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</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a> <span class="k">else</span><span class="p">:</span>
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</span><span id="L-581"><a href="#L-581"><span class="linenos">581</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>
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</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a>
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</span><span id="L-583"><a href="#L-583"><span class="linenos">583</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>
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</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a> <span class="n">corr</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y_all</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>
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</span><span id="L-585"><a href="#L-585"><span class="linenos">585</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>
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</span><span id="L-586"><a href="#L-586"><span class="linenos">586</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>
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</span><span id="L-587"><a href="#L-587"><span class="linenos">587</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>
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</span><span id="L-588"><a href="#L-588"><span class="linenos">588</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>
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</span><span id="L-589"><a href="#L-589"><span class="linenos">589</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>
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</span><span id="L-590"><a href="#L-590"><span class="linenos">590</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>
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</span><span id="L-591"><a href="#L-591"><span class="linenos">591</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>
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</span><span id="L-592"><a href="#L-592"><span class="linenos">592</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>
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</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a>
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</span><span id="L-594"><a href="#L-594"><span class="linenos">594</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>
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</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a> <span class="n">model</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">](</span><span class="n">p</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">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
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</span><span id="L-596"><a href="#L-596"><span class="linenos">596</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>
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</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a> <span class="k">return</span> <span class="n">chisq</span>
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</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a>
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</span><span id="L-599"><a href="#L-599"><span class="linenos">599</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>
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</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a> <span class="n">func_list</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">funcd</span><span class="p">[</span><span class="n">k</span><span class="p">]]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
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</span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">func_list</span><span class="p">[</span><span class="n">i</span><span class="p">](</span><span class="n">p</span><span class="p">,</span> <span class="n">x_all</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x_all</span><span class="p">))])</span>
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</span><span id="L-602"><a href="#L-602"><span class="linenos">602</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>
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</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a> <span class="k">return</span> <span class="n">chisq</span>
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</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a> <span class="k">def</span> <span class="nf">general_chisqfunc_uncorr</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">ivars</span><span class="p">):</span>
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</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">anp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">](</span><span class="n">p</span><span class="p">,</span> <span class="n">anp</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
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</span><span id="L-585"><a href="#L-585"><span class="linenos">585</span></a> <span class="k">return</span> <span class="p">((</span><span class="n">ivars</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><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a>
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</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a> <span class="k">def</span> <span class="nf">chisqfunc_uncorr</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
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</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a> <span class="k">return</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">general_chisqfunc_uncorr</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
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</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a>
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</span><span id="L-590"><a href="#L-590"><span class="linenos">590</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>
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</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a> <span class="n">corr</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y_all</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>
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</span><span id="L-592"><a href="#L-592"><span class="linenos">592</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>
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</span><span id="L-593"><a href="#L-593"><span class="linenos">593</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>
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</span><span id="L-594"><a href="#L-594"><span class="linenos">594</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>
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</span><span id="L-595"><a href="#L-595"><span class="linenos">595</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>
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</span><span id="L-596"><a href="#L-596"><span class="linenos">596</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>
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</span><span id="L-597"><a href="#L-597"><span class="linenos">597</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>
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</span><span id="L-598"><a href="#L-598"><span class="linenos">598</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>
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</span><span id="L-599"><a href="#L-599"><span class="linenos">599</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>
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</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>
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</span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a> <span class="k">def</span> <span class="nf">general_chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">ivars</span><span class="p">):</span>
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</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">concatenate</span><span class="p">([</span><span class="n">anp</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">](</span><span class="n">p</span><span class="p">,</span> <span class="n">anp</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
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</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a> <span class="k">return</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">ivars</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span>
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</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a>
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||||
</span><span id="L-605"><a href="#L-605"><span class="linenos">605</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>
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||||
</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
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</span><span id="L-607"><a href="#L-607"><span class="linenos">607</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>
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</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a>
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||||
</span><span id="L-609"><a href="#L-609"><span class="linenos">609</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>
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</span><span id="L-610"><a href="#L-610"><span class="linenos">610</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>
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</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a> <span class="n">tolerance</span> <span class="o">=</span> <span class="mf">1e-4</span> <span class="c1"># default value of 1e-1 set by iminuit can be problematic</span>
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</span><span id="L-612"><a href="#L-612"><span class="linenos">612</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>
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</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a> <span class="n">tolerance</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>
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</span><span id="L-614"><a href="#L-614"><span class="linenos">614</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="n">tolerance</span><span class="p">)</span> <span class="c1"># Stopping criterion 0.002 * tol * errordef</span>
|
||||
</span><span id="L-615"><a href="#L-615"><span class="linenos">615</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>
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||||
</span><span id="L-616"><a href="#L-616"><span class="linenos">616</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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-617"><a href="#L-617"><span class="linenos">617</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-618"><a href="#L-618"><span class="linenos">618</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a> <span class="n">tolerance</span> <span class="o">=</span> <span class="mf">1e-12</span>
|
||||
</span><span id="L-620"><a href="#L-620"><span class="linenos">620</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-621"><a href="#L-621"><span class="linenos">621</span></a> <span class="n">tolerance</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-622"><a href="#L-622"><span class="linenos">622</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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-623"><a href="#L-623"><span class="linenos">623</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-624"><a href="#L-624"><span class="linenos">624</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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-625"><a href="#L-625"><span class="linenos">625</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-626"><a href="#L-626"><span class="linenos">626</span></a>
|
||||
</span><span id="L-627"><a href="#L-627"><span class="linenos">627</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-628"><a href="#L-628"><span class="linenos">628</span></a>
|
||||
</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-630"><a href="#L-630"><span class="linenos">630</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-631"><a href="#L-631"><span class="linenos">631</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-632"><a href="#L-632"><span class="linenos">632</span></a> <span class="n">model</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">](</span><span class="n">p</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">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
|
||||
</span><span id="L-633"><a href="#L-633"><span class="linenos">633</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-634"><a href="#L-634"><span class="linenos">634</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||||
</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a>
|
||||
</span><span id="L-636"><a href="#L-636"><span class="linenos">636</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-637"><a href="#L-637"><span class="linenos">637</span></a> <span class="n">model</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">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">](</span><span class="n">p</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">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])))</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
|
||||
</span><span id="L-638"><a href="#L-638"><span class="linenos">638</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-639"><a href="#L-639"><span class="linenos">639</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||||
</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a>
|
||||
</span><span id="L-641"><a href="#L-641"><span class="linenos">641</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-642"><a href="#L-642"><span class="linenos">642</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'tol cannot be set for Levenberg-Marquardt'</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 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-645"><a href="#L-645"><span class="linenos">645</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-646"><a href="#L-646"><span class="linenos">646</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-605"><a href="#L-605"><span class="linenos">605</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-606"><a href="#L-606"><span class="linenos">606</span></a> <span class="k">return</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">general_chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||||
