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<h2>API Documentation</h2>
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<a class="class" href="#Fit_result">Fit_result</a>
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<li>
|
||
<a class="function" href="#Fit_result.gamma_method">gamma_method</a>
|
||
</li>
|
||
</ul>
|
||
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#least_squares">least_squares</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#total_least_squares">total_least_squares</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#fit_lin">fit_lin</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#qqplot">qqplot</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#residual_plot">residual_plot</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#error_band">error_band</a>
|
||
</li>
|
||
<li>
|
||
<a class="function" href="#ks_test">ks_test</a>
|
||
</li>
|
||
</ul>
|
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<section class="module-info">
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<h1 class="modulename">
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<a href="./../pyerrors.html">pyerrors</a><wbr>.fits </h1>
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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="nn">gc</span>
|
||
</span><span id="L-2"><a href="#L-2"><span class="linenos"> 2</span></a><span class="kn">from</span> <span class="nn">collections.abc</span> <span class="kn">import</span> <span class="n">Sequence</span>
|
||
</span><span id="L-3"><a href="#L-3"><span class="linenos"> 3</span></a><span class="kn">import</span> <span class="nn">warnings</span>
|
||
</span><span id="L-4"><a href="#L-4"><span class="linenos"> 4</span></a><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||
</span><span id="L-5"><a href="#L-5"><span class="linenos"> 5</span></a><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">anp</span>
|
||
</span><span id="L-6"><a href="#L-6"><span class="linenos"> 6</span></a><span class="kn">import</span> <span class="nn">scipy.optimize</span>
|
||
</span><span id="L-7"><a href="#L-7"><span class="linenos"> 7</span></a><span class="kn">import</span> <span class="nn">scipy.stats</span>
|
||
</span><span id="L-8"><a href="#L-8"><span class="linenos"> 8</span></a><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||
</span><span id="L-9"><a href="#L-9"><span class="linenos"> 9</span></a><span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">gridspec</span>
|
||
</span><span id="L-10"><a href="#L-10"><span class="linenos"> 10</span></a><span class="kn">from</span> <span class="nn">scipy.odr</span> <span class="kn">import</span> <span class="n">ODR</span><span class="p">,</span> <span class="n">Model</span><span class="p">,</span> <span class="n">RealData</span>
|
||
</span><span id="L-11"><a href="#L-11"><span class="linenos"> 11</span></a><span class="kn">import</span> <span class="nn">iminuit</span>
|
||
</span><span id="L-12"><a href="#L-12"><span class="linenos"> 12</span></a><span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">jacobian</span>
|
||
</span><span id="L-13"><a href="#L-13"><span class="linenos"> 13</span></a><span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">elementwise_grad</span> <span class="k">as</span> <span class="n">egrad</span>
|
||
</span><span id="L-14"><a href="#L-14"><span class="linenos"> 14</span></a><span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="n">Obs</span><span class="p">,</span> <span class="n">derived_observable</span><span class="p">,</span> <span class="n">covariance</span><span class="p">,</span> <span class="n">cov_Obs</span>
|
||
</span><span id="L-15"><a href="#L-15"><span class="linenos"> 15</span></a>
|
||
</span><span id="L-16"><a href="#L-16"><span class="linenos"> 16</span></a>
|
||
</span><span id="L-17"><a href="#L-17"><span class="linenos"> 17</span></a><span class="k">class</span> <span class="nc">Fit_result</span><span class="p">(</span><span class="n">Sequence</span><span class="p">):</span>
|
||
</span><span id="L-18"><a href="#L-18"><span class="linenos"> 18</span></a> <span class="sd">"""Represents fit results.</span>
|
||
</span><span id="L-19"><a href="#L-19"><span class="linenos"> 19</span></a>
|
||
</span><span id="L-20"><a href="#L-20"><span class="linenos"> 20</span></a><span class="sd"> Attributes</span>
|
||
</span><span id="L-21"><a href="#L-21"><span class="linenos"> 21</span></a><span class="sd"> ----------</span>
|
||
</span><span id="L-22"><a href="#L-22"><span class="linenos"> 22</span></a><span class="sd"> fit_parameters : list</span>
|
||
</span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a><span class="sd"> results for the individual fit parameters,</span>
|
||
</span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a><span class="sd"> also accessible via indices.</span>
|
||
</span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a><span class="sd"> """</span>
|
||
</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>
|
||
</span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
|
||
</span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a>
|
||
</span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a> <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
|
||
</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
|
||
</span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a>
|
||
</span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a> <span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">)</span>
|
||
</span><span id="L-35"><a href="#L-35"><span class="linenos"> 35</span></a>
|
||
</span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a> <span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a> <span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
||
</span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
||
</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a>
|
||
</span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a> <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a> <span class="n">my_str</span> <span class="o">=</span> <span class="s1">'Goodness of fit:</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-42"><a href="#L-42"><span class="linenos"> 42</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_dof'</span><span class="p">):</span>
|
||
</span><span id="L-43"><a href="#L-43"><span class="linenos"> 43</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/d.o.f. = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-44"><a href="#L-44"><span class="linenos"> 44</span></a> <span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'residual_variance'</span><span class="p">):</span>
|
||
</span><span id="L-45"><a href="#L-45"><span class="linenos"> 45</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'residual variance = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">residual_variance</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-46"><a href="#L-46"><span class="linenos"> 46</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_expected_chisquare'</span><span class="p">):</span>
|
||
</span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/</span><span class="se">\u03C7\u00b2</span><span class="s1">exp = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'p_value'</span><span class="p">):</span>
|
||
</span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'p-value = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">p_value</span><span class="si">:</span><span class="s1">2.4f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'Fit parameters:</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a> <span class="k">for</span> <span class="n">i_par</span><span class="p">,</span> <span class="n">par</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">):</span>
|
||
</span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_par</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\t</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">' '</span> <span class="o">*</span> <span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">par</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o"><</span> <span class="mf">0.0</span><span class="p">))</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a> <span class="k">return</span> <span class="n">my_str</span>
|
||
</span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a>
|
||
</span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a> <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a> <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())))</span> <span class="o">+</span> <span class="mi">1</span>
|
||
</span><span id="L-57"><a href="#L-57"><span class="linenos"> 57</span></a> <span class="k">return</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">key</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">+</span> <span class="s1">': '</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">items</span><span class="p">())])</span>
|
||
</span><span id="L-58"><a href="#L-58"><span class="linenos"> 58</span></a>
|
||
</span><span id="L-59"><a href="#L-59"><span class="linenos"> 59</span></a>
|
||
</span><span id="L-60"><a href="#L-60"><span class="linenos"> 60</span></a><span class="k">def</span> <span class="nf">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-61"><a href="#L-61"><span class="linenos"> 61</span></a> <span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x).</span>
|
||
</span><span id="L-62"><a href="#L-62"><span class="linenos"> 62</span></a>
|
||
</span><span id="L-63"><a href="#L-63"><span class="linenos"> 63</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a><span class="sd"> ----------</span>
|
||
</span><span id="L-65"><a href="#L-65"><span class="linenos"> 65</span></a><span class="sd"> x : list</span>
|
||
</span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a><span class="sd"> list of floats.</span>
|
||
</span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a><span class="sd"> y : list</span>
|
||
</span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a><span class="sd"> list of Obs.</span>
|
||
</span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a><span class="sd"> func : object</span>
|
||
</span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a><span class="sd"> fit function, has to be of the form</span>
|
||
</span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a>
|
||
</span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a><span class="sd"> ```python</span>
|
||
</span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a><span class="sd"> import autograd.numpy as anp</span>
|
||
</span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a>
|
||
</span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a><span class="sd"> return a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||
</span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a><span class="sd"> ```</span>
|
||
</span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a>
|
||
</span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a><span class="sd"> For multiple x values func can be of the form</span>
|
||
</span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a>
|
||
</span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a><span class="sd"> ```python</span>
|
||
</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a><span class="sd"> (x1, x2) = x</span>
|
||
</span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||
</span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="sd"> ```</span>
|
||
</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a>
|
||
</span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a><span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||
</span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a><span class="sd"> will not work.</span>
|
||
</span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a><span class="sd"> priors : list, optional</span>
|
||
</span><span id="L-90"><a href="#L-90"><span class="linenos"> 90</span></a><span class="sd"> priors has to be a list with an entry for every parameter in the fit. The entries can either be</span>
|
||
</span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a><span class="sd"> Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like</span>
|
||
</span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a><span class="sd"> 0.548(23), 500(40) or 0.5(0.4)</span>
|
||
</span><span id="L-93"><a href="#L-93"><span class="linenos"> 93</span></a><span class="sd"> silent : bool, optional</span>
|
||
</span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a><span class="sd"> If true all output to the console is omitted (default False).</span>
|
||
</span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a><span class="sd"> initial_guess : list</span>
|
||
</span><span id="L-96"><a href="#L-96"><span class="linenos"> 96</span></a><span class="sd"> can provide an initial guess for the input parameters. Relevant for</span>
|
||
</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a><span class="sd"> non-linear fits with many parameters. In case of correlated fits the guess is used to perform</span>
|
||
</span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a><span class="sd"> an uncorrelated fit which then serves as guess for the correlated fit.</span>
|
||
</span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a><span class="sd"> method : str, optional</span>
|
||
</span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a><span class="sd"> can be used to choose an alternative method for the minimization of chisquare.</span>
|
||
</span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a><span class="sd"> The possible methods are the ones which can be used for scipy.optimize.minimize and</span>
|
||
</span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a><span class="sd"> migrad of iminuit. If no method is specified, Levenberg-Marquard is used.</span>
|
||
</span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a><span class="sd"> Reliable alternatives are migrad, Powell and Nelder-Mead.</span>
|
||
</span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a><span class="sd"> correlated_fit : bool</span>
|
||
</span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a><span class="sd"> If True, use the full inverse covariance matrix in the definition of the chisquare cost function.</span>
|
||
</span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a><span class="sd"> For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.</span>
|
||
</span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a><span class="sd"> In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).</span>
|
||
</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a><span class="sd"> This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).</span>
|
||
</span><span id="L-109"><a href="#L-109"><span class="linenos">109</span></a><span class="sd"> At the moment this option only works for `prior==None` and when no `method` is given.</span>
|
||
</span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a><span class="sd"> expected_chisquare : bool</span>
|
||
</span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a><span class="sd"> If True estimates the expected chisquare which is</span>
|
||
</span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a><span class="sd"> corrected by effects caused by correlated input data (default False).</span>
|
||
</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a><span class="sd"> resplot : bool</span>
|
||
</span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a><span class="sd"> If True, a plot which displays fit, data and residuals is generated (default False).</span>
|
||
</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a><span class="sd"> qqplot : bool</span>
|
||
</span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a><span class="sd"> If True, a quantile-quantile plot of the fit result is generated (default False).</span>
|
||
</span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a><span class="sd"> '''</span>
|
||
</span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a> <span class="k">if</span> <span class="n">priors</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a> <span class="k">return</span> <span class="n">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="L-120"><a href="#L-120"><span class="linenos">120</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-121"><a href="#L-121"><span class="linenos">121</span></a> <span class="k">return</span> <span class="n">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a>
|
||
</span><span id="L-123"><a href="#L-123"><span class="linenos">123</span></a>
|
||
</span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a><span class="k">def</span> <span class="nf">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a> <span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
||
</span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a>
|
||
</span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a><span class="sd"> ----------</span>
|
||
</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a><span class="sd"> x : list</span>
|
||
</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a><span class="sd"> list of Obs, or a tuple of lists of Obs</span>
|
||
</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a><span class="sd"> y : list</span>
|
||
</span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a><span class="sd"> list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</span>
|
||
</span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a><span class="sd"> func : object</span>
|
||
</span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a><span class="sd"> func has to be of the form</span>
|
||
</span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a>
|
||
</span><span id="L-136"><a href="#L-136"><span class="linenos">136</span></a><span class="sd"> ```python</span>
|
||
</span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a><span class="sd"> import autograd.numpy as anp</span>
|
||
</span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a>
|
||
</span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a><span class="sd"> return a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||
</span><span id="L-141"><a href="#L-141"><span class="linenos">141</span></a><span class="sd"> ```</span>
|
||
</span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a>
|
||
</span><span id="L-143"><a href="#L-143"><span class="linenos">143</span></a><span class="sd"> For multiple x values func can be of the form</span>
|
||
</span><span id="L-144"><a href="#L-144"><span class="linenos">144</span></a>
|
||
</span><span id="L-145"><a href="#L-145"><span class="linenos">145</span></a><span class="sd"> ```python</span>
|
||
</span><span id="L-146"><a href="#L-146"><span class="linenos">146</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a><span class="sd"> (x1, x2) = x</span>
|
||
</span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a><span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||
</span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a><span class="sd"> ```</span>
|
||
</span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a>
|
||
</span><span id="L-151"><a href="#L-151"><span class="linenos">151</span></a><span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||
</span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a><span class="sd"> will not work.</span>
|
||
</span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a><span class="sd"> silent : bool, optional</span>
|
||
</span><span id="L-154"><a href="#L-154"><span class="linenos">154</span></a><span class="sd"> If true all output to the console is omitted (default False).</span>
|
||
</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a><span class="sd"> initial_guess : list</span>
|
||
</span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a><span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
||
</span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="sd"> fits with many parameters.</span>
|
||
</span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="sd"> expected_chisquare : bool</span>
|
||
</span><span id="L-159"><a href="#L-159"><span class="linenos">159</span></a><span class="sd"> If true prints the expected chisquare which is</span>
|
||
</span><span id="L-160"><a href="#L-160"><span class="linenos">160</span></a><span class="sd"> corrected by effects caused by correlated input data.</span>
|
||
</span><span id="L-161"><a href="#L-161"><span class="linenos">161</span></a><span class="sd"> This can take a while as the full correlation matrix</span>
|
||
</span><span id="L-162"><a href="#L-162"><span class="linenos">162</span></a><span class="sd"> has to be calculated (default False).</span>
|
||
</span><span id="L-163"><a href="#L-163"><span class="linenos">163</span></a>
|
||
</span><span id="L-164"><a href="#L-164"><span class="linenos">164</span></a><span class="sd"> Notes</span>
|
||
</span><span id="L-165"><a href="#L-165"><span class="linenos">165</span></a><span class="sd"> -----</span>
|
||
</span><span id="L-166"><a href="#L-166"><span class="linenos">166</span></a><span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||
</span><span id="L-167"><a href="#L-167"><span class="linenos">167</span></a><span class="sd"> '''</span>
|
||
</span><span id="L-168"><a href="#L-168"><span class="linenos">168</span></a>
|
||
</span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a> <span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||
</span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a>
|
||
</span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
||
</span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a>
|
||
</span><span id="L-173"><a href="#L-173"><span class="linenos">173</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-174"><a href="#L-174"><span class="linenos">174</span></a>
|
||
</span><span id="L-175"><a href="#L-175"><span class="linenos">175</span></a> <span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
||
</span><span id="L-176"><a href="#L-176"><span class="linenos">176</span></a>
|
||
</span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
||
</span><span id="L-178"><a href="#L-178"><span class="linenos">178</span></a> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
||
</span><span id="L-179"><a href="#L-179"><span class="linenos">179</span></a>
|
||
</span><span id="L-180"><a href="#L-180"><span class="linenos">180</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">42</span><span class="p">):</span>
|
||
</span><span id="L-181"><a href="#L-181"><span class="linenos">181</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-182"><a href="#L-182"><span class="linenos">182</span></a> <span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="L-183"><a href="#L-183"><span class="linenos">183</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="L-184"><a href="#L-184"><span class="linenos">184</span></a> <span class="k">continue</span>
|
||
</span><span id="L-185"><a href="#L-185"><span class="linenos">185</span></a> <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
|
||
</span><span id="L-186"><a href="#L-186"><span class="linenos">186</span></a> <span class="k">continue</span>
|
||
</span><span id="L-187"><a href="#L-187"><span class="linenos">187</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-188"><a href="#L-188"><span class="linenos">188</span></a> <span class="k">break</span>
|
||
</span><span id="L-189"><a href="#L-189"><span class="linenos">189</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-190"><a href="#L-190"><span class="linenos">190</span></a> <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Fit function is not valid."</span><span class="p">)</span>
|
||
</span><span id="L-191"><a href="#L-191"><span class="linenos">191</span></a>
|
||
</span><span id="L-192"><a href="#L-192"><span class="linenos">192</span></a> <span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
||
</span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-194"><a href="#L-194"><span class="linenos">194</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameter'</span> <span class="o">+</span> <span class="s1">'s'</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_parms</span> <span class="o">></span> <span class="mi">1</span><span class="p">))</span>
|
||
</span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a>
|
||
</span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a> <span class="n">x_f</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">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a> <span class="n">dx_f</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">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a> <span class="n">y_f</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">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a> <span class="n">dy_f</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">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="L-200"><a href="#L-200"><span class="linenos">200</span></a>
|
||
</span><span id="L-201"><a href="#L-201"><span class="linenos">201</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dx_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="L-202"><a href="#L-202"><span class="linenos">202</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No x errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="L-203"><a href="#L-203"><span class="linenos">203</span></a>
|
||
</span><span id="L-204"><a href="#L-204"><span class="linenos">204</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="L-205"><a href="#L-205"><span class="linenos">205</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="L-206"><a href="#L-206"><span class="linenos">206</span></a>
