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<h1 class="modulename">
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<a href="./../pyerrors.html">pyerrors</a><wbr>.integrate </h1>
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<input id="mod-integrate-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
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<div class="pdoc-code codehilite"><pre><span></span><span id="L-1"><a href="#L-1"><span class="linenos"> 1</span></a><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
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</span><span id="L-2"><a href="#L-2"><span class="linenos"> 2</span></a><span class="kn">from</span><span class="w"> </span><span class="nn">.obs</span><span class="w"> </span><span class="kn">import</span> <span class="n">derived_observable</span><span class="p">,</span> <span class="n">Obs</span>
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</span><span id="L-3"><a href="#L-3"><span class="linenos"> 3</span></a><span class="kn">from</span><span class="w"> </span><span class="nn">autograd</span><span class="w"> </span><span class="kn">import</span> <span class="n">jacobian</span>
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</span><span id="L-4"><a href="#L-4"><span class="linenos"> 4</span></a><span class="kn">from</span><span class="w"> </span><span class="nn">scipy.integrate</span><span class="w"> </span><span class="kn">import</span> <span class="n">quad</span> <span class="k">as</span> <span class="n">squad</span>
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</span><span id="L-5"><a href="#L-5"><span class="linenos"> 5</span></a>
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</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a>
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</span><span id="L-7"><a href="#L-7"><span class="linenos"> 7</span></a><span class="k">def</span><span class="w"> </span><span class="nf">quad</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
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</span><span id="L-8"><a href="#L-8"><span class="linenos"> 8</span></a><span class="w"> </span><span class="sd">'''Performs a (one-dimensional) numeric integration of f(p, x) from a to b.</span>
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</span><span id="L-9"><a href="#L-9"><span class="linenos"> 9</span></a>
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</span><span id="L-10"><a href="#L-10"><span class="linenos">10</span></a><span class="sd"> The integration is performed using scipy.integrate.quad().</span>
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</span><span id="L-11"><a href="#L-11"><span class="linenos">11</span></a><span class="sd"> All parameters that can be passed to scipy.integrate.quad may also be passed to this function.</span>
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</span><span id="L-12"><a href="#L-12"><span class="linenos">12</span></a><span class="sd"> The output is the same as for scipy.integrate.quad, the first element being an Obs.</span>
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</span><span id="L-13"><a href="#L-13"><span class="linenos">13</span></a>
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</span><span id="L-14"><a href="#L-14"><span class="linenos">14</span></a><span class="sd"> Parameters</span>
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</span><span id="L-15"><a href="#L-15"><span class="linenos">15</span></a><span class="sd"> ----------</span>
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</span><span id="L-16"><a href="#L-16"><span class="linenos">16</span></a><span class="sd"> func : object</span>
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</span><span id="L-17"><a href="#L-17"><span class="linenos">17</span></a><span class="sd"> function to integrate, has to be of the form</span>
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</span><span id="L-18"><a href="#L-18"><span class="linenos">18</span></a>
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</span><span id="L-19"><a href="#L-19"><span class="linenos">19</span></a><span class="sd"> ```python</span>
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</span><span id="L-20"><a href="#L-20"><span class="linenos">20</span></a><span class="sd"> import autograd.numpy as anp</span>
|
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</span><span id="L-21"><a href="#L-21"><span class="linenos">21</span></a>
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</span><span id="L-22"><a href="#L-22"><span class="linenos">22</span></a><span class="sd"> def func(p, x):</span>
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|
</span><span id="L-23"><a href="#L-23"><span class="linenos">23</span></a><span class="sd"> return p[0] + p[1] * x + p[2] * anp.sinh(x)</span>
|
|
</span><span id="L-24"><a href="#L-24"><span class="linenos">24</span></a><span class="sd"> ```</span>
|
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</span><span id="L-25"><a href="#L-25"><span class="linenos">25</span></a><span class="sd"> where x is the integration variable.</span>
|
|
</span><span id="L-26"><a href="#L-26"><span class="linenos">26</span></a><span class="sd"> p : list of floats or Obs</span>