</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a> <span class="n">general_chisqfunc</span> <span class="o">=</span> <span class="n">general_chisqfunc_uncorr</span>
|
||||
</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a> <span class="n">chisqfunc</span> <span class="o">=</span> <span class="n">chisqfunc_uncorr</span>
|
||||
</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a>
|
||||
</span><span id="L-611"><a href="#L-611"><span class="linenos">611</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-612"><a href="#L-612"><span class="linenos">612</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-613"><a href="#L-613"><span class="linenos">613</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-614"><a href="#L-614"><span class="linenos">614</span></a>
|
||||
</span><span id="L-615"><a href="#L-615"><span class="linenos">615</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-616"><a href="#L-616"><span class="linenos">616</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-617"><a href="#L-617"><span class="linenos">617</span></a> <span class="n">tolerance</span> <span class="o">=</span> <span class="mf">1e-4</span> <span class="c1"># default value of 1e-1 set by iminuit can be problematic</span>
|
||||
</span><span id="L-618"><a href="#L-618"><span class="linenos">618</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-619"><a href="#L-619"><span class="linenos">619</span></a> <span class="n">tolerance</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-620"><a href="#L-620"><span class="linenos">620</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_uncorr</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="n">tolerance</span><span class="p">)</span> <span class="c1"># Stopping criterion 0.002 * tol * errordef</span>
|
||||
</span><span id="L-621"><a href="#L-621"><span class="linenos">621</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-622"><a href="#L-622"><span class="linenos">622</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">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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-623"><a href="#L-623"><span class="linenos">623</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-624"><a href="#L-624"><span class="linenos">624</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a> <span class="n">tolerance</span> <span class="o">=</span> <span class="mf">1e-12</span>
|
||||
</span><span id="L-626"><a href="#L-626"><span class="linenos">626</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-627"><a href="#L-627"><span class="linenos">627</span></a> <span class="n">tolerance</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-628"><a href="#L-628"><span class="linenos">628</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_uncorr</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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-629"><a href="#L-629"><span class="linenos">629</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-630"><a href="#L-630"><span class="linenos">630</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">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="n">tolerance</span><span class="p">)</span>
|
||||
</span><span id="L-631"><a href="#L-631"><span class="linenos">631</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-632"><a href="#L-632"><span class="linenos">632</span></a>
|
||||
</span><span id="L-633"><a href="#L-633"><span class="linenos">633</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-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">else</span><span class="p">:</span>
|
||||
</span><span id="L-636"><a href="#L-636"><span class="linenos">636</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-637"><a href="#L-637"><span class="linenos">637</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'tol cannot be set for Levenberg-Marquardt'</span><span class="p">)</span>
|
||||
</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a>
|
||||
</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a> <span class="k">def</span> <span class="nf">chisqfunc_residuals_uncorr</span><span class="p">(</span><span class="n">p</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">general_chisqfunc_uncorr</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)</span>
|
||||
</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a>
|
||||
</span><span id="L-642"><a href="#L-642"><span class="linenos">642</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_uncorr</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-643"><a href="#L-643"><span class="linenos">643</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-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">chisqfunc_residuals</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="k">return</span> <span class="n">general_chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)</span>
|
||||
</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a>
|
||||
</span><span id="L-648"><a href="#L-648"><span class="linenos">648</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-649"><a href="#L-649"><span class="linenos">649</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-650"><a href="#L-650"><span class="linenos">650</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-651"><a href="#L-651"><span class="linenos">651</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-652"><a href="#L-652"><span class="linenos">652</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-653"><a href="#L-653"><span class="linenos">653</span></a>
|
||||
</span><span id="L-654"><a href="#L-654"><span class="linenos">654</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-655"><a href="#L-655"><span class="linenos">655</span></a>
|
||||
</span><span id="L-656"><a href="#L-656"><span class="linenos">656</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-657"><a href="#L-657"><span class="linenos">657</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-658"><a href="#L-658"><span class="linenos">658</span></a>
|
||||
</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a> <span class="k">if</span> <span class="n">x_all</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-660"><a href="#L-660"><span class="linenos">660</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-661"><a href="#L-661"><span class="linenos">661</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x_all</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-662"><a href="#L-662"><span class="linenos">662</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">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">/</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span>
|
||||
</span><span id="L-663"><a href="#L-663"><span class="linenos">663</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-664"><a href="#L-664"><span class="linenos">664</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-665"><a href="#L-665"><span class="linenos">665</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-666"><a href="#L-666"><span class="linenos">666</span></a>
|
||||
</span><span id="L-667"><a href="#L-667"><span class="linenos">667</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-668"><a href="#L-668"><span class="linenos">668</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-669"><a href="#L-669"><span class="linenos">669</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-670"><a href="#L-670"><span class="linenos">670</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-671"><a href="#L-671"><span class="linenos">671</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'fit parameters'</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><span id="L-672"><a href="#L-672"><span class="linenos">672</span></a>
|
||||
</span><span id="L-673"><a href="#L-673"><span class="linenos">673</span></a> <span class="k">def</span> <span class="nf">prepare_hat_matrix</span><span class="p">():</span>
|
||||
</span><span id="L-674"><a href="#L-674"><span class="linenos">674</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-675"><a href="#L-675"><span class="linenos">675</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-676"><a href="#L-676"><span class="linenos">676</span></a> <span class="n">x_array</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">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
|
||||
</span><span id="L-677"><a href="#L-677"><span class="linenos">677</span></a> <span class="k">if</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x_array</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">):</span>
|
||||
</span><span id="L-678"><a href="#L-678"><span class="linenos">678</span></a> <span class="n">hat_vector</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</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_array</span><span class="p">))</span>
|
||||
</span><span id="L-679"><a href="#L-679"><span class="linenos">679</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="p">[</span><span class="n">item</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="n">hat_vector</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">]</span>
|
||||
</span><span id="L-680"><a href="#L-680"><span class="linenos">680</span></a> <span class="k">return</span> <span class="n">hat_vector</span>
|
||||
</span><span id="L-681"><a href="#L-681"><span class="linenos">681</span></a>
|
||||
</span><span id="L-682"><a href="#L-682"><span class="linenos">682</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-683"><a href="#L-683"><span class="linenos">683</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-684"><a href="#L-684"><span class="linenos">684</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-685"><a href="#L-685"><span class="linenos">685</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y_all</span><span class="p">)</span>
|
||||
</span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="n">prepare_hat_matrix</span><span class="p">()</span>
|
||||
</span><span id="L-687"><a href="#L-687"><span class="linenos">687</span></a> <span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">hat_vector</span>
|
||||
</span><span id="L-688"><a href="#L-688"><span class="linenos">688</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-689"><a href="#L-689"><span class="linenos">689</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_all</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-690"><a href="#L-690"><span class="linenos">690</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">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
||||
</span><span id="L-691"><a href="#L-691"><span class="linenos">691</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-692"><a href="#L-692"><span class="linenos">692</span></a> <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><span id="L-693"><a href="#L-693"><span class="linenos">693</span></a>
|
||||
</span><span id="L-694"><a href="#L-694"><span class="linenos">694</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-695"><a href="#L-695"><span class="linenos">695</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-696"><a href="#L-696"><span class="linenos">696</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-697"><a href="#L-697"><span class="linenos">697</span></a>
|
||||
</span><span id="L-698"><a href="#L-698"><span class="linenos">698</span></a> <span class="k">try</span><span class="p">:</span>
|
||||
</span><span id="L-699"><a href="#L-699"><span class="linenos">699</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-700"><a href="#L-700"><span class="linenos">700</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">hessian</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-701"><a href="#L-701"><span class="linenos">701</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-702"><a href="#L-702"><span class="linenos">702</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">hessian</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-703"><a href="#L-703"><span class="linenos">703</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||||
</span><span id="L-704"><a href="#L-704"><span class="linenos">704</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-705"><a href="#L-705"><span class="linenos">705</span></a>
|
||||
</span><span id="L-706"><a href="#L-706"><span class="linenos">706</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-707"><a href="#L-707"><span class="linenos">707</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-708"><a href="#L-708"><span class="linenos">708</span></a> <span class="n">func_list</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">funcd</span><span class="p">[</span><span class="n">k</span><span class="p">]]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
|
||||
</span><span id="L-709"><a href="#L-709"><span class="linenos">709</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">func_list</span><span class="p">[</span><span class="n">i</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_all</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x_all</span><span class="p">))])</span>
|
||||
</span><span id="L-710"><a href="#L-710"><span class="linenos">710</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-711"><a href="#L-711"><span class="linenos">711</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||||
</span><span id="L-712"><a href="#L-712"><span class="linenos">712</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-713"><a href="#L-713"><span class="linenos">713</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-714"><a href="#L-714"><span class="linenos">714</span></a> <span class="n">func_list</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">funcd</span><span class="p">[</span><span class="n">k</span><span class="p">]]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">k</span><span class="p">])</span> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">])</span>
|
||||
</span><span id="L-715"><a href="#L-715"><span class="linenos">715</span></a> <span class="n">model</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">func_list</span><span class="p">[</span><span class="n">i</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_all</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x_all</span><span class="p">))])</span>
|
||||
</span><span id="L-716"><a href="#L-716"><span class="linenos">716</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-717"><a href="#L-717"><span class="linenos">717</span></a> <span class="k">return</span> <span class="n">chisq</span>
|
||||
</span><span id="L-648"><a href="#L-648"><span class="linenos">648</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">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-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">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-651"><a href="#L-651"><span class="linenos">651</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-652"><a href="#L-652"><span class="linenos">652</span></a>
|
||||
</span><span id="L-653"><a href="#L-653"><span class="linenos">653</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-654"><a href="#L-654"><span class="linenos">654</span></a>
|
||||
</span><span id="L-655"><a href="#L-655"><span class="linenos">655</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-656"><a href="#L-656"><span class="linenos">656</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-657"><a href="#L-657"><span class="linenos">657</span></a>
|
||||
</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a> <span class="k">if</span> <span class="n">x_all</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-659"><a href="#L-659"><span class="linenos">659</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-660"><a href="#L-660"><span class="linenos">660</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x_all</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-661"><a href="#L-661"><span class="linenos">661</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">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">/</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span>
|
||||
</span><span id="L-662"><a href="#L-662"><span class="linenos">662</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-663"><a href="#L-663"><span class="linenos">663</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-664"><a href="#L-664"><span class="linenos">664</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-665"><a href="#L-665"><span class="linenos">665</span></a>
|
||||
</span><span id="L-666"><a href="#L-666"><span class="linenos">666</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-667"><a href="#L-667"><span class="linenos">667</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-668"><a href="#L-668"><span class="linenos">668</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-669"><a href="#L-669"><span class="linenos">669</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-670"><a href="#L-670"><span class="linenos">670</span></a> <span class="nb">print</span><span class="p">(</span><span class="s1">'fit parameters'</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><span id="L-671"><a href="#L-671"><span class="linenos">671</span></a>
|
||||
</span><span id="L-672"><a href="#L-672"><span class="linenos">672</span></a> <span class="k">def</span> <span class="nf">prepare_hat_matrix</span><span class="p">():</span>
|
||||
</span><span id="L-673"><a href="#L-673"><span class="linenos">673</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-674"><a href="#L-674"><span class="linenos">674</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-675"><a href="#L-675"><span class="linenos">675</span></a> <span class="n">x_array</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">xd</span><span class="p">[</span><span class="n">key</span><span class="p">])</span>
|
||||
</span><span id="L-676"><a href="#L-676"><span class="linenos">676</span></a> <span class="k">if</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x_array</span><span class="p">)</span> <span class="o">!=</span> <span class="mi">0</span><span class="p">):</span>
|
||||
</span><span id="L-677"><a href="#L-677"><span class="linenos">677</span></a> <span class="n">hat_vector</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">funcd</span><span class="p">[</span><span class="n">key</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_array</span><span class="p">))</span>
|
||||
</span><span id="L-678"><a href="#L-678"><span class="linenos">678</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="p">[</span><span class="n">item</span> <span class="k">for</span> <span class="n">sublist</span> <span class="ow">in</span> <span class="n">hat_vector</span> <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">sublist</span><span class="p">]</span>
|
||||
</span><span id="L-679"><a href="#L-679"><span class="linenos">679</span></a> <span class="k">return</span> <span class="n">hat_vector</span>
|
||||
</span><span id="L-680"><a href="#L-680"><span class="linenos">680</span></a>
|
||||
</span><span id="L-681"><a href="#L-681"><span class="linenos">681</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-682"><a href="#L-682"><span class="linenos">682</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-683"><a href="#L-683"><span class="linenos">683</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-684"><a href="#L-684"><span class="linenos">684</span></a> <span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y_all</span><span class="p">)</span>
|
||||
</span><span id="L-685"><a href="#L-685"><span class="linenos">685</span></a> <span class="n">hat_vector</span> <span class="o">=</span> <span class="n">prepare_hat_matrix</span><span class="p">()</span>
|
||||
</span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a> <span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">hat_vector</span>
|
||||
</span><span id="L-687"><a href="#L-687"><span class="linenos">687</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-688"><a href="#L-688"><span class="linenos">688</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_all</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-689"><a href="#L-689"><span class="linenos">689</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">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
||||
</span><span id="L-690"><a href="#L-690"><span class="linenos">690</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-691"><a href="#L-691"><span class="linenos">691</span></a> <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><span id="L-692"><a href="#L-692"><span class="linenos">692</span></a>
|
||||
</span><span id="L-693"><a href="#L-693"><span class="linenos">693</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-694"><a href="#L-694"><span class="linenos">694</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-695"><a href="#L-695"><span class="linenos">695</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-696"><a href="#L-696"><span class="linenos">696</span></a>
|
||||
</span><span id="L-697"><a href="#L-697"><span class="linenos">697</span></a> <span class="k">try</span><span class="p">:</span>
|
||||
</span><span id="L-698"><a href="#L-698"><span class="linenos">698</span></a> <span class="n">hess</span> <span class="o">=</span> <span class="n">hessian</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-699"><a href="#L-699"><span class="linenos">699</span></a> <span class="k">except</span> <span class="ne">TypeError</span><span class="p">:</span>
|
||||
</span><span id="L-700"><a href="#L-700"><span class="linenos">700</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-701"><a href="#L-701"><span class="linenos">701</span></a>
|
||||
</span><span id="L-702"><a href="#L-702"><span class="linenos">702</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-703"><a href="#L-703"><span class="linenos">703</span></a> <span class="k">return</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">general_chisqfunc</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="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||||
</span><span id="L-704"><a href="#L-704"><span class="linenos">704</span></a>
|
||||
</span><span id="L-705"><a href="#L-705"><span class="linenos">705</span></a> <span class="n">jac_jac_y</span> <span class="o">=</span> <span class="n">hessian</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-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="c1"># Compute hess^{-1} @ jac_jac_y[:n_parms + m, n_parms + m:] using LAPACK dgesv</span>
|
||||
</span><span id="L-708"><a href="#L-708"><span class="linenos">708</span></a> <span class="k">try</span><span class="p">:</span>
|
||||
</span><span id="L-709"><a href="#L-709"><span class="linenos">709</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="p">,</span> <span class="n">n_parms</span><span class="p">:])</span>
|
||||
</span><span id="L-710"><a href="#L-710"><span class="linenos">710</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-711"><a href="#L-711"><span class="linenos">711</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-712"><a href="#L-712"><span class="linenos">712</span></a>
|
||||
</span><span id="L-713"><a href="#L-713"><span class="linenos">713</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-714"><a href="#L-714"><span class="linenos">714</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-715"><a href="#L-715"><span class="linenos">715</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_all</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_all</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_all</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">fitp</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_all</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_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||||
</span><span id="L-716"><a href="#L-716"><span class="linenos">716</span></a>
|
||||
</span><span id="L-717"><a href="#L-717"><span class="linenos">717</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-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="n">jac_jac_y</span> <span class="o">=</span> <span class="n">hessian</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-720"><a href="#L-720"><span class="linenos">720</span></a>
|
||||
</span><span id="L-721"><a href="#L-721"><span class="linenos">721</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-722"><a href="#L-722"><span class="linenos">722</span></a> <span class="k">try</span><span class="p">:</span>
|
||||
</span><span id="L-723"><a href="#L-723"><span class="linenos">723</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="p">,</span> <span class="n">n_parms</span><span class="p">:])</span>
|
||||
</span><span id="L-724"><a href="#L-724"><span class="linenos">724</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-725"><a href="#L-725"><span class="linenos">725</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-726"><a href="#L-726"><span class="linenos">726</span></a>
|
||||
</span><span id="L-727"><a href="#L-727"><span class="linenos">727</span></a> <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-728"><a href="#L-728"><span class="linenos">728</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-729"><a href="#L-729"><span class="linenos">729</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_all</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_all</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_all</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">fitp</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_all</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_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
||||
</span><span id="L-730"><a href="#L-730"><span class="linenos">730</span></a>
|
||||
</span><span id="L-731"><a href="#L-731"><span class="linenos">731</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-719"><a href="#L-719"><span class="linenos">719</span></a> <span class="c1"># Hotelling t-squared p-value for correlated fits.</span>
|
||||
</span><span id="L-720"><a href="#L-720"><span class="linenos">720</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-721"><a href="#L-721"><span class="linenos">721</span></a> <span class="n">n_cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x_all</span><span class="p">:</span> <span class="n">x_all</span><span class="o">.</span><span class="n">N</span><span class="p">)(</span><span class="n">y_all</span><span class="p">))</span>
|
||||
</span><span id="L-722"><a href="#L-722"><span class="linenos">722</span></a> <span class="n">output</span><span class="o">.</span><span class="n">t2_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">f</span><span class="o">.</span><span class="n">cdf</span><span class="p">((</span><span class="n">n_cov</span> <span class="o">-</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span> <span class="o">/</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="p">(</span><span class="n">n_cov</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare</span><span class="p">,</span>
|
||||
</span><span id="L-723"><a href="#L-723"><span class="linenos">723</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">,</span> <span class="n">n_cov</span> <span class="o">-</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span>
|
||||
</span><span id="L-724"><a href="#L-724"><span class="linenos">724</span></a>
|
||||
</span><span id="L-725"><a href="#L-725"><span class="linenos">725</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-726"><a href="#L-726"><span class="linenos">726</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-727"><a href="#L-727"><span class="linenos">727</span></a> <span class="n">residual_plot</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">yd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">result</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
|
||||
</span><span id="L-728"><a href="#L-728"><span class="linenos">728</span></a>
|
||||
</span><span id="L-729"><a href="#L-729"><span class="linenos">729</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-730"><a href="#L-730"><span class="linenos">730</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-731"><a href="#L-731"><span class="linenos">731</span></a> <span class="n">qqplot</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">yd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">result</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
|
||||
</span><span id="L-732"><a href="#L-732"><span class="linenos">732</span></a>
|
||||
</span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a> <span class="c1"># Hotelling t-squared p-value for correlated fits.</span>
|
||||
</span><span id="L-734"><a href="#L-734"><span class="linenos">734</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-735"><a href="#L-735"><span class="linenos">735</span></a> <span class="n">n_cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x_all</span><span class="p">:</span> <span class="n">x_all</span><span class="o">.</span><span class="n">N</span><span class="p">)(</span><span class="n">y_all</span><span class="p">))</span>
|
||||
</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a> <span class="n">output</span><span class="o">.</span><span class="n">t2_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">f</span><span class="o">.</span><span class="n">cdf</span><span class="p">((</span><span class="n">n_cov</span> <span class="o">-</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span> <span class="o">/</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="p">(</span><span class="n">n_cov</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare</span><span class="p">,</span>
