58:03 +00:00
parent 4859640b41
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3 changed files with 3927 additions and 3746 deletions

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@ -76,6 +76,9 @@
<li>
<a class="function" href="#eig">eig</a>
</li>
<li>
<a class="function" href="#eigv">eigv</a>
</li>
<li>
<a class="function" href="#pinv">pinv</a>
</li>
@ -376,17 +379,23 @@
</span><span id="L-271"><a href="#L-271"><span class="linenos">271</span></a> <span class="k">return</span> <span class="n">w</span>
</span><span id="L-272"><a href="#L-272"><span class="linenos">272</span></a>
</span><span id="L-273"><a href="#L-273"><span class="linenos">273</span></a>
</span><span id="L-274"><a href="#L-274"><span class="linenos">274</span></a><span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="L-275"><a href="#L-275"><span class="linenos">275</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Moore-Penrose pseudoinverse of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="L-276"><a href="#L-276"><span class="linenos">276</span></a> <span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</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="n">obs</span><span class="p">)</span>
</span><span id="L-277"><a href="#L-277"><span class="linenos">277</span></a>
</span><span id="L-274"><a href="#L-274"><span class="linenos">274</span></a><span class="k">def</span> <span class="nf">eigv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="L-275"><a href="#L-275"><span class="linenos">275</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.&quot;&quot;&quot;</span>
</span><span id="L-276"><a href="#L-276"><span class="linenos">276</span></a> <span class="n">v</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eigh</span><span class="p">(</span><span class="n">x</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-277"><a href="#L-277"><span class="linenos">277</span></a> <span class="k">return</span> <span class="n">v</span>
</span><span id="L-278"><a href="#L-278"><span class="linenos">278</span></a>
</span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a><span class="k">def</span> <span class="nf">svd</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the singular value decomposition of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a> <span class="n">u</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a> <span class="n">s</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a> <span class="n">vh</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vh</span><span class="p">)</span>
</span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a>
</span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a><span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Moore-Penrose pseudoinverse of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a> <span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</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="n">obs</span><span class="p">)</span>
</span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a>
</span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a>
</span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a><span class="k">def</span> <span class="nf">svd</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the singular value decomposition of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a> <span class="n">u</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a> <span class="n">s</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a> <span class="n">vh</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vh</span><span class="p">)</span>
</span></pre></div>
@ -775,6 +784,29 @@ Obs valued.</li>
</div>
</section>
<section id="eigv">
<input id="eigv-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
<div class="attr function">
<span class="def">def</span>
<span class="name">eigv</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">obs</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
<label class="view-source-button" for="eigv-view-source"><span>View Source</span></label>
</div>
<a class="headerlink" href="#eigv"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="eigv-275"><a href="#eigv-275"><span class="linenos">275</span></a><span class="k">def</span> <span class="nf">eigv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="eigv-276"><a href="#eigv-276"><span class="linenos">276</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.&quot;&quot;&quot;</span>
</span><span id="eigv-277"><a href="#eigv-277"><span class="linenos">277</span></a> <span class="n">v</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eigh</span><span class="p">(</span><span class="n">x</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="eigv-278"><a href="#eigv-278"><span class="linenos">278</span></a> <span class="k">return</span> <span class="n">v</span>
</span></pre></div>
<div class="docstring"><p>Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>
</div>
</section>
<section id="pinv">
<input id="pinv-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
@ -787,9 +819,9 @@ Obs valued.</li>
</div>
<a class="headerlink" href="#pinv"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="pinv-275"><a href="#pinv-275"><span class="linenos">275</span></a><span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="pinv-276"><a href="#pinv-276"><span class="linenos">276</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Moore-Penrose pseudoinverse of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="pinv-277"><a href="#pinv-277"><span class="linenos">277</span></a> <span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</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="n">obs</span><span class="p">)</span>
<div class="pdoc-code codehilite"><pre><span></span><span id="pinv-281"><a href="#pinv-281"><span class="linenos">281</span></a><span class="k">def</span> <span class="nf">pinv</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="pinv-282"><a href="#pinv-282"><span class="linenos">282</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the Moore-Penrose pseudoinverse of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="pinv-283"><a href="#pinv-283"><span class="linenos">283</span></a> <span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</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="n">obs</span><span class="p">)</span>
</span></pre></div>
@ -809,12 +841,12 @@ Obs valued.</li>
</div>
<a class="headerlink" href="#svd"></a>
<div class="pdoc-code codehilite"><pre><span></span><span id="svd-280"><a href="#svd-280"><span class="linenos">280</span></a><span class="k">def</span> <span class="nf">svd</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="svd-281"><a href="#svd-281"><span class="linenos">281</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the singular value decomposition of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="svd-282"><a href="#svd-282"><span class="linenos">282</span></a> <span class="n">u</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-283"><a href="#svd-283"><span class="linenos">283</span></a> <span class="n">s</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-284"><a href="#svd-284"><span class="linenos">284</span></a> <span class="n">vh</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-285"><a href="#svd-285"><span class="linenos">285</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vh</span><span class="p">)</span>
<div class="pdoc-code codehilite"><pre><span></span><span id="svd-286"><a href="#svd-286"><span class="linenos">286</span></a><span class="k">def</span> <span class="nf">svd</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
</span><span id="svd-287"><a href="#svd-287"><span class="linenos">287</span></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;Computes the singular value decomposition of a matrix of Obs.&quot;&quot;&quot;</span>
</span><span id="svd-288"><a href="#svd-288"><span class="linenos">288</span></a> <span class="n">u</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-289"><a href="#svd-289"><span class="linenos">289</span></a> <span class="n">s</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-290"><a href="#svd-290"><span class="linenos">290</span></a> <span class="n">vh</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">svd</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">full_matrices</span><span class="o">=</span><span class="kc">False</span><span class="p">)[</span><span class="mi">2</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
</span><span id="svd-291"><a href="#svd-291"><span class="linenos">291</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="n">vh</span><span class="p">)</span>
</span></pre></div>

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