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Documentation updated
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fjosw
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1 changed files with 1 additions and 236 deletions
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@ -311,8 +311,6 @@
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<span class="sd">"""Computes the matrix to scalar operation op to a given matrix of Obs."""</span>
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<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
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<span class="n">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
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<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">!=</span> <span class="n">dim</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Input has to have dim**2 entries'</span><span class="p">)</span>
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<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
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@ -325,8 +323,6 @@
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<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
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<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
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<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
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<span class="n">raveled_obs</span> <span class="o">=</span> <span class="n">obs</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
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@ -346,9 +342,6 @@
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<span class="n">A</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">entry</span>
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<span class="n">B</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
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<span class="n">big_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">block</span><span class="p">([[</span><span class="n">A</span><span class="p">,</span> <span class="o">-</span><span class="n">B</span><span class="p">],</span> <span class="p">[</span><span class="n">B</span><span class="p">,</span> <span class="n">A</span><span class="p">]])</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="n">op_big_matrix</span> <span class="o">=</span> <span class="n">_num_diff_mat_mat_op</span><span class="p">(</span><span class="n">op</span><span class="p">,</span> <span class="n">big_matrix</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">op_big_matrix</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">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">big_matrix</span><span class="p">],</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
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<span class="n">dim</span> <span class="o">=</span> <span class="n">op_big_matrix</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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<span class="n">op_A</span> <span class="o">=</span> <span class="n">op_big_matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span> <span class="n">dim</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span> <span class="n">dim</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span>
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@ -358,15 +351,11 @@
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<span class="n">res</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">CObs</span><span class="p">(</span><span class="n">op_A</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">],</span> <span class="n">op_B</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">])</span>
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<span class="k">return</span> <span class="n">res</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">_num_diff_mat_mat_op</span><span class="p">(</span><span class="n">op</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>
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<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">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">obs</span><span class="p">],</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
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<span class="k">def</span> <span class="nf">eigh</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>
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<span class="sd">"""Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">_num_diff_eigh</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>
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<span class="n">w</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">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
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<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>
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<span class="k">return</span> <span class="n">w</span><span class="p">,</span> <span class="n">v</span>
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@ -374,235 +363,21 @@
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<span class="k">def</span> <span class="nf">eig</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>
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<span class="sd">"""Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig."""</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">_num_diff_eig</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>
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<span class="c1"># Note: Automatic differentiation of eig is implemented in the git of autograd</span>
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<span class="c1"># but not yet released to PyPi (1.3)</span>
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<span class="n">w</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">real</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">eig</span><span class="p">(</span><span class="n">x</span><span class="p">)[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">obs</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">w</span>
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<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>
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<span class="sd">"""Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">_num_diff_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>
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<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>
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<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>
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<span class="sd">"""Computes the singular value decomposition of a matrix of Obs."""</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="k">return</span> <span class="n">_num_diff_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>
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<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>
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<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>
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<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>
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<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>
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<span class="c1"># Variants for numerical differentiation</span>
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<span class="k">def</span> <span class="nf">_num_diff_mat_mat_op</span><span class="p">(</span><span class="n">op</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>
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<span class="sd">"""Computes the matrix to matrix operation op to a given matrix of Obs elementwise</span>
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<span class="sd"> which is suitable for numerical differentiation."""</span>
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<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
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<span class="n">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
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<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">!=</span> <span class="n">dim</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Input has to have dim**2 entries'</span><span class="p">)</span>
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<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
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<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
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<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
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<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">dim</span> <span class="o">*</span> <span class="n">i</span><span class="p">])</span>
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<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">op</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</span><span class="p">))[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'j'</span><span class="p">)]</span>
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<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
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<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
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<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
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<span class="n">raveled_obs</span> <span class="o">=</span> <span class="n">obs</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
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<span class="n">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">raveled_obs</span><span class="p">)))</span>
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<span class="n">res_mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">=</span><span class="n">j</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
<span class="n">res_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_num_diff_eigh</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 class="sd">"""Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh</span>
|
||||
<span class="sd"> elementwise which is suitable for numerical differentiation."""</span>
|
||||