|
||||
</span><span id="L-737"><a href="#L-737"><span class="linenos">737</span></a> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">,</span> <span class="n">n_cov</span> <span class="o">-</span> <span class="n">output</span><span class="o">.</span><span class="n">dof</span><span class="p">)</span>
|
||||
</span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a> <span class="k">return</span> <span class="n">output</span>
|
||||
</span><span id="L-734"><a href="#L-734"><span class="linenos">734</span></a>
|
||||
</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="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-737"><a href="#L-737"><span class="linenos">737</span></a><span class="w"> </span><span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||||
</span><span id="L-738"><a href="#L-738"><span class="linenos">738</span></a>
|
||||
</span><span id="L-739"><a href="#L-739"><span class="linenos">739</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-740"><a href="#L-740"><span class="linenos">740</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-741"><a href="#L-741"><span class="linenos">741</span></a> <span class="n">residual_plot</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">yd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">result</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
|
||||
</span><span id="L-742"><a href="#L-742"><span class="linenos">742</span></a>
|
||||
</span><span id="L-743"><a href="#L-743"><span class="linenos">743</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-744"><a href="#L-744"><span class="linenos">744</span></a> <span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">key_ls</span><span class="p">:</span>
|
||||
</span><span id="L-745"><a href="#L-745"><span class="linenos">745</span></a> <span class="n">qqplot</span><span class="p">(</span><span class="n">xd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">yd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">funcd</span><span class="p">[</span><span class="n">key</span><span class="p">],</span> <span class="n">result</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="n">key</span><span class="p">)</span>
|
||||
</span><span id="L-739"><a href="#L-739"><span class="linenos">739</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="L-740"><a href="#L-740"><span class="linenos">740</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="L-741"><a href="#L-741"><span class="linenos">741</span></a><span class="sd"> x : list</span>
|
||||
</span><span id="L-742"><a href="#L-742"><span class="linenos">742</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-743"><a href="#L-743"><span class="linenos">743</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-744"><a href="#L-744"><span class="linenos">744</span></a><span class="sd"> y : list</span>
|
||||
</span><span id="L-745"><a href="#L-745"><span class="linenos">745</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-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="k">return</span> <span class="n">output</span>
|
||||
</span><span id="L-748"><a href="#L-748"><span class="linenos">748</span></a>
|
||||
</span><span id="L-749"><a href="#L-749"><span class="linenos">749</span></a>
|
||||
</span><span id="L-750"><a href="#L-750"><span class="linenos">750</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-751"><a href="#L-751"><span class="linenos">751</span></a><span class="w"> </span><span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||||
</span><span id="L-747"><a href="#L-747"><span class="linenos">747</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-748"><a href="#L-748"><span class="linenos">748</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-749"><a href="#L-749"><span class="linenos">749</span></a><span class="sd"> fit_parameters : list[Obs]</span>
|
||||
</span><span id="L-750"><a href="#L-750"><span class="linenos">750</span></a><span class="sd"> LIist of fitted observables.</span>
|
||||
</span><span id="L-751"><a href="#L-751"><span class="linenos">751</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-752"><a href="#L-752"><span class="linenos">752</span></a>
|
||||
</span><span id="L-753"><a href="#L-753"><span class="linenos">753</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="L-754"><a href="#L-754"><span class="linenos">754</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a><span class="sd"> x : list</span>
|
||||
</span><span id="L-756"><a href="#L-756"><span class="linenos">756</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-757"><a href="#L-757"><span class="linenos">757</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-758"><a href="#L-758"><span class="linenos">758</span></a><span class="sd"> y : list</span>
|
||||
</span><span id="L-759"><a href="#L-759"><span class="linenos">759</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-760"><a href="#L-760"><span class="linenos">760</span></a>
|
||||
</span><span id="L-761"><a href="#L-761"><span class="linenos">761</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-762"><a href="#L-762"><span class="linenos">762</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-763"><a href="#L-763"><span class="linenos">763</span></a><span class="sd"> fit_parameters : list[Obs]</span>
|
||||
</span><span id="L-764"><a href="#L-764"><span class="linenos">764</span></a><span class="sd"> LIist of fitted observables.</span>
|
||||
</span><span id="L-765"><a href="#L-765"><span class="linenos">765</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-753"><a href="#L-753"><span class="linenos">753</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-754"><a href="#L-754"><span class="linenos">754</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-755"><a href="#L-755"><span class="linenos">755</span></a> <span class="k">return</span> <span class="n">y</span>
|
||||
</span><span id="L-756"><a href="#L-756"><span class="linenos">756</span></a>
|
||||
</span><span id="L-757"><a href="#L-757"><span class="linenos">757</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-758"><a href="#L-758"><span class="linenos">758</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-759"><a href="#L-759"><span class="linenos">759</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-760"><a href="#L-760"><span class="linenos">760</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-761"><a href="#L-761"><span class="linenos">761</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-762"><a href="#L-762"><span class="linenos">762</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-763"><a href="#L-763"><span class="linenos">763</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-764"><a href="#L-764"><span class="linenos">764</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-765"><a href="#L-765"><span class="linenos">765</span></a>
|
||||
</span><span id="L-766"><a href="#L-766"><span class="linenos">766</span></a>
|
||||
</span><span id="L-767"><a href="#L-767"><span class="linenos">767</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-768"><a href="#L-768"><span class="linenos">768</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-769"><a href="#L-769"><span class="linenos">769</span></a> <span class="k">return</span> <span class="n">y</span>
|
||||
</span><span id="L-767"><a href="#L-767"><span class="linenos">767</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="L-768"><a href="#L-768"><span class="linenos">768</span></a><span class="w"> </span><span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||||
</span><span id="L-769"><a href="#L-769"><span class="linenos">769</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||||
</span><span id="L-770"><a href="#L-770"><span class="linenos">770</span></a>
|
||||
</span><span id="L-771"><a href="#L-771"><span class="linenos">771</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-772"><a href="#L-772"><span class="linenos">772</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-773"><a href="#L-773"><span class="linenos">773</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-774"><a href="#L-774"><span class="linenos">774</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-775"><a href="#L-775"><span class="linenos">775</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-776"><a href="#L-776"><span class="linenos">776</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-777"><a href="#L-777"><span class="linenos">777</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-778"><a href="#L-778"><span class="linenos">778</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-779"><a href="#L-779"><span class="linenos">779</span></a>
|
||||
</span><span id="L-780"><a href="#L-780"><span class="linenos">780</span></a>
|
||||
</span><span id="L-781"><a href="#L-781"><span class="linenos">781</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="L-782"><a href="#L-782"><span class="linenos">782</span></a><span class="w"> </span><span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||||
</span><span id="L-783"><a href="#L-783"><span class="linenos">783</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||||
</span><span id="L-784"><a href="#L-784"><span class="linenos">784</span></a>
|
||||
</span><span id="L-785"><a href="#L-785"><span class="linenos">785</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-786"><a href="#L-786"><span class="linenos">786</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-787"><a href="#L-787"><span class="linenos">787</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-788"><a href="#L-788"><span class="linenos">788</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-789"><a href="#L-789"><span class="linenos">789</span></a>
|
||||
</span><span id="L-790"><a href="#L-790"><span class="linenos">790</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-791"><a href="#L-791"><span class="linenos">791</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-792"><a href="#L-792"><span class="linenos">792</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-793"><a href="#L-793"><span class="linenos">793</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-794"><a href="#L-794"><span class="linenos">794</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-795"><a href="#L-795"><span class="linenos">795</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-796"><a href="#L-796"><span class="linenos">796</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-797"><a href="#L-797"><span class="linenos">797</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-798"><a href="#L-798"><span class="linenos">798</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-799"><a href="#L-799"><span class="linenos">799</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-800"><a href="#L-800"><span class="linenos">800</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-801"><a href="#L-801"><span class="linenos">801</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-802"><a href="#L-802"><span class="linenos">802</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-803"><a href="#L-803"><span class="linenos">803</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-804"><a href="#L-804"><span class="linenos">804</span></a>
|
||||
</span><span id="L-805"><a href="#L-805"><span class="linenos">805</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-806"><a href="#L-806"><span class="linenos">806</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-807"><a href="#L-807"><span class="linenos">807</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="L-808"><a href="#L-808"><span class="linenos">808</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-809"><a href="#L-809"><span class="linenos">809</span></a>
|
||||
</span><span id="L-771"><a href="#L-771"><span class="linenos">771</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-772"><a href="#L-772"><span class="linenos">772</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-773"><a href="#L-773"><span class="linenos">773</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-774"><a href="#L-774"><span class="linenos">774</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-775"><a href="#L-775"><span class="linenos">775</span></a>
|
||||
</span><span id="L-776"><a href="#L-776"><span class="linenos">776</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-777"><a href="#L-777"><span class="linenos">777</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-778"><a href="#L-778"><span class="linenos">778</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-779"><a href="#L-779"><span class="linenos">779</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-780"><a href="#L-780"><span class="linenos">780</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-781"><a href="#L-781"><span class="linenos">781</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-782"><a href="#L-782"><span class="linenos">782</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-783"><a href="#L-783"><span class="linenos">783</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-784"><a href="#L-784"><span class="linenos">784</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-785"><a href="#L-785"><span class="linenos">785</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-786"><a href="#L-786"><span class="linenos">786</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-787"><a href="#L-787"><span class="linenos">787</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-788"><a href="#L-788"><span class="linenos">788</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-789"><a href="#L-789"><span class="linenos">789</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-790"><a href="#L-790"><span class="linenos">790</span></a>
|
||||
</span><span id="L-791"><a href="#L-791"><span class="linenos">791</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-792"><a href="#L-792"><span class="linenos">792</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-793"><a href="#L-793"><span class="linenos">793</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="L-794"><a href="#L-794"><span class="linenos">794</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-795"><a href="#L-795"><span class="linenos">795</span></a>
|
||||
</span><span id="L-796"><a href="#L-796"><span class="linenos">796</span></a>
|
||||
</span><span id="L-797"><a href="#L-797"><span class="linenos">797</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="L-798"><a href="#L-798"><span class="linenos">798</span></a><span class="w"> </span><span class="sd">"""Generates a plot which compares the fit to the data and displays the corresponding residuals</span>
|
||||