|
||
</span><span id="L-207"><a href="#L-207"><span class="linenos">207</span></a> <span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||
</span><span id="L-208"><a href="#L-208"><span class="linenos">208</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
||
</span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
||
</span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
||
</span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
||
</span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a>
|
||
</span><span id="L-214"><a href="#L-214"><span class="linenos">214</span></a> <span class="n">data</span> <span class="o">=</span> <span class="n">RealData</span><span class="p">(</span><span class="n">x_f</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">sx</span><span class="o">=</span><span class="n">dx_f</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="n">dy_f</span><span class="p">)</span>
|
||
</span><span id="L-215"><a href="#L-215"><span class="linenos">215</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">Model</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
|
||
</span><span id="L-216"><a href="#L-216"><span class="linenos">216</span></a> <span class="n">odr</span> <span class="o">=</span> <span class="n">ODR</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">partol</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><span id="L-217"><a href="#L-217"><span class="linenos">217</span></a> <span class="n">odr</span><span class="o">.</span><span class="n">set_job</span><span class="p">(</span><span class="n">fit_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">deriv</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="L-218"><a href="#L-218"><span class="linenos">218</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">odr</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
|
||
</span><span id="L-219"><a href="#L-219"><span class="linenos">219</span></a>
|
||
</span><span id="L-220"><a href="#L-220"><span class="linenos">220</span></a> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">res_var</span>
|
||
</span><span id="L-221"><a href="#L-221"><span class="linenos">221</span></a>
|
||
</span><span id="L-222"><a href="#L-222"><span class="linenos">222</span></a> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'ODR'</span>
|
||
</span><span id="L-223"><a href="#L-223"><span class="linenos">223</span></a>
|
||
</span><span id="L-224"><a href="#L-224"><span class="linenos">224</span></a> <span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">stopreason</span>
|
||
</span><span id="L-225"><a href="#L-225"><span class="linenos">225</span></a>
|
||
</span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a> <span class="n">output</span><span class="o">.</span><span class="n">xplus</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span>
|
||
</span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a>
|
||
</span><span id="L-228"><a href="#L-228"><span class="linenos">228</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-229"><a href="#L-229"><span class="linenos">229</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Method: ODR'</span><span class="p">)</span>
|
||
</span><span id="L-230"><a href="#L-230"><span class="linenos">230</span></a> <span class="nb">print</span><span class="p">(</span><span class="o">*</span><span class="n">out</span><span class="o">.</span><span class="n">stopreason</span><span class="p">)</span>
|
||
</span><span id="L-231"><a href="#L-231"><span class="linenos">231</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Residual variance:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span><span class="p">)</span>
|
||
</span><span id="L-232"><a href="#L-232"><span class="linenos">232</span></a>
|
||
</span><span id="L-233"><a href="#L-233"><span class="linenos">233</span></a> <span class="k">if</span> <span class="n">out</span><span class="o">.</span><span class="n">info</span> <span class="o">></span> <span class="mi">3</span><span class="p">:</span>
|
||
</span><span id="L-234"><a href="#L-234"><span class="linenos">234</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
||
</span><span id="L-235"><a href="#L-235"><span class="linenos">235</span></a>
|
||
</span><span id="L-236"><a href="#L-236"><span class="linenos">236</span></a> <span class="n">m</span> <span class="o">=</span> <span class="n">x_f</span><span class="o">.</span><span class="n">size</span>
|
||
</span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a>
|
||
</span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a> <span class="k">def</span> <span class="nf">odr_chisquare</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-239"><a href="#L-239"><span class="linenos">239</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="L-240"><a href="#L-240"><span class="linenos">240</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-242"><a href="#L-242"><span class="linenos">242</span></a>
|
||
</span><span id="L-243"><a href="#L-243"><span class="linenos">243</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-244"><a href="#L-244"><span class="linenos">244</span></a> <span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">dy_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">dx_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
||
</span><span id="L-245"><a href="#L-245"><span class="linenos">245</span></a>
|
||
</span><span id="L-246"><a href="#L-246"><span class="linenos">246</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="L-247"><a href="#L-247"><span class="linenos">247</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
||
</span><span id="L-248"><a href="#L-248"><span class="linenos">248</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-249"><a href="#L-249"><span class="linenos">249</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="L-250"><a href="#L-250"><span class="linenos">250</span></a>
|
||
</span><span id="L-251"><a href="#L-251"><span class="linenos">251</span></a> <span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||
</span><span id="L-252"><a href="#L-252"><span class="linenos">252</span></a>
|
||
</span><span id="L-253"><a href="#L-253"><span class="linenos">253</span></a> <span class="n">old_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 class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">)</span>
|
||
</span><span id="L-254"><a href="#L-254"><span class="linenos">254</span></a> <span class="n">fused_row1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">old_jac</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">)]),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)))</span>
|
||
</span><span id="L-255"><a href="#L-255"><span class="linenos">255</span></a> <span class="n">fused_row2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">jacobian</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">))(</span><span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">number_of_x_parameters</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])))</span>
|
||
</span><span id="L-256"><a href="#L-256"><span class="linenos">256</span></a> <span class="n">new_jac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fused_row1</span><span class="p">,</span> <span class="n">fused_row2</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="L-257"><a href="#L-257"><span class="linenos">257</span></a>
|
||
</span><span id="L-258"><a href="#L-258"><span class="linenos">258</span></a> <span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">new_jac</span>
|
||
</span><span id="L-259"><a href="#L-259"><span class="linenos">259</span></a> <span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
||
</span><span id="L-260"><a href="#L-260"><span class="linenos">260</span></a> <span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">P_phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
||
</span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a> <span class="k">if</span> <span class="n">expected_chisquare</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">:</span>
|
||
</span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a> <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Negative expected_chisquare."</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||
</span><span id="L-263"><a href="#L-263"><span class="linenos">263</span></a> <span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">expected_chisquare</span><span class="p">)</span>
|
||
</span><span id="L-264"><a href="#L-264"><span class="linenos">264</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
||
</span><span id="L-265"><a href="#L-265"><span class="linenos">265</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-266"><a href="#L-266"><span class="linenos">266</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
||
</span><span id="L-267"><a href="#L-267"><span class="linenos">267</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
||
</span><span id="L-268"><a href="#L-268"><span class="linenos">268</span></a>
|
||
</span><span id="L-269"><a href="#L-269"><span class="linenos">269</span></a> <span class="n">fitp</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span>
|
||
</span><span id="L-270"><a href="#L-270"><span class="linenos">270</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-271"><a href="#L-271"><span class="linenos">271</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="L-272"><a href="#L-272"><span class="linenos">272</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="L-273"><a href="#L-273"><span class="linenos">273</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details."</span><span class="p">)</span> <span class="kn">from</span> <span class="bp">None</span>
|
||
</span><span id="L-274"><a href="#L-274"><span class="linenos">274</span></a>
|
||
</span><span id="L-275"><a href="#L-275"><span class="linenos">275</span></a> <span class="k">def</span> <span class="nf">odr_chisquare_compact_x</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="L-276"><a href="#L-276"><span class="linenos">276</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="L-277"><a href="#L-277"><span class="linenos">277</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-278"><a href="#L-278"><span class="linenos">278</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a>
|
||
</span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a> <span class="n">jac_jac_x</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_x</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">x_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a>
|
||
</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a> <span class="c1"># Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv</span>
|
||
</span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a> <span class="n">deriv_x</span> <span class="o">=</span> <span class="o">-</span><span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">hess</span><span class="p">,</span> <span class="n">jac_jac_x</span><span class="p">[:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:])</span>
|
||
</span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a> <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
|
||
</span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"Cannot invert hessian matrix."</span><span class="p">)</span>
|
||
</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a>
|
||
</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a> <span class="k">def</span> <span class="nf">odr_chisquare_compact_y</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-292"><a href="#L-292"><span class="linenos">292</span></a>
|
||
</span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a> <span class="n">jac_jac_y</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_y</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">y_f</span><span class="p">)))</span>
|
||
</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a>
|
||
</span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a> <span class="c1"># Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv</span>
|
||
</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a> <span class="n">deriv_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">hess</span><span class="p">,</span> <span class="n">jac_jac_y</span><span class="p">[:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:])</span>
|
||
</span><span id="L-298"><a href="#L-298"><span class="linenos">298</span></a> <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
|
||
</span><span id="L-299"><a href="#L-299"><span class="linenos">299</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"Cannot invert hessian matrix."</span><span class="p">)</span>
|
||
</span><span id="L-300"><a href="#L-300"><span class="linenos">300</span></a>
|
||
</span><span id="L-301"><a href="#L-301"><span class="linenos">301</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-302"><a href="#L-302"><span class="linenos">302</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">n_parms</span><span class="p">):</span>
|
||
</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">my_var</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">my_var</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">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</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">out</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv_x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">deriv_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||
</span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a>
|
||
</span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||
</span><span id="L-306"><a href="#L-306"><span class="linenos">306</span></a>
|
||
</span><span id="L-307"><a href="#L-307"><span class="linenos">307</span></a> <span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="L-308"><a href="#L-308"><span class="linenos">308</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
|
||
</span><span id="L-309"><a href="#L-309"><span class="linenos">309</span></a> <span class="n">output</span><span class="o">.</span><span class="n">p_value</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span>
|
||
</span><span id="L-310"><a href="#L-310"><span class="linenos">310</span></a>
|
||
</span><span id="L-311"><a href="#L-311"><span class="linenos">311</span></a> <span class="k">return</span> <span class="n">output</span>
|
||
</span><span id="L-312"><a href="#L-312"><span class="linenos">312</span></a>
|
||
</span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a>
|
||
</span><span id="L-314"><a href="#L-314"><span class="linenos">314</span></a><span class="k">def</span> <span class="nf">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-315"><a href="#L-315"><span class="linenos">315</span></a> <span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||
</span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a>
|
||
</span><span id="L-317"><a href="#L-317"><span class="linenos">317</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
||
</span><span id="L-318"><a href="#L-318"><span class="linenos">318</span></a>
|
||
</span><span id="L-319"><a href="#L-319"><span class="linenos">319</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-320"><a href="#L-320"><span class="linenos">320</span></a>
|
||
</span><span id="L-321"><a href="#L-321"><span class="linenos">321</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
||
</span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
||
</span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a>
|
||
</span><span id="L-324"><a href="#L-324"><span class="linenos">324</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">100</span><span class="p">):</span>
|
||
</span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a> <span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
|
||
</span><span id="L-327"><a href="#L-327"><span class="linenos">327</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="L-328"><a href="#L-328"><span class="linenos">328</span></a> <span class="k">continue</span>
|
||
</span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a> <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
|
||
</span><span id="L-330"><a href="#L-330"><span class="linenos">330</span></a> <span class="k">continue</span>
|
||
</span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a> <span class="k">break</span>
|
||
</span><span id="L-333"><a href="#L-333"><span class="linenos">333</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-334"><a href="#L-334"><span class="linenos">334</span></a> <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Fit function is not valid."</span><span class="p">)</span>
|
||
</span><span id="L-335"><a href="#L-335"><span class="linenos">335</span></a>
|
||
</span><span id="L-336"><a href="#L-336"><span class="linenos">336</span></a> <span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
||
</span><span id="L-337"><a href="#L-337"><span class="linenos">337</span></a>
|
||
</span><span id="L-338"><a href="#L-338"><span class="linenos">338</span></a> <span class="k">if</span> <span class="n">n_parms</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">priors</span><span class="p">):</span>
|
||
</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Priors does not have the correct length.'</span><span class="p">)</span>
|
||
</span><span id="L-340"><a href="#L-340"><span class="linenos">340</span></a>
|
||
</span><span id="L-341"><a href="#L-341"><span class="linenos">341</span></a> <span class="k">def</span> <span class="nf">extract_val_and_dval</span><span class="p">(</span><span class="n">string</span><span class="p">):</span>
|
||
</span><span id="L-342"><a href="#L-342"><span class="linenos">342</span></a> <span class="n">split_string</span> <span class="o">=</span> <span class="n">string</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">'('</span><span class="p">)</span>
|
||
</span><span id="L-343"><a href="#L-343"><span class="linenos">343</span></a> <span class="k">if</span> <span class="s1">'.'</span> <span class="ow">in</span> <span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span> <span class="s1">'.'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">split_string</span><span class="p">[</span><span class="mi">1</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
|
||
</span><span id="L-344"><a href="#L-344"><span class="linenos">344</span></a> <span class="n">factor</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">**</span> <span class="o">-</span><span class="nb">len</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="s1">'.'</span><span class="p">)[</span><span class="mi">2</span><span class="p">])</span>
|
||
</span><span id="L-345"><a href="#L-345"><span class="linenos">345</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-346"><a href="#L-346"><span class="linenos">346</span></a> <span class="n">factor</span> <span class="o">=</span> <span class="mi">1</span>
|
||
</span><span id="L-347"><a href="#L-347"><span class="linenos">347</span></a> <span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="nb">float</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">1</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">factor</span>
|
||
</span><span id="L-348"><a href="#L-348"><span class="linenos">348</span></a>
|
||
</span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a> <span class="n">loc_priors</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-350"><a href="#L-350"><span class="linenos">350</span></a> <span class="k">for</span> <span class="n">i_n</span><span class="p">,</span> <span class="n">i_prior</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">priors</span><span class="p">):</span>
|
||
</span><span id="L-351"><a href="#L-351"><span class="linenos">351</span></a> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_prior</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
|
||
</span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a> <span class="n">loc_priors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i_prior</span><span class="p">)</span>
|
||
</span><span id="L-353"><a href="#L-353"><span class="linenos">353</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-354"><a href="#L-354"><span class="linenos">354</span></a> <span class="n">loc_val</span><span class="p">,</span> <span class="n">loc_dval</span> <span class="o">=</span> <span class="n">extract_val_and_dval</span><span class="p">(</span><span class="n">i_prior</span><span class="p">)</span>
|
||
</span><span id="L-355"><a href="#L-355"><span class="linenos">355</span></a> <span class="n">loc_priors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">cov_Obs</span><span class="p">(</span><span class="n">loc_val</span><span class="p">,</span> <span class="n">loc_dval</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="s1">'#prior'</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_n</span><span class="p">)</span> <span class="o">+</span> <span class="sa">f</span><span class="s2">"_</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">2147483647</span><span class="p">)</span><span class="si">:</span><span class="s2">010d</span><span class="si">}</span><span class="s2">"</span><span class="p">))</span>
|
||
</span><span id="L-356"><a href="#L-356"><span class="linenos">356</span></a>
|
||
</span><span id="L-357"><a href="#L-357"><span class="linenos">357</span></a> <span class="n">output</span><span class="o">.</span><span class="n">priors</span> <span class="o">=</span> <span class="n">loc_priors</span>
|
||
</span><span id="L-358"><a href="#L-358"><span class="linenos">358</span></a>
|
||
</span><span id="L-359"><a href="#L-359"><span class="linenos">359</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-360"><a href="#L-360"><span class="linenos">360</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameter'</span> <span class="o">+</span> <span class="s1">'s'</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_parms</span> <span class="o">></span> <span class="mi">1</span><span class="p">))</span>
|
||
</span><span id="L-361"><a href="#L-361"><span class="linenos">361</span></a>
|
||
</span><span id="L-362"><a href="#L-362"><span class="linenos">362</span></a> <span class="n">y_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
||
</span><span id="L-363"><a href="#L-363"><span class="linenos">363</span></a> <span class="n">dy_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
||
</span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a>
|
||
</span><span id="L-365"><a href="#L-365"><span class="linenos">365</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a>
|
||
</span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a> <span class="n">p_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">loc_priors</span><span class="p">]</span>
|
||
</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a> <span class="n">dp_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">loc_priors</span><span class="p">]</span>
|
||
</span><span id="L-370"><a href="#L-370"><span class="linenos">370</span></a>
|
||
</span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dp_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No prior errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="L-373"><a href="#L-373"><span class="linenos">373</span></a>
|
||
</span><span id="L-374"><a href="#L-374"><span class="linenos">374</span></a> <span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||
</span><span id="L-375"><a href="#L-375"><span class="linenos">375</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
||
</span><span id="L-376"><a href="#L-376"><span class="linenos">376</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
||
</span><span id="L-377"><a href="#L-377"><span class="linenos">377</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length.'</span><span class="p">)</span>
|
||
</span><span id="L-378"><a href="#L-378"><span class="linenos">378</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-379"><a href="#L-379"><span class="linenos">379</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="n">p_f</span>
|
||
</span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a>
|
||
</span><span id="L-381"><a href="#L-381"><span class="linenos">381</span></a> <span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">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><span id="L-383"><a href="#L-383"><span class="linenos">383</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">p_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span> <span class="o">/</span> <span class="n">dp_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-384"><a href="#L-384"><span class="linenos">384</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-385"><a href="#L-385"><span class="linenos">385</span></a>
|
||
</span><span id="L-386"><a href="#L-386"><span class="linenos">386</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-387"><a href="#L-387"><span class="linenos">387</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Method: migrad'</span><span class="p">)</span>
|
||
</span><span id="L-388"><a href="#L-388"><span class="linenos">388</span></a>
|
||
</span><span id="L-389"><a href="#L-389"><span class="linenos">389</span></a> <span class="n">m</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">Minuit</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">)</span>
|
||
</span><span id="L-390"><a href="#L-390"><span class="linenos">390</span></a> <span class="n">m</span><span class="o">.</span><span class="n">errordef</span> <span class="o">=</span> <span class="mi">1</span>
|
||