<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</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">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">!=</span> <span class="n">dim</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Input has to have dim**2 entries'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">dim</span> <span class="o">*</span> <span class="n">i</span><span class="p">])</span>
|
||||
<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'n'</span><span class="p">)</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">np</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</span><span class="p">))[</span><span class="n">n</span><span class="p">]</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)]</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'j'</span><span class="p">)]</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
||||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="n">obs</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">raveled_obs</span><span class="p">)))</span>
|
||||
|
||||
<span class="n">res_vec</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">res_vec</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
|
||||
<span class="n">res_mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">=</span><span class="n">j</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
<span class="n">res_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_vec</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">dim</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">dim</span><span class="p">))</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_num_diff_eig</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 class="sd">"""Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig</span>
|
||||
<span class="sd"> elementwise which is suitable for numerical differentiation."""</span>
|
||||
<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</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">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span>
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">))</span> <span class="o">!=</span> <span class="n">dim</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Input has to have dim**2 entries'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">dim</span> <span class="o">*</span> <span class="n">i</span><span class="p">])</span>
|
||||
<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'n'</span><span class="p">)</span>
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</span><span class="p">))[</span><span class="n">n</span><span class="p">]</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||||
<span class="c1"># Discard imaginary part of eigenvalue here</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">real</span><span class="p">(</span><span class="n">res</span><span class="p">[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)])</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'j'</span><span class="p">)]</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
||||
<span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="n">obs</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">dim</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">raveled_obs</span><span class="p">)))</span>
|
||||
|
||||
<span class="n">res_vec</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">dim</span><span class="p">):</span>
|
||||
<span class="c1"># Note: Automatic differentiation of eig is implemented in the git of autograd</span>
|
||||
<span class="c1"># but not yet released to PyPi (1.3)</span>
|
||||
<span class="n">res_vec</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_vec</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">dim</span><span class="p">)</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_num_diff_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 class="sd">"""Computes the Moore-Penrose pseudoinverse of a matrix of Obs elementwise which is suitable</span>
|
||||
<span class="sd"> for numerical differentiation."""</span>
|
||||
<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</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">shape</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'shape'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">i</span><span class="p">])</span>
|
||||
<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">np</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</span><span class="p">))[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'j'</span><span class="p">)]</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||||
<span class="n">shape</span> <span class="o">=</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">res_mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">=</span><span class="n">j</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
<span class="n">res_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_num_diff_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 class="sd">"""Computes the singular value decomposition of a matrix of Obs elementwise which</span>
|
||||
<span class="sd"> is suitable for numerical differentiation."""</span>
|
||||
<span class="k">def</span> <span class="nf">_mat</span><span class="p">(</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">shape</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'shape'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mat</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">i</span><span class="p">])</span>
|
||||
<span class="n">mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="n">res</span> <span class="o">=</span> <span class="n">np</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">mat</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="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'n'</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)]</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'n'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'i'</span><span class="p">)][</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'j'</span><span class="p">)]</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||||
<span class="n">shape</span> <span class="o">=</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span>
|
||||
<span class="n">raveled_obs</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))</span><span class="o">.</span><span class="n">tolist</span><span class="p">()</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'Unproper type of input.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">mid_index</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||||
|
||||
<span class="n">res_mat0</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">mid_index</span><span class="p">):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">=</span><span class="n">j</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
<span class="n">res_mat0</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="n">res_mat1</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">mid_index</span><span class="p">):</span>
|
||||
<span class="n">res_mat1</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
|
||||
<span class="n">res_mat2</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">mid_index</span><span class="p">):</span>
|
||||
<span class="n">row</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="n">_mat</span><span class="p">,</span> <span class="n">raveled_obs</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="n">shape</span><span class="p">,</span> <span class="n">n</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">i</span><span class="o">=</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="o">=</span><span class="n">j</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">))</span>
|
||||
<span class="n">res_mat2</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">row</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat0</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">mid_index</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat1</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">mid_index</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">res_mat2</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
|
@ -956,8 +731,6 @@ Obs valued.</li>
|
|||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">eigh</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 class="sd">"""Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh."""</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">_num_diff_eigh</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 class="n">w</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">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">)</span>
|
||||
<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 class="k">return</span> <span class="n">w</span><span class="p">,</span> <span class="n">v</span>
|
||||
|
|
@ -982,10 +755,6 @@ Obs valued.</li>
|
|||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">eig</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 class="sd">"""Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig."""</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">_num_diff_eig</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 class="c1"># Note: Automatic differentiation of eig is implemented in the git of autograd</span>
|
||||
<span class="c1"># but not yet released to PyPi (1.3)</span>
|
||||
<span class="n">w</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">real</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">eig</span><span class="p">(</span><span class="n">x</span><span class="p">)[</span><span class="mi">0</span><span class="p">]),</span> <span class="n">obs</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">w</span>
|
||||
</pre></div>
|
||||
|
|
@ -1009,8 +778,6 @@ Obs valued.</li>
|
|||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><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 class="sd">"""Computes the Moore-Penrose pseudoinverse of a matrix of Obs."""</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">_num_diff_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 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>
|
||||
</pre></div>
|
||||
|
||||
|
|
@ -1033,8 +800,6 @@ Obs valued.</li>
|
|||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><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 class="sd">"""Computes the singular value decomposition of a matrix of Obs."""</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'num_grad'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">_num_diff_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 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 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 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>
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue