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<div>
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<a class="pdoc-button module-list-button" href="../pyerrors.html">
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<svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-box-arrow-in-left" viewBox="0 0 16 16">
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<path fill-rule="evenodd" d="M10 3.5a.5.5 0 0 0-.5-.5h-8a.5.5 0 0 0-.5.5v9a.5.5 0 0 0 .5.5h8a.5.5 0 0 0 .5-.5v-2a.5.5 0 0 1 1 0v2A1.5 1.5 0 0 1 9.5 14h-8A1.5 1.5 0 0 1 0 12.5v-9A1.5 1.5 0 0 1 1.5 2h8A1.5 1.5 0 0 1 11 3.5v2a.5.5 0 0 1-1 0v-2z"/>
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</svg> pyerrors</a>
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<input type="search" placeholder="Search..." role="searchbox" aria-label="search"
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pattern=".+" required>
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<h2>API Documentation</h2>
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<ul class="memberlist">
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<li>
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<a class="class" href="#Fit_result">Fit_result</a>
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<ul class="memberlist">
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<li>
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<a class="function" href="#Fit_result.__init__">Fit_result</a>
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</li>
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<li>
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<a class="function" href="#Fit_result.gamma_method">gamma_method</a>
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</li>
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<li>
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<a class="function" href="#least_squares">least_squares</a>
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|
</li>
|
|
<li>
|
|
<a class="function" href="#total_least_squares">total_least_squares</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#prior_fit">prior_fit</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#standard_fit">standard_fit</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#odr_fit">odr_fit</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#fit_lin">fit_lin</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#qqplot">qqplot</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#residual_plot">residual_plot</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#covariance_matrix">covariance_matrix</a>
|
|
</li>
|
|
<li>
|
|
<a class="function" href="#error_band">error_band</a>
|
|
</li>
|
|
</ul>
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src="data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A//www.w3.org/2000/svg%22%20role%3D%22img%22%20aria-label%3D%22pdoc%20logo%22%20width%3D%22300%22%20height%3D%22150%22%20viewBox%3D%22-1%200%2060%2030%22%3E%3Ctitle%3Epdoc%3C/title%3E%3Cpath%20d%3D%22M29.621%2021.293c-.011-.273-.214-.475-.511-.481a.5.5%200%200%200-.489.503l-.044%201.393c-.097.551-.695%201.215-1.566%201.704-.577.428-1.306.486-2.193.182-1.426-.617-2.467-1.654-3.304-2.487l-.173-.172a3.43%203.43%200%200%200-.365-.306.49.49%200%200%200-.286-.196c-1.718-1.06-4.931-1.47-7.353.191l-.219.15c-1.707%201.187-3.413%202.131-4.328%201.03-.02-.027-.49-.685-.141-1.763.233-.721.546-2.408.772-4.076.042-.09.067-.187.046-.288.166-1.347.277-2.625.241-3.351%201.378-1.008%202.271-2.586%202.271-4.362%200-.976-.272-1.935-.788-2.774-.057-.094-.122-.18-.184-.268.033-.167.052-.339.052-.516%200-1.477-1.202-2.679-2.679-2.679-.791%200-1.496.352-1.987.9a6.3%206.3%200%200%200-1.001.029c-.492-.564-1.207-.929-2.012-.929-1.477%200-2.679%201.202-2.679%202.679A2.65%202.65%200%200%200%20.97%206.554c-.383.747-.595%201.572-.595%202.41%200%202.311%201.507%204.29%203.635%205.107-.037.699-.147%202.27-.423%203.294l-.137.461c-.622%202.042-2.515%208.257%201.727%2010.643%201.614.908%203.06%201.248%204.317%201.248%202.665%200%204.492-1.524%205.322-2.401%201.476-1.559%202.886-1.854%206.491.82%201.877%201.393%203.514%201.753%204.861%201.068%202.223-1.713%202.811-3.867%203.399-6.374.077-.846.056-1.469.054-1.537zm-4.835%204.313c-.054.305-.156.586-.242.629-.034-.007-.131-.022-.307-.157-.145-.111-.314-.478-.456-.908.221.121.432.25.675.355.115.039.219.051.33.081zm-2.251-1.238c-.05.33-.158.648-.252.694-.022.001-.125-.018-.307-.157-.217-.166-.488-.906-.639-1.573.358.344.754.693%201.198%201.036zm-3.887-2.337c-.006-.116-.018-.231-.041-.342.635.145%201.189.368%201.599.625.097.231.166.481.174.642-.03.049-.055.101-.067.158-.046.013-.128.026-.298.004-.278-.037-.901-.57-1.367-1.087zm-1.127-.497c.116.306.176.625.12.71-.019.014-.117.045-.345.016-.206-.027-.604-.332-.986-.695.41-.051.816-.056%201.211-.031zm-4.535%201.535c.209.22.379.47.358.598-.006.041-.088.138-.351.234-.144.055-.539-.063-.979-.259a11.66%2011.66%200%200%200%20.972-.573zm.983-.664c.359-.237.738-.418%201.126-.554.25.237.479.548.457.694-.006.042-.087.138-.351.235-.174.064-.694-.105-1.232-.375zm-3.381%201.794c-.022.145-.061.29-.149.401-.133.166-.358.248-.69.251h-.002c-.133%200-.306-.26-.45-.621.417.091.854.07%201.291-.031zm-2.066-8.077a4.78%204.78%200%200%201-.775-.584c.172-.115.505-.254.88-.378l-.105.962zm-.331%202.302a10.32%2010.32%200%200%201-.828-.502c.202-.143.576-.328.984-.49l-.156.992zm-.45%202.157l-.701-.403c.214-.115.536-.249.891-.376a11.57%2011.57%200%200%201-.19.779zm-.181%201.716c.064.398.194.702.298.893-.194-.051-.435-.162-.736-.398.061-.119.224-.3.438-.495zM8.87%204.141c0%20.152-.123.276-.276.276s-.275-.124-.275-.276.123-.276.276-.276.275.124.275.276zm-.735-.389a1.15%201.15%200%200%200-.314.783%201.16%201.16%200%200%200%201.162%201.162c.457%200%20.842-.27%201.032-.653.026.117.042.238.042.362a1.68%201.68%200%200%201-1.679%201.679%201.68%201.68%200%200%201-1.679-1.679c0-.843.626-1.535%201.436-1.654zM5.059%205.406A1.68%201.68%200%200%201%203.38%207.085a1.68%201.68%200%200%201-1.679-1.679c0-.037.009-.072.011-.109.21.3.541.508.935.508a1.16%201.16%200%200%200%201.162-1.162%201.14%201.14%200%200%200-.474-.912c.015%200%20.03-.005.045-.005.926.001%201.679.754%201.679%201.68zM3.198%204.141c0%20.152-.123.276-.276.276s-.275-.124-.275-.276.123-.276.276-.276.275.124.275.276zM1.375%208.964c0-.52.103-1.035.288-1.52.466.394%201.06.64%201.717.64%201.144%200%202.116-.725%202.499-1.738.383%201.012%201.355%201.738%202.499%201.738.867%200%201.631-.421%202.121-1.062.307.605.478%201.267.478%201.942%200%202.486-2.153%204.51-4.801%204.51s-4.801-2.023-4.801-4.51zm24.342%2019.349c-.985.498-2.267.168-3.813-.979-3.073-2.281-5.453-3.199-7.813-.705-1.315%201.391-4.163%203.365-8.423.97-3.174-1.786-2.239-6.266-1.261-9.479l.146-.492c.276-1.02.395-2.457.444-3.268a6.11%206.11%200%200%200%201.18.115%206.01%206.01%200%200%200%202.536-.562l-.006.175c-.802.215-1.848.612-2.021%201.25-.079.295.021.601.274.837.219.203.415.364.598.501-.667.304-1.243.698-1.311%201.179-.02.144-.022.507.393.787.213.144.395.26.564.365-1.285.521-1.361.96-1.381%201.126-.018.142-.011.496.427.746l.854.489c-.473.389-.971.914-.999%201.429-.018.278.095.532.316.713.675.556%201.231.721%201.653.721.059%200%20.104-.014.158-.02.207.707.641%201.64%201.513%201.64h.013c.8-.008%201.236-.345%201.462-.626.173-.216.268-.457.325-.692.424.195.93.374%201.372.374.151%200%20.294-.021.423-.068.732-.27.944-.704.993-1.021.009-.061.003-.119.002-.179.266.086.538.147.789.147.15%200%20.294-.021.423-.069.542-.2.797-.489.914-.754.237.147.478.258.704.288.106.014.205.021.296.021.356%200%20.595-.101.767-.229.438.435%201.094.992%201.656%201.067.106.014.205.021.296.021a1.56%201.56%200%200%200%20.323-.035c.17.575.453%201.289.866%201.605.358.273.665.362.914.362a.99.99%200%200%200%20.421-.093%201.03%201.03%200%200%200%20.245-.164c.168.42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</nav>
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<main class="pdoc">
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<section>
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<h1 class="modulename">
|
|
<a href="./../pyerrors.html">pyerrors</a><wbr>.fits </h1>
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<details>
|
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<summary>View Source</summary>
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<div class="codehilite"><pre><span></span><span class="kn">from</span> <span class="nn">collections.abc</span> <span class="kn">import</span> <span class="n">Sequence</span>
|
|
<span class="kn">import</span> <span class="nn">warnings</span>
|
|
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
|
<span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">anp</span>
|
|
<span class="kn">import</span> <span class="nn">scipy.optimize</span>
|
|
<span class="kn">import</span> <span class="nn">scipy.stats</span>
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<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
|
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">gridspec</span>
|
|
<span class="kn">from</span> <span class="nn">scipy.odr</span> <span class="kn">import</span> <span class="n">ODR</span><span class="p">,</span> <span class="n">Model</span><span class="p">,</span> <span class="n">RealData</span>
|
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<span class="kn">import</span> <span class="nn">iminuit</span>
|
|
<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">jacobian</span>
|
|
<span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">elementwise_grad</span> <span class="k">as</span> <span class="n">egrad</span>
|
|
<span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="n">Obs</span><span class="p">,</span> <span class="n">derived_observable</span><span class="p">,</span> <span class="n">covariance</span><span class="p">,</span> <span class="n">cov_Obs</span>
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<span class="k">class</span> <span class="nc">Fit_result</span><span class="p">(</span><span class="n">Sequence</span><span class="p">):</span>
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<span class="sd">"""Represents fit results.</span>
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|
<span class="sd"> Attributes</span>
|
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<span class="sd"> ----------</span>
|
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<span class="sd"> fit_parameters : list</span>
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<span class="sd"> results for the individual fit parameters,</span>
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|
<span class="sd"> also accessible via indices.</span>
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<span class="sd"> """</span>
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|
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<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
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<span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
|
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<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
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<span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">)</span>
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|
<span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
|
<span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="bp">self</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span>
|
|
<span class="n">my_str</span> <span class="o">=</span> <span class="s1">'Goodness of fit:</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_dof'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/d.o.f. = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'residual_variance'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'residual variance = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">residual_variance</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_expected_chisquare'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/</span><span class="se">\u03C7\u00b2</span><span class="s1">exp = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'Fit parameters:</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">for</span> <span class="n">i_par</span><span class="p">,</span> <span class="n">par</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_par</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\t</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">' '</span> <span class="o">*</span> <span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">par</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o"><</span> <span class="mf">0.0</span><span class="p">))</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">return</span> <span class="n">my_str</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())))</span> <span class="o">+</span> <span class="mi">1</span>
|
|
<span class="k">return</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">key</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">+</span> <span class="s1">': '</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">items</span><span class="p">())])</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x).</span>
|
|
|
|
<span class="sd"> Parameters</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> x : list</span>
|
|
<span class="sd"> list of floats.</span>
|
|
<span class="sd"> y : list</span>
|
|
<span class="sd"> list of Obs.</span>
|
|
<span class="sd"> func : object</span>
|
|
<span class="sd"> fit function, has to be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
|
<span class="sd"> return y</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> For multiple x values func can be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> (x1, x2) = x</span>
|
|
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
|
<span class="sd"> will not work</span>
|
|
<span class="sd"> priors : list, optional</span>
|
|
<span class="sd"> priors has to be a list with an entry for every parameter in the fit. The entries can either be</span>
|
|
<span class="sd"> Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like</span>
|
|
<span class="sd"> 0.548(23), 500(40) or 0.5(0.4)</span>
|
|
<span class="sd"> silent : bool, optional</span>
|
|
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
|
<span class="sd"> initial_guess : list</span>
|
|
<span class="sd"> can provide an initial guess for the input parameters. Relevant for</span>
|
|
<span class="sd"> non-linear fits with many parameters.</span>
|
|
<span class="sd"> method : str</span>
|
|
<span class="sd"> can be used to choose an alternative method for the minimization of chisquare.</span>
|
|
<span class="sd"> The possible methods are the ones which can be used for scipy.optimize.minimize and</span>
|
|
<span class="sd"> migrad of iminuit. If no method is specified, Levenberg-Marquard is used.</span>
|
|
<span class="sd"> Reliable alternatives are migrad, Powell and Nelder-Mead.</span>
|
|
<span class="sd"> resplot : bool</span>
|
|
<span class="sd"> If true, a plot which displays fit, data and residuals is generated (default False).</span>
|
|
<span class="sd"> qqplot : bool</span>
|
|
<span class="sd"> If true, a quantile-quantile plot of the fit result is generated (default False).</span>
|
|
<span class="sd"> expected_chisquare : bool</span>
|
|
<span class="sd"> If true prints the expected chisquare which is</span>
|
|
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
|
<span class="sd"> This can take a while as the full correlation matrix</span>
|
|
<span class="sd"> has to be calculated (default False).</span>
|
|
<span class="sd"> correlated_fit : bool</span>
|
|
<span class="sd"> If true, use the full correlation matrix in the definition of the chisquare</span>
|
|
<span class="sd"> (only works for prior==None and when no method is given, at the moment).</span>
|
|
<span class="sd"> const_par : list, optional</span>
|
|
<span class="sd"> List of N Obs that are used to constrain the last N fit parameters of func.</span>
|
|
<span class="sd"> '''</span>
|
|
<span class="k">if</span> <span class="n">priors</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
|
|
|
<span class="sd"> Parameters</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> x : list</span>
|
|
<span class="sd"> list of Obs, or a tuple of lists of Obs</span>
|
|
<span class="sd"> y : list</span>
|
|
<span class="sd"> list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</span>
|
|
<span class="sd"> func : object</span>
|
|
<span class="sd"> func has to be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
|
<span class="sd"> return y</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> For multiple x values func can be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> (x1, x2) = x</span>
|
|
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
|
<span class="sd"> will not work.</span>
|
|
<span class="sd"> silent : bool, optional</span>
|
|
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
|
<span class="sd"> initial_guess : list</span>
|
|
<span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
|
<span class="sd"> fits with many parameters.</span>
|
|
<span class="sd"> expected_chisquare : bool</span>
|
|
<span class="sd"> If true prints the expected chisquare which is</span>
|
|
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
|
<span class="sd"> This can take a while as the full correlation matrix</span>
|
|
<span class="sd"> has to be calculated (default False).</span>
|
|
<span class="sd"> const_par : list, optional</span>
|
|
<span class="sd"> List of N Obs that are used to constrain the last N fit parameters of func.</span>
|
|
|
|
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
|
<span class="sd"> '''</span>
|
|
|
|
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
|
|
|
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
|
|
<span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
|
|
|
<span class="n">func_aug</span> <span class="o">=</span> <span class="n">func</span>
|
|
<span class="k">if</span> <span class="s1">'const_par'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'const_par'</span><span class="p">]</span>
|
|
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">const_par</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[</span><span class="n">const_par</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="n">func_aug</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">p</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">const_par</span><span class="p">])),</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[]</span>
|
|
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">25</span><span class="p">):</span>
|
|
<span class="k">try</span><span class="p">:</span>
|
|
<span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
<span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
|
|
<span class="k">pass</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">break</span>
|
|
|
|
<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameters'</span><span class="p">)</span>
|
|
<span class="k">if</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">):</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\t</span><span class="s1"> and </span><span class="si">%d</span><span class="s1"> constrained parameter</span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">),</span> <span class="s1">'s'</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span> <span class="k">else</span> <span class="s1">''</span><span class="p">),</span> <span class="n">const_par</span><span class="p">)</span>
|
|
|
|
<span class="n">x_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="n">dx_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="n">y_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
|
<span class="n">dy_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dx_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No x errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
|
|
|
<span class="n">data</span> <span class="o">=</span> <span class="n">RealData</span><span class="p">(</span><span class="n">x_f</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">sx</span><span class="o">=</span><span class="n">dx_f</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="n">dy_f</span><span class="p">)</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">Model</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
|
|
<span class="n">odr</span> <span class="o">=</span> <span class="n">ODR</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">partol</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span>
|
|
<span class="n">odr</span><span class="o">.</span><span class="n">set_job</span><span class="p">(</span><span class="n">fit_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">deriv</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
|
<span class="n">out</span> <span class="o">=</span> <span class="n">odr</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">res_var</span>
|
|
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|
<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'ODR'</span>
|
|
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|
<span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">stopreason</span>
|
|
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|
<span class="n">output</span><span class="o">.</span><span class="n">xplus</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: ODR'</span><span class="p">)</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="o">*</span><span class="n">out</span><span class="o">.</span><span class="n">stopreason</span><span class="p">)</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Residual variance:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span><span class="p">)</span>
|
|
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<span class="k">if</span> <span class="n">out</span><span class="o">.</span><span class="n">info</span> <span class="o">></span> <span class="mi">3</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
|
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|
<span class="n">m</span> <span class="o">=</span> <span class="n">x_f</span><span class="o">.</span><span class="n">size</span>
|
|
<span class="n">n_parms_aug</span> <span class="o">=</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span>
|
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<span class="k">def</span> <span class="nf">odr_chisquare</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
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<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
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|
<span class="k">def</span> <span class="nf">odr_chisquare_aug</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</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">p</span><span class="p">[:</span><span class="n">n_parms_aug</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">const_par</span><span class="p">])),</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">dy_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">dx_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
|
|
<span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
|
|
|
<span class="n">old_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">)</span>
|
|
<span class="n">fused_row1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">old_jac</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">)]),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)))</span>
|
|
<span class="n">fused_row2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">jacobian</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">))(</span><span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">number_of_x_parameters</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])))</span>
|
|
<span class="n">new_jac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fused_row1</span><span class="p">,</span> <span class="n">fused_row2</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
|
|
|
<span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">new_jac</span>
|
|
<span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
|
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">P_phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">expected_chisquare</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">:</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Negative expected_chisquare."</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
|
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">expected_chisquare</span><span class="p">)</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
|
|
|
<span class="n">fitp</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">out</span><span class="o">.</span><span class="n">beta</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">const_par</span><span class="p">]))</span>
|
|
<span class="n">hess_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_aug</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare_compact_x</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">jac_jac_x</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_x</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">x_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
|
|
<span class="n">deriv_x</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac_x</span><span class="p">[:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare_compact_y</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="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_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">jac_jac_y</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_y</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">y_f</span><span class="p">)))</span>
|
|
|
|
<span class="n">deriv_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac_y</span><span class="p">[:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span>
|
|
|
|
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
|
<span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">my_var</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">my_var</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv_x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">deriv_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span> <span class="o">+</span> <span class="n">const_par</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
|
|
|
|
<span class="k">return</span> <span class="n">output</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"prior_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
|
|
|
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
|
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
|
|
<span class="k">try</span><span class="p">:</span>
|
|
<span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
|
|
<span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
|
|
<span class="k">pass</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">break</span>
|
|
|
|
<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
|
|
|
<span class="k">if</span> <span class="n">n_parms</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">priors</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Priors does not have the correct length.'</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">extract_val_and_dval</span><span class="p">(</span><span class="n">string</span><span class="p">):</span>
|
|
<span class="n">split_string</span> <span class="o">=</span> <span class="n">string</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s1">'('</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="s1">'.'</span> <span class="ow">in</span> <span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="ow">and</span> <span class="s1">'.'</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">split_string</span><span class="p">[</span><span class="mi">1</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
|
|
<span class="n">factor</span> <span class="o">=</span> <span class="mi">10</span> <span class="o">**</span> <span class="o">-</span><span class="nb">len</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="s1">'.'</span><span class="p">)[</span><span class="mi">2</span><span class="p">])</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">factor</span> <span class="o">=</span> <span class="mi">1</span>
|
|
<span class="k">return</span> <span class="nb">float</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="nb">float</span><span class="p">(</span><span class="n">split_string</span><span class="p">[</span><span class="mi">1</span><span class="p">][:</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">factor</span>
|
|
|
|
<span class="n">loc_priors</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="k">for</span> <span class="n">i_n</span><span class="p">,</span> <span class="n">i_prior</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">priors</span><span class="p">):</span>
|
|
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_prior</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
|
|
<span class="n">loc_priors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i_prior</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">loc_val</span><span class="p">,</span> <span class="n">loc_dval</span> <span class="o">=</span> <span class="n">extract_val_and_dval</span><span class="p">(</span><span class="n">i_prior</span><span class="p">)</span>
|
|
<span class="n">loc_priors</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">cov_Obs</span><span class="p">(</span><span class="n">loc_val</span><span class="p">,</span> <span class="n">loc_dval</span> <span class="o">**</span> <span class="mi">2</span><span class="p">,</span> <span class="s1">'#prior'</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_n</span><span class="p">)</span> <span class="o">+</span> <span class="sa">f</span><span class="s2">"_</span><span class="si">{</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">2147483647</span><span class="p">)</span><span class="si">:</span><span class="s2">010d</span><span class="si">}</span><span class="s2">"</span><span class="p">))</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">priors</span> <span class="o">=</span> <span class="n">loc_priors</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameters'</span><span class="p">)</span>
|
|
|
|
<span class="n">y_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
|
<span class="n">dy_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="n">p_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">loc_priors</span><span class="p">]</span>
|
|
<span class="n">dp_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">loc_priors</span><span class="p">]</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dp_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No prior errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length.'</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="n">p_f</span>
|
|
|
|
<span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">p_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span> <span class="o">/</span> <span class="n">dp_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: migrad'</span><span class="p">)</span>
|
|
|
|
<span class="n">m</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">Minuit</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">)</span>
|
|
<span class="n">m</span><span class="o">.</span><span class="n">errordef</span> <span class="o">=</span> <span class="mi">1</span>
|
|
<span class="n">m</span><span class="o">.</span><span class="n">print_level</span> <span class="o">=</span> <span class="mi">0</span>
|
|
<span class="k">if</span> <span class="s1">'tol'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">m</span><span class="o">.</span><span class="n">tol</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'tol'</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">m</span><span class="o">.</span><span class="n">tol</span> <span class="o">=</span> <span class="mf">1e-4</span>
|
|
<span class="n">m</span><span class="o">.</span><span class="n">migrad</span><span class="p">()</span>
|
|
<span class="n">params</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">m</span><span class="o">.</span><span class="n">values</span><span class="p">)</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="n">m</span><span class="o">.</span><span class="n">fval</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'migrad'</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/d.o.f.:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">m</span><span class="o">.</span><span class="n">fmin</span><span class="o">.</span><span class="n">is_valid</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
|
|
|
<span class="n">hess_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">))(</span><span class="n">params</span><span class="p">))</span>
|
|
|
|
<span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">):]</span> <span class="o">-</span> <span class="n">d</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">])</span> <span class="o">/</span> <span class="n">dp_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
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|
<span class="n">jac_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_compact</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">params</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">p_f</span><span class="p">)))</span>
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|
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|
<span class="n">deriv</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">:]</span>
|
|
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|
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
|
<span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="n">params</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">loc_priors</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
|
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|
<span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">=</span> <span class="n">chisqfunc</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">params</span><span class="p">))</span>
|
|
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|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'resplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="n">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'qqplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="n">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
|
|
|
|
<span class="k">return</span> <span class="n">output</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
|
|
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
|
|
|
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'x and y input have to have the same length'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span> <span class="o">></span> <span class="mi">2</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unknown format for x values'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
|
|
|
<span class="n">func_aug</span> <span class="o">=</span> <span class="n">func</span>
|
|
<span class="k">if</span> <span class="s1">'const_par'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'const_par'</span><span class="p">]</span>
|
|
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">const_par</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[</span><span class="n">const_par</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="n">func_aug</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">p</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">const_par</span><span class="p">])),</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[]</span>
|
|
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">25</span><span class="p">):</span>
|
|
<span class="k">try</span><span class="p">:</span>
|
|
<span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
<span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
|
|
<span class="k">pass</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">break</span>
|
|
|
|
<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameters'</span><span class="p">)</span>
|
|
<span class="k">if</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">):</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\t</span><span class="s1"> and </span><span class="si">%d</span><span class="s1"> constrained parameter</span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">),</span> <span class="s1">'s'</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span> <span class="k">else</span> <span class="s1">''</span><span class="p">),</span> <span class="n">const_par</span><span class="p">)</span>
|
|
|
|
<span class="n">y_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
|
<span class="n">dy_f</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
|
|
|
<span class="k">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 class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
<span class="n">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="mf">1.</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span>
|
|
<span class="n">corr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">cov</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">y</span><span class="p">)):</span>
|
|
<span class="k">for</span> <span class="n">j</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">y</span><span class="p">)):</span>
|
|
<span class="n">corr</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">cov</span><span class="p">[</span><span class="n">i</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="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">j</span><span class="p">])</span>
|
|
<span class="n">condn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mf">1e4</span><span class="p">:</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Correlation matrix may be ill-conditioned! condition number: </span><span class="si">%1.2e</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">condn</span><span class="p">),</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
|
<span class="n">chol</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
|
<span class="n">chol_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">chol</span><span class="p">)</span>
|
|
<span class="n">chol_inv</span> <span class="o">=</span> <span class="n">np</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="n">covdiag</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="p">(</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">def</span> <span class="nf">chisqfunc_aug</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</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">p</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">const_par</span><span class="p">])),</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="p">(</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">def</span> <span class="nf">chisqfunc</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">def</span> <span class="nf">chisqfunc_aug</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</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">p</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">const_par</span><span class="p">])),</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">if</span> <span class="s1">'method'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method:'</span><span class="p">,</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">))</span>
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">)</span> <span class="o">==</span> <span class="s1">'migrad'</span><span class="p">:</span>
|
|
<span class="n">fit_result</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">)</span>
|
|
<span class="n">fit_result</span> <span class="o">=</span> <span class="n">iminuit</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">))</span>
|
|
<span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">minimize</span><span class="p">(</span><span class="n">chisqfunc</span><span class="p">,</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'method'</span><span class="p">),</span> <span class="n">tol</span><span class="o">=</span><span class="mf">1e-12</span><span class="p">)</span>
|
|
|
|
<span class="n">chisquare</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">nit</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'Levenberg-Marquardt'</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: Levenberg-Marquardt'</span><span class="p">)</span>
|
|
|
|
<span class="k">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 class="k">def</span> <span class="nf">chisqfunc_residuals</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="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="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">def</span> <span class="nf">chisqfunc_residuals</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="p">((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">fit_result</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">optimize</span><span class="o">.</span><span class="n">least_squares</span><span class="p">(</span><span class="n">chisqfunc_residuals</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">'lm'</span><span class="p">,</span> <span class="n">ftol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">gtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">,</span> <span class="n">xtol</span><span class="o">=</span><span class="mf">1e-15</span><span class="p">)</span>
|
|
|
|
<span class="n">chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">fun</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">iterations</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">nfev</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">success</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="n">chisquare</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'nan'</span><span class="p">)</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">message</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">message</span><span class="p">)</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/d.o.f.:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="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 class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">))</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
<span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
|
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">chisquare</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
|
|
|
<span class="n">fitp</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">fit_result</span><span class="o">.</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">const_par</span><span class="p">]))</span>
|
|
<span class="n">hess_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_aug</span><span class="p">))(</span><span class="n">fitp</span><span class="p">))</span>
|
|
|
|
<span class="n">n_parms_aug</span> <span class="o">=</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">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_aug</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 class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">def</span> <span class="nf">chisqfunc_compact</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">jac_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">chisqfunc_compact</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">y_f</span><span class="p">)))</span>
|
|
|
|
<span class="n">deriv</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">,</span> <span class="n">n_parms_aug</span><span class="p">:]</span>
|
|
|
|
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
|
<span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
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<span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span> <span class="o">+</span> <span class="n">const_par</span>
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<span class="n">output</span><span class="o">.</span><span class="n">chisquare</span> <span class="o">=</span> <span class="n">chisqfunc</span><span class="p">(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
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<span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'resplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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|
<span class="n">residual_plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'qqplot'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
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|
<span class="n">qqplot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">result</span><span class="p">)</span>
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|
<span class="k">return</span> <span class="n">output</span>
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<span class="k">def</span> <span class="nf">odr_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
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|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
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|
<span class="k">return</span> <span class="n">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
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<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>
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<span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
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<span class="sd"> y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.</span>
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<span class="sd"> x can either be a list of floats in which case no xerror is assumed, or</span>
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<span class="sd"> a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</span>
|
|
<span class="sd"> """</span>
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<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>
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<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>
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|
<span class="k">return</span> <span class="n">y</span>
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<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>
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<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>
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<span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
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|
<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>
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<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>
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|
<span class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unsupported types for x'</span><span class="p">)</span>
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<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>