</span><span id="L-391"><a href="#L-391"><span class="linenos">391</span></a> <span class="n">m</span><span class="o">.</span><span class="n">print_level</span> <span class="o">=</span> <span class="mi">0</span>
|
||
</span><span id="L-392"><a href="#L-392"><span class="linenos">392</span></a> <span class="k">if</span> <span class="s1">'tol'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||
</span><span id="L-393"><a href="#L-393"><span class="linenos">393</span></a> <span class="n">m</span><span class="o">.</span><span class="n">tol</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'tol'</span><span class="p">)</span>
|
||
</span><span id="L-394"><a href="#L-394"><span class="linenos">394</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a> <span class="n">m</span><span class="o">.</span><span class="n">tol</span> <span class="o">=</span> <span class="mf">1e-4</span>
|
||
</span><span id="L-396"><a href="#L-396"><span class="linenos">396</span></a> <span class="n">m</span><span class="o">.</span><span class="n">migrad</span><span class="p">()</span>
|
||
</span><span id="L-397"><a href="#L-397"><span class="linenos">397</span></a> <span class="n">params</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
|
||
</span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a>
|
||
</span><span id="L-399"><a href="#L-399"><span class="linenos">399</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">fval</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-400"><a href="#L-400"><span class="linenos">400</span></a>
|
||
</span><span id="L-401"><a href="#L-401"><span class="linenos">401</span></a> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'migrad'</span>
|
||
</span><span id="L-402"><a href="#L-402"><span class="linenos">402</span></a>
|
||
</span><span id="L-403"><a href="#L-403"><span class="linenos">403</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-404"><a href="#L-404"><span class="linenos">404</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/d.o.f.:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="p">)</span>
|
||
</span><span id="L-405"><a href="#L-405"><span class="linenos">405</span></a>
|
||
</span><span id="L-406"><a href="#L-406"><span class="linenos">406</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">m</span><span class="o">.</span><span class="n">fmin</span><span class="o">.</span><span class="n">is_valid</span><span class="p">:</span>
|
||
</span><span id="L-407"><a href="#L-407"><span class="linenos">407</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
||
</span><span id="L-408"><a href="#L-408"><span class="linenos">408</span></a>
|
||
</span><span id="L-409"><a href="#L-409"><span class="linenos">409</span></a> <span class="n">hess_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">))(</span><span class="n">params</span><span class="p">))</span>
|
||
</span><span id="L-410"><a href="#L-410"><span class="linenos">410</span></a>
|
||
</span><span id="L-411"><a href="#L-411"><span class="linenos">411</span></a> <span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="L-412"><a href="#L-412"><span class="linenos">412</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">):]</span> <span class="o">-</span> <span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">])</span> <span class="o">/</span> <span class="n">dp_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a>
|
||
</span><span id="L-416"><a href="#L-416"><span class="linenos">416</span></a> <span class="n">jac_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_compact</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">params</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">p_f</span><span class="p">)))</span>
|
||
</span><span id="L-417"><a href="#L-417"><span class="linenos">417</span></a>
|
||
</span><span id="L-418"><a href="#L-418"><span class="linenos">418</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">:]</span>
|
||
</span><span id="L-419"><a href="#L-419"><span class="linenos">419</span></a>
|
||
</span><span id="L-420"><a href="#L-420"><span class="linenos">420</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-421"><a href="#L-421"><span class="linenos">421</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">n_parms</span><span class="p">):</span>
|
||
</span><span id="L-422"><a href="#L-422"><span class="linenos">422</span></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="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="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">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</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">params</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">loc_priors</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||
</span><span id="L-423"><a href="#L-423"><span class="linenos">423</span></a>
|
||
</span><span id="L-424"><a href="#L-424"><span class="linenos">424</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||
</span><span id="L-425"><a href="#L-425"><span class="linenos">425</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">=</span> <span class="n">chisqfunc</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">params</span><span class="p">))</span>
|
||
</span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a>
|
||
</span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'resplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a> <span class="n">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
||
</span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a>
|
||
</span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'qqplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-431"><a href="#L-431"><span class="linenos">431</span></a> <span class="n">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
||
</span><span id="L-432"><a href="#L-432"><span class="linenos">432</span></a>
|
||
</span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a> <span class="k">return</span> <span class="n">output</span>
|
||
</span><span id="L-434"><a href="#L-434"><span class="linenos">434</span></a>
|
||
</span><span id="L-435"><a href="#L-435"><span class="linenos">435</span></a>
|
||
</span><span id="L-436"><a href="#L-436"><span class="linenos">436</span></a><span class="k">def</span> <span class="nf">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-437"><a href="#L-437"><span class="linenos">437</span></a>
|
||
</span><span id="L-438"><a href="#L-438"><span class="linenos">438</span></a> <span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||
</span><span id="L-439"><a href="#L-439"><span class="linenos">439</span></a>
|
||
</span><span id="L-440"><a href="#L-440"><span class="linenos">440</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
||
</span><span id="L-441"><a href="#L-441"><span class="linenos">441</span></a>
|
||
</span><span id="L-442"><a href="#L-442"><span class="linenos">442</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-443"><a href="#L-443"><span class="linenos">443</span></a>
|
||
</span><span id="L-444"><a href="#L-444"><span class="linenos">444</span></a> <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
||
</span><span id="L-445"><a href="#L-445"><span class="linenos">445</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'x and y input have to have the same length'</span><span class="p">)</span>
|
||
</span><span id="L-446"><a href="#L-446"><span class="linenos">446</span></a>
|
||
</span><span id="L-447"><a href="#L-447"><span class="linenos">447</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
|
||
</span><span id="L-448"><a href="#L-448"><span class="linenos">448</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unknown format for x values'</span><span class="p">)</span>
|
||
</span><span id="L-449"><a href="#L-449"><span class="linenos">449</span></a>
|
||
</span><span id="L-450"><a href="#L-450"><span class="linenos">450</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
||
</span><span id="L-451"><a href="#L-451"><span class="linenos">451</span></a> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
||
</span><span id="L-452"><a href="#L-452"><span class="linenos">452</span></a>
|
||
</span><span id="L-453"><a href="#L-453"><span class="linenos">453</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">42</span><span class="p">):</span>
|
||
</span><span id="L-454"><a href="#L-454"><span class="linenos">454</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a> <span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="L-456"><a href="#L-456"><span class="linenos">456</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="L-457"><a href="#L-457"><span class="linenos">457</span></a> <span class="k">continue</span>
|
||
</span><span id="L-458"><a href="#L-458"><span class="linenos">458</span></a> <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
|
||
</span><span id="L-459"><a href="#L-459"><span class="linenos">459</span></a> <span class="k">continue</span>
|
||
</span><span id="L-460"><a href="#L-460"><span class="linenos">460</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-461"><a href="#L-461"><span class="linenos">461</span></a> <span class="k">break</span>
|
||
</span><span id="L-462"><a href="#L-462"><span class="linenos">462</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-463"><a href="#L-463"><span class="linenos">463</span></a> <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Fit function is not valid."</span><span class="p">)</span>
|
||
</span><span id="L-464"><a href="#L-464"><span class="linenos">464</span></a>
|
||
</span><span id="L-465"><a href="#L-465"><span class="linenos">465</span></a> <span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
||
</span><span id="L-466"><a href="#L-466"><span class="linenos">466</span></a>
|
||
</span><span id="L-467"><a href="#L-467"><span class="linenos">467</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-468"><a href="#L-468"><span class="linenos">468</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameter'</span> <span class="o">+</span> <span class="s1">'s'</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_parms</span> <span class="o">></span> <span class="mi">1</span><span class="p">))</span>
|
||
</span><span id="L-469"><a href="#L-469"><span class="linenos">469</span></a>
|
||
</span><span id="L-470"><a href="#L-470"><span class="linenos">470</span></a> <span class="n">y_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
||
</span><span id="L-471"><a href="#L-471"><span class="linenos">471</span></a> <span class="n">dy_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
||
</span><span id="L-472"><a href="#L-472"><span class="linenos">472</span></a>
|
||
</span><span id="L-473"><a href="#L-473"><span class="linenos">473</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="L-474"><a href="#L-474"><span class="linenos">474</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="L-475"><a href="#L-475"><span class="linenos">475</span></a>
|
||
</span><span id="L-476"><a href="#L-476"><span class="linenos">476</span></a> <span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||
</span><span id="L-477"><a href="#L-477"><span class="linenos">477</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
||
</span><span id="L-478"><a href="#L-478"><span class="linenos">478</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
||
</span><span id="L-479"><a href="#L-479"><span class="linenos">479</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
||
</span><span id="L-480"><a href="#L-480"><span class="linenos">480</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-481"><a href="#L-481"><span class="linenos">481</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
||
</span><span id="L-482"><a href="#L-482"><span class="linenos">482</span></a>
|
||
</span><span id="L-483"><a href="#L-483"><span class="linenos">483</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-484"><a href="#L-484"><span class="linenos">484</span></a> <span class="n">corr</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="L-485"><a href="#L-485"><span class="linenos">485</span></a> <span class="n">covdiag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">))</span>
|
||
</span><span id="L-486"><a href="#L-486"><span class="linenos">486</span></a> <span class="n">condn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
||
</span><span id="L-487"><a href="#L-487"><span class="linenos">487</span></a> <span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mf">0.1</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="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">:</span>
|
||
</span><span id="L-488"><a href="#L-488"><span class="linenos">488</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Cannot invert correlation matrix as its condition number exceeds machine precision (</span><span class="si">{</span><span class="n">condn</span><span class="si">:</span><span class="s2">1.2e</span><span class="si">}</span><span class="s2">)"</span><span class="p">)</span>
|
||
</span><span id="L-489"><a href="#L-489"><span class="linenos">489</span></a> <span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mf">1e13</span><span class="p">:</span>
|
||
</span><span id="L-490"><a href="#L-490"><span class="linenos">490</span></a> <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Correlation matrix may be ill-conditioned, condition number: {</span><span class="si">%1.2e</span><span class="s2">}"</span> <span class="o">%</span> <span class="p">(</span><span class="n">condn</span><span class="p">),</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||
</span><span id="L-491"><a href="#L-491"><span class="linenos">491</span></a> <span class="n">chol</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
||
</span><span id="L-492"><a href="#L-492"><span class="linenos">492</span></a> <span class="n">chol_inv</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve_triangular</span><span class="p">(</span><span class="n">chol</span><span class="p">,</span> <span class="n">covdiag</span><span class="p">,</span> <span class="n">lower</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</span><span id="L-493"><a href="#L-493"><span class="linenos">493</span></a>
|
||
</span><span id="L-494"><a href="#L-494"><span class="linenos">494</span></a> <span class="k">def</span> <span class="nf">chisqfunc_corr</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-495"><a href="#L-495"><span class="linenos">495</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">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><span id="L-496"><a href="#L-496"><span class="linenos">496</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="p">(</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-497"><a href="#L-497"><span class="linenos">497</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-498"><a href="#L-498"><span class="linenos">498</span></a>
|
||
</span><span id="L-499"><a href="#L-499"><span class="linenos">499</span></a> <span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-500"><a href="#L-500"><span class="linenos">500</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">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><span id="L-501"><a href="#L-501"><span class="linenos">501</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-502"><a href="#L-502"><span class="linenos">502</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-503"><a href="#L-503"><span class="linenos">503</span></a>
|
||
</span><span id="L-504"><a href="#L-504"><span class="linenos">504</span></a> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">,</span> <span class="s1">'Levenberg-Marquardt'</span><span class="p">)</span>
|
||
</span><span id="L-505"><a href="#L-505"><span class="linenos">505</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-506"><a href="#L-506"><span class="linenos">506</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Method:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">method</span><span class="p">)</span>
|
||
</span><span id="L-507"><a href="#L-507"><span class="linenos">507</span></a>
|
||
</span><span id="L-508"><a href="#L-508"><span class="linenos">508</span></a> <span class="k">if</span> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">!=</span> <span class="s1">'Levenberg-Marquardt'</span><span class="p">:</span>
|
||
</span><span id="L-509"><a href="#L-509"><span class="linenos">509</span></a> <span class="k">if</span> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">==</span> <span class="s1">'migrad'</span><span class="p">:</span>
|
||
</span><span id="L-510"><a href="#L-510"><span class="linenos">510</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span> <span class="c1"># Stopping criterion 0.002 * tol * errordef</span>
|
||
</span><span id="L-511"><a href="#L-511"><span class="linenos">511</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-512"><a href="#L-512"><span class="linenos">512</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc_corr</span><span class="p">,</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-4</span><span class="p">)</span> <span class="c1"># Stopping criterion 0.002 * tol * errordef</span>
|
||
</span><span id="L-513"><a href="#L-513"><span class="linenos">513</span></a> <span class="n">output</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">nfev</span>
|
||
</span><span id="L-514"><a href="#L-514"><span class="linenos">514</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-515"><a href="#L-515"><span class="linenos">515</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">),</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">)</span>
|
||
</span><span id="L-516"><a href="#L-516"><span class="linenos">516</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-517"><a href="#L-517"><span class="linenos">517</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc_corr</span><span class="p">,</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">),</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">)</span>
|
||
</span><span id="L-518"><a href="#L-518"><span class="linenos">518</span></a> <span class="n">output</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">nit</span>
|
||
</span><span id="L-519"><a href="#L-519"><span class="linenos">519</span></a>
|
||
</span><span id="L-520"><a href="#L-520"><span class="linenos">520</span></a> <span class="n">chisquare</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span>
|
||
</span><span id="L-521"><a href="#L-521"><span class="linenos">521</span></a>
|
||
</span><span id="L-522"><a href="#L-522"><span class="linenos">522</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-523"><a href="#L-523"><span class="linenos">523</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-524"><a href="#L-524"><span class="linenos">524</span></a> <span class="k">def</span> <span class="nf">chisqfunc_residuals_corr</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-525"><a href="#L-525"><span class="linenos">525</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">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><span id="L-526"><a href="#L-526"><span class="linenos">526</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="p">(</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span>
|
||
</span><span id="L-527"><a href="#L-527"><span class="linenos">527</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-528"><a href="#L-528"><span class="linenos">528</span></a>
|
||
</span><span id="L-529"><a href="#L-529"><span class="linenos">529</span></a> <span class="k">def</span> <span class="nf">chisqfunc_residuals</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-530"><a href="#L-530"><span class="linenos">530</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">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><span id="L-531"><a href="#L-531"><span class="linenos">531</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="p">((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span>
|
||
</span><span id="L-532"><a href="#L-532"><span class="linenos">532</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-533"><a href="#L-533"><span class="linenos">533</span></a>
|
||
</span><span id="L-534"><a href="#L-534"><span class="linenos">534</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">least_squares</span><span class="p">(</span><span class="n">chisqfunc_residuals</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'lm'</span><span class="p">,</span> <span class="n">ftol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">gtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">xtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">)</span>
|
||
</span><span id="L-535"><a href="#L-535"><span class="linenos">535</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-536"><a href="#L-536"><span class="linenos">536</span></a> <span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">least_squares</span><span class="p">(</span><span class="n">chisqfunc_residuals_corr</span><span class="p">,</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'lm'</span><span class="p">,</span> <span class="n">ftol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">gtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">xtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">)</span>
|
||
</span><span id="L-537"><a href="#L-537"><span class="linenos">537</span></a>
|
||
</span><span id="L-538"><a href="#L-538"><span class="linenos">538</span></a> <span class="n">chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-539"><a href="#L-539"><span class="linenos">539</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-540"><a href="#L-540"><span class="linenos">540</span></a> <span class="k">assert</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">chisquare</span><span class="p">,</span> <span class="n">chisqfunc_corr</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">),</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-14</span><span class="p">)</span>
|
||
</span><span id="L-541"><a href="#L-541"><span class="linenos">541</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-542"><a href="#L-542"><span class="linenos">542</span></a> <span class="k">assert</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">chisquare</span><span class="p">,</span> <span class="n">chisqfunc</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">),</span> <span class="n">atol</span><span class="o">=</span><span class="mf">1e-14</span><span class="p">)</span>
|
||
</span><span id="L-543"><a href="#L-543"><span class="linenos">543</span></a>
|
||
</span><span id="L-544"><a href="#L-544"><span class="linenos">544</span></a> <span class="n">output</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">nfev</span>
|
||
</span><span id="L-545"><a href="#L-545"><span class="linenos">545</span></a>
|
||
</span><span id="L-546"><a href="#L-546"><span class="linenos">546</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">success</span><span class="p">:</span>
|
||
</span><span id="L-547"><a href="#L-547"><span class="linenos">547</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
||
</span><span id="L-548"><a href="#L-548"><span class="linenos">548</span></a>
|
||
</span><span id="L-549"><a href="#L-549"><span class="linenos">549</span></a> <span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
||
</span><span id="L-550"><a href="#L-550"><span class="linenos">550</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="n">chisquare</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span><span class="p">)</span>
|
||
</span><span id="L-551"><a href="#L-551"><span class="linenos">551</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-552"><a href="#L-552"><span class="linenos">552</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">)</span>
|
||
</span><span id="L-553"><a href="#L-553"><span class="linenos">553</span></a>
|
||
</span><span id="L-554"><a href="#L-554"><span class="linenos">554</span></a> <span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">message</span>
|
||
</span><span id="L-555"><a href="#L-555"><span class="linenos">555</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-556"><a href="#L-556"><span class="linenos">556</span></a> <span class="nb">print</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">message</span><span class="p">)</span>
|
||
</span><span id="L-557"><a href="#L-557"><span class="linenos">557</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/d.o.f.:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="p">)</span>
|
||
</span><span id="L-558"><a href="#L-558"><span class="linenos">558</span></a>
|
||
</span><span id="L-559"><a href="#L-559"><span class="linenos">559</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-560"><a href="#L-560"><span class="linenos">560</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-561"><a href="#L-561"><span class="linenos">561</span></a> <span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">))</span>
|
||
</span><span id="L-562"><a href="#L-562"><span class="linenos">562</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||
</span><span id="L-563"><a href="#L-563"><span class="linenos">563</span></a> <span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-564"><a href="#L-564"><span class="linenos">564</span></a> <span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
||
</span><span id="L-565"><a href="#L-565"><span class="linenos">565</span></a> <span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
||
</span><span id="L-566"><a href="#L-566"><span class="linenos">566</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">chisquare</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
||