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|
</span><span id="L-27"><a href="#L-27"><span class="linenos">27</span></a><span class="sd"> parameters of the function func.</span>
|
|
</span><span id="L-28"><a href="#L-28"><span class="linenos">28</span></a><span class="sd"> a: float or Obs</span>
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|
</span><span id="L-29"><a href="#L-29"><span class="linenos">29</span></a><span class="sd"> Lower limit of integration (use -numpy.inf for -infinity).</span>
|
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</span><span id="L-30"><a href="#L-30"><span class="linenos">30</span></a><span class="sd"> b: float or Obs</span>
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|
</span><span id="L-31"><a href="#L-31"><span class="linenos">31</span></a><span class="sd"> Upper limit of integration (use -numpy.inf for -infinity).</span>
|
|
</span><span id="L-32"><a href="#L-32"><span class="linenos">32</span></a><span class="sd"> All parameters of scipy.integrate.quad</span>
|
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</span><span id="L-33"><a href="#L-33"><span class="linenos">33</span></a>
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|
</span><span id="L-34"><a href="#L-34"><span class="linenos">34</span></a><span class="sd"> Returns</span>
|
|
</span><span id="L-35"><a href="#L-35"><span class="linenos">35</span></a><span class="sd"> -------</span>
|
|
</span><span id="L-36"><a href="#L-36"><span class="linenos">36</span></a><span class="sd"> y : Obs</span>
|
|
</span><span id="L-37"><a href="#L-37"><span class="linenos">37</span></a><span class="sd"> The integral of func from `a` to `b`.</span>
|
|
</span><span id="L-38"><a href="#L-38"><span class="linenos">38</span></a><span class="sd"> abserr : float</span>
|
|
</span><span id="L-39"><a href="#L-39"><span class="linenos">39</span></a><span class="sd"> An estimate of the absolute error in the result.</span>
|
|
</span><span id="L-40"><a href="#L-40"><span class="linenos">40</span></a><span class="sd"> infodict : dict</span>
|
|
</span><span id="L-41"><a href="#L-41"><span class="linenos">41</span></a><span class="sd"> A dictionary containing additional information.</span>
|
|
</span><span id="L-42"><a href="#L-42"><span class="linenos">42</span></a><span class="sd"> Run scipy.integrate.quad_explain() for more information.</span>
|
|
</span><span id="L-43"><a href="#L-43"><span class="linenos">43</span></a><span class="sd"> message</span>
|
|
</span><span id="L-44"><a href="#L-44"><span class="linenos">44</span></a><span class="sd"> A convergence message.</span>
|
|
</span><span id="L-45"><a href="#L-45"><span class="linenos">45</span></a><span class="sd"> explain</span>
|
|
</span><span id="L-46"><a href="#L-46"><span class="linenos">46</span></a><span class="sd"> Appended only with 'cos' or 'sin' weighting and infinite</span>
|
|
</span><span id="L-47"><a href="#L-47"><span class="linenos">47</span></a><span class="sd"> integration limits, it contains an explanation of the codes in</span>
|
|
</span><span id="L-48"><a href="#L-48"><span class="linenos">48</span></a><span class="sd"> infodict['ierlst']</span>
|
|
</span><span id="L-49"><a href="#L-49"><span class="linenos">49</span></a><span class="sd"> '''</span>
|
|
</span><span id="L-50"><a href="#L-50"><span class="linenos">50</span></a>
|
|
</span><span id="L-51"><a href="#L-51"><span class="linenos">51</span></a> <span class="n">Np</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
|
|
</span><span id="L-52"><a href="#L-52"><span class="linenos">52</span></a> <span class="n">isobs</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">pi</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">else</span> <span class="kc">False</span> <span class="k">for</span> <span class="n">pi</span> <span class="ow">in</span> <span class="n">p</span><span class="p">]</span>
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</span><span id="L-53"><a href="#L-53"><span class="linenos">53</span></a> <span class="n">pval</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="n">p</span><span class="p">[</span><span class="n">i</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">Np</span><span class="p">)],)</span>
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</span><span id="L-54"><a href="#L-54"><span class="linenos">54</span></a> <span class="n">pobs</span> <span class="o">=</span> <span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="n">i</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">Np</span><span class="p">)</span> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
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</span><span id="L-55"><a href="#L-55"><span class="linenos">55</span></a>
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</span><span id="L-56"><a href="#L-56"><span class="linenos">56</span></a> <span class="n">bounds</span> <span class="o">=</span> <span class="p">[</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">]</span>
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</span><span id="L-57"><a href="#L-57"><span class="linenos">57</span></a> <span class="n">isobs_b</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">bi</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">else</span> <span class="kc">False</span> <span class="k">for</span> <span class="n">bi</span> <span class="ow">in</span> <span class="n">bounds</span><span class="p">]</span>
