Documentation updated

This commit is contained in:
fjosw 2022-01-31 17:31:32 +00:00
parent 3df59fc7bc
commit db66a3c08a
2 changed files with 218 additions and 80 deletions

View file

@ -666,25 +666,16 @@
<span class="k">return</span> <span class="p">(</span><span class="bp">self</span> <span class="o">+</span> <span class="n">T_partner</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symmetric</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the first derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> symmetric : bool</span>
<span class="sd"> decides whether symmetric of simple finite differences are used. Default: True</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, forward, backward, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -694,9 +685,49 @@
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;forward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;backward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.&quot;&quot;&quot;</span>
<span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -706,6 +737,18 @@
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">30</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">m_eff</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s1">&#39;log&#39;</span><span class="p">,</span> <span class="n">guess</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Returns the effective mass of the correlator as correlator object</span>
@ -1707,25 +1750,16 @@
<span class="k">return</span> <span class="p">(</span><span class="bp">self</span> <span class="o">+</span> <span class="n">T_partner</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span>
<span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symmetric</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the first derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> symmetric : bool</span>
<span class="sd"> decides whether symmetric of simple finite differences are used. Default: True</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, forward, backward, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -1735,9 +1769,49 @@
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;forward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;backward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.&quot;&quot;&quot;</span>
<span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -1747,6 +1821,18 @@
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">30</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">m_eff</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s1">&#39;log&#39;</span><span class="p">,</span> <span class="n">guess</span><span class="o">=</span><span class="mf">1.0</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Returns the effective mass of the correlator as correlator object</span>
@ -3082,30 +3168,21 @@ Parity quantum number of the correlator, can be +1 or -1</li>
<span class="def">def</span>
<span class="name">deriv</span><span class="signature">(self, symmetric=True)</span>:
<span class="name">deriv</span><span class="signature">(self, variant=&#39;symmetric&#39;)</span>:
</div>
<details>
<summary>View Source</summary>
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">symmetric</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the first derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> symmetric : bool</span>
<span class="sd"> decides whether symmetric of simple finite differences are used. Default: True</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, forward, backward, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="ow">not</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span> <span class="n">symmetric</span><span class="p">:</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -3115,6 +3192,38 @@ Parity quantum number of the correlator, can be +1 or -1</li>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;forward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;backward&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Derivative is undefined at all timeslices&#39;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
</pre></div>
</details>
@ -3124,8 +3233,9 @@ Parity quantum number of the correlator, can be +1 or -1</li>
<h6 id="parameters">Parameters</h6>
<ul>
<li><strong>symmetric</strong> (bool):
decides whether symmetric of simple finite differences are used. Default: True</li>
<li><strong>variant</strong> (str):
decides which definition of the finite differences derivative is used.
Available choice: symmetric, forward, backward, improved, default: symmetric</li>
</ul>
</div>
@ -3136,13 +3246,21 @@ decides whether symmetric of simple finite differences are used. Default: True</
<span class="def">def</span>
<span class="name">second_deriv</span><span class="signature">(self)</span>:
<span class="name">second_deriv</span><span class="signature">(self, variant=&#39;symmetric&#39;)</span>:
</div>
<details>
<summary>View Source</summary>
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.&quot;&quot;&quot;</span>
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">second_deriv</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">variant</span><span class="o">=</span><span class="s2">&quot;symmetric&quot;</span><span class="p">):</span>
<span class="sd">&quot;&quot;&quot;Return the second derivative of the correlator with respect to x0.</span>
<span class="sd"> Parameters</span>
<span class="sd"> ----------</span>
<span class="sd"> variant : str</span>
<span class="sd"> decides which definition of the finite differences derivative is used.</span>
<span class="sd"> Available choice: symmetric, improved, default: symmetric</span>
<span class="sd"> &quot;&quot;&quot;</span>
<span class="k">if</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;symmetric&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
@ -3152,11 +3270,31 @@ decides whether symmetric of simple finite differences are used. Default: True</
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="k">elif</span> <span class="n">variant</span> <span class="o">==</span> <span class="s2">&quot;improved&quot;</span><span class="p">:</span>
<span class="n">newcontent</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">T</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
<span class="k">if</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">):</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="k">else</span><span class="p">:</span>
<span class="n">newcontent</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="mi">1</span> <span class="o">/</span> <span class="mi">12</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span><span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="mi">30</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span><span class="p">]</span> <span class="o">+</span> <span class="mi">16</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">content</span><span class="p">[</span><span class="n">t</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]))</span>
<span class="k">if</span><span class="p">(</span><span class="nb">all</span><span class="p">([</span><span class="n">x</span> <span class="ow">is</span> <span class="kc">None</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">newcontent</span><span class="p">])):</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Derivative is undefined at all timeslices&quot;</span><span class="p">)</span>
<span class="k">return</span> <span class="n">Corr</span><span class="p">(</span><span class="n">newcontent</span><span class="p">,</span> <span class="n">padding</span><span class="o">=</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">&quot;Unknown variant.&quot;</span><span class="p">)</span>
</pre></div>
</details>
<div class="docstring"><p>Return the second derivative of the correlator with respect to x0.</p>
<h6 id="parameters">Parameters</h6>
<ul>
<li><strong>variant</strong> (str):
decides which definition of the finite differences derivative is used.
Available choice: symmetric, improved, default: symmetric</li>
</ul>
</div>

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