</span><span id="L-567"><a href="#L-567"><span class="linenos">567</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="L-568"><a href="#L-568"><span class="linenos">568</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
||
</span><span id="L-569"><a href="#L-569"><span class="linenos">569</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
||
</span><span id="L-570"><a href="#L-570"><span class="linenos">570</span></a>
|
||
</span><span id="L-571"><a href="#L-571"><span class="linenos">571</span></a> <span class="n">fitp</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span>
|
||
</span><span id="L-572"><a href="#L-572"><span class="linenos">572</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-573"><a href="#L-573"><span class="linenos">573</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-574"><a href="#L-574"><span class="linenos">574</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_corr</span><span class="p">))(</span><span class="n">fitp</span><span class="p">)</span>
|
||
</span><span id="L-575"><a href="#L-575"><span class="linenos">575</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-576"><a href="#L-576"><span class="linenos">576</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">))(</span><span class="n">fitp</span><span class="p">)</span>
|
||
</span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details."</span><span class="p">)</span> <span class="kn">from</span> <span class="bp">None</span>
|
||
</span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a>
|
||
</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a> <span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="p">(</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-585"><a href="#L-585"><span class="linenos">585</span></a>
|
||
</span><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a> <span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="L-590"><a href="#L-590"><span class="linenos">590</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a>
|
||
</span><span id="L-592"><a href="#L-592"><span class="linenos">592</span></a> <span class="n">jac_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_compact</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)))</span>
|
||
</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a>
|
||
</span><span id="L-594"><a href="#L-594"><span class="linenos">594</span></a> <span class="c1"># Compute hess^{-1} @ jac_jac[:n_parms, n_parms:] using LAPACK dgesv</span>
|
||
</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="L-596"><a href="#L-596"><span class="linenos">596</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="o">-</span><span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">hess</span><span class="p">,</span> <span class="n">jac_jac</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">:])</span>
|
||
</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a> <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
|
||
</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"Cannot invert hessian matrix."</span><span class="p">)</span>
|
||
</span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>
|
||
</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-601"><a href="#L-601"><span class="linenos">601</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">n_parms</span><span class="p">):</span>
|
||
</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="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="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">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||
</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a>
|
||
</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||
</span><span id="L-605"><a href="#L-605"><span class="linenos">605</span></a>
|
||
</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">=</span> <span class="n">chisquare</span>
|
||
</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
|
||
</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a> <span class="n">output</span><span class="o">.</span><span class="n">p_value</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">chisquare</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span>
|
||
</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a>
|
||
</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'resplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a> <span class="n">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
||
</span><span id="L-612"><a href="#L-612"><span class="linenos">612</span></a>
|
||
</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'qqplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="L-614"><a href="#L-614"><span class="linenos">614</span></a> <span class="n">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
||
</span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>
|
||
</span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a> <span class="k">return</span> <span class="n">output</span>
|
||
</span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a>
|
||
</span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a>
|
||
</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a><span class="k">def</span> <span class="nf">fit_lin</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a> <span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||
</span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a>
|
||
</span><span id="L-622"><a href="#L-622"><span class="linenos">622</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="L-623"><a href="#L-623"><span class="linenos">623</span></a><span class="sd"> ----------</span>
|
||
</span><span id="L-624"><a href="#L-624"><span class="linenos">624</span></a><span class="sd"> x : list</span>
|
||
</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a><span class="sd"> Can either be a list of floats in which case no xerror is assumed, or</span>
|
||
</span><span id="L-626"><a href="#L-626"><span class="linenos">626</span></a><span class="sd"> a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</span>
|
||
</span><span id="L-627"><a href="#L-627"><span class="linenos">627</span></a><span class="sd"> y : list</span>
|
||
</span><span id="L-628"><a href="#L-628"><span class="linenos">628</span></a><span class="sd"> List of Obs, the dvalues of the Obs are used as yerror for the fit.</span>
|
||
</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a><span class="sd"> """</span>
|
||
</span><span id="L-630"><a href="#L-630"><span class="linenos">630</span></a>
|
||
</span><span id="L-631"><a href="#L-631"><span class="linenos">631</span></a> <span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
</span><span id="L-632"><a href="#L-632"><span class="linenos">632</span></a> <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span>
|
||
</span><span id="L-633"><a href="#L-633"><span class="linenos">633</span></a> <span class="k">return</span> <span class="n">y</span>
|
||
</span><span id="L-634"><a href="#L-634"><span class="linenos">634</span></a>
|
||
</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a> <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">x</span><span class="p">):</span>
|
||
</span><span id="L-636"><a href="#L-636"><span class="linenos">636</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="L-637"><a href="#L-637"><span class="linenos">637</span></a> <span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
||
</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a> <span class="k">elif</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">float</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">x</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||
</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a> <span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
||
</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unsupported types for x'</span><span class="p">)</span>
|
||
</span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a>
|
||
</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a>
|
||
</span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a><span class="k">def</span> <span class="nf">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">o_y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
|
||
</span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a> <span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||
</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||
</span><span id="L-648"><a href="#L-648"><span class="linenos">648</span></a><span class="sd"> """</span>
|
||
</span><span id="L-649"><a href="#L-649"><span class="linenos">649</span></a>
|
||
</span><span id="L-650"><a href="#L-650"><span class="linenos">650</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-651"><a href="#L-651"><span class="linenos">651</span></a> <span class="k">for</span> <span class="n">i_x</span><span class="p">,</span> <span class="n">i_y</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">o_y</span><span class="p">):</span>
|
||
</span><span id="L-652"><a href="#L-652"><span class="linenos">652</span></a> <span class="n">residuals</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">i_y</span> <span class="o">-</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">i_x</span><span class="p">))</span> <span class="o">/</span> <span class="n">i_y</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)</span>
|
||
</span><span id="L-653"><a href="#L-653"><span class="linenos">653</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">residuals</span><span class="p">)</span>
|
||
</span><span id="L-654"><a href="#L-654"><span class="linenos">654</span></a> <span class="n">my_y</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">residuals</span><span class="p">]</span>
|
||
</span><span id="L-655"><a href="#L-655"><span class="linenos">655</span></a> <span class="n">probplot</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">my_y</span><span class="p">)</span>
|
||
</span><span id="L-656"><a href="#L-656"><span class="linenos">656</span></a> <span class="n">my_x</span> <span class="o">=</span> <span class="n">probplot</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||
</span><span id="L-657"><a href="#L-657"><span class="linenos">657</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span> <span class="o">/</span> <span class="mf">1.618</span><span class="p">))</span>
|
||
</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">my_x</span><span class="p">,</span> <span class="n">my_y</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">'o'</span><span class="p">)</span>
|
||
</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a> <span class="n">fit_start</span> <span class="o">=</span> <span class="n">my_x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
</span><span id="L-660"><a href="#L-660"><span class="linenos">660</span></a> <span class="n">fit_stop</span> <span class="o">=</span> <span class="n">my_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||
</span><span id="L-661"><a href="#L-661"><span class="linenos">661</span></a> <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">fit_start</span><span class="p">,</span> <span class="n">fit_stop</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
|
||
</span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">samples</span><span class="p">,</span> <span class="n">samples</span><span class="p">,</span> <span class="s1">'k--'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Standard normal distribution'</span><span class="p">)</span>
|
||
</span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">samples</span><span class="p">,</span> <span class="n">probplot</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="o">*</span> <span class="n">samples</span> <span class="o">+</span> <span class="n">probplot</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="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Least squares fit, r='</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">around</span><span class="p">(</span><span class="n">probplot</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">],</span> <span class="mi">3</span><span class="p">)),</span> <span class="n">marker</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'-'</span><span class="p">)</span>
|
||
</span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>
|
||
</span><span id="L-665"><a href="#L-665"><span class="linenos">665</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'Theoretical quantiles'</span><span class="p">)</span>
|
||
</span><span id="L-666"><a href="#L-666"><span class="linenos">666</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Ordered Values'</span><span class="p">)</span>
|
||
</span><span id="L-667"><a href="#L-667"><span class="linenos">667</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
</span><span id="L-668"><a href="#L-668"><span class="linenos">668</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span><span id="L-669"><a href="#L-669"><span class="linenos">669</span></a>
|
||
</span><span id="L-670"><a href="#L-670"><span class="linenos">670</span></a>
|
||
</span><span id="L-671"><a href="#L-671"><span class="linenos">671</span></a><span class="k">def</span> <span class="nf">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">fit_res</span><span class="p">):</span>
|
||
</span><span id="L-672"><a href="#L-672"><span class="linenos">672</span></a> <span class="sd">""" Generates a plot which compares the fit to the data and displays the corresponding residuals"""</span>
|
||
</span><span id="L-673"><a href="#L-673"><span class="linenos">673</span></a> <span class="n">sorted_x</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="L-674"><a href="#L-674"><span class="linenos">674</span></a> <span class="n">xstart</span> <span class="o">=</span> <span class="n">sorted_x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">sorted_x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">sorted_x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="L-675"><a href="#L-675"><span class="linenos">675</span></a> <span class="n">xstop</span> <span class="o">=</span> <span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
|
||
</span><span id="L-676"><a href="#L-676"><span class="linenos">676</span></a> <span class="n">x_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span> <span class="o">+</span> <span class="mf">0.01</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
|
||
</span><span id="L-677"><a href="#L-677"><span class="linenos">677</span></a>
|
||
</span><span id="L-678"><a href="#L-678"><span class="linenos">678</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span> <span class="o">/</span> <span class="mf">1.618</span><span class="p">))</span>
|
||
</span><span id="L-679"><a href="#L-679"><span class="linenos">679</span></a> <span class="n">gs</span> <span class="o">=</span> <span class="n">gridspec</span><span class="o">.</span><span class="n">GridSpec</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">height_ratios</span><span class="o">=</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">wspace</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
|
||
</span><span id="L-680"><a href="#L-680"><span class="linenos">680</span></a> <span class="n">ax0</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="n">gs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="L-681"><a href="#L-681"><span class="linenos">681</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">],</span> <span class="n">yerr</span><span class="o">=</span><span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">],</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'none'</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">'o'</span><span class="p">,</span> <span class="n">capsize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Data'</span><span class="p">)</span>
|
||
</span><span id="L-682"><a href="#L-682"><span class="linenos">682</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_samples</span><span class="p">,</span> <span class="n">func</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">fit_res</span><span class="p">],</span> <span class="n">x_samples</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Fit'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
</span><span id="L-683"><a href="#L-683"><span class="linenos">683</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
||
</span><span id="L-684"><a href="#L-684"><span class="linenos">684</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span><span class="p">])</span>
|
||
</span><span id="L-685"><a href="#L-685"><span class="linenos">685</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
||
</span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
</span><span id="L-687"><a href="#L-687"><span class="linenos">687</span></a>
|
||
</span><span id="L-688"><a href="#L-688"><span class="linenos">688</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span> <span class="o">-</span> <span class="n">func</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">fit_res</span><span class="p">],</span> <span class="n">x</span><span class="p">))</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="L-689"><a href="#L-689"><span class="linenos">689</span></a> <span class="n">ax1</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="n">gs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
</span><span id="L-690"><a href="#L-690"><span class="linenos">690</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">residuals</span><span class="p">,</span> <span class="s1">'ko'</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'none'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
|
||
</span><span id="L-691"><a href="#L-691"><span class="linenos">691</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">direction</span><span class="o">=</span><span class="s1">'out'</span><span class="p">)</span>
|
||
</span><span id="L-692"><a href="#L-692"><span class="linenos">692</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">labelbottom</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</span><span id="L-693"><a href="#L-693"><span class="linenos">693</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'--'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span>
|
||
</span><span id="L-694"><a href="#L-694"><span class="linenos">694</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">x_samples</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
|
||
</span><span id="L-695"><a href="#L-695"><span class="linenos">695</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span><span class="p">])</span>
|
||
</span><span id="L-696"><a href="#L-696"><span class="linenos">696</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'Residuals'</span><span class="p">)</span>
|
||
</span><span id="L-697"><a href="#L-697"><span class="linenos">697</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
|
||
</span><span id="L-698"><a href="#L-698"><span class="linenos">698</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span><span id="L-699"><a href="#L-699"><span class="linenos">699</span></a>
|
||
</span><span id="L-700"><a href="#L-700"><span class="linenos">700</span></a>
|
||
</span><span id="L-701"><a href="#L-701"><span class="linenos">701</span></a><span class="k">def</span> <span class="nf">error_band</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
|
||
</span><span id="L-702"><a href="#L-702"><span class="linenos">702</span></a> <span class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
||
</span><span id="L-703"><a href="#L-703"><span class="linenos">703</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||
</span><span id="L-704"><a href="#L-704"><span class="linenos">704</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">cov</span> <span class="o">-</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">></span> <span class="mi">1000</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><span id="L-705"><a href="#L-705"><span class="linenos">705</span></a> <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Covariance matrix is not symmetric within floating point precision"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||
</span><span id="L-706"><a href="#L-706"><span class="linenos">706</span></a>
|
||
</span><span id="L-707"><a href="#L-707"><span class="linenos">707</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-708"><a href="#L-708"><span class="linenos">708</span></a> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
|
||
</span><span id="L-709"><a href="#L-709"><span class="linenos">709</span></a> <span class="n">deriv</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">egrad</span><span class="p">(</span><span class="n">func</span><span class="p">)([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">beta</span><span class="p">],</span> <span class="n">item</span><span class="p">)))</span>
|
||
</span><span id="L-710"><a href="#L-710"><span class="linenos">710</span></a>
|
||
</span><span id="L-711"><a href="#L-711"><span class="linenos">711</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-712"><a href="#L-712"><span class="linenos">712</span></a> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
|
||
</span><span id="L-713"><a href="#L-713"><span class="linenos">713</span></a> <span class="n">err</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
|
||
</span><span id="L-714"><a href="#L-714"><span class="linenos">714</span></a> <span class="n">err</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">err</span><span class="p">)</span>
|
||
</span><span id="L-715"><a href="#L-715"><span class="linenos">715</span></a>
|
||
</span><span id="L-716"><a href="#L-716"><span class="linenos">716</span></a> <span class="k">return</span> <span class="n">err</span>
|
||
</span><span id="L-717"><a href="#L-717"><span class="linenos">717</span></a>
|
||
</span><span id="L-718"><a href="#L-718"><span class="linenos">718</span></a>
|
||
</span><span id="L-719"><a href="#L-719"><span class="linenos">719</span></a><span class="k">def</span> <span class="nf">ks_test</span><span class="p">(</span><span class="n">objects</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||
</span><span id="L-720"><a href="#L-720"><span class="linenos">720</span></a> <span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||
</span><span id="L-721"><a href="#L-721"><span class="linenos">721</span></a>
|
||
</span><span id="L-722"><a href="#L-722"><span class="linenos">722</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="L-723"><a href="#L-723"><span class="linenos">723</span></a><span class="sd"> ----------</span>
|
||
</span><span id="L-724"><a href="#L-724"><span class="linenos">724</span></a><span class="sd"> objects : list</span>
|
||
</span><span id="L-725"><a href="#L-725"><span class="linenos">725</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||
</span><span id="L-726"><a href="#L-726"><span class="linenos">726</span></a><span class="sd"> """</span>
|
||
</span><span id="L-727"><a href="#L-727"><span class="linenos">727</span></a>
|
||
</span><span id="L-728"><a href="#L-728"><span class="linenos">728</span></a> <span class="k">if</span> <span class="n">objects</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="L-729"><a href="#L-729"><span class="linenos">729</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="L-730"><a href="#L-730"><span class="linenos">730</span></a> <span class="k">for</span> <span class="n">obj</span> <span class="ow">in</span> <span class="n">gc</span><span class="o">.</span><span class="n">get_objects</span><span class="p">():</span>
|
||
</span><span id="L-731"><a href="#L-731"><span class="linenos">731</span></a> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">Fit_result</span><span class="p">):</span>
|
||
</span><span id="L-732"><a href="#L-732"><span class="linenos">732</span></a> <span class="n">obs_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
|
||
</span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="L-734"><a href="#L-734"><span class="linenos">734</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||
</span><span id="L-735"><a href="#L-735"><span class="linenos">735</span></a>
|
||
</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a> <span class="n">p_values</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">p_value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">obs_list</span><span class="p">]</span>
|
||
</span><span id="L-737"><a href="#L-737"><span class="linenos">737</span></a>
|
||
</span><span id="L-738"><a href="#L-738"><span class="linenos">738</span></a> <span class="n">bins</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">p_values</span><span class="p">)</span>
|
||
</span><span id="L-739"><a href="#L-739"><span class="linenos">739</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.001</span><span class="p">,</span> <span class="mf">0.001</span><span class="p">)</span>
|
||
</span><span id="L-740"><a href="#L-740"><span class="linenos">740</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="L-741"><a href="#L-741"><span class="linenos">741</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="L-742"><a href="#L-742"><span class="linenos">742</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="L-743"><a href="#L-743"><span class="linenos">743</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'p-value'</span><span class="p">)</span>
|
||
</span><span id="L-744"><a href="#L-744"><span class="linenos">744</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Cumulative probability'</span><span class="p">)</span>
|
||
</span><span id="L-745"><a href="#L-745"><span class="linenos">745</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">bins</span><span class="p">)</span> <span class="o">+</span> <span class="s1">' p-values'</span><span class="p">)</span>
|
||