</span><span id="L-799"><a href="#L-799"><span class="linenos">799</span></a>
|
||||
</span><span id="L-800"><a href="#L-800"><span class="linenos">800</span></a><span class="sd"> For uncorrelated data the residuals are expected to be distributed ~N(0,1).</span>
|
||||
</span><span id="L-801"><a href="#L-801"><span class="linenos">801</span></a>
|
||||
</span><span id="L-802"><a href="#L-802"><span class="linenos">802</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-803"><a href="#L-803"><span class="linenos">803</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-804"><a href="#L-804"><span class="linenos">804</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-805"><a href="#L-805"><span class="linenos">805</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-806"><a href="#L-806"><span class="linenos">806</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-807"><a href="#L-807"><span class="linenos">807</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-808"><a href="#L-808"><span class="linenos">808</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-809"><a href="#L-809"><span class="linenos">809</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-810"><a href="#L-810"><span class="linenos">810</span></a>
|
||||
</span><span id="L-811"><a href="#L-811"><span class="linenos">811</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="L-812"><a href="#L-812"><span class="linenos">812</span></a><span class="w"> </span><span class="sd">"""Generates a plot which compares the fit to the data and displays the corresponding residuals</span>
|
||||
</span><span id="L-813"><a href="#L-813"><span class="linenos">813</span></a>
|
||||
</span><span id="L-814"><a href="#L-814"><span class="linenos">814</span></a><span class="sd"> For uncorrelated data the residuals are expected to be distributed ~N(0,1).</span>
|
||||
</span><span id="L-815"><a href="#L-815"><span class="linenos">815</span></a>
|
||||
</span><span id="L-816"><a href="#L-816"><span class="linenos">816</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-817"><a href="#L-817"><span class="linenos">817</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-818"><a href="#L-818"><span class="linenos">818</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-819"><a href="#L-819"><span class="linenos">819</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-820"><a href="#L-820"><span class="linenos">820</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-821"><a href="#L-821"><span class="linenos">821</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-822"><a href="#L-822"><span class="linenos">822</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-823"><a href="#L-823"><span class="linenos">823</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-824"><a href="#L-824"><span class="linenos">824</span></a>
|
||||
</span><span id="L-825"><a href="#L-825"><span class="linenos">825</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-826"><a href="#L-826"><span class="linenos">826</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-827"><a href="#L-827"><span class="linenos">827</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-828"><a href="#L-828"><span class="linenos">828</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-829"><a href="#L-829"><span class="linenos">829</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-830"><a href="#L-830"><span class="linenos">830</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-831"><a href="#L-831"><span class="linenos">831</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-832"><a href="#L-832"><span class="linenos">832</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-833"><a href="#L-833"><span class="linenos">833</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="L-834"><a href="#L-834"><span class="linenos">834</span></a>
|
||||
</span><span id="L-835"><a href="#L-835"><span class="linenos">835</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-836"><a href="#L-836"><span class="linenos">836</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-837"><a href="#L-837"><span class="linenos">837</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-838"><a href="#L-838"><span class="linenos">838</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-839"><a href="#L-839"><span class="linenos">839</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-840"><a href="#L-840"><span class="linenos">840</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-841"><a href="#L-841"><span class="linenos">841</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-842"><a href="#L-842"><span class="linenos">842</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-843"><a href="#L-843"><span class="linenos">843</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-844"><a href="#L-844"><span class="linenos">844</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-845"><a href="#L-845"><span class="linenos">845</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-846"><a href="#L-846"><span class="linenos">846</span></a>
|
||||
</span><span id="L-847"><a href="#L-847"><span class="linenos">847</span></a>
|
||||
</span><span id="L-848"><a href="#L-848"><span class="linenos">848</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-849"><a href="#L-849"><span class="linenos">849</span></a><span class="w"> </span><span class="sd">"""Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.</span>
|
||||
</span><span id="L-850"><a href="#L-850"><span class="linenos">850</span></a>
|
||||
</span><span id="L-851"><a href="#L-851"><span class="linenos">851</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-852"><a href="#L-852"><span class="linenos">852</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-853"><a href="#L-853"><span class="linenos">853</span></a><span class="sd"> err : np.array(Obs)</span>
|
||||
</span><span id="L-854"><a href="#L-854"><span class="linenos">854</span></a><span class="sd"> Error band for an array of sample values x</span>
|
||||
</span><span id="L-855"><a href="#L-855"><span class="linenos">855</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-856"><a href="#L-856"><span class="linenos">856</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-857"><a href="#L-857"><span class="linenos">857</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-858"><a href="#L-858"><span class="linenos">858</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-859"><a href="#L-859"><span class="linenos">859</span></a>
|
||||
</span><span id="L-860"><a href="#L-860"><span class="linenos">860</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-861"><a href="#L-861"><span class="linenos">861</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-862"><a href="#L-862"><span class="linenos">862</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-863"><a href="#L-863"><span class="linenos">863</span></a>
|
||||
</span><span id="L-864"><a href="#L-864"><span class="linenos">864</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-865"><a href="#L-865"><span class="linenos">865</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-866"><a href="#L-866"><span class="linenos">866</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-867"><a href="#L-867"><span class="linenos">867</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-868"><a href="#L-868"><span class="linenos">868</span></a>
|
||||
</span><span id="L-869"><a href="#L-869"><span class="linenos">869</span></a> <span class="k">return</span> <span class="n">err</span>
|
||||
</span><span id="L-811"><a href="#L-811"><span class="linenos">811</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-812"><a href="#L-812"><span class="linenos">812</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-813"><a href="#L-813"><span class="linenos">813</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-814"><a href="#L-814"><span class="linenos">814</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-815"><a href="#L-815"><span class="linenos">815</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-816"><a href="#L-816"><span class="linenos">816</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-817"><a href="#L-817"><span class="linenos">817</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-818"><a href="#L-818"><span class="linenos">818</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-819"><a href="#L-819"><span class="linenos">819</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="L-820"><a href="#L-820"><span class="linenos">820</span></a>
|
||||
</span><span id="L-821"><a href="#L-821"><span class="linenos">821</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-822"><a href="#L-822"><span class="linenos">822</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-823"><a href="#L-823"><span class="linenos">823</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-824"><a href="#L-824"><span class="linenos">824</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-825"><a href="#L-825"><span class="linenos">825</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-826"><a href="#L-826"><span class="linenos">826</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-827"><a href="#L-827"><span class="linenos">827</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-828"><a href="#L-828"><span class="linenos">828</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-829"><a href="#L-829"><span class="linenos">829</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-830"><a href="#L-830"><span class="linenos">830</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-831"><a href="#L-831"><span class="linenos">831</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-832"><a href="#L-832"><span class="linenos">832</span></a>
|
||||
</span><span id="L-833"><a href="#L-833"><span class="linenos">833</span></a>
|
||||
</span><span id="L-834"><a href="#L-834"><span class="linenos">834</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-835"><a href="#L-835"><span class="linenos">835</span></a><span class="w"> </span><span class="sd">"""Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.</span>
|
||||
</span><span id="L-836"><a href="#L-836"><span class="linenos">836</span></a>
|
||||
</span><span id="L-837"><a href="#L-837"><span class="linenos">837</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-838"><a href="#L-838"><span class="linenos">838</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-839"><a href="#L-839"><span class="linenos">839</span></a><span class="sd"> err : np.array(Obs)</span>
|
||||
</span><span id="L-840"><a href="#L-840"><span class="linenos">840</span></a><span class="sd"> Error band for an array of sample values x</span>
|
||||
</span><span id="L-841"><a href="#L-841"><span class="linenos">841</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-842"><a href="#L-842"><span class="linenos">842</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-843"><a href="#L-843"><span class="linenos">843</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-844"><a href="#L-844"><span class="linenos">844</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-845"><a href="#L-845"><span class="linenos">845</span></a>
|
||||
</span><span id="L-846"><a href="#L-846"><span class="linenos">846</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-847"><a href="#L-847"><span class="linenos">847</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-848"><a href="#L-848"><span class="linenos">848</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-849"><a href="#L-849"><span class="linenos">849</span></a>
|
||||
</span><span id="L-850"><a href="#L-850"><span class="linenos">850</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-851"><a href="#L-851"><span class="linenos">851</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-852"><a href="#L-852"><span class="linenos">852</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-853"><a href="#L-853"><span class="linenos">853</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-854"><a href="#L-854"><span class="linenos">854</span></a>
|
||||
</span><span id="L-855"><a href="#L-855"><span class="linenos">855</span></a> <span class="k">return</span> <span class="n">err</span>
|
||||
</span><span id="L-856"><a href="#L-856"><span class="linenos">856</span></a>
|
||||
</span><span id="L-857"><a href="#L-857"><span class="linenos">857</span></a>
|
||||
</span><span id="L-858"><a href="#L-858"><span class="linenos">858</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-859"><a href="#L-859"><span class="linenos">859</span></a><span class="w"> </span><span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||||
</span><span id="L-860"><a href="#L-860"><span class="linenos">860</span></a>
|
||||
</span><span id="L-861"><a href="#L-861"><span class="linenos">861</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="L-862"><a href="#L-862"><span class="linenos">862</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="L-863"><a href="#L-863"><span class="linenos">863</span></a><span class="sd"> objects : list</span>
|
||||
</span><span id="L-864"><a href="#L-864"><span class="linenos">864</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||||
</span><span id="L-865"><a href="#L-865"><span class="linenos">865</span></a>
|
||||
</span><span id="L-866"><a href="#L-866"><span class="linenos">866</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-867"><a href="#L-867"><span class="linenos">867</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-868"><a href="#L-868"><span class="linenos">868</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-869"><a href="#L-869"><span class="linenos">869</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-870"><a href="#L-870"><span class="linenos">870</span></a>
|
||||
</span><span id="L-871"><a href="#L-871"><span class="linenos">871</span></a>
|
||||
</span><span id="L-872"><a href="#L-872"><span class="linenos">872</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-873"><a href="#L-873"><span class="linenos">873</span></a><span class="w"> </span><span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||||
</span><span id="L-874"><a href="#L-874"><span class="linenos">874</span></a>
|
||||
</span><span id="L-875"><a href="#L-875"><span class="linenos">875</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="L-876"><a href="#L-876"><span class="linenos">876</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="L-877"><a href="#L-877"><span class="linenos">877</span></a><span class="sd"> objects : list</span>
|
||||
</span><span id="L-878"><a href="#L-878"><span class="linenos">878</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||||
</span><span id="L-879"><a href="#L-879"><span class="linenos">879</span></a>
|
||||
</span><span id="L-880"><a href="#L-880"><span class="linenos">880</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="L-881"><a href="#L-881"><span class="linenos">881</span></a><span class="sd"> -------</span>
