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Documentation updated
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fjosw
parent
e4391b707a
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2 changed files with 213 additions and 201 deletions
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@ -62,18 +62,18 @@
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<li>
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<a class="function" href="#least_squares">least_squares</a>
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</li>
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<li>
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<a class="function" href="#standard_fit">standard_fit</a>
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</li>
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<li>
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<a class="function" href="#odr_fit">odr_fit</a>
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</li>
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<li>
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<a class="function" href="#total_least_squares">total_least_squares</a>
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</li>
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<li>
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<a class="function" href="#prior_fit">prior_fit</a>
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</li>
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<li>
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<a class="function" href="#standard_fit">standard_fit</a>
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</li>
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<li>
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<a class="function" href="#odr_fit">odr_fit</a>
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</li>
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<li>
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<a class="function" href="#fit_lin">fit_lin</a>
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</li>
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@ -227,149 +227,8 @@
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<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>
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<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>
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<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
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<span class="k">return</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">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>
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<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>
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<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
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<span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
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<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>
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<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>
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<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>
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<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>
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<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unkown format for x values'</span><span class="p">)</span>
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<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>
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<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>
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<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">25</span><span class="p">):</span>
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<span class="k">try</span><span class="p">:</span>
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<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>
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<span class="k">except</span><span class="p">:</span>
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<span class="k">pass</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="k">break</span>
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<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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<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">'parameters'</span><span class="p">)</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="k">else</span><span class="p">:</span>
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<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>
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<span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
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<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>
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<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>
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<span class="k">return</span> <span class="n">chisq</span>
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<span class="k">if</span> <span class="s1">'method'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
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<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>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'Method:'</span><span class="p">,</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">))</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">)</span> <span class="o">==</span> <span class="s1">'migrad'</span><span class="p">:</span>
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<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>
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<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">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>
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<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">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>
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<span class="n">chisquare</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span>
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<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>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'Levenberg-Marquardt'</span>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: Levenberg-Marquardt'</span><span class="p">)</span>
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<span class="k">def</span> <span class="nf">chisqfunc_residuals</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
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<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>
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<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>
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<span class="k">return</span> <span class="n">chisq</span>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="k">else</span><span class="p">:</span>
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<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>
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<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>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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<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>
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<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>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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<span class="n">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>
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<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
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<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>
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<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">inv</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>
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<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>
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<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>
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<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
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<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
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|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">))</span>
|
||||
|
||||
<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 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 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 class="k">return</span> <span class="n">chisq</span>
|
||||
|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)))</span>
|
||||
|
||||
<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 class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
||||
<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="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="n">pseudo_Obs</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">i</span><span class="p">],</span> <span class="mf">0.0</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">names</span><span class="p">[</span><span class="mi">0</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">shape</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">names</span><span class="p">[</span><span class="mi">0</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="p">[</span><span class="mi">0</span><span class="p">]</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 class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||||
|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
|
||||
<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 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 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 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 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 class="k">return</span> <span class="n">output</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">odr_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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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 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 class="sd">"""Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
||||
<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 class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
|
|
@ -380,21 +239,24 @@
|
|||
<span class="sd"> func : object</span>
|
||||
<span class="sd"> func has to be of the form</span>
|
||||
|
||||
<span class="sd"> ```python</span>
|
||||
<span class="sd"> def func(a, x):</span>
|
||||
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||||
<span class="sd"> return y</span>
|
||||
<span class="sd"> ```</span>
|
||||
|
||||
<span class="sd"> For multiple x values func can be of the form</span>
|
||||
|
||||
<span class="sd"> ```python</span>
|
||||
<span class="sd"> def func(a, x):</span>
|
||||
<span class="sd"> (x1, x2) = x</span>
|
||||
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||||
<span class="sd"> ```</span>
|
||||
|
||||
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||||
<span class="sd"> will not work.</span>
|
||||
<span class="sd"> silent : bool, optional</span>
|
||||
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
||||
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||||
<span class="sd"> initial_guess : list</span>
|
||||
<span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
||||
<span class="sd"> fits with many parameters.</span>
|
||||
|
|
@ -403,7 +265,9 @@
|
|||
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
||||
<span class="sd"> This can take a while as the full correlation matrix</span>
|
||||