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</span><span id="L-58"><a href="#L-58"><span class="linenos">58</span></a> <span class="n">bval</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="n">bounds</span><span class="p">[</span><span class="n">i</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="mi">2</span><span class="p">)])</span>
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</span><span id="L-59"><a href="#L-59"><span class="linenos">59</span></a> <span class="n">bobs</span> <span class="o">=</span> <span class="p">[</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</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="mi">2</span><span class="p">)</span> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
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</span><span id="L-60"><a href="#L-60"><span class="linenos">60</span></a> <span class="n">bsign</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
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</span><span id="L-61"><a href="#L-61"><span class="linenos">61</span></a>
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</span><span id="L-62"><a href="#L-62"><span class="linenos">62</span></a> <span class="n">ifunc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
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</span><span id="L-63"><a href="#L-63"><span class="linenos">63</span></a>
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</span><span id="L-64"><a href="#L-64"><span class="linenos">64</span></a> <span class="n">intpars</span> <span class="o">=</span> <span class="n">squad</span><span class="o">.</span><span class="vm">__code__</span><span class="o">.</span><span class="n">co_varnames</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">squad</span><span class="o">.</span><span class="vm">__defaults__</span><span class="p">)]</span>
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</span><span id="L-65"><a href="#L-65"><span class="linenos">65</span></a> <span class="n">ikwargs</span> <span class="o">=</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">kwargs</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">intpars</span> <span class="k">if</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">}</span>
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</span><span id="L-66"><a href="#L-66"><span class="linenos">66</span></a>
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</span><span id="L-67"><a href="#L-67"><span class="linenos">67</span></a> <span class="n">integration_result</span> <span class="o">=</span> <span class="n">squad</span><span class="p">(</span><span class="n">ifunc</span><span class="p">,</span> <span class="n">bval</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bval</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">**</span><span class="n">ikwargs</span><span class="p">)</span>
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</span><span id="L-68"><a href="#L-68"><span class="linenos">68</span></a> <span class="n">val</span> <span class="o">=</span> <span class="n">integration_result</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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</span><span id="L-69"><a href="#L-69"><span class="linenos">69</span></a>
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</span><span id="L-70"><a href="#L-70"><span class="linenos">70</span></a> <span class="n">jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
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</span><span id="L-71"><a href="#L-71"><span class="linenos">71</span></a>
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</span><span id="L-72"><a href="#L-72"><span class="linenos">72</span></a> <span class="n">derivint</span> <span class="o">=</span> <span class="p">[]</span>
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</span><span id="L-73"><a href="#L-73"><span class="linenos">73</span></a> <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">Np</span><span class="p">):</span>
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</span><span id="L-74"><a href="#L-74"><span class="linenos">74</span></a> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
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</span><span id="L-75"><a href="#L-75"><span class="linenos">75</span></a> <span class="n">ifunc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">jac</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">x</span><span class="p">)[</span><span class="n">i</span><span class="p">])</span>
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</span><span id="L-76"><a href="#L-76"><span class="linenos">76</span></a> <span class="n">derivint</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">squad</span><span class="p">(</span><span class="n">ifunc</span><span class="p">,</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">**</span><span class="n">ikwargs</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
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</span><span id="L-77"><a href="#L-77"><span class="linenos">77</span></a>
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</span><span id="L-78"><a href="#L-78"><span class="linenos">78</span></a> <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="mi">2</span><span class="p">):</span>
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</span><span id="L-79"><a href="#L-79"><span class="linenos">79</span></a> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
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</span><span id="L-80"><a href="#L-80"><span class="linenos">80</span></a> <span class="n">derivint</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">bsign</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">func</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">bval</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
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</span><span id="L-81"><a href="#L-81"><span class="linenos">81</span></a>
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</span><span id="L-82"><a href="#L-82"><span class="linenos">82</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">derivint</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
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</span><span id="L-83"><a href="#L-83"><span class="linenos">83</span></a> <span class="k">return</span> <span class="n">integration_result</span>
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</span><span id="L-84"><a href="#L-84"><span class="linenos">84</span></a>
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</span><span id="L-85"><a href="#L-85"><span class="linenos">85</span></a> <span class="n">res</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="mi">0</span> <span class="o">*</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="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">pval</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">+</span> <span class="n">val</span><span class="p">,</span> <span class="n">pobs</span> <span class="o">+</span> <span class="n">bobs</span><span class="p">,</span> <span class="n">man_grad</span><span class="o">=</span><span class="n">derivint</span><span class="p">)</span>
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</span><span id="L-86"><a href="#L-86"><span class="linenos">86</span></a>
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</span><span id="L-87"><a href="#L-87"><span class="linenos">87</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="o">*</span><span class="n">integration_result</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
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</span></pre></div>
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</section>
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<section id="quad">
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<input id="quad-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
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<div class="attr function">
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<span class="def">def</span>
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<span class="name">quad</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">p</span>, </span><span class="param"><span class="n">a</span>, </span><span class="param"><span class="n">b</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
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<label class="view-source-button" for="quad-view-source"><span>View Source</span></label>
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</div>
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<a class="headerlink" href="#quad"></a>
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<div class="pdoc-code codehilite"><pre><span></span><span id="quad-8"><a href="#quad-8"><span class="linenos"> 8</span></a><span class="k">def</span><span class="w"> </span><span class="nf">quad</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
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</span><span id="quad-9"><a href="#quad-9"><span class="linenos"> 9</span></a><span class="w"> </span><span class="sd">'''Performs a (one-dimensional) numeric integration of f(p, x) from a to b.</span>
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</span><span id="quad-10"><a href="#quad-10"><span class="linenos">10</span></a>
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</span><span id="quad-11"><a href="#quad-11"><span class="linenos">11</span></a><span class="sd"> The integration is performed using scipy.integrate.quad().</span>
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</span><span id="quad-12"><a href="#quad-12"><span class="linenos">12</span></a><span class="sd"> All parameters that can be passed to scipy.integrate.quad may also be passed to this function.</span>
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</span><span id="quad-13"><a href="#quad-13"><span class="linenos">13</span></a><span class="sd"> The output is the same as for scipy.integrate.quad, the first element being an Obs.</span>
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</span><span id="quad-14"><a href="#quad-14"><span class="linenos">14</span></a>