</span><span id="L-746"><a href="#L-746"><span class="linenos">746</span></a>
|
||
</span><span id="L-747"><a href="#L-747"><span class="linenos">747</span></a> <span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">bins</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">(</span><span class="n">bins</span><span class="p">)</span>
|
||
</span><span id="L-748"><a href="#L-748"><span class="linenos">748</span></a> <span class="n">Xs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">p_values</span><span class="p">)</span>
|
||
</span><span id="L-749"><a href="#L-749"><span class="linenos">749</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">Xs</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||
</span><span id="L-750"><a href="#L-750"><span class="linenos">750</span></a> <span class="n">diffs</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">Xs</span>
|
||
</span><span id="L-751"><a href="#L-751"><span class="linenos">751</span></a> <span class="n">loc_max_diff</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">diffs</span><span class="p">))</span>
|
||
</span><span id="L-752"><a href="#L-752"><span class="linenos">752</span></a> <span class="n">loc</span> <span class="o">=</span> <span class="n">Xs</span><span class="p">[</span><span class="n">loc_max_diff</span><span class="p">]</span>
|
||
</span><span id="L-753"><a href="#L-753"><span class="linenos">753</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">''</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">loc</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">loc</span> <span class="o">+</span> <span class="n">diffs</span><span class="p">[</span><span class="n">loc_max_diff</span><span class="p">]),</span> <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">arrowstyle</span><span class="o">=</span><span class="s1">'<->'</span><span class="p">,</span> <span class="n">shrinkA</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">shrinkB</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span>
|
||
</span><span id="L-754"><a href="#L-754"><span class="linenos">754</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a>
|
||
</span><span id="L-756"><a href="#L-756"><span class="linenos">756</span></a> <span class="nb">print</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">kstest</span><span class="p">(</span><span class="n">p_values</span><span class="p">,</span> <span class="s1">'uniform'</span><span class="p">))</span>
|
||
</span></pre></div>
|
||
|
||
|
||
</section>
|
||
<section id="Fit_result">
|
||
<input id="Fit_result-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr class">
|
||
|
||
<span class="def">class</span>
|
||
<span class="name">Fit_result</span><wbr>(<span class="base">collections.abc.Sequence</span>):
|
||
|
||
<label class="view-source-button" for="Fit_result-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#Fit_result"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="Fit_result-18"><a href="#Fit_result-18"><span class="linenos">18</span></a><span class="k">class</span> <span class="nc">Fit_result</span><span class="p">(</span><span class="n">Sequence</span><span class="p">):</span>
|
||
</span><span id="Fit_result-19"><a href="#Fit_result-19"><span class="linenos">19</span></a> <span class="sd">"""Represents fit results.</span>
|
||
</span><span id="Fit_result-20"><a href="#Fit_result-20"><span class="linenos">20</span></a>
|
||
</span><span id="Fit_result-21"><a href="#Fit_result-21"><span class="linenos">21</span></a><span class="sd"> Attributes</span>
|
||
</span><span id="Fit_result-22"><a href="#Fit_result-22"><span class="linenos">22</span></a><span class="sd"> ----------</span>
|
||
</span><span id="Fit_result-23"><a href="#Fit_result-23"><span class="linenos">23</span></a><span class="sd"> fit_parameters : list</span>
|
||
</span><span id="Fit_result-24"><a href="#Fit_result-24"><span class="linenos">24</span></a><span class="sd"> results for the individual fit parameters,</span>
|
||
</span><span id="Fit_result-25"><a href="#Fit_result-25"><span class="linenos">25</span></a><span class="sd"> also accessible via indices.</span>
|
||
</span><span id="Fit_result-26"><a href="#Fit_result-26"><span class="linenos">26</span></a><span class="sd"> """</span>
|
||
</span><span id="Fit_result-27"><a href="#Fit_result-27"><span class="linenos">27</span></a>
|
||
</span><span id="Fit_result-28"><a href="#Fit_result-28"><span class="linenos">28</span></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="Fit_result-29"><a href="#Fit_result-29"><span class="linenos">29</span></a> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
|
||
</span><span id="Fit_result-30"><a href="#Fit_result-30"><span class="linenos">30</span></a>
|
||
</span><span id="Fit_result-31"><a href="#Fit_result-31"><span class="linenos">31</span></a> <span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
|
||
</span><span id="Fit_result-32"><a href="#Fit_result-32"><span class="linenos">32</span></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
|
||
</span><span id="Fit_result-33"><a href="#Fit_result-33"><span class="linenos">33</span></a>
|
||
</span><span id="Fit_result-34"><a href="#Fit_result-34"><span class="linenos">34</span></a> <span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="Fit_result-35"><a href="#Fit_result-35"><span class="linenos">35</span></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">)</span>
|
||
</span><span id="Fit_result-36"><a href="#Fit_result-36"><span class="linenos">36</span></a>
|
||
</span><span id="Fit_result-37"><a href="#Fit_result-37"><span class="linenos">37</span></a> <span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="Fit_result-38"><a href="#Fit_result-38"><span class="linenos">38</span></a> <span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
||
</span><span id="Fit_result-39"><a href="#Fit_result-39"><span class="linenos">39</span></a> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
||
</span><span id="Fit_result-40"><a href="#Fit_result-40"><span class="linenos">40</span></a>
|
||
</span><span id="Fit_result-41"><a href="#Fit_result-41"><span class="linenos">41</span></a> <span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="Fit_result-42"><a href="#Fit_result-42"><span class="linenos">42</span></a> <span class="n">my_str</span> <span class="o">=</span> <span class="s1">'Goodness of fit:</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-43"><a href="#Fit_result-43"><span class="linenos">43</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_dof'</span><span class="p">):</span>
|
||
</span><span id="Fit_result-44"><a href="#Fit_result-44"><span class="linenos">44</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/d.o.f. = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-45"><a href="#Fit_result-45"><span class="linenos">45</span></a> <span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'residual_variance'</span><span class="p">):</span>
|
||
</span><span id="Fit_result-46"><a href="#Fit_result-46"><span class="linenos">46</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'residual variance = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">residual_variance</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-47"><a href="#Fit_result-47"><span class="linenos">47</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_expected_chisquare'</span><span class="p">):</span>
|
||
</span><span id="Fit_result-48"><a href="#Fit_result-48"><span class="linenos">48</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/</span><span class="se">\u03C7\u00b2</span><span class="s1">exp = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-49"><a href="#Fit_result-49"><span class="linenos">49</span></a> <span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'p_value'</span><span class="p">):</span>
|
||
</span><span id="Fit_result-50"><a href="#Fit_result-50"><span class="linenos">50</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'p-value = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">p_value</span><span class="si">:</span><span class="s1">2.4f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-51"><a href="#Fit_result-51"><span class="linenos">51</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'Fit parameters:</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-52"><a href="#Fit_result-52"><span class="linenos">52</span></a> <span class="k">for</span> <span class="n">i_par</span><span class="p">,</span> <span class="n">par</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">):</span>
|
||
</span><span id="Fit_result-53"><a href="#Fit_result-53"><span class="linenos">53</span></a> <span class="n">my_str</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_par</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\t</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">' '</span> <span class="o">*</span> <span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">par</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o"><</span> <span class="mf">0.0</span><span class="p">))</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
||
</span><span id="Fit_result-54"><a href="#Fit_result-54"><span class="linenos">54</span></a> <span class="k">return</span> <span class="n">my_str</span>
|
||
</span><span id="Fit_result-55"><a href="#Fit_result-55"><span class="linenos">55</span></a>
|
||
</span><span id="Fit_result-56"><a href="#Fit_result-56"><span class="linenos">56</span></a> <span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="Fit_result-57"><a href="#Fit_result-57"><span class="linenos">57</span></a> <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())))</span> <span class="o">+</span> <span class="mi">1</span>
|
||
</span><span id="Fit_result-58"><a href="#Fit_result-58"><span class="linenos">58</span></a> <span class="k">return</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">key</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">+</span> <span class="s1">': '</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">items</span><span class="p">())])</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Represents fit results.</p>
|
||
|
||
<h6 id="attributes">Attributes</h6>
|
||
|
||
<ul>
|
||
<li><strong>fit_parameters</strong> (list):
|
||
results for the individual fit parameters,
|
||
also accessible via indices.</li>
|
||
</ul>
|
||
</div>
|
||
|
||
|
||
<div id="Fit_result.__init__" class="classattr">
|
||
<input id="Fit_result.__init__-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="name">Fit_result</span><span class="signature pdoc-code condensed">()</span>
|
||
|
||
<label class="view-source-button" for="Fit_result.__init__-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#Fit_result.__init__"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="Fit_result.__init__-28"><a href="#Fit_result.__init__-28"><span class="linenos">28</span></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
||
</span><span id="Fit_result.__init__-29"><a href="#Fit_result.__init__-29"><span class="linenos">29</span></a> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
|
||
</span></pre></div>
|
||
|
||
|
||
|
||
|
||
</div>
|
||
<div id="Fit_result.gamma_method" class="classattr">
|
||
<input id="Fit_result.gamma_method-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">gamma_method</span><span class="signature pdoc-code condensed">(<span class="param"><span class="bp">self</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="Fit_result.gamma_method-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#Fit_result.gamma_method"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="Fit_result.gamma_method-37"><a href="#Fit_result.gamma_method-37"><span class="linenos">37</span></a> <span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="Fit_result.gamma_method-38"><a href="#Fit_result.gamma_method-38"><span class="linenos">38</span></a> <span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
||
</span><span id="Fit_result.gamma_method-39"><a href="#Fit_result.gamma_method-39"><span class="linenos">39</span></a> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">(</span><span class="o">**</span><span class="n">kwargs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Apply the gamma method to all fit parameters</p>
|
||
</div>
|
||
|
||
|
||
</div>
|
||
<div class="inherited">
|
||
<h5>Inherited Members</h5>
|
||
<dl>
|
||
<div><dt>collections.abc.Sequence</dt>
|
||
<dd id="Fit_result.index" class="function">index</dd>
|
||
<dd id="Fit_result.count" class="function">count</dd>
|
||
|
||
</div>
|
||
</dl>
|
||
</div>
|
||
</section>
|
||
<section id="least_squares">
|
||
<input id="least_squares-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">least_squares</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">y</span>, </span><span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">priors</span><span class="o">=</span><span class="kc">None</span>, </span><span class="param"><span class="n">silent</span><span class="o">=</span><span class="kc">False</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="least_squares-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#least_squares"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="least_squares-61"><a href="#least_squares-61"><span class="linenos"> 61</span></a><span class="k">def</span> <span class="nf">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="least_squares-62"><a href="#least_squares-62"><span class="linenos"> 62</span></a> <span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x).</span>
|
||
</span><span id="least_squares-63"><a href="#least_squares-63"><span class="linenos"> 63</span></a>
|
||
</span><span id="least_squares-64"><a href="#least_squares-64"><span class="linenos"> 64</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="least_squares-65"><a href="#least_squares-65"><span class="linenos"> 65</span></a><span class="sd"> ----------</span>
|
||
</span><span id="least_squares-66"><a href="#least_squares-66"><span class="linenos"> 66</span></a><span class="sd"> x : list</span>
|
||
</span><span id="least_squares-67"><a href="#least_squares-67"><span class="linenos"> 67</span></a><span class="sd"> list of floats.</span>
|
||
</span><span id="least_squares-68"><a href="#least_squares-68"><span class="linenos"> 68</span></a><span class="sd"> y : list</span>
|
||
</span><span id="least_squares-69"><a href="#least_squares-69"><span class="linenos"> 69</span></a><span class="sd"> list of Obs.</span>
|
||
</span><span id="least_squares-70"><a href="#least_squares-70"><span class="linenos"> 70</span></a><span class="sd"> func : object</span>
|
||
</span><span id="least_squares-71"><a href="#least_squares-71"><span class="linenos"> 71</span></a><span class="sd"> fit function, has to be of the form</span>
|
||
</span><span id="least_squares-72"><a href="#least_squares-72"><span class="linenos"> 72</span></a>
|
||
</span><span id="least_squares-73"><a href="#least_squares-73"><span class="linenos"> 73</span></a><span class="sd"> ```python</span>
|
||
</span><span id="least_squares-74"><a href="#least_squares-74"><span class="linenos"> 74</span></a><span class="sd"> import autograd.numpy as anp</span>
|
||
</span><span id="least_squares-75"><a href="#least_squares-75"><span class="linenos"> 75</span></a>
|
||
</span><span id="least_squares-76"><a href="#least_squares-76"><span class="linenos"> 76</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="least_squares-77"><a href="#least_squares-77"><span class="linenos"> 77</span></a><span class="sd"> return a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||
</span><span id="least_squares-78"><a href="#least_squares-78"><span class="linenos"> 78</span></a><span class="sd"> ```</span>
|
||
</span><span id="least_squares-79"><a href="#least_squares-79"><span class="linenos"> 79</span></a>
|
||
</span><span id="least_squares-80"><a href="#least_squares-80"><span class="linenos"> 80</span></a><span class="sd"> For multiple x values func can be of the form</span>
|
||
</span><span id="least_squares-81"><a href="#least_squares-81"><span class="linenos"> 81</span></a>
|
||
</span><span id="least_squares-82"><a href="#least_squares-82"><span class="linenos"> 82</span></a><span class="sd"> ```python</span>
|
||
</span><span id="least_squares-83"><a href="#least_squares-83"><span class="linenos"> 83</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="least_squares-84"><a href="#least_squares-84"><span class="linenos"> 84</span></a><span class="sd"> (x1, x2) = x</span>
|
||
</span><span id="least_squares-85"><a href="#least_squares-85"><span class="linenos"> 85</span></a><span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||
</span><span id="least_squares-86"><a href="#least_squares-86"><span class="linenos"> 86</span></a><span class="sd"> ```</span>
|
||
</span><span id="least_squares-87"><a href="#least_squares-87"><span class="linenos"> 87</span></a>
|
||
</span><span id="least_squares-88"><a href="#least_squares-88"><span class="linenos"> 88</span></a><span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||
</span><span id="least_squares-89"><a href="#least_squares-89"><span class="linenos"> 89</span></a><span class="sd"> will not work.</span>
|
||
</span><span id="least_squares-90"><a href="#least_squares-90"><span class="linenos"> 90</span></a><span class="sd"> priors : list, optional</span>
|
||
</span><span id="least_squares-91"><a href="#least_squares-91"><span class="linenos"> 91</span></a><span class="sd"> priors has to be a list with an entry for every parameter in the fit. The entries can either be</span>
|
||
</span><span id="least_squares-92"><a href="#least_squares-92"><span class="linenos"> 92</span></a><span class="sd"> Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like</span>
|
||
</span><span id="least_squares-93"><a href="#least_squares-93"><span class="linenos"> 93</span></a><span class="sd"> 0.548(23), 500(40) or 0.5(0.4)</span>
|
||
</span><span id="least_squares-94"><a href="#least_squares-94"><span class="linenos"> 94</span></a><span class="sd"> silent : bool, optional</span>
|
||
</span><span id="least_squares-95"><a href="#least_squares-95"><span class="linenos"> 95</span></a><span class="sd"> If true all output to the console is omitted (default False).</span>
|
||
</span><span id="least_squares-96"><a href="#least_squares-96"><span class="linenos"> 96</span></a><span class="sd"> initial_guess : list</span>
|
||
</span><span id="least_squares-97"><a href="#least_squares-97"><span class="linenos"> 97</span></a><span class="sd"> can provide an initial guess for the input parameters. Relevant for</span>
|
||
</span><span id="least_squares-98"><a href="#least_squares-98"><span class="linenos"> 98</span></a><span class="sd"> non-linear fits with many parameters. In case of correlated fits the guess is used to perform</span>
|
||
</span><span id="least_squares-99"><a href="#least_squares-99"><span class="linenos"> 99</span></a><span class="sd"> an uncorrelated fit which then serves as guess for the correlated fit.</span>
|
||
</span><span id="least_squares-100"><a href="#least_squares-100"><span class="linenos">100</span></a><span class="sd"> method : str, optional</span>
|
||
</span><span id="least_squares-101"><a href="#least_squares-101"><span class="linenos">101</span></a><span class="sd"> can be used to choose an alternative method for the minimization of chisquare.</span>
|
||
</span><span id="least_squares-102"><a href="#least_squares-102"><span class="linenos">102</span></a><span class="sd"> The possible methods are the ones which can be used for scipy.optimize.minimize and</span>
|
||
</span><span id="least_squares-103"><a href="#least_squares-103"><span class="linenos">103</span></a><span class="sd"> migrad of iminuit. If no method is specified, Levenberg-Marquard is used.</span>
|
||
</span><span id="least_squares-104"><a href="#least_squares-104"><span class="linenos">104</span></a><span class="sd"> Reliable alternatives are migrad, Powell and Nelder-Mead.</span>
|
||
</span><span id="least_squares-105"><a href="#least_squares-105"><span class="linenos">105</span></a><span class="sd"> correlated_fit : bool</span>
|
||
</span><span id="least_squares-106"><a href="#least_squares-106"><span class="linenos">106</span></a><span class="sd"> If True, use the full inverse covariance matrix in the definition of the chisquare cost function.</span>
|
||
</span><span id="least_squares-107"><a href="#least_squares-107"><span class="linenos">107</span></a><span class="sd"> For details about how the covariance matrix is estimated see `pyerrors.obs.covariance`.</span>
|
||
</span><span id="least_squares-108"><a href="#least_squares-108"><span class="linenos">108</span></a><span class="sd"> In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).</span>
|
||
</span><span id="least_squares-109"><a href="#least_squares-109"><span class="linenos">109</span></a><span class="sd"> This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).</span>
|
||
</span><span id="least_squares-110"><a href="#least_squares-110"><span class="linenos">110</span></a><span class="sd"> At the moment this option only works for `prior==None` and when no `method` is given.</span>
|
||
</span><span id="least_squares-111"><a href="#least_squares-111"><span class="linenos">111</span></a><span class="sd"> expected_chisquare : bool</span>
|
||
</span><span id="least_squares-112"><a href="#least_squares-112"><span class="linenos">112</span></a><span class="sd"> If True estimates the expected chisquare which is</span>
|
||
</span><span id="least_squares-113"><a href="#least_squares-113"><span class="linenos">113</span></a><span class="sd"> corrected by effects caused by correlated input data (default False).</span>
|
||
</span><span id="least_squares-114"><a href="#least_squares-114"><span class="linenos">114</span></a><span class="sd"> resplot : bool</span>
|
||
</span><span id="least_squares-115"><a href="#least_squares-115"><span class="linenos">115</span></a><span class="sd"> If True, a plot which displays fit, data and residuals is generated (default False).</span>
|
||
</span><span id="least_squares-116"><a href="#least_squares-116"><span class="linenos">116</span></a><span class="sd"> qqplot : bool</span>
|
||
</span><span id="least_squares-117"><a href="#least_squares-117"><span class="linenos">117</span></a><span class="sd"> If True, a quantile-quantile plot of the fit result is generated (default False).</span>
|
||
</span><span id="least_squares-118"><a href="#least_squares-118"><span class="linenos">118</span></a><span class="sd"> '''</span>
|
||
</span><span id="least_squares-119"><a href="#least_squares-119"><span class="linenos">119</span></a> <span class="k">if</span> <span class="n">priors</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="least_squares-120"><a href="#least_squares-120"><span class="linenos">120</span></a> <span class="k">return</span> <span class="n">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="least_squares-121"><a href="#least_squares-121"><span class="linenos">121</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="least_squares-122"><a href="#least_squares-122"><span class="linenos">122</span></a> <span class="k">return</span> <span class="n">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Performs a non-linear fit to y = func(x).</p>
|
||
|
||
<h6 id="parameters">Parameters</h6>
|
||
|
||
<ul>
|
||
<li><strong>x</strong> (list):
|
||
list of floats.</li>
|
||
<li><strong>y</strong> (list):
|
||
list of Obs.</li>
|
||
<li><p><strong>func</strong> (object):
|
||
fit function, has to be of the form</p>
|
||
|
||
<div class="pdoc-code codehilite">
|
||
<pre><span></span><code><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">anp</span>
|
||
|
||
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</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">a</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>For multiple x values func can be of the form</p>
|
||
|
||
<div class="pdoc-code codehilite">
|
||
<pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
<span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
|
||
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x2</span>
|
||
</code></pre>
|
||
</div>
|
||
|
||
<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
|
||
will not work.</p></li>
|
||
<li><strong>priors</strong> (list, optional):
|
||
priors has to be a list with an entry for every parameter in the fit. The entries can either be
|
||
Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
|
||
0.548(23), 500(40) or 0.5(0.4)</li>
|
||
<li><strong>silent</strong> (bool, optional):
|
||
If true all output to the console is omitted (default False).</li>
|
||
<li><strong>initial_guess</strong> (list):
|
||
can provide an initial guess for the input parameters. Relevant for
|
||
non-linear fits with many parameters. In case of correlated fits the guess is used to perform
|
||
an uncorrelated fit which then serves as guess for the correlated fit.</li>
|
||
<li><strong>method</strong> (str, optional):
|
||
can be used to choose an alternative method for the minimization of chisquare.
|
||
The possible methods are the ones which can be used for scipy.optimize.minimize and
|
||
migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
|
||
Reliable alternatives are migrad, Powell and Nelder-Mead.</li>
|
||
<li><strong>correlated_fit</strong> (bool):
|
||
If True, use the full inverse covariance matrix in the definition of the chisquare cost function.
|
||
For details about how the covariance matrix is estimated see <code><a href="obs.html#covariance">pyerrors.obs.covariance</a></code>.
|
||
In practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).
|
||
This procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).