<span class="sd"> has to be calculated (default False).</span>
|
||||
<span class="sd"> """</span>
|
||||
|
||||
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||||
<span class="sd"> '''</span>
|
||||
|
||||
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||||
|
||||
|
|
@ -657,6 +521,147 @@
|
|||
<span class="k">return</span> <span class="n">output</span>
|
||||
|
||||
|
||||
<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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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 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 class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||||
|
||||
<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 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 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 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 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 class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unkown format for x values'</span><span class="p">)</span>
|
||||
|
||||
<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 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 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">25</span><span class="p">):</span>
|
||||
<span class="k">try</span><span class="p">:</span>
|
||||
<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 class="k">except</span><span class="p">:</span>
|
||||
<span class="k">pass</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">break</span>
|
||||
|
||||
<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
||||
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||||
<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">'parameters'</span><span class="p">)</span>
|
||||
|
||||
<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 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 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 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 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 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 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 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 class="k">else</span><span class="p">:</span>
|
||||
<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 class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
||||
<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 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="k">return</span> <span class="n">chisq</span>
|
||||
|
||||
<span class="k">if</span> <span class="s1">'method'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
||||
<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="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method:'</span><span class="p">,</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">))</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">)</span> <span class="o">==</span> <span class="s1">'migrad'</span><span class="p">:</span>
|
||||
<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">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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<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">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">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 class="n">chisquare</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span>
|
||||
|
||||
<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 class="k">else</span><span class="p">:</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="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: Levenberg-Marquardt'</span><span class="p">)</span>
|
||||
|
||||
<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 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 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 class="k">return</span> <span class="n">chisq</span>
|
||||
|
||||
<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 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 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 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 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 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 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 class="k">else</span><span class="p">:</span>
|
||||
<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 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 class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||||
<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 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 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 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 class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<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 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">inv</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 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 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 class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
||||
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
||||
|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">))</span>
|
||||
|
||||
<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 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 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 class="k">return</span> <span class="n">chisq</span>
|
||||
|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)))</span>
|
||||
|
||||
<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 class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
||||
<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="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="n">pseudo_Obs</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">i</span><span class="p">],</span> <span class="mf">0.0</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">names</span><span class="p">[</span><span class="mi">0</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">shape</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">names</span><span class="p">[</span><span class="mi">0</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="p">[</span><span class="mi">0</span><span class="p">]</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 class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
||||
|
||||
<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">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
|
||||
<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 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 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 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 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 class="k">return</span> <span class="n">output</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">odr_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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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 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 class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||||
|
||||
|
|
@ -1152,46 +1157,6 @@ has to be calculated (default False).</li>
|
|||
</div>
|
||||
|
||||
|
||||
</section>
|
||||
<section id="standard_fit">
|
||||
<div class="attr function"><a class="headerlink" href="#standard_fit">#  </a>
|
||||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">standard_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
|
||||
|
||||
</section>
|
||||
<section id="odr_fit">
|
||||
<div class="attr function"><a class="headerlink" href="#odr_fit">#  </a>
|
||||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">odr_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">odr_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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
|
||||
|
||||
</section>
|
||||
<section id="total_least_squares">
|
||||
<div class="attr function"><a class="headerlink" href="#total_least_squares">#  </a>
|
||||
|
|
@ -1204,7 +1169,7 @@ has to be calculated (default False).</li>
|
|||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><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 class="sd">"""Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
||||
<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 class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
|
|
@ -1215,21 +1180,24 @@ has to be calculated (default False).</li>
|
|||
<span class="sd"> func : object</span>
|
||||
<span class="sd"> func has to be of the form</span>
|
||||
|
||||
<span class="sd"> ```python</span>
|
||||
<span class="sd"> def func(a, x):</span>
|
||||
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
||||
<span class="sd"> return y</span>
|
||||
<span class="sd"> ```</span>
|
||||
|
||||
<span class="sd"> For multiple x values func can be of the form</span>
|
||||
|
||||
<span class="sd"> ```python</span>
|
||||
<span class="sd"> def func(a, x):</span>
|
||||
<span class="sd"> (x1, x2) = x</span>
|
||||
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
||||
<span class="sd"> ```</span>
|
||||
|
||||
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
||||
<span class="sd"> will not work.</span>
|
||||
<span class="sd"> silent : bool, optional</span>
|
||||
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
||||
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||||
<span class="sd"> initial_guess : list</span>
|
||||
<span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
||||
<span class="sd"> fits with many parameters.</span>
|
||||
|
|
@ -1238,7 +1206,9 @@ has to be calculated (default False).</li>
|
|||
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
||||
<span class="sd"> This can take a while as the full correlation matrix</span>
|
||||
<span class="sd"> has to be calculated (default False).</span>
|
||||
<span class="sd"> """</span>
|
||||
|
||||
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
||||
<span class="sd"> '''</span>
|
||||
|
||||
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
||||
|
||||
|
|
@ -1382,21 +1352,22 @@ 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>
|
||||
|
||||
<p>def func(a, x):
|
||||
y = a[0] + a[1] * x + a[2] * anp.sinh(x)
|
||||
return y</p>
|
||||
<div class="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="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 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>
|
||||
<span class="k">return</span> <span class="n">y</span>
|
||||
</code></pre></div>
|
||||
|
||||
<p>For multiple x values func can be of the form</p>
|
||||
|
||||
<p>def func(a, x):
|
||||
(x1, x2) = x
|
||||
return a[0] * x1 ** 2 + a[1] * x2</p>
|
||||
<div class="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>Based on the orthogonal distance regression module of scipy</strong></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>
|
||||
|
|
@ -1405,6 +1376,7 @@ 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>
|
||||
<li><strong>Based on the orthogonal distance regression module of scipy</strong></li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
|
|
@ -1429,6 +1401,46 @@ has to be calculated (default False).</li>
|
|||
|
||||
|
||||
|
||||
</section>
|
||||
<section id="standard_fit">
|
||||
<div class="attr function"><a class="headerlink" href="#standard_fit">#  </a>
|
||||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">standard_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
|
||||
|
||||
</section>
|
||||
<section id="odr_fit">
|
||||
<div class="attr function"><a class="headerlink" href="#odr_fit">#  </a>
|
||||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">odr_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">odr_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 class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
||||
<span class="k">return</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">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>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
|
||||
|
||||
</section>
|
||||
<section id="fit_lin">
|
||||
<div class="attr function"><a class="headerlink" href="#fit_lin">#  </a>
|
||||
|
|
|
|||
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