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</span><span id="quad-15"><a href="#quad-15"><span class="linenos">15</span></a><span class="sd"> Parameters</span>
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</span><span id="quad-16"><a href="#quad-16"><span class="linenos">16</span></a><span class="sd"> ----------</span>
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</span><span id="quad-17"><a href="#quad-17"><span class="linenos">17</span></a><span class="sd"> func : object</span>
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</span><span id="quad-18"><a href="#quad-18"><span class="linenos">18</span></a><span class="sd"> function to integrate, has to be of the form</span>
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</span><span id="quad-19"><a href="#quad-19"><span class="linenos">19</span></a>
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</span><span id="quad-20"><a href="#quad-20"><span class="linenos">20</span></a><span class="sd"> ```python</span>
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</span><span id="quad-21"><a href="#quad-21"><span class="linenos">21</span></a><span class="sd"> import autograd.numpy as anp</span>
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</span><span id="quad-22"><a href="#quad-22"><span class="linenos">22</span></a>
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</span><span id="quad-23"><a href="#quad-23"><span class="linenos">23</span></a><span class="sd"> def func(p, x):</span>
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</span><span id="quad-24"><a href="#quad-24"><span class="linenos">24</span></a><span class="sd"> return p[0] + p[1] * x + p[2] * anp.sinh(x)</span>
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</span><span id="quad-25"><a href="#quad-25"><span class="linenos">25</span></a><span class="sd"> ```</span>
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</span><span id="quad-26"><a href="#quad-26"><span class="linenos">26</span></a><span class="sd"> where x is the integration variable.</span>
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</span><span id="quad-27"><a href="#quad-27"><span class="linenos">27</span></a><span class="sd"> p : list of floats or Obs</span>
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</span><span id="quad-28"><a href="#quad-28"><span class="linenos">28</span></a><span class="sd"> parameters of the function func.</span>
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</span><span id="quad-29"><a href="#quad-29"><span class="linenos">29</span></a><span class="sd"> a: float or Obs</span>
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</span><span id="quad-30"><a href="#quad-30"><span class="linenos">30</span></a><span class="sd"> Lower limit of integration (use -numpy.inf for -infinity).</span>
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</span><span id="quad-31"><a href="#quad-31"><span class="linenos">31</span></a><span class="sd"> b: float or Obs</span>
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</span><span id="quad-32"><a href="#quad-32"><span class="linenos">32</span></a><span class="sd"> Upper limit of integration (use -numpy.inf for -infinity).</span>
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</span><span id="quad-33"><a href="#quad-33"><span class="linenos">33</span></a><span class="sd"> All parameters of scipy.integrate.quad</span>
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</span><span id="quad-34"><a href="#quad-34"><span class="linenos">34</span></a>
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</span><span id="quad-35"><a href="#quad-35"><span class="linenos">35</span></a><span class="sd"> Returns</span>
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</span><span id="quad-36"><a href="#quad-36"><span class="linenos">36</span></a><span class="sd"> -------</span>
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</span><span id="quad-37"><a href="#quad-37"><span class="linenos">37</span></a><span class="sd"> y : Obs</span>
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</span><span id="quad-38"><a href="#quad-38"><span class="linenos">38</span></a><span class="sd"> The integral of func from `a` to `b`.</span>
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</span><span id="quad-39"><a href="#quad-39"><span class="linenos">39</span></a><span class="sd"> abserr : float</span>
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</span><span id="quad-40"><a href="#quad-40"><span class="linenos">40</span></a><span class="sd"> An estimate of the absolute error in the result.</span>
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</span><span id="quad-41"><a href="#quad-41"><span class="linenos">41</span></a><span class="sd"> infodict : dict</span>
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</span><span id="quad-42"><a href="#quad-42"><span class="linenos">42</span></a><span class="sd"> A dictionary containing additional information.</span>
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</span><span id="quad-43"><a href="#quad-43"><span class="linenos">43</span></a><span class="sd"> Run scipy.integrate.quad_explain() for more information.</span>
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</span><span id="quad-44"><a href="#quad-44"><span class="linenos">44</span></a><span class="sd"> message</span>