|
||
At the moment this option only works for <code>prior==None</code> and when no <code>method</code> is given.</li>
|
||
<li><strong>expected_chisquare</strong> (bool):
|
||
If True estimates the expected chisquare which is
|
||
corrected by effects caused by correlated input data (default False).</li>
|
||
<li><strong>resplot</strong> (bool):
|
||
If True, a plot which displays fit, data and residuals is generated (default False).</li>
|
||
<li><strong>qqplot</strong> (bool):
|
||
If True, a quantile-quantile plot of the fit result is generated (default False).</li>
|
||
</ul>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="total_least_squares">
|
||
<input id="total_least_squares-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">total_least_squares</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">y</span>, </span><span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">silent</span><span class="o">=</span><span class="kc">False</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="total_least_squares-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#total_least_squares"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="total_least_squares-125"><a href="#total_least_squares-125"><span class="linenos">125</span></a><span class="k">def</span> <span class="nf">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-126"><a href="#total_least_squares-126"><span class="linenos">126</span></a> <span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
||
</span><span id="total_least_squares-127"><a href="#total_least_squares-127"><span class="linenos">127</span></a>
|
||
</span><span id="total_least_squares-128"><a href="#total_least_squares-128"><span class="linenos">128</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="total_least_squares-129"><a href="#total_least_squares-129"><span class="linenos">129</span></a><span class="sd"> ----------</span>
|
||
</span><span id="total_least_squares-130"><a href="#total_least_squares-130"><span class="linenos">130</span></a><span class="sd"> x : list</span>
|
||
</span><span id="total_least_squares-131"><a href="#total_least_squares-131"><span class="linenos">131</span></a><span class="sd"> list of Obs, or a tuple of lists of Obs</span>
|
||
</span><span id="total_least_squares-132"><a href="#total_least_squares-132"><span class="linenos">132</span></a><span class="sd"> y : list</span>
|
||
</span><span id="total_least_squares-133"><a href="#total_least_squares-133"><span class="linenos">133</span></a><span class="sd"> list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</span>
|
||
</span><span id="total_least_squares-134"><a href="#total_least_squares-134"><span class="linenos">134</span></a><span class="sd"> func : object</span>
|
||
</span><span id="total_least_squares-135"><a href="#total_least_squares-135"><span class="linenos">135</span></a><span class="sd"> func has to be of the form</span>
|
||
</span><span id="total_least_squares-136"><a href="#total_least_squares-136"><span class="linenos">136</span></a>
|
||
</span><span id="total_least_squares-137"><a href="#total_least_squares-137"><span class="linenos">137</span></a><span class="sd"> ```python</span>
|
||
</span><span id="total_least_squares-138"><a href="#total_least_squares-138"><span class="linenos">138</span></a><span class="sd"> import autograd.numpy as anp</span>
|
||
</span><span id="total_least_squares-139"><a href="#total_least_squares-139"><span class="linenos">139</span></a>
|
||
</span><span id="total_least_squares-140"><a href="#total_least_squares-140"><span class="linenos">140</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="total_least_squares-141"><a href="#total_least_squares-141"><span class="linenos">141</span></a><span class="sd"> return a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||
</span><span id="total_least_squares-142"><a href="#total_least_squares-142"><span class="linenos">142</span></a><span class="sd"> ```</span>
|
||
</span><span id="total_least_squares-143"><a href="#total_least_squares-143"><span class="linenos">143</span></a>
|
||
</span><span id="total_least_squares-144"><a href="#total_least_squares-144"><span class="linenos">144</span></a><span class="sd"> For multiple x values func can be of the form</span>
|
||
</span><span id="total_least_squares-145"><a href="#total_least_squares-145"><span class="linenos">145</span></a>
|
||
</span><span id="total_least_squares-146"><a href="#total_least_squares-146"><span class="linenos">146</span></a><span class="sd"> ```python</span>
|
||
</span><span id="total_least_squares-147"><a href="#total_least_squares-147"><span class="linenos">147</span></a><span class="sd"> def func(a, x):</span>
|
||
</span><span id="total_least_squares-148"><a href="#total_least_squares-148"><span class="linenos">148</span></a><span class="sd"> (x1, x2) = x</span>
|
||
</span><span id="total_least_squares-149"><a href="#total_least_squares-149"><span class="linenos">149</span></a><span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||
</span><span id="total_least_squares-150"><a href="#total_least_squares-150"><span class="linenos">150</span></a><span class="sd"> ```</span>
|
||
</span><span id="total_least_squares-151"><a href="#total_least_squares-151"><span class="linenos">151</span></a>
|
||
</span><span id="total_least_squares-152"><a href="#total_least_squares-152"><span class="linenos">152</span></a><span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||
</span><span id="total_least_squares-153"><a href="#total_least_squares-153"><span class="linenos">153</span></a><span class="sd"> will not work.</span>
|
||
</span><span id="total_least_squares-154"><a href="#total_least_squares-154"><span class="linenos">154</span></a><span class="sd"> silent : bool, optional</span>
|
||
</span><span id="total_least_squares-155"><a href="#total_least_squares-155"><span class="linenos">155</span></a><span class="sd"> If true all output to the console is omitted (default False).</span>
|
||
</span><span id="total_least_squares-156"><a href="#total_least_squares-156"><span class="linenos">156</span></a><span class="sd"> initial_guess : list</span>
|
||
</span><span id="total_least_squares-157"><a href="#total_least_squares-157"><span class="linenos">157</span></a><span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
||
</span><span id="total_least_squares-158"><a href="#total_least_squares-158"><span class="linenos">158</span></a><span class="sd"> fits with many parameters.</span>
|
||
</span><span id="total_least_squares-159"><a href="#total_least_squares-159"><span class="linenos">159</span></a><span class="sd"> expected_chisquare : bool</span>
|
||
</span><span id="total_least_squares-160"><a href="#total_least_squares-160"><span class="linenos">160</span></a><span class="sd"> If true prints the expected chisquare which is</span>
|
||
</span><span id="total_least_squares-161"><a href="#total_least_squares-161"><span class="linenos">161</span></a><span class="sd"> corrected by effects caused by correlated input data.</span>
|
||
</span><span id="total_least_squares-162"><a href="#total_least_squares-162"><span class="linenos">162</span></a><span class="sd"> This can take a while as the full correlation matrix</span>
|
||
</span><span id="total_least_squares-163"><a href="#total_least_squares-163"><span class="linenos">163</span></a><span class="sd"> has to be calculated (default False).</span>
|
||
</span><span id="total_least_squares-164"><a href="#total_least_squares-164"><span class="linenos">164</span></a>
|
||
</span><span id="total_least_squares-165"><a href="#total_least_squares-165"><span class="linenos">165</span></a><span class="sd"> Notes</span>
|
||
</span><span id="total_least_squares-166"><a href="#total_least_squares-166"><span class="linenos">166</span></a><span class="sd"> -----</span>
|
||
</span><span id="total_least_squares-167"><a href="#total_least_squares-167"><span class="linenos">167</span></a><span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||
</span><span id="total_least_squares-168"><a href="#total_least_squares-168"><span class="linenos">168</span></a><span class="sd"> '''</span>
|
||
</span><span id="total_least_squares-169"><a href="#total_least_squares-169"><span class="linenos">169</span></a>
|
||
</span><span id="total_least_squares-170"><a href="#total_least_squares-170"><span class="linenos">170</span></a> <span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||
</span><span id="total_least_squares-171"><a href="#total_least_squares-171"><span class="linenos">171</span></a>
|
||
</span><span id="total_least_squares-172"><a href="#total_least_squares-172"><span class="linenos">172</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
||
</span><span id="total_least_squares-173"><a href="#total_least_squares-173"><span class="linenos">173</span></a>
|
||
</span><span id="total_least_squares-174"><a href="#total_least_squares-174"><span class="linenos">174</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-175"><a href="#total_least_squares-175"><span class="linenos">175</span></a>
|
||
</span><span id="total_least_squares-176"><a href="#total_least_squares-176"><span class="linenos">176</span></a> <span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
||
</span><span id="total_least_squares-177"><a href="#total_least_squares-177"><span class="linenos">177</span></a>
|
||
</span><span id="total_least_squares-178"><a href="#total_least_squares-178"><span class="linenos">178</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-179"><a href="#total_least_squares-179"><span class="linenos">179</span></a> <span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-180"><a href="#total_least_squares-180"><span class="linenos">180</span></a>
|
||
</span><span id="total_least_squares-181"><a href="#total_least_squares-181"><span class="linenos">181</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">42</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-182"><a href="#total_least_squares-182"><span class="linenos">182</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-183"><a href="#total_least_squares-183"><span class="linenos">183</span></a> <span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="total_least_squares-184"><a href="#total_least_squares-184"><span class="linenos">184</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-185"><a href="#total_least_squares-185"><span class="linenos">185</span></a> <span class="k">continue</span>
|
||
</span><span id="total_least_squares-186"><a href="#total_least_squares-186"><span class="linenos">186</span></a> <span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-187"><a href="#total_least_squares-187"><span class="linenos">187</span></a> <span class="k">continue</span>
|
||
</span><span id="total_least_squares-188"><a href="#total_least_squares-188"><span class="linenos">188</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-189"><a href="#total_least_squares-189"><span class="linenos">189</span></a> <span class="k">break</span>
|
||
</span><span id="total_least_squares-190"><a href="#total_least_squares-190"><span class="linenos">190</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-191"><a href="#total_least_squares-191"><span class="linenos">191</span></a> <span class="k">raise</span> <span class="ne">RuntimeError</span><span class="p">(</span><span class="s2">"Fit function is not valid."</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-192"><a href="#total_least_squares-192"><span class="linenos">192</span></a>
|
||
</span><span id="total_least_squares-193"><a href="#total_least_squares-193"><span class="linenos">193</span></a> <span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
||
</span><span id="total_least_squares-194"><a href="#total_least_squares-194"><span class="linenos">194</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-195"><a href="#total_least_squares-195"><span class="linenos">195</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameter'</span> <span class="o">+</span> <span class="s1">'s'</span> <span class="o">*</span> <span class="p">(</span><span class="n">n_parms</span> <span class="o">></span> <span class="mi">1</span><span class="p">))</span>
|
||
</span><span id="total_least_squares-196"><a href="#total_least_squares-196"><span class="linenos">196</span></a>
|
||
</span><span id="total_least_squares-197"><a href="#total_least_squares-197"><span class="linenos">197</span></a> <span class="n">x_f</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">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-198"><a href="#total_least_squares-198"><span class="linenos">198</span></a> <span class="n">dx_f</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">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-199"><a href="#total_least_squares-199"><span class="linenos">199</span></a> <span class="n">y_f</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">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="total_least_squares-200"><a href="#total_least_squares-200"><span class="linenos">200</span></a> <span class="n">dy_f</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">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="total_least_squares-201"><a href="#total_least_squares-201"><span class="linenos">201</span></a>
|
||
</span><span id="total_least_squares-202"><a href="#total_least_squares-202"><span class="linenos">202</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dx_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-203"><a href="#total_least_squares-203"><span class="linenos">203</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No x errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-204"><a href="#total_least_squares-204"><span class="linenos">204</span></a>
|
||
</span><span id="total_least_squares-205"><a href="#total_least_squares-205"><span class="linenos">205</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-206"><a href="#total_least_squares-206"><span class="linenos">206</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-207"><a href="#total_least_squares-207"><span class="linenos">207</span></a>
|
||
</span><span id="total_least_squares-208"><a href="#total_least_squares-208"><span class="linenos">208</span></a> <span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-209"><a href="#total_least_squares-209"><span class="linenos">209</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-210"><a href="#total_least_squares-210"><span class="linenos">210</span></a> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-211"><a href="#total_least_squares-211"><span class="linenos">211</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
||
</span><span id="total_least_squares-212"><a href="#total_least_squares-212"><span class="linenos">212</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-213"><a href="#total_least_squares-213"><span class="linenos">213</span></a> <span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
||
</span><span id="total_least_squares-214"><a href="#total_least_squares-214"><span class="linenos">214</span></a>
|
||
</span><span id="total_least_squares-215"><a href="#total_least_squares-215"><span class="linenos">215</span></a> <span class="n">data</span> <span class="o">=</span> <span class="n">RealData</span><span class="p">(</span><span class="n">x_f</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">sx</span><span class="o">=</span><span class="n">dx_f</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="n">dy_f</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-216"><a href="#total_least_squares-216"><span class="linenos">216</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">Model</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-217"><a href="#total_least_squares-217"><span class="linenos">217</span></a> <span class="n">odr</span> <span class="o">=</span> <span class="n">ODR</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">partol</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><span id="total_least_squares-218"><a href="#total_least_squares-218"><span class="linenos">218</span></a> <span class="n">odr</span><span class="o">.</span><span class="n">set_job</span><span class="p">(</span><span class="n">fit_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">deriv</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-219"><a href="#total_least_squares-219"><span class="linenos">219</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">odr</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
|
||
</span><span id="total_least_squares-220"><a href="#total_least_squares-220"><span class="linenos">220</span></a>
|
||
</span><span id="total_least_squares-221"><a href="#total_least_squares-221"><span class="linenos">221</span></a> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">res_var</span>
|
||
</span><span id="total_least_squares-222"><a href="#total_least_squares-222"><span class="linenos">222</span></a>
|
||
</span><span id="total_least_squares-223"><a href="#total_least_squares-223"><span class="linenos">223</span></a> <span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'ODR'</span>
|
||
</span><span id="total_least_squares-224"><a href="#total_least_squares-224"><span class="linenos">224</span></a>
|
||
</span><span id="total_least_squares-225"><a href="#total_least_squares-225"><span class="linenos">225</span></a> <span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">stopreason</span>
|
||
</span><span id="total_least_squares-226"><a href="#total_least_squares-226"><span class="linenos">226</span></a>
|
||
</span><span id="total_least_squares-227"><a href="#total_least_squares-227"><span class="linenos">227</span></a> <span class="n">output</span><span class="o">.</span><span class="n">xplus</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span>
|
||
</span><span id="total_least_squares-228"><a href="#total_least_squares-228"><span class="linenos">228</span></a>
|
||
</span><span id="total_least_squares-229"><a href="#total_least_squares-229"><span class="linenos">229</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-230"><a href="#total_least_squares-230"><span class="linenos">230</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Method: ODR'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-231"><a href="#total_least_squares-231"><span class="linenos">231</span></a> <span class="nb">print</span><span class="p">(</span><span class="o">*</span><span class="n">out</span><span class="o">.</span><span class="n">stopreason</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-232"><a href="#total_least_squares-232"><span class="linenos">232</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'Residual variance:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-233"><a href="#total_least_squares-233"><span class="linenos">233</span></a>
|
||
</span><span id="total_least_squares-234"><a href="#total_least_squares-234"><span class="linenos">234</span></a> <span class="k">if</span> <span class="n">out</span><span class="o">.</span><span class="n">info</span> <span class="o">></span> <span class="mi">3</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-235"><a href="#total_least_squares-235"><span class="linenos">235</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-236"><a href="#total_least_squares-236"><span class="linenos">236</span></a>
|
||
</span><span id="total_least_squares-237"><a href="#total_least_squares-237"><span class="linenos">237</span></a> <span class="n">m</span> <span class="o">=</span> <span class="n">x_f</span><span class="o">.</span><span class="n">size</span>
|
||
</span><span id="total_least_squares-238"><a href="#total_least_squares-238"><span class="linenos">238</span></a>
|
||
</span><span id="total_least_squares-239"><a href="#total_least_squares-239"><span class="linenos">239</span></a> <span class="k">def</span> <span class="nf">odr_chisquare</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-240"><a href="#total_least_squares-240"><span class="linenos">240</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="total_least_squares-241"><a href="#total_least_squares-241"><span class="linenos">241</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-242"><a href="#total_least_squares-242"><span class="linenos">242</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="total_least_squares-243"><a href="#total_least_squares-243"><span class="linenos">243</span></a>
|
||
</span><span id="total_least_squares-244"><a href="#total_least_squares-244"><span class="linenos">244</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-245"><a href="#total_least_squares-245"><span class="linenos">245</span></a> <span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">dy_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">dx_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
||
</span><span id="total_least_squares-246"><a href="#total_least_squares-246"><span class="linenos">246</span></a>
|
||
</span><span id="total_least_squares-247"><a href="#total_least_squares-247"><span class="linenos">247</span></a> <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-248"><a href="#total_least_squares-248"><span class="linenos">248</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-249"><a href="#total_least_squares-249"><span class="linenos">249</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-250"><a href="#total_least_squares-250"><span class="linenos">250</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="total_least_squares-251"><a href="#total_least_squares-251"><span class="linenos">251</span></a>
|
||
</span><span id="total_least_squares-252"><a href="#total_least_squares-252"><span class="linenos">252</span></a> <span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||
</span><span id="total_least_squares-253"><a href="#total_least_squares-253"><span class="linenos">253</span></a>
|
||
</span><span id="total_least_squares-254"><a href="#total_least_squares-254"><span class="linenos">254</span></a> <span class="n">old_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 class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-255"><a href="#total_least_squares-255"><span class="linenos">255</span></a> <span class="n">fused_row1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">old_jac</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">)]),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)))</span>
|
||
</span><span id="total_least_squares-256"><a href="#total_least_squares-256"><span class="linenos">256</span></a> <span class="n">fused_row2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">jacobian</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">))(</span><span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">number_of_x_parameters</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])))</span>
|
||
</span><span id="total_least_squares-257"><a href="#total_least_squares-257"><span class="linenos">257</span></a> <span class="n">new_jac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fused_row1</span><span class="p">,</span> <span class="n">fused_row2</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-258"><a href="#total_least_squares-258"><span class="linenos">258</span></a>
|
||
</span><span id="total_least_squares-259"><a href="#total_least_squares-259"><span class="linenos">259</span></a> <span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">new_jac</span>
|
||
</span><span id="total_least_squares-260"><a href="#total_least_squares-260"><span class="linenos">260</span></a> <span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
||