|
||||
</span><span id="L-882"><a href="#L-882"><span class="linenos">882</span></a><span class="sd"> None</span>
|
||||
</span><span id="L-883"><a href="#L-883"><span class="linenos">883</span></a><span class="sd"> """</span>
|
||||
</span><span id="L-884"><a href="#L-884"><span class="linenos">884</span></a>
|
||||
</span><span id="L-885"><a href="#L-885"><span class="linenos">885</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-886"><a href="#L-886"><span class="linenos">886</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-887"><a href="#L-887"><span class="linenos">887</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-888"><a href="#L-888"><span class="linenos">888</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-889"><a href="#L-889"><span class="linenos">889</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-890"><a href="#L-890"><span class="linenos">890</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-891"><a href="#L-891"><span class="linenos">891</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||||
</span><span id="L-892"><a href="#L-892"><span class="linenos">892</span></a>
|
||||
</span><span id="L-893"><a href="#L-893"><span class="linenos">893</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-894"><a href="#L-894"><span class="linenos">894</span></a>
|
||||
</span><span id="L-895"><a href="#L-895"><span class="linenos">895</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-896"><a href="#L-896"><span class="linenos">896</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-897"><a href="#L-897"><span class="linenos">897</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-898"><a href="#L-898"><span class="linenos">898</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-899"><a href="#L-899"><span class="linenos">899</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-900"><a href="#L-900"><span class="linenos">900</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-901"><a href="#L-901"><span class="linenos">901</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-902"><a href="#L-902"><span class="linenos">902</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-903"><a href="#L-903"><span class="linenos">903</span></a>
|
||||
</span><span id="L-904"><a href="#L-904"><span class="linenos">904</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-905"><a href="#L-905"><span class="linenos">905</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-906"><a href="#L-906"><span class="linenos">906</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-907"><a href="#L-907"><span class="linenos">907</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-908"><a href="#L-908"><span class="linenos">908</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-909"><a href="#L-909"><span class="linenos">909</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-910"><a href="#L-910"><span class="linenos">910</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-911"><a href="#L-911"><span class="linenos">911</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-912"><a href="#L-912"><span class="linenos">912</span></a>
|
||||
</span><span id="L-913"><a href="#L-913"><span class="linenos">913</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><span id="L-871"><a href="#L-871"><span class="linenos">871</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-872"><a href="#L-872"><span class="linenos">872</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="L-873"><a href="#L-873"><span class="linenos">873</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-874"><a href="#L-874"><span class="linenos">874</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-875"><a href="#L-875"><span class="linenos">875</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-876"><a href="#L-876"><span class="linenos">876</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="L-877"><a href="#L-877"><span class="linenos">877</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||||
</span><span id="L-878"><a href="#L-878"><span class="linenos">878</span></a>
|
||||
</span><span id="L-879"><a href="#L-879"><span class="linenos">879</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-880"><a href="#L-880"><span class="linenos">880</span></a>
|
||||
</span><span id="L-881"><a href="#L-881"><span class="linenos">881</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-882"><a href="#L-882"><span class="linenos">882</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-883"><a href="#L-883"><span class="linenos">883</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-884"><a href="#L-884"><span class="linenos">884</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-885"><a href="#L-885"><span class="linenos">885</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-886"><a href="#L-886"><span class="linenos">886</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-887"><a href="#L-887"><span class="linenos">887</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-888"><a href="#L-888"><span class="linenos">888</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-889"><a href="#L-889"><span class="linenos">889</span></a>
|
||||
</span><span id="L-890"><a href="#L-890"><span class="linenos">890</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-891"><a href="#L-891"><span class="linenos">891</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-892"><a href="#L-892"><span class="linenos">892</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-893"><a href="#L-893"><span class="linenos">893</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-894"><a href="#L-894"><span class="linenos">894</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-895"><a href="#L-895"><span class="linenos">895</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-896"><a href="#L-896"><span class="linenos">896</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-897"><a href="#L-897"><span class="linenos">897</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span><span id="L-898"><a href="#L-898"><span class="linenos">898</span></a>
|
||||
</span><span id="L-899"><a href="#L-899"><span class="linenos">899</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>
|
||||
|
||||
|
||||
|
|
@ -1662,35 +1648,35 @@ Parameters and information on the fitted result.</li>
|
|||
|
||||
</div>
|
||||
<a class="headerlink" href="#fit_lin"></a>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="fit_lin-751"><a href="#fit_lin-751"><span class="linenos">751</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-752"><a href="#fit_lin-752"><span class="linenos">752</span></a><span class="w"> </span><span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="fit_lin-737"><a href="#fit_lin-737"><span class="linenos">737</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-738"><a href="#fit_lin-738"><span class="linenos">738</span></a><span class="w"> </span><span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
||||
</span><span id="fit_lin-739"><a href="#fit_lin-739"><span class="linenos">739</span></a>
|
||||
</span><span id="fit_lin-740"><a href="#fit_lin-740"><span class="linenos">740</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="fit_lin-741"><a href="#fit_lin-741"><span class="linenos">741</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="fit_lin-742"><a href="#fit_lin-742"><span class="linenos">742</span></a><span class="sd"> x : list</span>
|
||||
</span><span id="fit_lin-743"><a href="#fit_lin-743"><span class="linenos">743</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-744"><a href="#fit_lin-744"><span class="linenos">744</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-745"><a href="#fit_lin-745"><span class="linenos">745</span></a><span class="sd"> y : list</span>
|
||||
</span><span id="fit_lin-746"><a href="#fit_lin-746"><span class="linenos">746</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-747"><a href="#fit_lin-747"><span class="linenos">747</span></a>
|
||||
</span><span id="fit_lin-748"><a href="#fit_lin-748"><span class="linenos">748</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="fit_lin-749"><a href="#fit_lin-749"><span class="linenos">749</span></a><span class="sd"> -------</span>
|
||||
</span><span id="fit_lin-750"><a href="#fit_lin-750"><span class="linenos">750</span></a><span class="sd"> fit_parameters : list[Obs]</span>
|
||||
</span><span id="fit_lin-751"><a href="#fit_lin-751"><span class="linenos">751</span></a><span class="sd"> LIist of fitted observables.</span>
|
||||
</span><span id="fit_lin-752"><a href="#fit_lin-752"><span class="linenos">752</span></a><span class="sd"> """</span>
|
||||
</span><span id="fit_lin-753"><a href="#fit_lin-753"><span class="linenos">753</span></a>
|
||||
</span><span id="fit_lin-754"><a href="#fit_lin-754"><span class="linenos">754</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="fit_lin-755"><a href="#fit_lin-755"><span class="linenos">755</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="fit_lin-756"><a href="#fit_lin-756"><span class="linenos">756</span></a><span class="sd"> x : list</span>
|
||||
</span><span id="fit_lin-757"><a href="#fit_lin-757"><span class="linenos">757</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-758"><a href="#fit_lin-758"><span class="linenos">758</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-759"><a href="#fit_lin-759"><span class="linenos">759</span></a><span class="sd"> y : list</span>
|
||||
</span><span id="fit_lin-760"><a href="#fit_lin-760"><span class="linenos">760</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-761"><a href="#fit_lin-761"><span class="linenos">761</span></a>
|
||||
</span><span id="fit_lin-762"><a href="#fit_lin-762"><span class="linenos">762</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="fit_lin-763"><a href="#fit_lin-763"><span class="linenos">763</span></a><span class="sd"> -------</span>
|
||||
</span><span id="fit_lin-764"><a href="#fit_lin-764"><span class="linenos">764</span></a><span class="sd"> fit_parameters : list[Obs]</span>
|
||||
</span><span id="fit_lin-765"><a href="#fit_lin-765"><span class="linenos">765</span></a><span class="sd"> LIist of fitted observables.</span>
|
||||
</span><span id="fit_lin-766"><a href="#fit_lin-766"><span class="linenos">766</span></a><span class="sd"> """</span>
|
||||
</span><span id="fit_lin-767"><a href="#fit_lin-767"><span class="linenos">767</span></a>
|
||||
</span><span id="fit_lin-768"><a href="#fit_lin-768"><span class="linenos">768</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-769"><a href="#fit_lin-769"><span class="linenos">769</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-770"><a href="#fit_lin-770"><span class="linenos">770</span></a> <span class="k">return</span> <span class="n">y</span>
|
||||
</span><span id="fit_lin-771"><a href="#fit_lin-771"><span class="linenos">771</span></a>
|
||||
</span><span id="fit_lin-772"><a href="#fit_lin-772"><span class="linenos">772</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-773"><a href="#fit_lin-773"><span class="linenos">773</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-774"><a href="#fit_lin-774"><span class="linenos">774</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-775"><a href="#fit_lin-775"><span class="linenos">775</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-776"><a href="#fit_lin-776"><span class="linenos">776</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-777"><a href="#fit_lin-777"><span class="linenos">777</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-778"><a href="#fit_lin-778"><span class="linenos">778</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="fit_lin-779"><a href="#fit_lin-779"><span class="linenos">779</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="fit_lin-754"><a href="#fit_lin-754"><span class="linenos">754</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-755"><a href="#fit_lin-755"><span class="linenos">755</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-756"><a href="#fit_lin-756"><span class="linenos">756</span></a> <span class="k">return</span> <span class="n">y</span>
|
||||
</span><span id="fit_lin-757"><a href="#fit_lin-757"><span class="linenos">757</span></a>
|
||||
</span><span id="fit_lin-758"><a href="#fit_lin-758"><span class="linenos">758</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-759"><a href="#fit_lin-759"><span class="linenos">759</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-760"><a href="#fit_lin-760"><span class="linenos">760</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-761"><a href="#fit_lin-761"><span class="linenos">761</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-762"><a href="#fit_lin-762"><span class="linenos">762</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-763"><a href="#fit_lin-763"><span class="linenos">763</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-764"><a href="#fit_lin-764"><span class="linenos">764</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="fit_lin-765"><a href="#fit_lin-765"><span class="linenos">765</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>
|
||||
|
||||
|
||||
|
|
@ -1727,34 +1713,34 @@ LIist of fitted observables.</li>
|
|||
|
||||
</div>
|
||||
<a class="headerlink" href="#qqplot"></a>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="qqplot-782"><a href="#qqplot-782"><span class="linenos">782</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="qqplot-783"><a href="#qqplot-783"><span class="linenos">783</span></a><span class="w"> </span><span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||||
</span><span id="qqplot-784"><a href="#qqplot-784"><span class="linenos">784</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||||
</span><span id="qqplot-785"><a href="#qqplot-785"><span class="linenos">785</span></a>
|
||||
</span><span id="qqplot-786"><a href="#qqplot-786"><span class="linenos">786</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="qqplot-787"><a href="#qqplot-787"><span class="linenos">787</span></a><span class="sd"> -------</span>
|
||||
</span><span id="qqplot-788"><a href="#qqplot-788"><span class="linenos">788</span></a><span class="sd"> None</span>
|
||||
</span><span id="qqplot-789"><a href="#qqplot-789"><span class="linenos">789</span></a><span class="sd"> """</span>
|
||||
</span><span id="qqplot-790"><a href="#qqplot-790"><span class="linenos">790</span></a>
|
||||