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</span><span id="quad-45"><a href="#quad-45"><span class="linenos">45</span></a><span class="sd"> A convergence message.</span>
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</span><span id="quad-46"><a href="#quad-46"><span class="linenos">46</span></a><span class="sd"> explain</span>
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</span><span id="quad-47"><a href="#quad-47"><span class="linenos">47</span></a><span class="sd"> Appended only with 'cos' or 'sin' weighting and infinite</span>
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</span><span id="quad-48"><a href="#quad-48"><span class="linenos">48</span></a><span class="sd"> integration limits, it contains an explanation of the codes in</span>
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</span><span id="quad-49"><a href="#quad-49"><span class="linenos">49</span></a><span class="sd"> infodict['ierlst']</span>
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</span><span id="quad-50"><a href="#quad-50"><span class="linenos">50</span></a><span class="sd"> '''</span>
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</span><span id="quad-51"><a href="#quad-51"><span class="linenos">51</span></a>
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</span><span id="quad-52"><a href="#quad-52"><span class="linenos">52</span></a> <span class="n">Np</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
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</span><span id="quad-53"><a href="#quad-53"><span class="linenos">53</span></a> <span class="n">isobs</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">pi</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">else</span> <span class="kc">False</span> <span class="k">for</span> <span class="n">pi</span> <span class="ow">in</span> <span class="n">p</span><span class="p">]</span>
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</span><span id="quad-54"><a href="#quad-54"><span class="linenos">54</span></a> <span class="n">pval</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">p</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="n">p</span><span class="p">[</span><span class="n">i</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">Np</span><span class="p">)],)</span>
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|
</span><span id="quad-55"><a href="#quad-55"><span class="linenos">55</span></a> <span class="n">pobs</span> <span class="o">=</span> <span class="p">[</span><span class="n">p</span><span class="p">[</span><span class="n">i</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">Np</span><span class="p">)</span> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
|
|
</span><span id="quad-56"><a href="#quad-56"><span class="linenos">56</span></a>
|
|
</span><span id="quad-57"><a href="#quad-57"><span class="linenos">57</span></a> <span class="n">bounds</span> <span class="o">=</span> <span class="p">[</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">]</span>
|
|
</span><span id="quad-58"><a href="#quad-58"><span class="linenos">58</span></a> <span class="n">isobs_b</span> <span class="o">=</span> <span class="p">[</span><span class="kc">True</span> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">bi</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">else</span> <span class="kc">False</span> <span class="k">for</span> <span class="n">bi</span> <span class="ow">in</span> <span class="n">bounds</span><span class="p">]</span>
|
|
</span><span id="quad-59"><a href="#quad-59"><span class="linenos">59</span></a> <span class="n">bval</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">else</span> <span class="n">bounds</span><span class="p">[</span><span class="n">i</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="mi">2</span><span class="p">)])</span>
|
|
</span><span id="quad-60"><a href="#quad-60"><span class="linenos">60</span></a> <span class="n">bobs</span> <span class="o">=</span> <span class="p">[</span><span class="n">bounds</span><span class="p">[</span><span class="n">i</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="mi">2</span><span class="p">)</span> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
|
|
</span><span id="quad-61"><a href="#quad-61"><span class="linenos">61</span></a> <span class="n">bsign</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
|
|
</span><span id="quad-62"><a href="#quad-62"><span class="linenos">62</span></a>
|
|
</span><span id="quad-63"><a href="#quad-63"><span class="linenos">63</span></a> <span class="n">ifunc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">x</span><span class="p">))</span>
|
|
</span><span id="quad-64"><a href="#quad-64"><span class="linenos">64</span></a>
|
|
</span><span id="quad-65"><a href="#quad-65"><span class="linenos">65</span></a> <span class="n">intpars</span> <span class="o">=</span> <span class="n">squad</span><span class="o">.</span><span class="vm">__code__</span><span class="o">.</span><span class="n">co_varnames</span><span class="p">[</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">squad</span><span class="o">.</span><span class="vm">__defaults__</span><span class="p">)]</span>
|
|