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<span class="sd">""" Generates a quantile-quantile plot of the fit result which can be used to</span>
|
|
<span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
|
<span class="sd"> """</span>
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|
<span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
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|
<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>
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|
<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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|
<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>
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<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>
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|
<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>
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|
<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>
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|
<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>
|
|
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|
<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>
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|
<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 class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
|
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|
|
|
<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="sd">""" Generates a plot which compares the fit to the data and displays the corresponding residuals"""</span>
|
|
<span class="n">xstart</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span>
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|
<span class="n">xstop</span> <span class="o">=</span> <span class="n">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="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="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
|
|
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|
<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 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 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 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>
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|
<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 class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
|
<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 class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
|
<span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
|
|
|
<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 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 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 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 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 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 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 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 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 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 class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
|
|
|
|
|
<span class="k">def</span> <span class="nf">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
|
<span class="sd">"""Returns the covariance matrix of y."""</span>
|
|
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
|
<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">y</span><span class="p">):</span>
|
|
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">jtem</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">[:</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]):</span>
|
|
<span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
|
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">**</span> <span class="mi">2</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">jtem</span><span class="p">)</span>
|
|
<span class="k">return</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="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
|
|
|
|
|
<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 class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">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 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 class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<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 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 class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<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 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 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 class="k">return</span> <span class="n">err</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
</section>
|
|
<section id="Fit_result">
|
|
<div class="attr class">
|
|
<a class="headerlink" href="#Fit_result">#  </a>
|
|
|
|
|
|
<span class="def">class</span>
|
|
<span class="name">Fit_result</span><wbr>(<span class="base">collections.abc.Sequence</span>):
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">class</span> <span class="nc">Fit_result</span><span class="p">(</span><span class="n">Sequence</span><span class="p">):</span>
|
|
<span class="sd">"""Represents fit results.</span>
|
|
|
|
<span class="sd"> Attributes</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> fit_parameters : list</span>
|
|
<span class="sd"> results for the individual fit parameters,</span>
|
|
<span class="sd"> also accessible via indices.</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__getitem__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">idx</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">[</span><span class="n">idx</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__len__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
|
<span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__str__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="bp">self</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span>
|
|
<span class="n">my_str</span> <span class="o">=</span> <span class="s1">'Goodness of fit:</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_dof'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/d.o.f. = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_dof</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">elif</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'residual_variance'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'residual variance = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">residual_variance</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">if</span> <span class="nb">hasattr</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="s1">'chisquare_by_expected_chisquare'</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'</span><span class="se">\u03C7\u00b2</span><span class="s1">/</span><span class="se">\u03C7\u00b2</span><span class="s1">exp = '</span> <span class="o">+</span> <span class="sa">f</span><span class="s1">'</span><span class="si">{</span><span class="bp">self</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="si">:</span><span class="s1">2.6f</span><span class="si">}</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="s1">'Fit parameters:</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">for</span> <span class="n">i_par</span><span class="p">,</span> <span class="n">par</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">):</span>
|
|
<span class="n">my_str</span> <span class="o">+=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i_par</span><span class="p">)</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\t</span><span class="s1">'</span> <span class="o">+</span> <span class="s1">' '</span> <span class="o">*</span> <span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">par</span><span class="p">)</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">par</span> <span class="o"><</span> <span class="mf">0.0</span><span class="p">))</span> <span class="o">+</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span>
|
|
<span class="k">return</span> <span class="n">my_str</span>
|
|
|
|
<span class="k">def</span> <span class="fm">__repr__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">map</span><span class="p">(</span><span class="nb">len</span><span class="p">,</span> <span class="nb">list</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">keys</span><span class="p">())))</span> <span class="o">+</span> <span class="mi">1</span>
|
|
<span class="k">return</span> <span class="s1">'</span><span class="se">\n</span><span class="s1">'</span><span class="o">.</span><span class="n">join</span><span class="p">([</span><span class="n">key</span><span class="o">.</span><span class="n">rjust</span><span class="p">(</span><span class="n">m</span><span class="p">)</span> <span class="o">+</span> <span class="s1">': '</span> <span class="o">+</span> <span class="nb">repr</span><span class="p">(</span><span class="n">value</span><span class="p">)</span> <span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="nb">sorted</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="vm">__dict__</span><span class="o">.</span><span class="n">items</span><span class="p">())])</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Represents fit results.</p>
|
|
|
|
<h6 id="attributes">Attributes</h6>
|
|
|
|
<ul>
|
|
<li><strong>fit_parameters</strong> (list):
|
|
results for the individual fit parameters,
|
|
also accessible via indices.</li>
|
|
</ul>
|
|
</div>
|
|
|
|
|
|
<div id="Fit_result.__init__" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#Fit_result.__init__">#  </a>
|
|
|
|
|
|
<span class="name">Fit_result</span><span class="signature">()</span>
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="kc">None</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
|
|
|
|
</div>
|
|
<div id="Fit_result.gamma_method" class="classattr">
|
|
<div class="attr function"><a class="headerlink" href="#Fit_result.gamma_method">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">gamma_method</span><span class="signature">(self)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span> <span class="k">def</span> <span class="nf">gamma_method</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<span class="sd">"""Apply the gamma method to all fit parameters"""</span>
|
|
<span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">fit_parameters</span><span class="p">]</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Apply the gamma method to all fit parameters</p>
|
|
</div>
|
|
|
|
|
|
</div>
|
|
<div class="inherited">
|
|
<h5>Inherited Members</h5>
|
|
<dl>
|
|
<div><dt>collections.abc.Sequence</dt>
|
|
<dd id="Fit_result.index" class="function">index</dd>
|
|
<dd id="Fit_result.count" class="function">count</dd>
|
|
|
|
</div>
|
|
</dl>
|
|
</div>
|
|
</section>
|
|
<section id="least_squares">
|
|
<div class="attr function"><a class="headerlink" href="#least_squares">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">least_squares</span><span class="signature">(x, y, func, priors=None, silent=False, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x).</span>
|
|
|
|
<span class="sd"> Parameters</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> x : list</span>
|
|
<span class="sd"> list of floats.</span>
|
|
<span class="sd"> y : list</span>
|
|
<span class="sd"> list of Obs.</span>
|
|
<span class="sd"> func : object</span>
|
|
<span class="sd"> fit function, has to be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
|
<span class="sd"> return y</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> For multiple x values func can be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> (x1, x2) = x</span>
|
|
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