</span><span id="qqplot-791"><a href="#qqplot-791"><span class="linenos">791</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="qqplot-792"><a href="#qqplot-792"><span class="linenos">792</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-793"><a href="#qqplot-793"><span class="linenos">793</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-794"><a href="#qqplot-794"><span class="linenos">794</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-795"><a href="#qqplot-795"><span class="linenos">795</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-796"><a href="#qqplot-796"><span class="linenos">796</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-797"><a href="#qqplot-797"><span class="linenos">797</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-798"><a href="#qqplot-798"><span class="linenos">798</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-799"><a href="#qqplot-799"><span class="linenos">799</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-800"><a href="#qqplot-800"><span class="linenos">800</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-801"><a href="#qqplot-801"><span class="linenos">801</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-802"><a href="#qqplot-802"><span class="linenos">802</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-803"><a href="#qqplot-803"><span class="linenos">803</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-804"><a href="#qqplot-804"><span class="linenos">804</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-805"><a href="#qqplot-805"><span class="linenos">805</span></a>
|
||||
</span><span id="qqplot-806"><a href="#qqplot-806"><span class="linenos">806</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-807"><a href="#qqplot-807"><span class="linenos">807</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-808"><a href="#qqplot-808"><span class="linenos">808</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="qqplot-809"><a href="#qqplot-809"><span class="linenos">809</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="qqplot-768"><a href="#qqplot-768"><span class="linenos">768</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="qqplot-769"><a href="#qqplot-769"><span class="linenos">769</span></a><span class="w"> </span><span class="sd">"""Generates a quantile-quantile plot of the fit result which can be used to</span>
|
||||
</span><span id="qqplot-770"><a href="#qqplot-770"><span class="linenos">770</span></a><span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
||||
</span><span id="qqplot-771"><a href="#qqplot-771"><span class="linenos">771</span></a>
|
||||
</span><span id="qqplot-772"><a href="#qqplot-772"><span class="linenos">772</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="qqplot-773"><a href="#qqplot-773"><span class="linenos">773</span></a><span class="sd"> -------</span>
|
||||
</span><span id="qqplot-774"><a href="#qqplot-774"><span class="linenos">774</span></a><span class="sd"> None</span>
|
||||
</span><span id="qqplot-775"><a href="#qqplot-775"><span class="linenos">775</span></a><span class="sd"> """</span>
|
||||
</span><span id="qqplot-776"><a href="#qqplot-776"><span class="linenos">776</span></a>
|
||||
</span><span id="qqplot-777"><a href="#qqplot-777"><span class="linenos">777</span></a> <span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="qqplot-778"><a href="#qqplot-778"><span class="linenos">778</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-779"><a href="#qqplot-779"><span class="linenos">779</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-780"><a href="#qqplot-780"><span class="linenos">780</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-781"><a href="#qqplot-781"><span class="linenos">781</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-782"><a href="#qqplot-782"><span class="linenos">782</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-783"><a href="#qqplot-783"><span class="linenos">783</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-784"><a href="#qqplot-784"><span class="linenos">784</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-785"><a href="#qqplot-785"><span class="linenos">785</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-786"><a href="#qqplot-786"><span class="linenos">786</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-787"><a href="#qqplot-787"><span class="linenos">787</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-788"><a href="#qqplot-788"><span class="linenos">788</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-789"><a href="#qqplot-789"><span class="linenos">789</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-790"><a href="#qqplot-790"><span class="linenos">790</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-791"><a href="#qqplot-791"><span class="linenos">791</span></a>
|
||||
</span><span id="qqplot-792"><a href="#qqplot-792"><span class="linenos">792</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-793"><a href="#qqplot-793"><span class="linenos">793</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-794"><a href="#qqplot-794"><span class="linenos">794</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="qqplot-795"><a href="#qqplot-795"><span class="linenos">795</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span></pre></div>
|
||||
|
||||
|
||||
|
|
@ -1781,41 +1767,41 @@ LIist of fitted observables.</li>
|
|||
|
||||
</div>
|
||||
<a class="headerlink" href="#residual_plot"></a>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="residual_plot-812"><a href="#residual_plot-812"><span class="linenos">812</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="residual_plot-813"><a href="#residual_plot-813"><span class="linenos">813</span></a><span class="w"> </span><span class="sd">"""Generates a plot which compares the fit to the data and displays the corresponding residuals</span>
|
||||
</span><span id="residual_plot-814"><a href="#residual_plot-814"><span class="linenos">814</span></a>
|
||||
</span><span id="residual_plot-815"><a href="#residual_plot-815"><span class="linenos">815</span></a><span class="sd"> For uncorrelated data the residuals are expected to be distributed ~N(0,1).</span>
|
||||
</span><span id="residual_plot-816"><a href="#residual_plot-816"><span class="linenos">816</span></a>
|
||||
</span><span id="residual_plot-817"><a href="#residual_plot-817"><span class="linenos">817</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="residual_plot-818"><a href="#residual_plot-818"><span class="linenos">818</span></a><span class="sd"> -------</span>
|
||||
</span><span id="residual_plot-819"><a href="#residual_plot-819"><span class="linenos">819</span></a><span class="sd"> None</span>
|
||||
</span><span id="residual_plot-820"><a href="#residual_plot-820"><span class="linenos">820</span></a><span class="sd"> """</span>
|
||||
</span><span id="residual_plot-821"><a href="#residual_plot-821"><span class="linenos">821</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-822"><a href="#residual_plot-822"><span class="linenos">822</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-823"><a href="#residual_plot-823"><span class="linenos">823</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-824"><a href="#residual_plot-824"><span class="linenos">824</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-825"><a href="#residual_plot-825"><span class="linenos">825</span></a>
|
||||
</span><span id="residual_plot-826"><a href="#residual_plot-826"><span class="linenos">826</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-827"><a href="#residual_plot-827"><span class="linenos">827</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-828"><a href="#residual_plot-828"><span class="linenos">828</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-829"><a href="#residual_plot-829"><span class="linenos">829</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-830"><a href="#residual_plot-830"><span class="linenos">830</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-831"><a href="#residual_plot-831"><span class="linenos">831</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-832"><a href="#residual_plot-832"><span class="linenos">832</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-833"><a href="#residual_plot-833"><span class="linenos">833</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-834"><a href="#residual_plot-834"><span class="linenos">834</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="residual_plot-835"><a href="#residual_plot-835"><span class="linenos">835</span></a>
|
||||
</span><span id="residual_plot-836"><a href="#residual_plot-836"><span class="linenos">836</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-837"><a href="#residual_plot-837"><span class="linenos">837</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-838"><a href="#residual_plot-838"><span class="linenos">838</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-839"><a href="#residual_plot-839"><span class="linenos">839</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-840"><a href="#residual_plot-840"><span class="linenos">840</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-841"><a href="#residual_plot-841"><span class="linenos">841</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-842"><a href="#residual_plot-842"><span class="linenos">842</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-843"><a href="#residual_plot-843"><span class="linenos">843</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-844"><a href="#residual_plot-844"><span class="linenos">844</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-845"><a href="#residual_plot-845"><span class="linenos">845</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-846"><a href="#residual_plot-846"><span class="linenos">846</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="residual_plot-798"><a href="#residual_plot-798"><span class="linenos">798</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 class="n">title</span><span class="o">=</span><span class="s2">""</span><span class="p">):</span>
|
||||
</span><span id="residual_plot-799"><a href="#residual_plot-799"><span class="linenos">799</span></a><span class="w"> </span><span class="sd">"""Generates a plot which compares the fit to the data and displays the corresponding residuals</span>
|
||||
</span><span id="residual_plot-800"><a href="#residual_plot-800"><span class="linenos">800</span></a>
|
||||
</span><span id="residual_plot-801"><a href="#residual_plot-801"><span class="linenos">801</span></a><span class="sd"> For uncorrelated data the residuals are expected to be distributed ~N(0,1).</span>
|
||||
</span><span id="residual_plot-802"><a href="#residual_plot-802"><span class="linenos">802</span></a>
|
||||
</span><span id="residual_plot-803"><a href="#residual_plot-803"><span class="linenos">803</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="residual_plot-804"><a href="#residual_plot-804"><span class="linenos">804</span></a><span class="sd"> -------</span>
|
||||
</span><span id="residual_plot-805"><a href="#residual_plot-805"><span class="linenos">805</span></a><span class="sd"> None</span>
|
||||
</span><span id="residual_plot-806"><a href="#residual_plot-806"><span class="linenos">806</span></a><span class="sd"> """</span>
|
||||
</span><span id="residual_plot-807"><a href="#residual_plot-807"><span class="linenos">807</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-808"><a href="#residual_plot-808"><span class="linenos">808</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-809"><a href="#residual_plot-809"><span class="linenos">809</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-810"><a href="#residual_plot-810"><span class="linenos">810</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-811"><a href="#residual_plot-811"><span class="linenos">811</span></a>
|
||||
</span><span id="residual_plot-812"><a href="#residual_plot-812"><span class="linenos">812</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-813"><a href="#residual_plot-813"><span class="linenos">813</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-814"><a href="#residual_plot-814"><span class="linenos">814</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-815"><a href="#residual_plot-815"><span class="linenos">815</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-816"><a href="#residual_plot-816"><span class="linenos">816</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-817"><a href="#residual_plot-817"><span class="linenos">817</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-818"><a href="#residual_plot-818"><span class="linenos">818</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-819"><a href="#residual_plot-819"><span class="linenos">819</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-820"><a href="#residual_plot-820"><span class="linenos">820</span></a> <span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="n">title</span><span class="p">)</span>
|
||||
</span><span id="residual_plot-821"><a href="#residual_plot-821"><span class="linenos">821</span></a>
|
||||
</span><span id="residual_plot-822"><a href="#residual_plot-822"><span class="linenos">822</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-823"><a href="#residual_plot-823"><span class="linenos">823</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-824"><a href="#residual_plot-824"><span class="linenos">824</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-825"><a href="#residual_plot-825"><span class="linenos">825</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-826"><a href="#residual_plot-826"><span class="linenos">826</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-827"><a href="#residual_plot-827"><span class="linenos">827</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-828"><a href="#residual_plot-828"><span class="linenos">828</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-829"><a href="#residual_plot-829"><span class="linenos">829</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-830"><a href="#residual_plot-830"><span class="linenos">830</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-831"><a href="#residual_plot-831"><span class="linenos">831</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-832"><a href="#residual_plot-832"><span class="linenos">832</span></a> <span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
</span></pre></div>
|
||||
|
||||
|
||||
|
|
@ -1843,28 +1829,28 @@ LIist of fitted observables.</li>
|
|||
|
||||
</div>
|
||||
<a class="headerlink" href="#error_band"></a>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="error_band-849"><a href="#error_band-849"><span class="linenos">849</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-850"><a href="#error_band-850"><span class="linenos">850</span></a><span class="w"> </span><span class="sd">"""Calculate 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-851"><a href="#error_band-851"><span class="linenos">851</span></a>
|
||||
</span><span id="error_band-852"><a href="#error_band-852"><span class="linenos">852</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="error_band-853"><a href="#error_band-853"><span class="linenos">853</span></a><span class="sd"> -------</span>