</span><span id="total_least_squares-261"><a href="#total_least_squares-261"><span class="linenos">261</span></a> <span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">P_phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-262"><a href="#total_least_squares-262"><span class="linenos">262</span></a> <span class="k">if</span> <span class="n">expected_chisquare</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-263"><a href="#total_least_squares-263"><span class="linenos">263</span></a> <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Negative expected_chisquare."</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-264"><a href="#total_least_squares-264"><span class="linenos">264</span></a> <span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">expected_chisquare</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-265"><a href="#total_least_squares-265"><span class="linenos">265</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
||
</span><span id="total_least_squares-266"><a href="#total_least_squares-266"><span class="linenos">266</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-267"><a href="#total_least_squares-267"><span class="linenos">267</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
||
</span><span id="total_least_squares-268"><a href="#total_least_squares-268"><span class="linenos">268</span></a> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-269"><a href="#total_least_squares-269"><span class="linenos">269</span></a>
|
||
</span><span id="total_least_squares-270"><a href="#total_least_squares-270"><span class="linenos">270</span></a> <span class="n">fitp</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span>
|
||
</span><span id="total_least_squares-271"><a href="#total_least_squares-271"><span class="linenos">271</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-272"><a href="#total_least_squares-272"><span class="linenos">272</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="total_least_squares-273"><a href="#total_least_squares-273"><span class="linenos">273</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-274"><a href="#total_least_squares-274"><span class="linenos">274</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"It is required to use autograd.numpy instead of numpy within fit functions, see the documentation for details."</span><span class="p">)</span> <span class="kn">from</span> <span class="bp">None</span>
|
||
</span><span id="total_least_squares-275"><a href="#total_least_squares-275"><span class="linenos">275</span></a>
|
||
</span><span id="total_least_squares-276"><a href="#total_least_squares-276"><span class="linenos">276</span></a> <span class="k">def</span> <span class="nf">odr_chisquare_compact_x</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-277"><a href="#total_least_squares-277"><span class="linenos">277</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="total_least_squares-278"><a href="#total_least_squares-278"><span class="linenos">278</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-279"><a href="#total_least_squares-279"><span class="linenos">279</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="total_least_squares-280"><a href="#total_least_squares-280"><span class="linenos">280</span></a>
|
||
</span><span id="total_least_squares-281"><a href="#total_least_squares-281"><span class="linenos">281</span></a> <span class="n">jac_jac_x</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_x</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">x_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="total_least_squares-282"><a href="#total_least_squares-282"><span class="linenos">282</span></a>
|
||
</span><span id="total_least_squares-283"><a href="#total_least_squares-283"><span class="linenos">283</span></a> <span class="c1"># Compute hess^{-1} @ jac_jac_x[:n_parms + m, n_parms + m:] using LAPACK dgesv</span>
|
||
</span><span id="total_least_squares-284"><a href="#total_least_squares-284"><span class="linenos">284</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-285"><a href="#total_least_squares-285"><span class="linenos">285</span></a> <span class="n">deriv_x</span> <span class="o">=</span> <span class="o">-</span><span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">hess</span><span class="p">,</span> <span class="n">jac_jac_x</span><span class="p">[:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:])</span>
|
||
</span><span id="total_least_squares-286"><a href="#total_least_squares-286"><span class="linenos">286</span></a> <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-287"><a href="#total_least_squares-287"><span class="linenos">287</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"Cannot invert hessian matrix."</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-288"><a href="#total_least_squares-288"><span class="linenos">288</span></a>
|
||
</span><span id="total_least_squares-289"><a href="#total_least_squares-289"><span class="linenos">289</span></a> <span class="k">def</span> <span class="nf">odr_chisquare_compact_y</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-290"><a href="#total_least_squares-290"><span class="linenos">290</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
||
</span><span id="total_least_squares-291"><a href="#total_least_squares-291"><span class="linenos">291</span></a> <span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</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">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-292"><a href="#total_least_squares-292"><span class="linenos">292</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||
</span><span id="total_least_squares-293"><a href="#total_least_squares-293"><span class="linenos">293</span></a>
|
||
</span><span id="total_least_squares-294"><a href="#total_least_squares-294"><span class="linenos">294</span></a> <span class="n">jac_jac_y</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_y</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">y_f</span><span class="p">)))</span>
|
||
</span><span id="total_least_squares-295"><a href="#total_least_squares-295"><span class="linenos">295</span></a>
|
||
</span><span id="total_least_squares-296"><a href="#total_least_squares-296"><span class="linenos">296</span></a> <span class="c1"># Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv</span>
|
||
</span><span id="total_least_squares-297"><a href="#total_least_squares-297"><span class="linenos">297</span></a> <span class="k">try</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-298"><a href="#total_least_squares-298"><span class="linenos">298</span></a> <span class="n">deriv_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">scipy</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">hess</span><span class="p">,</span> <span class="n">jac_jac_y</span><span class="p">[:</span><span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="n">m</span><span class="p">:])</span>
|
||
</span><span id="total_least_squares-299"><a href="#total_least_squares-299"><span class="linenos">299</span></a> <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
|
||
</span><span id="total_least_squares-300"><a href="#total_least_squares-300"><span class="linenos">300</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s2">"Cannot invert hessian matrix."</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-301"><a href="#total_least_squares-301"><span class="linenos">301</span></a>
|
||
</span><span id="total_least_squares-302"><a href="#total_least_squares-302"><span class="linenos">302</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="total_least_squares-303"><a href="#total_least_squares-303"><span class="linenos">303</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">n_parms</span><span class="p">):</span>
|
||
</span><span id="total_least_squares-304"><a href="#total_least_squares-304"><span class="linenos">304</span></a> <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">my_var</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">my_var</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">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</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">out</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv_x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">deriv_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||
</span><span id="total_least_squares-305"><a href="#total_least_squares-305"><span class="linenos">305</span></a>
|
||
</span><span id="total_least_squares-306"><a href="#total_least_squares-306"><span class="linenos">306</span></a> <span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||
</span><span id="total_least_squares-307"><a href="#total_least_squares-307"><span class="linenos">307</span></a>
|
||
</span><span id="total_least_squares-308"><a href="#total_least_squares-308"><span class="linenos">308</span></a> <span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||
</span><span id="total_least_squares-309"><a href="#total_least_squares-309"><span class="linenos">309</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
|
||
</span><span id="total_least_squares-310"><a href="#total_least_squares-310"><span class="linenos">310</span></a> <span class="n">output</span><span class="o">.</span><span class="n">p_value</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">chi2</span><span class="o">.</span><span class="n">cdf</span><span class="p">(</span><span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span>
|
||
</span><span id="total_least_squares-311"><a href="#total_least_squares-311"><span class="linenos">311</span></a>
|
||
</span><span id="total_least_squares-312"><a href="#total_least_squares-312"><span class="linenos">312</span></a> <span class="k">return</span> <span class="n">output</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</p>
|
||
|
||
<h6 id="parameters">Parameters</h6>
|
||
|
||
<ul>
|
||
<li><strong>x</strong> (list):
|
||
list of Obs, or a tuple of lists of Obs</li>
|
||
<li><strong>y</strong> (list):
|
||
list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</li>
|
||
<li><p><strong>func</strong> (object):
|
||
func has to be of the form</p>
|
||
|
||
<div class="pdoc-code codehilite">
|
||
<pre><span></span><code><span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">anp</span>
|
||
|
||
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</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">a</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>For multiple x values func can be of the form</p>
|
||
|
||
<div class="pdoc-code codehilite">
|
||
<pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
<span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
|
||
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x2</span>
|
||
</code></pre>
|
||
</div>
|
||
|
||
<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
|
||
will not work.</p></li>
|
||
<li><strong>silent</strong> (bool, optional):
|
||
If true all output to the console is omitted (default False).</li>
|
||
<li><strong>initial_guess</strong> (list):
|
||
can provide an initial guess for the input parameters. Relevant for non-linear
|
||
fits with many parameters.</li>
|
||
<li><strong>expected_chisquare</strong> (bool):
|
||
If true prints the expected chisquare which is
|
||
corrected by effects caused by correlated input data.
|
||
This can take a while as the full correlation matrix
|
||
has to be calculated (default False).</li>
|
||
</ul>
|
||
|
||
<h6 id="notes">Notes</h6>
|
||
|
||
<p>Based on the orthogonal distance regression module of scipy</p>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="fit_lin">
|
||
<input id="fit_lin-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">fit_lin</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">y</span>, </span><span class="param"><span class="o">**</span><span class="n">kwargs</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="fit_lin-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#fit_lin"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="fit_lin-620"><a href="#fit_lin-620"><span class="linenos">620</span></a><span class="k">def</span> <span class="nf">fit_lin</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||
</span><span id="fit_lin-621"><a href="#fit_lin-621"><span class="linenos">621</span></a> <span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||
</span><span id="fit_lin-622"><a href="#fit_lin-622"><span class="linenos">622</span></a>
|
||
</span><span id="fit_lin-623"><a href="#fit_lin-623"><span class="linenos">623</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="fit_lin-624"><a href="#fit_lin-624"><span class="linenos">624</span></a><span class="sd"> ----------</span>
|
||
</span><span id="fit_lin-625"><a href="#fit_lin-625"><span class="linenos">625</span></a><span class="sd"> x : list</span>
|
||
</span><span id="fit_lin-626"><a href="#fit_lin-626"><span class="linenos">626</span></a><span class="sd"> Can either be a list of floats in which case no xerror is assumed, or</span>
|
||
</span><span id="fit_lin-627"><a href="#fit_lin-627"><span class="linenos">627</span></a><span class="sd"> a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</span>
|
||
</span><span id="fit_lin-628"><a href="#fit_lin-628"><span class="linenos">628</span></a><span class="sd"> y : list</span>
|
||
</span><span id="fit_lin-629"><a href="#fit_lin-629"><span class="linenos">629</span></a><span class="sd"> List of Obs, the dvalues of the Obs are used as yerror for the fit.</span>
|
||
</span><span id="fit_lin-630"><a href="#fit_lin-630"><span class="linenos">630</span></a><span class="sd"> """</span>
|
||
</span><span id="fit_lin-631"><a href="#fit_lin-631"><span class="linenos">631</span></a>
|
||
</span><span id="fit_lin-632"><a href="#fit_lin-632"><span class="linenos">632</span></a> <span class="k">def</span> <span class="nf">f</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
||
</span><span id="fit_lin-633"><a href="#fit_lin-633"><span class="linenos">633</span></a> <span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span>
|
||
</span><span id="fit_lin-634"><a href="#fit_lin-634"><span class="linenos">634</span></a> <span class="k">return</span> <span class="n">y</span>
|
||
</span><span id="fit_lin-635"><a href="#fit_lin-635"><span class="linenos">635</span></a>
|
||
</span><span id="fit_lin-636"><a href="#fit_lin-636"><span class="linenos">636</span></a> <span class="k">if</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">x</span><span class="p">):</span>
|
||
</span><span id="fit_lin-637"><a href="#fit_lin-637"><span class="linenos">637</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="fit_lin-638"><a href="#fit_lin-638"><span class="linenos">638</span></a> <span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
||
</span><span id="fit_lin-639"><a href="#fit_lin-639"><span class="linenos">639</span></a> <span class="k">elif</span> <span class="nb">all</span><span class="p">(</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">float</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">int</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">x</span><span class="p">)</span> <span class="ow">or</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">):</span>
|
||
</span><span id="fit_lin-640"><a href="#fit_lin-640"><span class="linenos">640</span></a> <span class="n">out</span> <span class="o">=</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">f</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
||
</span><span id="fit_lin-641"><a href="#fit_lin-641"><span class="linenos">641</span></a> <span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
||
</span><span id="fit_lin-642"><a href="#fit_lin-642"><span class="linenos">642</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="fit_lin-643"><a href="#fit_lin-643"><span class="linenos">643</span></a> <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unsupported types for x'</span><span class="p">)</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>
|
||
|
||
<h6 id="parameters">Parameters</h6>
|
||
|
||
<ul>
|
||
<li><strong>x</strong> (list):
|
||
Can either be a list of floats in which case no xerror is assumed, or
|
||
a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</li>
|
||
<li><strong>y</strong> (list):
|
||
List of Obs, the dvalues of the Obs are used as yerror for the fit.</li>
|
||
</ul>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="qqplot">
|
||
<input id="qqplot-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">qqplot</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">o_y</span>, </span><span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">p</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="qqplot-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#qqplot"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="qqplot-646"><a href="#qqplot-646"><span class="linenos">646</span></a><span class="k">def</span> <span class="nf">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">o_y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
|
||
</span><span id="qqplot-647"><a href="#qqplot-647"><span class="linenos">647</span></a> <span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||
</span><span id="qqplot-648"><a href="#qqplot-648"><span class="linenos">648</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||
</span><span id="qqplot-649"><a href="#qqplot-649"><span class="linenos">649</span></a><span class="sd"> """</span>
|
||
</span><span id="qqplot-650"><a href="#qqplot-650"><span class="linenos">650</span></a>
|
||
</span><span id="qqplot-651"><a href="#qqplot-651"><span class="linenos">651</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="qqplot-652"><a href="#qqplot-652"><span class="linenos">652</span></a> <span class="k">for</span> <span class="n">i_x</span><span class="p">,</span> <span class="n">i_y</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">o_y</span><span class="p">):</span>
|
||
</span><span id="qqplot-653"><a href="#qqplot-653"><span class="linenos">653</span></a> <span class="n">residuals</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">i_y</span> <span class="o">-</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">i_x</span><span class="p">))</span> <span class="o">/</span> <span class="n">i_y</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)</span>
|
||
</span><span id="qqplot-654"><a href="#qqplot-654"><span class="linenos">654</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">residuals</span><span class="p">)</span>
|
||
</span><span id="qqplot-655"><a href="#qqplot-655"><span class="linenos">655</span></a> <span class="n">my_y</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">residuals</span><span class="p">]</span>
|
||
</span><span id="qqplot-656"><a href="#qqplot-656"><span class="linenos">656</span></a> <span class="n">probplot</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">probplot</span><span class="p">(</span><span class="n">my_y</span><span class="p">)</span>
|
||
</span><span id="qqplot-657"><a href="#qqplot-657"><span class="linenos">657</span></a> <span class="n">my_x</span> <span class="o">=</span> <span class="n">probplot</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||
</span><span id="qqplot-658"><a href="#qqplot-658"><span class="linenos">658</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span> <span class="o">/</span> <span class="mf">1.618</span><span class="p">))</span>
|
||
</span><span id="qqplot-659"><a href="#qqplot-659"><span class="linenos">659</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">my_x</span><span class="p">,</span> <span class="n">my_y</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">'o'</span><span class="p">)</span>
|
||
</span><span id="qqplot-660"><a href="#qqplot-660"><span class="linenos">660</span></a> <span class="n">fit_start</span> <span class="o">=</span> <span class="n">my_x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
|
||
</span><span id="qqplot-661"><a href="#qqplot-661"><span class="linenos">661</span></a> <span class="n">fit_stop</span> <span class="o">=</span> <span class="n">my_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||
</span><span id="qqplot-662"><a href="#qqplot-662"><span class="linenos">662</span></a> <span class="n">samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">fit_start</span><span class="p">,</span> <span class="n">fit_stop</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
|
||
</span><span id="qqplot-663"><a href="#qqplot-663"><span class="linenos">663</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">samples</span><span class="p">,</span> <span class="n">samples</span><span class="p">,</span> <span class="s1">'k--'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">11</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Standard normal distribution'</span><span class="p">)</span>
|
||
</span><span id="qqplot-664"><a href="#qqplot-664"><span class="linenos">664</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">samples</span><span class="p">,</span> <span class="n">probplot</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="o">*</span> <span class="n">samples</span> <span class="o">+</span> <span class="n">probplot</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="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Least squares fit, r='</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">around</span><span class="p">(</span><span class="n">probplot</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">],</span> <span class="mi">3</span><span class="p">)),</span> <span class="n">marker</span><span class="o">=</span><span class="s1">''</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'-'</span><span class="p">)</span>
|
||
</span><span id="qqplot-665"><a href="#qqplot-665"><span class="linenos">665</span></a>
|
||
</span><span id="qqplot-666"><a href="#qqplot-666"><span class="linenos">666</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'Theoretical quantiles'</span><span class="p">)</span>
|
||
</span><span id="qqplot-667"><a href="#qqplot-667"><span class="linenos">667</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Ordered Values'</span><span class="p">)</span>
|
||
</span><span id="qqplot-668"><a href="#qqplot-668"><span class="linenos">668</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
</span><span id="qqplot-669"><a href="#qqplot-669"><span class="linenos">669</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Generates a quantile-quantile plot of the fit result which can be used to
|
||
check if the residuals of the fit are gaussian distributed.</p>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="residual_plot">
|
||
<input id="residual_plot-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">residual_plot</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">y</span>, </span><span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">fit_res</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="residual_plot-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#residual_plot"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="residual_plot-672"><a href="#residual_plot-672"><span class="linenos">672</span></a><span class="k">def</span> <span class="nf">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">fit_res</span><span class="p">):</span>
|
||
</span><span id="residual_plot-673"><a href="#residual_plot-673"><span class="linenos">673</span></a> <span class="sd">""" Generates a plot which compares the fit to the data and displays the corresponding residuals"""</span>
|
||
</span><span id="residual_plot-674"><a href="#residual_plot-674"><span class="linenos">674</span></a> <span class="n">sorted_x</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||
</span><span id="residual_plot-675"><a href="#residual_plot-675"><span class="linenos">675</span></a> <span class="n">xstart</span> <span class="o">=</span> <span class="n">sorted_x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">sorted_x</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">sorted_x</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="residual_plot-676"><a href="#residual_plot-676"><span class="linenos">676</span></a> <span class="n">xstop</span> <span class="o">=</span> <span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span><span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">sorted_x</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