|
<span class="sd"> will not work</span>
|
|
<span class="sd"> priors : list, optional</span>
|
|
<span class="sd"> priors has to be a list with an entry for every parameter in the fit. The entries can either be</span>
|
|
<span class="sd"> Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like</span>
|
|
<span class="sd"> 0.548(23), 500(40) or 0.5(0.4)</span>
|
|
<span class="sd"> silent : bool, optional</span>
|
|
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
|
<span class="sd"> initial_guess : list</span>
|
|
<span class="sd"> can provide an initial guess for the input parameters. Relevant for</span>
|
|
<span class="sd"> non-linear fits with many parameters.</span>
|
|
<span class="sd"> method : str</span>
|
|
<span class="sd"> can be used to choose an alternative method for the minimization of chisquare.</span>
|
|
<span class="sd"> The possible methods are the ones which can be used for scipy.optimize.minimize and</span>
|
|
<span class="sd"> migrad of iminuit. If no method is specified, Levenberg-Marquard is used.</span>
|
|
<span class="sd"> Reliable alternatives are migrad, Powell and Nelder-Mead.</span>
|
|
<span class="sd"> resplot : bool</span>
|
|
<span class="sd"> If true, a plot which displays fit, data and residuals is generated (default False).</span>
|
|
<span class="sd"> qqplot : bool</span>
|
|
<span class="sd"> If true, a quantile-quantile plot of the fit result is generated (default False).</span>
|
|
<span class="sd"> expected_chisquare : bool</span>
|
|
<span class="sd"> If true prints the expected chisquare which is</span>
|
|
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
|
<span class="sd"> This can take a while as the full correlation matrix</span>
|
|
<span class="sd"> has to be calculated (default False).</span>
|
|
<span class="sd"> correlated_fit : bool</span>
|
|
<span class="sd"> If true, use the full correlation matrix in the definition of the chisquare</span>
|
|
<span class="sd"> (only works for prior==None and when no method is given, at the moment).</span>
|
|
<span class="sd"> const_par : list, optional</span>
|
|
<span class="sd"> List of N Obs that are used to constrain the last N fit parameters of func.</span>
|
|
<span class="sd"> '''</span>
|
|
<span class="k">if</span> <span class="n">priors</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">return</span> <span class="n">_standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Performs a non-linear fit to y = func(x).</p>
|
|
|
|
<h6 id="parameters">Parameters</h6>
|
|
|
|
<ul>
|
|
<li><strong>x</strong> (list):
|
|
list of floats.</li>
|
|
<li><strong>y</strong> (list):
|
|
list of Obs.</li>
|
|
<li><p><strong>func</strong> (object):
|
|
fit function, has to be of the form</p>
|
|
|
|
<div class="codehilite"><pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">anp</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">y</span>
|
|
</code></pre></div>
|
|
|
|
<p>For multiple x values func can be of the form</p>
|
|
|
|
<div class="codehilite"><pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
|
|
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x2</span>
|
|
</code></pre></div>
|
|
|
|
<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
|
|
will not work</p></li>
|
|
<li><strong>priors</strong> (list, optional):
|
|
priors has to be a list with an entry for every parameter in the fit. The entries can either be
|
|
Obs (e.g. results from a previous fit) or strings containing a value and an error formatted like
|
|
0.548(23), 500(40) or 0.5(0.4)</li>
|
|
<li><strong>silent</strong> (bool, optional):
|
|
If true all output to the console is omitted (default False).</li>
|
|
<li><strong>initial_guess</strong> (list):
|
|
can provide an initial guess for the input parameters. Relevant for
|
|
non-linear fits with many parameters.</li>
|
|
<li><strong>method</strong> (str):
|
|
can be used to choose an alternative method for the minimization of chisquare.
|
|
The possible methods are the ones which can be used for scipy.optimize.minimize and
|
|
migrad of iminuit. If no method is specified, Levenberg-Marquard is used.
|
|
Reliable alternatives are migrad, Powell and Nelder-Mead.</li>
|
|
<li><strong>resplot</strong> (bool):
|
|
If true, a plot which displays fit, data and residuals is generated (default False).</li>
|
|
<li><strong>qqplot</strong> (bool):
|
|
If true, a quantile-quantile plot of the fit result is generated (default False).</li>
|
|
<li><strong>expected_chisquare</strong> (bool):
|
|
If true prints the expected chisquare which is
|
|
corrected by effects caused by correlated input data.
|
|
This can take a while as the full correlation matrix
|
|
has to be calculated (default False).</li>
|
|
<li><strong>correlated_fit</strong> (bool):
|
|
If true, use the full correlation matrix in the definition of the chisquare
|
|
(only works for prior==None and when no method is given, at the moment).</li>
|
|
<li><strong>const_par</strong> (list, optional):
|
|
List of N Obs that are used to constrain the last N fit parameters of func.</li>
|
|
</ul>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="total_least_squares">
|
|
<div class="attr function"><a class="headerlink" href="#total_least_squares">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">total_least_squares</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="sa">r</span><span class="sd">'''Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</span>
|
|
|
|
<span class="sd"> Parameters</span>
|
|
<span class="sd"> ----------</span>
|
|
<span class="sd"> x : list</span>
|
|
<span class="sd"> list of Obs, or a tuple of lists of Obs</span>
|
|
<span class="sd"> y : list</span>
|
|
<span class="sd"> list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</span>
|
|
<span class="sd"> func : object</span>
|
|
<span class="sd"> func has to be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> y = a[0] + a[1] * x + a[2] * anp.sinh(x)</span>
|
|
<span class="sd"> return y</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> For multiple x values func can be of the form</span>
|
|
|
|
<span class="sd"> ```python</span>
|
|
<span class="sd"> def func(a, x):</span>
|
|
<span class="sd"> (x1, x2) = x</span>
|
|
<span class="sd"> return a[0] * x1 ** 2 + a[1] * x2</span>
|
|
<span class="sd"> ```</span>
|
|
|
|
<span class="sd"> It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation</span>
|
|
<span class="sd"> will not work.</span>
|
|
<span class="sd"> silent : bool, optional</span>
|
|
<span class="sd"> If true all output to the console is omitted (default False).</span>
|
|
<span class="sd"> initial_guess : list</span>
|
|
<span class="sd"> can provide an initial guess for the input parameters. Relevant for non-linear</span>
|
|
<span class="sd"> fits with many parameters.</span>
|
|
<span class="sd"> expected_chisquare : bool</span>
|
|
<span class="sd"> If true prints the expected chisquare which is</span>
|
|
<span class="sd"> corrected by effects caused by correlated input data.</span>
|
|
<span class="sd"> This can take a while as the full correlation matrix</span>
|
|
<span class="sd"> has to be calculated (default False).</span>
|
|
<span class="sd"> const_par : list, optional</span>
|
|
<span class="sd"> List of N Obs that are used to constrain the last N fit parameters of func.</span>
|
|
|
|
<span class="sd"> Based on the orthogonal distance regression module of scipy</span>
|
|
<span class="sd"> '''</span>
|
|
|
|
<span class="n">output</span> <span class="o">=</span> <span class="n">Fit_result</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_function</span> <span class="o">=</span> <span class="n">func</span>
|
|
|
|
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
|
|
<span class="n">x_shape</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">callable</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'func has to be a function.'</span><span class="p">)</span>
|
|
|
|
<span class="n">func_aug</span> <span class="o">=</span> <span class="n">func</span>
|
|
<span class="k">if</span> <span class="s1">'const_par'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="n">kwargs</span><span class="p">[</span><span class="s1">'const_par'</span><span class="p">]</span>
|
|
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">const_par</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[</span><span class="n">const_par</span><span class="p">]</span>
|
|
|
|
<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="k">return</span> <span class="n">func_aug</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">p</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">const_par</span><span class="p">])),</span> <span class="n">x</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">const_par</span> <span class="o">=</span> <span class="p">[]</span>
|
|
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">25</span><span class="p">):</span>
|
|
<span class="k">try</span><span class="p">:</span>
|
|
<span class="n">func</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
|
|
<span class="k">except</span> <span class="ne">Exception</span><span class="p">:</span>
|
|
<span class="k">pass</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">break</span>
|
|
|
|
<span class="n">n_parms</span> <span class="o">=</span> <span class="n">i</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Fit with'</span><span class="p">,</span> <span class="n">n_parms</span><span class="p">,</span> <span class="s1">'parameters'</span><span class="p">)</span>
|
|
<span class="k">if</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">):</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'</span><span class="se">\t</span><span class="s1"> and </span><span class="si">%d</span><span class="s1"> constrained parameter</span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">),</span> <span class="s1">'s'</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span> <span class="o">></span> <span class="mi">1</span> <span class="k">else</span> <span class="s1">''</span><span class="p">),</span> <span class="n">const_par</span><span class="p">)</span>
|
|
|
|
<span class="n">x_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="n">dx_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="n">y_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">value</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
|
<span class="n">dy_f</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">y</span><span class="p">])</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dx_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No x errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">)</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">):</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'No y errors available, run the gamma method first.'</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="s1">'initial_guess'</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'initial_guess'</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_parms</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Initial guess does not have the correct length: </span><span class="si">%d</span><span class="s1"> vs. </span><span class="si">%d</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">x0</span><span class="p">),</span> <span class="n">n_parms</span><span class="p">))</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
|
|
|
<span class="n">data</span> <span class="o">=</span> <span class="n">RealData</span><span class="p">(</span><span class="n">x_f</span><span class="p">,</span> <span class="n">y_f</span><span class="p">,</span> <span class="n">sx</span><span class="o">=</span><span class="n">dx_f</span><span class="p">,</span> <span class="n">sy</span><span class="o">=</span><span class="n">dy_f</span><span class="p">)</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">Model</span><span class="p">(</span><span class="n">func</span><span class="p">)</span>