</span><span id="quad-66"><a href="#quad-66"><span class="linenos">66</span></a> <span class="n">ikwargs</span> <span class="o">=</span> <span class="p">{</span><span class="n">k</span><span class="p">:</span> <span class="n">kwargs</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">intpars</span> <span class="k">if</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">}</span>
|
|
</span><span id="quad-67"><a href="#quad-67"><span class="linenos">67</span></a>
|
|
</span><span id="quad-68"><a href="#quad-68"><span class="linenos">68</span></a> <span class="n">integration_result</span> <span class="o">=</span> <span class="n">squad</span><span class="p">(</span><span class="n">ifunc</span><span class="p">,</span> <span class="n">bval</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bval</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">**</span><span class="n">ikwargs</span><span class="p">)</span>
|
|
</span><span id="quad-69"><a href="#quad-69"><span class="linenos">69</span></a> <span class="n">val</span> <span class="o">=</span> <span class="n">integration_result</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
|
</span><span id="quad-70"><a href="#quad-70"><span class="linenos">70</span></a>
|
|
</span><span id="quad-71"><a href="#quad-71"><span class="linenos">71</span></a> <span class="n">jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
|
|
</span><span id="quad-72"><a href="#quad-72"><span class="linenos">72</span></a>
|
|
</span><span id="quad-73"><a href="#quad-73"><span class="linenos">73</span></a> <span class="n">derivint</span> <span class="o">=</span> <span class="p">[]</span>
|
|
</span><span id="quad-74"><a href="#quad-74"><span class="linenos">74</span></a> <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">Np</span><span class="p">):</span>
|
|
</span><span id="quad-75"><a href="#quad-75"><span class="linenos">75</span></a> <span class="k">if</span> <span class="n">isobs</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
|
|
</span><span id="quad-76"><a href="#quad-76"><span class="linenos">76</span></a> <span class="n">ifunc</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">jac</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">x</span><span class="p">)[</span><span class="n">i</span><span class="p">])</span>
|
|
</span><span id="quad-77"><a href="#quad-77"><span class="linenos">77</span></a> <span class="n">derivint</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">squad</span><span class="p">(</span><span class="n">ifunc</span><span class="p">,</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">bounds</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">**</span><span class="n">ikwargs</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
|
|
</span><span id="quad-78"><a href="#quad-78"><span class="linenos">78</span></a>
|
|
</span><span id="quad-79"><a href="#quad-79"><span class="linenos">79</span></a> <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="mi">2</span><span class="p">):</span>
|
|
</span><span id="quad-80"><a href="#quad-80"><span class="linenos">80</span></a> <span class="k">if</span> <span class="n">isobs_b</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
|
|
</span><span id="quad-81"><a href="#quad-81"><span class="linenos">81</span></a> <span class="n">derivint</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">bsign</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">func</span><span class="p">(</span><span class="n">pval</span><span class="p">,</span> <span class="n">bval</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
|
|
</span><span id="quad-82"><a href="#quad-82"><span class="linenos">82</span></a>
|
|
</span><span id="quad-83"><a href="#quad-83"><span class="linenos">83</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">derivint</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
|
</span><span id="quad-84"><a href="#quad-84"><span class="linenos">84</span></a> <span class="k">return</span> <span class="n">integration_result</span>
|
|
</span><span id="quad-85"><a href="#quad-85"><span class="linenos">85</span></a>
|
|
</span><span id="quad-86"><a href="#quad-86"><span class="linenos">86</span></a> <span class="n">res</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="mi">0</span> <span class="o">*</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="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">pval</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">+</span> <span class="n">val</span><span class="p">,</span> <span class="n">pobs</span> <span class="o">+</span> <span class="n">bobs</span><span class="p">,</span> <span class="n">man_grad</span><span class="o">=</span><span class="n">derivint</span><span class="p">)</span>
|
|
</span><span id="quad-87"><a href="#quad-87"><span class="linenos">87</span></a>
|
|
</span><span id="quad-88"><a href="#quad-88"><span class="linenos">88</span></a> <span class="k">return</span> <span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="o">*</span><span class="n">integration_result</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span>
|
|
</span></pre></div>
|
|
|
|
|
|
<div class="docstring"><p>Performs a (one-dimensional) numeric integration of f(p, x) from a to b.</p>
|
|
|
|
<p>The integration is performed using scipy.integrate.quad().