|
||||
</span><span id="error_band-854"><a href="#error_band-854"><span class="linenos">854</span></a><span class="sd"> err : np.array(Obs)</span>
|
||||
</span><span id="error_band-855"><a href="#error_band-855"><span class="linenos">855</span></a><span class="sd"> Error band for an array of sample values x</span>
|
||||
</span><span id="error_band-856"><a href="#error_band-856"><span class="linenos">856</span></a><span class="sd"> """</span>
|
||||
</span><span id="error_band-857"><a href="#error_band-857"><span class="linenos">857</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-858"><a href="#error_band-858"><span class="linenos">858</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-859"><a href="#error_band-859"><span class="linenos">859</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-860"><a href="#error_band-860"><span class="linenos">860</span></a>
|
||||
</span><span id="error_band-861"><a href="#error_band-861"><span class="linenos">861</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="error_band-862"><a href="#error_band-862"><span class="linenos">862</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-863"><a href="#error_band-863"><span class="linenos">863</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-864"><a href="#error_band-864"><span class="linenos">864</span></a>
|
||||
</span><span id="error_band-865"><a href="#error_band-865"><span class="linenos">865</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="error_band-866"><a href="#error_band-866"><span class="linenos">866</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-867"><a href="#error_band-867"><span class="linenos">867</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-868"><a href="#error_band-868"><span class="linenos">868</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-869"><a href="#error_band-869"><span class="linenos">869</span></a>
|
||||
</span><span id="error_band-870"><a href="#error_band-870"><span class="linenos">870</span></a> <span class="k">return</span> <span class="n">err</span>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="error_band-835"><a href="#error_band-835"><span class="linenos">835</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-836"><a href="#error_band-836"><span class="linenos">836</span></a><span class="w"> </span><span class="sd">"""Calculate 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-837"><a href="#error_band-837"><span class="linenos">837</span></a>
|
||||
</span><span id="error_band-838"><a href="#error_band-838"><span class="linenos">838</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="error_band-839"><a href="#error_band-839"><span class="linenos">839</span></a><span class="sd"> -------</span>
|
||||
</span><span id="error_band-840"><a href="#error_band-840"><span class="linenos">840</span></a><span class="sd"> err : np.array(Obs)</span>
|
||||
</span><span id="error_band-841"><a href="#error_band-841"><span class="linenos">841</span></a><span class="sd"> Error band for an array of sample values x</span>
|
||||
</span><span id="error_band-842"><a href="#error_band-842"><span class="linenos">842</span></a><span class="sd"> """</span>
|
||||
</span><span id="error_band-843"><a href="#error_band-843"><span class="linenos">843</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-844"><a href="#error_band-844"><span class="linenos">844</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-845"><a href="#error_band-845"><span class="linenos">845</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-846"><a href="#error_band-846"><span class="linenos">846</span></a>
|
||||
</span><span id="error_band-847"><a href="#error_band-847"><span class="linenos">847</span></a> <span class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="error_band-848"><a href="#error_band-848"><span class="linenos">848</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-849"><a href="#error_band-849"><span class="linenos">849</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-850"><a href="#error_band-850"><span class="linenos">850</span></a>
|
||||
</span><span id="error_band-851"><a href="#error_band-851"><span class="linenos">851</span></a> <span class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="error_band-852"><a href="#error_band-852"><span class="linenos">852</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-853"><a href="#error_band-853"><span class="linenos">853</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-854"><a href="#error_band-854"><span class="linenos">854</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-855"><a href="#error_band-855"><span class="linenos">855</span></a>
|
||||
</span><span id="error_band-856"><a href="#error_band-856"><span class="linenos">856</span></a> <span class="k">return</span> <span class="n">err</span>
|
||||
</span></pre></div>
|
||||
|
||||
|
||||
|
|
@ -1891,48 +1877,48 @@ Error band for an array of sample values x</li>
|
|||
|
||||
</div>
|
||||
<a class="headerlink" href="#ks_test"></a>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="ks_test-873"><a href="#ks_test-873"><span class="linenos">873</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-874"><a href="#ks_test-874"><span class="linenos">874</span></a><span class="w"> </span><span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||||
</span><span id="ks_test-875"><a href="#ks_test-875"><span class="linenos">875</span></a>
|
||||
</span><span id="ks_test-876"><a href="#ks_test-876"><span class="linenos">876</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="ks_test-877"><a href="#ks_test-877"><span class="linenos">877</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="ks_test-878"><a href="#ks_test-878"><span class="linenos">878</span></a><span class="sd"> objects : list</span>
|
||||
</span><span id="ks_test-879"><a href="#ks_test-879"><span class="linenos">879</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||||
</span><span id="ks_test-880"><a href="#ks_test-880"><span class="linenos">880</span></a>
|
||||
</span><span id="ks_test-881"><a href="#ks_test-881"><span class="linenos">881</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="ks_test-882"><a href="#ks_test-882"><span class="linenos">882</span></a><span class="sd"> -------</span>
|
||||
</span><span id="ks_test-883"><a href="#ks_test-883"><span class="linenos">883</span></a><span class="sd"> None</span>
|
||||
</span><span id="ks_test-884"><a href="#ks_test-884"><span class="linenos">884</span></a><span class="sd"> """</span>
|
||||
</span><span id="ks_test-885"><a href="#ks_test-885"><span class="linenos">885</span></a>
|
||||
</span><span id="ks_test-886"><a href="#ks_test-886"><span class="linenos">886</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-887"><a href="#ks_test-887"><span class="linenos">887</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="ks_test-888"><a href="#ks_test-888"><span class="linenos">888</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-889"><a href="#ks_test-889"><span class="linenos">889</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-890"><a href="#ks_test-890"><span class="linenos">890</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-891"><a href="#ks_test-891"><span class="linenos">891</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="ks_test-892"><a href="#ks_test-892"><span class="linenos">892</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||||
</span><span id="ks_test-893"><a href="#ks_test-893"><span class="linenos">893</span></a>
|
||||
</span><span id="ks_test-894"><a href="#ks_test-894"><span class="linenos">894</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-895"><a href="#ks_test-895"><span class="linenos">895</span></a>
|
||||
</span><span id="ks_test-896"><a href="#ks_test-896"><span class="linenos">896</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-897"><a href="#ks_test-897"><span class="linenos">897</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-898"><a href="#ks_test-898"><span class="linenos">898</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-899"><a href="#ks_test-899"><span class="linenos">899</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-900"><a href="#ks_test-900"><span class="linenos">900</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-901"><a href="#ks_test-901"><span class="linenos">901</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-902"><a href="#ks_test-902"><span class="linenos">902</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-903"><a href="#ks_test-903"><span class="linenos">903</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-904"><a href="#ks_test-904"><span class="linenos">904</span></a>
|
||||
</span><span id="ks_test-905"><a href="#ks_test-905"><span class="linenos">905</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-906"><a href="#ks_test-906"><span class="linenos">906</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-907"><a href="#ks_test-907"><span class="linenos">907</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-908"><a href="#ks_test-908"><span class="linenos">908</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-909"><a href="#ks_test-909"><span class="linenos">909</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-910"><a href="#ks_test-910"><span class="linenos">910</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-911"><a href="#ks_test-911"><span class="linenos">911</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-912"><a href="#ks_test-912"><span class="linenos">912</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-913"><a href="#ks_test-913"><span class="linenos">913</span></a>
|
||||
</span><span id="ks_test-914"><a href="#ks_test-914"><span class="linenos">914</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>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span id="ks_test-859"><a href="#ks_test-859"><span class="linenos">859</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-860"><a href="#ks_test-860"><span class="linenos">860</span></a><span class="w"> </span><span class="sd">"""Performs a Kolmogorov–Smirnov test for the p-values of all fit object.</span>
|
||||
</span><span id="ks_test-861"><a href="#ks_test-861"><span class="linenos">861</span></a>
|
||||
</span><span id="ks_test-862"><a href="#ks_test-862"><span class="linenos">862</span></a><span class="sd"> Parameters</span>
|
||||
</span><span id="ks_test-863"><a href="#ks_test-863"><span class="linenos">863</span></a><span class="sd"> ----------</span>
|
||||
</span><span id="ks_test-864"><a href="#ks_test-864"><span class="linenos">864</span></a><span class="sd"> objects : list</span>
|
||||
</span><span id="ks_test-865"><a href="#ks_test-865"><span class="linenos">865</span></a><span class="sd"> List of fit results to include in the analysis (optional).</span>
|
||||
</span><span id="ks_test-866"><a href="#ks_test-866"><span class="linenos">866</span></a>
|
||||
</span><span id="ks_test-867"><a href="#ks_test-867"><span class="linenos">867</span></a><span class="sd"> Returns</span>
|
||||
</span><span id="ks_test-868"><a href="#ks_test-868"><span class="linenos">868</span></a><span class="sd"> -------</span>
|
||||
</span><span id="ks_test-869"><a href="#ks_test-869"><span class="linenos">869</span></a><span class="sd"> None</span>
|
||||
</span><span id="ks_test-870"><a href="#ks_test-870"><span class="linenos">870</span></a><span class="sd"> """</span>
|
||||
</span><span id="ks_test-871"><a href="#ks_test-871"><span class="linenos">871</span></a>
|
||||
</span><span id="ks_test-872"><a href="#ks_test-872"><span class="linenos">872</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-873"><a href="#ks_test-873"><span class="linenos">873</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
</span><span id="ks_test-874"><a href="#ks_test-874"><span class="linenos">874</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-875"><a href="#ks_test-875"><span class="linenos">875</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-876"><a href="#ks_test-876"><span class="linenos">876</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-877"><a href="#ks_test-877"><span class="linenos">877</span></a> <span class="k">else</span><span class="p">:</span>
|
||||
</span><span id="ks_test-878"><a href="#ks_test-878"><span class="linenos">878</span></a> <span class="n">obs_list</span> <span class="o">=</span> <span class="n">objects</span>
|
||||
</span><span id="ks_test-879"><a href="#ks_test-879"><span class="linenos">879</span></a>
|
||||
</span><span id="ks_test-880"><a href="#ks_test-880"><span class="linenos">880</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-881"><a href="#ks_test-881"><span class="linenos">881</span></a>
|
||||
</span><span id="ks_test-882"><a href="#ks_test-882"><span class="linenos">882</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-883"><a href="#ks_test-883"><span class="linenos">883</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-884"><a href="#ks_test-884"><span class="linenos">884</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-885"><a href="#ks_test-885"><span class="linenos">885</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-886"><a href="#ks_test-886"><span class="linenos">886</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-887"><a href="#ks_test-887"><span class="linenos">887</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-888"><a href="#ks_test-888"><span class="linenos">888</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-889"><a href="#ks_test-889"><span class="linenos">889</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-890"><a href="#ks_test-890"><span class="linenos">890</span></a>
|
||||
</span><span id="ks_test-891"><a href="#ks_test-891"><span class="linenos">891</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-892"><a href="#ks_test-892"><span class="linenos">892</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-893"><a href="#ks_test-893"><span class="linenos">893</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-894"><a href="#ks_test-894"><span class="linenos">894</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-895"><a href="#ks_test-895"><span class="linenos">895</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-896"><a href="#ks_test-896"><span class="linenos">896</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-897"><a href="#ks_test-897"><span class="linenos">897</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-898"><a href="#ks_test-898"><span class="linenos">898</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-899"><a href="#ks_test-899"><span class="linenos">899</span></a>
|
||||
</span><span id="ks_test-900"><a href="#ks_test-900"><span class="linenos">900</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>
|
||||
|
||||
|
||||
|
|
|
|||
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