|
|
<span class="n">odr</span> <span class="o">=</span> <span class="n">ODR</span><span class="p">(</span><span class="n">data</span><span class="p">,</span> <span class="n">model</span><span class="p">,</span> <span class="n">x0</span><span class="p">,</span> <span class="n">partol</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span>
|
|
<span class="n">odr</span><span class="o">.</span><span class="n">set_job</span><span class="p">(</span><span class="n">fit_type</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">deriv</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
|
<span class="n">out</span> <span class="o">=</span> <span class="n">odr</span><span class="o">.</span><span class="n">run</span><span class="p">()</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">res_var</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">method</span> <span class="o">=</span> <span class="s1">'ODR'</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">message</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">stopreason</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">xplus</span> <span class="o">=</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span>
|
|
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Method: ODR'</span><span class="p">)</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="o">*</span><span class="n">out</span><span class="o">.</span><span class="n">stopreason</span><span class="p">)</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'Residual variance:'</span><span class="p">,</span> <span class="n">output</span><span class="o">.</span><span class="n">residual_variance</span><span class="p">)</span>
|
|
|
|
<span class="k">if</span> <span class="n">out</span><span class="o">.</span><span class="n">info</span> <span class="o">></span> <span class="mi">3</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The minimization procedure did not converge.'</span><span class="p">)</span>
|
|
|
|
<span class="n">m</span> <span class="o">=</span> <span class="n">x_f</span><span class="o">.</span><span class="n">size</span>
|
|
<span class="n">n_parms_aug</span> <span class="o">=</span> <span class="n">n_parms</span> <span class="o">+</span> <span class="nb">len</span><span class="p">(</span><span class="n">const_par</span><span class="p">)</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">p</span><span class="p">[:</span><span class="n">n_parms</span><span class="p">],</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare_aug</span><span class="p">(</span><span class="n">p</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</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">p</span><span class="p">[:</span><span class="n">n_parms_aug</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">const_par</span><span class="p">])),</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">p</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
|
<span class="n">W</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">dy_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">dx_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
|
|
|
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
|
|
<span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
|
|
|
<span class="n">old_jac</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">)</span>
|
|
<span class="n">fused_row1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">old_jac</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">)]),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)))</span>
|
|
<span class="n">fused_row2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">jacobian</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">func</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="p">))(</span><span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">number_of_x_parameters</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">number_of_x_parameters</span> <span class="o">*</span> <span class="n">old_jac</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])))</span>
|
|
<span class="n">new_jac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fused_row1</span><span class="p">,</span> <span class="n">fused_row2</span><span class="p">),</span> <span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
|
|
|
<span class="n">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">new_jac</span>
|
|
<span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
|
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">P_phi</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">expected_chisquare</span> <span class="o"><=</span> <span class="mf">0.0</span><span class="p">:</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Negative expected_chisquare."</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
|
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">expected_chisquare</span><span class="p">)</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span> <span class="o">/</span> <span class="n">expected_chisquare</span>
|
|
<span class="k">if</span> <span class="ow">not</span> <span class="n">silent</span><span class="p">:</span>
|
|
<span class="nb">print</span><span class="p">(</span><span class="s1">'chisquare/expected_chisquare:'</span><span class="p">,</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">chisquare_by_expected_chisquare</span><span class="p">)</span>
|
|
|
|
<span class="n">fitp</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">out</span><span class="o">.</span><span class="n">beta</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">const_par</span><span class="p">]))</span>
|
|
<span class="n">hess_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_aug</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">()))))</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare_compact_x</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="n">chisq</span> <span class="o">=</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">y_f</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">)</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">jac_jac_x</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_x</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">x_f</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
|
|
<span class="n">deriv_x</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac_x</span><span class="p">[:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span>
|
|
|
|
<span class="k">def</span> <span class="nf">odr_chisquare_compact_y</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
|
|
<span class="n">model</span> <span class="o">=</span> <span class="n">func_aug</span><span class="p">(</span><span class="n">d</span><span class="p">[:</span><span class="n">n_parms_aug</span><span class="p">],</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span>
|
|
<span class="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_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span> <span class="o">-</span> <span class="n">model</span><span class="p">)</span> <span class="o">/</span> <span class="n">dy_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">anp</span><span class="o">.</span><span class="n">sum</span><span class="p">(((</span><span class="n">x_f</span> <span class="o">-</span> <span class="n">d</span><span class="p">[</span><span class="n">n_parms_aug</span><span class="p">:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">x_shape</span><span class="p">))</span> <span class="o">/</span> <span class="n">dx_f</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">chisq</span>
|
|
|
|
<span class="n">jac_jac_y</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">jacobian</span><span class="p">(</span><span class="n">odr_chisquare_compact_y</span><span class="p">))(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">fitp</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">y_f</span><span class="p">)))</span>
|
|
|
|
<span class="n">deriv_y</span> <span class="o">=</span> <span class="o">-</span><span class="n">hess_inv</span> <span class="o">@</span> <span class="n">jac_jac_y</span><span class="p">[:</span><span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">,</span> <span class="n">n_parms_aug</span> <span class="o">+</span> <span class="n">m</span><span class="p">:]</span>
|
|
|
|
<span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_parms</span><span class="p">):</span>
|
|
<span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">my_var</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="p">(</span><span class="n">my_var</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">value</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">float64</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">)</span> <span class="o">*</span> <span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="nb">list</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">y</span><span class="p">),</span> <span class="n">man_grad</span><span class="o">=</span><span class="nb">list</span><span class="p">(</span><span class="n">deriv_x</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="n">deriv_y</span><span class="p">[</span><span class="n">i</span><span class="p">])))</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">fit_parameters</span> <span class="o">=</span> <span class="n">result</span> <span class="o">+</span> <span class="n">const_par</span>
|
|
|
|
<span class="n">output</span><span class="o">.</span><span class="n">odr_chisquare</span> <span class="o">=</span> <span class="n">odr_chisquare</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">out</span><span class="o">.</span><span class="n">beta</span><span class="p">,</span> <span class="n">out</span><span class="o">.</span><span class="n">xplus</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
|
<span class="n">output</span><span class="o">.</span><span class="n">dof</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">n_parms</span>
|
|
|
|
<span class="k">return</span> <span class="n">output</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</p>
|
|
|
|
<h6 id="parameters">Parameters</h6>
|
|
|
|
<ul>
|
|
<li><strong>x</strong> (list):
|
|
list of Obs, or a tuple of lists of Obs</li>
|
|
<li><strong>y</strong> (list):
|
|
list of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</li>
|
|
<li><p><strong>func</strong> (object):
|
|
func has to be of the form</p>
|
|
|
|
<div class="codehilite"><pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">anp</span><span class="o">.</span><span class="n">sinh</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">y</span>
|
|
</code></pre></div>
|
|
|
|
<p>For multiple x values func can be of the form</p>
|
|
|
|
<div class="codehilite"><pre><span></span><code><span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
|
|
<span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">)</span> <span class="o">=</span> <span class="n">x</span>
|
|
<span class="k">return</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">x1</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x2</span>
|
|
</code></pre></div>
|
|
|
|
<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation
|
|
will not work.</p></li>
|
|
<li><strong>silent</strong> (bool, optional):
|
|
If true all output to the console is omitted (default False).</li>
|
|
<li><strong>initial_guess</strong> (list):
|
|
can provide an initial guess for the input parameters. Relevant for non-linear
|
|
fits with many parameters.</li>
|
|
<li><strong>expected_chisquare</strong> (bool):
|
|
If true prints the expected chisquare which is
|
|
corrected by effects caused by correlated input data.