|
|
All parameters that can be passed to scipy.integrate.quad may also be passed to this function.
|
|
The output is the same as for scipy.integrate.quad, the first element being an Obs.</p>
|
|
|
|
<h6 id="parameters">Parameters</h6>
|
|
|
|
<ul>
|
|
<li><p><strong>func</strong> (object):
|
|
function to integrate, has to be of the form</p>
|
|
|
|
<div class="pdoc-code codehilite">
|
|
<pre><span></span><code><span class="kn">import</span><span class="w"> </span><span class="nn">autograd.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">anp</span>
|
|
|
|
<span class="k">def</span><span class="w"> </span><span class="nf">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="n">p</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">p</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">p</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">anp</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
</code></pre>
|
|
</div>
|
|
|
|
<p>where x is the integration variable.</p></li>
|
|
<li><strong>p</strong> (list of floats or Obs):
|
|
parameters of the function func.</li>
|
|
<li><strong>a</strong> (float or Obs):
|
|
Lower limit of integration (use -numpy.inf for -infinity).</li>
|
|
<li><strong>b</strong> (float or Obs):
|
|
Upper limit of integration (use -numpy.inf for -infinity).</li>
|
|
<li><strong>All parameters of scipy.integrate.quad</strong></li>
|
|
</ul>
|
|
|
|
<h6 id="returns">Returns</h6>
|
|
|
|
<ul>
|
|
<li><strong>y</strong> (Obs):
|
|
The integral of func from <code>a</code> to <code>b</code>.</li>
|
|
<li><strong>abserr</strong> (float):
|
|
An estimate of the absolute error in the result.</li>
|
|
<li><strong>infodict</strong> (dict):
|
|
A dictionary containing additional information.
|
|
Run scipy.integrate.quad_explain() for more information.</li>
|
|
<li><strong>message</strong>: A convergence message.</li>
|
|
<li><strong>explain</strong>: Appended only with 'cos' or 'sin' weighting and infinite
|
|
integration limits, it contains an explanation of the codes in
|
|
infodict['ierlst']</li>
|
|
</ul>
|
|
</div>
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|
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case "class":
|
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heading = `<span class="def">class</span> <span class="name">${doc.fullname}</span>`;
|
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if (doc.bases)
|
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heading += `<wbr>(<span class="base">${doc.bases}</span>)`;
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heading += `:`;
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|
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heading += `<span class="annotation">${doc.annotation}</span>`;
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<a href="${url}" class="attr ${doc.kind}">${heading}</a>
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block: "nearest",
|
|
inline: "nearest"
|
|
});
|
|
} else if (
|
|
e.key === "ArrowUp"
|
|
&& focused.previousElementSibling
|
|
&& focused.previousElementSibling.classList.contains("search-result")
|
|
) {
|
|
focused.classList.remove("focused");
|
|
focused.previousElementSibling.classList.add("focused");
|
|
focused.previousElementSibling.scrollIntoView({
|
|
behavior: "smooth",
|
|
block: "nearest",
|
|
inline: "nearest"
|
|
});
|
|
} else if (
|
|
e.key === "Enter"
|
|
) {
|
|
focused.querySelector("a").click();
|
|
}
|
|
}
|
|
});
|
|
</script></body>
|
|
</html> |