|
||
</span><span id="residual_plot-677"><a href="#residual_plot-677"><span class="linenos">677</span></a> <span class="n">x_samples</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span> <span class="o">+</span> <span class="mf">0.01</span><span class="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
|
||
</span><span id="residual_plot-678"><a href="#residual_plot-678"><span class="linenos">678</span></a>
|
||
</span><span id="residual_plot-679"><a href="#residual_plot-679"><span class="linenos">679</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">8</span><span class="p">,</span> <span class="mi">8</span> <span class="o">/</span> <span class="mf">1.618</span><span class="p">))</span>
|
||
</span><span id="residual_plot-680"><a href="#residual_plot-680"><span class="linenos">680</span></a> <span class="n">gs</span> <span class="o">=</span> <span class="n">gridspec</span><span class="o">.</span><span class="n">GridSpec</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="n">height_ratios</span><span class="o">=</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">wspace</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span>
|
||
</span><span id="residual_plot-681"><a href="#residual_plot-681"><span class="linenos">681</span></a> <span class="n">ax0</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="n">gs</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
||
</span><span id="residual_plot-682"><a href="#residual_plot-682"><span class="linenos">682</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">errorbar</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">],</span> <span class="n">yerr</span><span class="o">=</span><span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">],</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'none'</span><span class="p">,</span> <span class="n">fmt</span><span class="o">=</span><span class="s1">'o'</span><span class="p">,</span> <span class="n">capsize</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Data'</span><span class="p">)</span>
|
||
</span><span id="residual_plot-683"><a href="#residual_plot-683"><span class="linenos">683</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_samples</span><span class="p">,</span> <span class="n">func</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">fit_res</span><span class="p">],</span> <span class="n">x_samples</span><span class="p">),</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Fit'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'-'</span><span class="p">,</span> <span class="n">ms</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
|
||
</span><span id="residual_plot-684"><a href="#residual_plot-684"><span class="linenos">684</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
||
</span><span id="residual_plot-685"><a href="#residual_plot-685"><span class="linenos">685</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span><span class="p">])</span>
|
||
</span><span id="residual_plot-686"><a href="#residual_plot-686"><span class="linenos">686</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
||
</span><span id="residual_plot-687"><a href="#residual_plot-687"><span class="linenos">687</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
||
</span><span id="residual_plot-688"><a href="#residual_plot-688"><span class="linenos">688</span></a>
|
||
</span><span id="residual_plot-689"><a href="#residual_plot-689"><span class="linenos">689</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span> <span class="o">-</span> <span class="n">func</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">fit_res</span><span class="p">],</span> <span class="n">x</span><span class="p">))</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
||
</span><span id="residual_plot-690"><a href="#residual_plot-690"><span class="linenos">690</span></a> <span class="n">ax1</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="n">gs</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
|
||
</span><span id="residual_plot-691"><a href="#residual_plot-691"><span class="linenos">691</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">residuals</span><span class="p">,</span> <span class="s1">'ko'</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'none'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
|
||
</span><span id="residual_plot-692"><a href="#residual_plot-692"><span class="linenos">692</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">direction</span><span class="o">=</span><span class="s1">'out'</span><span class="p">)</span>
|
||
</span><span id="residual_plot-693"><a href="#residual_plot-693"><span class="linenos">693</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">tick_params</span><span class="p">(</span><span class="n">axis</span><span class="o">=</span><span class="s2">"x"</span><span class="p">,</span> <span class="n">bottom</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">top</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">labelbottom</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||
</span><span id="residual_plot-694"><a href="#residual_plot-694"><span class="linenos">694</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="n">y</span><span class="o">=</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">ls</span><span class="o">=</span><span class="s1">'--'</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">marker</span><span class="o">=</span><span class="s2">" "</span><span class="p">)</span>
|
||
</span><span id="residual_plot-695"><a href="#residual_plot-695"><span class="linenos">695</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">fill_between</span><span class="p">(</span><span class="n">x_samples</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
|
||
</span><span id="residual_plot-696"><a href="#residual_plot-696"><span class="linenos">696</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">([</span><span class="n">xstart</span><span class="p">,</span> <span class="n">xstop</span><span class="p">])</span>
|
||
</span><span id="residual_plot-697"><a href="#residual_plot-697"><span class="linenos">697</span></a> <span class="n">ax1</span><span class="o">.</span><span class="n">set_ylabel</span><span class="p">(</span><span class="s1">'Residuals'</span><span class="p">)</span>
|
||
</span><span id="residual_plot-698"><a href="#residual_plot-698"><span class="linenos">698</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">wspace</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">hspace</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
|
||
</span><span id="residual_plot-699"><a href="#residual_plot-699"><span class="linenos">699</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="error_band">
|
||
<input id="error_band-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">error_band</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">x</span>, </span><span class="param"><span class="n">func</span>, </span><span class="param"><span class="n">beta</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="error_band-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#error_band"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="error_band-702"><a href="#error_band-702"><span class="linenos">702</span></a><span class="k">def</span> <span class="nf">error_band</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
|
||
</span><span id="error_band-703"><a href="#error_band-703"><span class="linenos">703</span></a> <span class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
||
</span><span id="error_band-704"><a href="#error_band-704"><span class="linenos">704</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||
</span><span id="error_band-705"><a href="#error_band-705"><span class="linenos">705</span></a> <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">cov</span> <span class="o">-</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">></span> <span class="mi">1000</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><span id="error_band-706"><a href="#error_band-706"><span class="linenos">706</span></a> <span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Covariance matrix is not symmetric within floating point precision"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||
</span><span id="error_band-707"><a href="#error_band-707"><span class="linenos">707</span></a>
|
||
</span><span id="error_band-708"><a href="#error_band-708"><span class="linenos">708</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="error_band-709"><a href="#error_band-709"><span class="linenos">709</span></a> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
|
||
</span><span id="error_band-710"><a href="#error_band-710"><span class="linenos">710</span></a> <span class="n">deriv</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">egrad</span><span class="p">(</span><span class="n">func</span><span class="p">)([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">beta</span><span class="p">],</span> <span class="n">item</span><span class="p">)))</span>
|
||
</span><span id="error_band-711"><a href="#error_band-711"><span class="linenos">711</span></a>
|
||
</span><span id="error_band-712"><a href="#error_band-712"><span class="linenos">712</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="error_band-713"><a href="#error_band-713"><span class="linenos">713</span></a> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
|
||
</span><span id="error_band-714"><a href="#error_band-714"><span class="linenos">714</span></a> <span class="n">err</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span>
|
||
</span><span id="error_band-715"><a href="#error_band-715"><span class="linenos">715</span></a> <span class="n">err</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">err</span><span class="p">)</span>
|
||
</span><span id="error_band-716"><a href="#error_band-716"><span class="linenos">716</span></a>
|
||
</span><span id="error_band-717"><a href="#error_band-717"><span class="linenos">717</span></a> <span class="k">return</span> <span class="n">err</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
<section id="ks_test">
|
||
<input id="ks_test-view-source" class="view-source-toggle-state" type="checkbox" aria-hidden="true" tabindex="-1">
|
||
<div class="attr function">
|
||
|
||
<span class="def">def</span>
|
||
<span class="name">ks_test</span><span class="signature pdoc-code condensed">(<span class="param"><span class="n">objects</span><span class="o">=</span><span class="kc">None</span></span><span class="return-annotation">):</span></span>
|
||
|
||
<label class="view-source-button" for="ks_test-view-source"><span>View Source</span></label>
|
||
|
||
</div>
|
||
<a class="headerlink" href="#ks_test"></a>
|
||
<div class="pdoc-code codehilite"><pre><span></span><span id="ks_test-720"><a href="#ks_test-720"><span class="linenos">720</span></a><span class="k">def</span> <span class="nf">ks_test</span><span class="p">(</span><span class="n">objects</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
|
||
</span><span id="ks_test-721"><a href="#ks_test-721"><span class="linenos">721</span></a> <span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||
</span><span id="ks_test-722"><a href="#ks_test-722"><span class="linenos">722</span></a>
|
||
</span><span id="ks_test-723"><a href="#ks_test-723"><span class="linenos">723</span></a><span class="sd"> Parameters</span>
|
||
</span><span id="ks_test-724"><a href="#ks_test-724"><span class="linenos">724</span></a><span class="sd"> ----------</span>
|
||
</span><span id="ks_test-725"><a href="#ks_test-725"><span class="linenos">725</span></a><span class="sd"> objects : list</span>
|
||
</span><span id="ks_test-726"><a href="#ks_test-726"><span class="linenos">726</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||
</span><span id="ks_test-727"><a href="#ks_test-727"><span class="linenos">727</span></a><span class="sd"> """</span>
|
||
</span><span id="ks_test-728"><a href="#ks_test-728"><span class="linenos">728</span></a>
|
||
</span><span id="ks_test-729"><a href="#ks_test-729"><span class="linenos">729</span></a> <span class="k">if</span> <span class="n">objects</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
||
</span><span id="ks_test-730"><a href="#ks_test-730"><span class="linenos">730</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||
</span><span id="ks_test-731"><a href="#ks_test-731"><span class="linenos">731</span></a> <span class="k">for</span> <span class="n">obj</span> <span class="ow">in</span> <span class="n">gc</span><span class="o">.</span><span class="n">get_objects</span><span class="p">():</span>
|
||
</span><span id="ks_test-732"><a href="#ks_test-732"><span class="linenos">732</span></a> <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">obj</span><span class="p">,</span> <span class="n">Fit_result</span><span class="p">):</span>
|
||
</span><span id="ks_test-733"><a href="#ks_test-733"><span class="linenos">733</span></a> <span class="n">obs_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
|
||
</span><span id="ks_test-734"><a href="#ks_test-734"><span class="linenos">734</span></a> <span class="k">else</span><span class="p">:</span>
|
||
</span><span id="ks_test-735"><a href="#ks_test-735"><span class="linenos">735</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||
</span><span id="ks_test-736"><a href="#ks_test-736"><span class="linenos">736</span></a>
|
||
</span><span id="ks_test-737"><a href="#ks_test-737"><span class="linenos">737</span></a> <span class="n">p_values</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">p_value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">obs_list</span><span class="p">]</span>
|
||
</span><span id="ks_test-738"><a href="#ks_test-738"><span class="linenos">738</span></a>
|
||
</span><span id="ks_test-739"><a href="#ks_test-739"><span class="linenos">739</span></a> <span class="n">bins</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">p_values</span><span class="p">)</span>
|
||
</span><span id="ks_test-740"><a href="#ks_test-740"><span class="linenos">740</span></a> <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.001</span><span class="p">,</span> <span class="mf">0.001</span><span class="p">)</span>
|
||
</span><span id="ks_test-741"><a href="#ks_test-741"><span class="linenos">741</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="s1">'k'</span><span class="p">,</span> <span class="n">zorder</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="ks_test-742"><a href="#ks_test-742"><span class="linenos">742</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="ks_test-743"><a href="#ks_test-743"><span class="linenos">743</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||
</span><span id="ks_test-744"><a href="#ks_test-744"><span class="linenos">744</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s1">'p-value'</span><span class="p">)</span>
|
||
</span><span id="ks_test-745"><a href="#ks_test-745"><span class="linenos">745</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s1">'Cumulative probability'</span><span class="p">)</span>
|
||
</span><span id="ks_test-746"><a href="#ks_test-746"><span class="linenos">746</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">bins</span><span class="p">)</span> <span class="o">+</span> <span class="s1">' p-values'</span><span class="p">)</span>
|
||
</span><span id="ks_test-747"><a href="#ks_test-747"><span class="linenos">747</span></a>
|
||
</span><span id="ks_test-748"><a href="#ks_test-748"><span class="linenos">748</span></a> <span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">bins</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">(</span><span class="n">bins</span><span class="p">)</span>
|
||
</span><span id="ks_test-749"><a href="#ks_test-749"><span class="linenos">749</span></a> <span class="n">Xs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">p_values</span><span class="p">)</span>
|
||
</span><span id="ks_test-750"><a href="#ks_test-750"><span class="linenos">750</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">step</span><span class="p">(</span><span class="n">Xs</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
|
||
</span><span id="ks_test-751"><a href="#ks_test-751"><span class="linenos">751</span></a> <span class="n">diffs</span> <span class="o">=</span> <span class="n">n</span> <span class="o">-</span> <span class="n">Xs</span>
|
||
</span><span id="ks_test-752"><a href="#ks_test-752"><span class="linenos">752</span></a> <span class="n">loc_max_diff</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argmax</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">diffs</span><span class="p">))</span>
|
||
</span><span id="ks_test-753"><a href="#ks_test-753"><span class="linenos">753</span></a> <span class="n">loc</span> <span class="o">=</span> <span class="n">Xs</span><span class="p">[</span><span class="n">loc_max_diff</span><span class="p">]</span>
|
||
</span><span id="ks_test-754"><a href="#ks_test-754"><span class="linenos">754</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s1">''</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">loc</span><span class="p">),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="n">loc</span><span class="p">,</span> <span class="n">loc</span> <span class="o">+</span> <span class="n">diffs</span><span class="p">[</span><span class="n">loc_max_diff</span><span class="p">]),</span> <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">arrowstyle</span><span class="o">=</span><span class="s1">'<->'</span><span class="p">,</span> <span class="n">shrinkA</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">shrinkB</span><span class="o">=</span><span class="mi">0</span><span class="p">))</span>
|
||
</span><span id="ks_test-755"><a href="#ks_test-755"><span class="linenos">755</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||
</span><span id="ks_test-756"><a href="#ks_test-756"><span class="linenos">756</span></a>
|
||
</span><span id="ks_test-757"><a href="#ks_test-757"><span class="linenos">757</span></a> <span class="nb">print</span><span class="p">(</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">kstest</span><span class="p">(</span><span class="n">p_values</span><span class="p">,</span> <span class="s1">'uniform'</span><span class="p">))</span>
|
||
</span></pre></div>
|
||
|
||
|
||
<div class="docstring"><p>Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</p>
|
||
|
||
<h6 id="parameters">Parameters</h6>
|
||
|
||
<ul>
|
||
<li><strong>objects</strong> (list):
|
||
List of fit results to include in the analysis (optional).</li>
|
||
</ul>
|
||
</div>
|
||
|
||
|
||
</section>
|
||
</main>
|
||
<script>
|
||
function escapeHTML(html) {
|
||
return document.createElement('div').appendChild(document.createTextNode(html)).parentNode.innerHTML;
|
||
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|
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||
const originalContent = document.querySelector("main.pdoc");
|
||
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|
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|
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|
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|
||
} else {
|
||
elem = originalContent;
|
||
}
|
||
if (currentContent !== elem) {
|
||
currentContent.replaceWith(elem);
|
||
currentContent = elem;
|
||
}
|
||
}
|
||
|
||
function getSearchTerm() {
|
||
return (new URL(window.location)).searchParams.get("search");
|
||
}
|
||
|
||
const searchBox = document.querySelector(".pdoc input[type=search]");
|
||
searchBox.addEventListener("input", function () {
|
||
let url = new URL(window.location);
|
||
if (searchBox.value.trim()) {
|
||
url.hash = "";
|
||
url.searchParams.set("search", searchBox.value);
|
||
} else {
|
||
url.searchParams.delete("search");
|
||
}
|
||
history.replaceState("", "", url.toString());
|
||
onInput();
|
||
});
|
||
window.addEventListener("popstate", onInput);
|
||
|
||
|
||
let search, searchErr;
|
||
|
||
async function initialize() {
|
||
try {
|
||
search = await new Promise((resolve, reject) => {
|
||
const script = document.createElement("script");
|
||
script.type = "text/javascript";
|
||
script.async = true;
|
||
script.onload = () => resolve(window.pdocSearch);
|
||
script.onerror = (e) => reject(e);
|
||
script.src = "../search.js";
|
||
document.getElementsByTagName("head")[0].appendChild(script);
|
||
});
|
||
} catch (e) {
|
||
console.error("Cannot fetch pdoc search index");
|
||
searchErr = "Cannot fetch search index.";
|
||
}
|
||
onInput();
|
||
|
||
document.querySelector("nav.pdoc").addEventListener("click", e => {
|
||
if (e.target.hash) {
|
||
searchBox.value = "";
|
||
searchBox.dispatchEvent(new Event("input"));
|
||
}
|
||
});
|
||
}
|
||
|
||
function onInput() {
|
||
setContent((() => {
|
||
const term = getSearchTerm();
|
||
if (!term) {
|
||
return null
|
||
}
|
||
if (searchErr) {
|
||
return `<h3>Error: ${searchErr}</h3>`
|
||
}
|
||
if (!search) {
|
||
return "<h3>Searching...</h3>"
|
||
}
|
||
|
||
window.scrollTo({top: 0, left: 0, behavior: 'auto'});
|
||
|
||
const results = search(term);
|
||
|
||
let html;
|
||
if (results.length === 0) {
|
||
html = `No search results for '${escapeHTML(term)}'.`
|
||
} else {
|
||
html = `<h4>${results.length} search result${results.length > 1 ? "s" : ""} for '${escapeHTML(term)}'.</h4>`;
|
||
}
|
||
for (let result of results.slice(0, 10)) {
|
||
let doc = result.doc;
|
||
let url = `../${doc.modulename.replaceAll(".", "/")}.html`;
|
||
if (doc.qualname) {
|
||
url += `#${doc.qualname}`;
|
||
}
|
||
|
||
let heading;
|
||
switch (result.doc.type) {
|
||
case "function":
|
||
if (doc.fullname.endsWith(".__init__")) {
|
||
heading = `<span class="name">${doc.fullname.replace(/\.__init__$/, "")}</span>${doc.signature}`;
|
||
} else {
|
||
heading = `<span class="def">${doc.funcdef}</span> <span class="name">${doc.fullname}</span>${doc.signature}`;
|
||
}
|
||
break;
|
||
case "class":
|
||
heading = `<span class="def">class</span> <span class="name">${doc.fullname}</span>`;
|
||
if (doc.bases)
|
||
heading += `<wbr>(<span class="base">${doc.bases}</span>)`;
|
||
heading += `:`;
|
||
break;
|
||
case "variable":
|
||
heading = `<span class="name">${doc.fullname}</span>`;
|
||
if (doc.annotation)
|
||
heading += `<span class="annotation">${doc.annotation}</span>`;
|
||
if (doc.default_value)
|
||
heading += `<span class="default_value">${doc.default_value}</span>`;
|
||
break;
|
||
default:
|
||
heading = `<span class="name">${doc.fullname}</span>`;
|
||
break;
|
||
}
|
||
html += `
|
||
<section class="search-result">
|
||
<a href="${url}" class="attr ${doc.type}">${heading}</a>
|
||
<div class="docstring">${doc.doc}</div>
|
||
</section>
|
||
`;
|
||
|
||
}
|
||
return html;
|
||
})());
|
||
}
|
||
|
||
if (getSearchTerm()) {
|
||
initialize();
|
||
searchBox.value = getSearchTerm();
|
||
onInput();
|
||
} else {
|
||
searchBox.addEventListener("focus", initialize, {once: true});
|
||
}
|
||
|
||
searchBox.addEventListener("keydown", e => {
|
||
if (["ArrowDown", "ArrowUp", "Enter"].includes(e.key)) {
|
||
let focused = currentContent.querySelector(".search-result.focused");
|
||
if (!focused) {
|
||
currentContent.querySelector(".search-result").classList.add("focused");
|
||
} else if (
|
||
e.key === "ArrowDown"
|
||
&& focused.nextElementSibling
|
||
&& focused.nextElementSibling.classList.contains("search-result")
|
||
) {
|
||
focused.classList.remove("focused");
|
||
focused.nextElementSibling.classList.add("focused");
|
||
focused.nextElementSibling.scrollIntoView({
|
||
behavior: "smooth",
|
||
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> |