|
|
This can take a while as the full correlation matrix
|
|
has to be calculated (default False).</li>
|
|
<li><strong>const_par</strong> (list, optional):
|
|
List of N Obs that are used to constrain the last N fit parameters of func.</li>
|
|
<li><strong>Based on the orthogonal distance regression module of scipy</strong></li>
|
|
</ul>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="prior_fit">
|
|
<div class="attr function"><a class="headerlink" href="#prior_fit">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">prior_fit</span><span class="signature">(x, y, func, priors, silent=False, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">prior_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"prior_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">priors</span><span class="o">=</span><span class="n">priors</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
|
|
|
|
</section>
|
|
<section id="standard_fit">
|
|
<div class="attr function"><a class="headerlink" href="#standard_fit">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">standard_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">standard_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"standard_fit renamed to least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
|
|
|
|
</section>
|
|
<section id="odr_fit">
|
|
<div class="attr function"><a class="headerlink" href="#odr_fit">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">odr_fit</span><span class="signature">(x, y, func, silent=False, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">odr_fit</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"odr_fit renamed to total_least_squares"</span><span class="p">,</span> <span class="ne">DeprecationWarning</span><span class="p">)</span>
|
|
<span class="k">return</span> <span class="n">total_least_squares</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">silent</span><span class="o">=</span><span class="n">silent</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
|
|
|
|
</section>
|
|
<section id="fit_lin">
|
|
<div class="attr function"><a class="headerlink" href="#fit_lin">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">fit_lin</span><span class="signature">(x, y, **kwargs)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">fit_lin</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
|
<span class="sd">"""Performs a linear fit to y = n + m * x and returns two Obs n, m.</span>
|
|
|
|
<span class="sd"> y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.</span>
|
|
<span class="sd"> x can either be a list of floats in which case no xerror is assumed, or</span>
|
|
<span class="sd"> a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<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 class="n">y</span> <span class="o">=</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">x</span>
|
|
<span class="k">return</span> <span class="n">y</span>
|
|
|
|
<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 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 class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
|
<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 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 class="k">return</span> <span class="n">out</span><span class="o">.</span><span class="n">fit_parameters</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'Unsupported types for x'</span><span class="p">)</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>
|
|
|
|
<p>y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.
|
|
x can either be a list of floats in which case no xerror is assumed, or
|
|
a list of Obs, where the dvalues of the Obs are used as xerror for the fit.</p>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="qqplot">
|
|
<div class="attr function"><a class="headerlink" href="#qqplot">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">qqplot</span><span class="signature">(x, o_y, func, p)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><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="sd">""" Generates a quantile-quantile plot of the fit result which can be used to</span>
|
|
<span class="sd"> check if the residuals of the fit are gaussian distributed.</span>
|
|
<span class="sd"> """</span>
|
|
|
|
<span class="n">residuals</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<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 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 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>
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|
<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>
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|
<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>
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|
<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>
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|
<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>
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|
<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>
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|
<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>
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|
<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>
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|
<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>
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|
<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 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">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 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 class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
|
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Generates a quantile-quantile plot of the fit result which can be used to
|
|
check if the residuals of the fit are gaussian distributed.</p>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="residual_plot">
|
|
<div class="attr function"><a class="headerlink" href="#residual_plot">#  </a>
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|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">residual_plot</span><span class="signature">(x, y, func, fit_res)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><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="sd">""" Generates a plot which compares the fit to the data and displays the corresponding residuals"""</span>
|
|
<span class="n">xstart</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mf">0.5</span>
|
|
<span class="n">xstop</span> <span class="o">=</span> <span class="n">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="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="p">,</span> <span class="mf">0.01</span><span class="p">)</span>
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|
|
|
<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 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 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 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 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 class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
|
<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 class="n">ax0</span><span class="o">.</span><span class="n">set_xticklabels</span><span class="p">([])</span>
|
|
<span class="n">ax0</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
|
|
|
|
<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 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 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 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 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 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 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 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 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 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 class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="covariance_matrix">
|
|
<div class="attr function"><a class="headerlink" href="#covariance_matrix">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">covariance_matrix</span><span class="signature">(y)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
|
<span class="sd">"""Returns the covariance matrix of y."""</span>
|
|
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
|
<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">y</span><span class="p">):</span>
|
|
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">jtem</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">[:</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]):</span>
|
|
<span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
|
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">**</span> <span class="mi">2</span>
|
|
<span class="k">else</span><span class="p">:</span>
|
|
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">jtem</span><span class="p">)</span>
|
|
<span class="k">return</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="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Returns the covariance matrix of y.</p>
|
|
</div>
|
|
|
|
|
|
</section>
|
|
<section id="error_band">
|
|
<div class="attr function"><a class="headerlink" href="#error_band">#  </a>
|
|
|
|
|
|
<span class="def">def</span>
|
|
<span class="name">error_band</span><span class="signature">(x, func, beta)</span>:
|
|
</div>
|
|
|
|
<details>
|
|
<summary>View Source</summary>
|
|
<div class="codehilite"><pre><span></span><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 class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
|
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
|
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">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 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 class="n">deriv</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<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 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 class="n">err</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<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 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 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 class="k">return</span> <span class="n">err</span>
|
|
</pre></div>
|
|
|
|
</details>
|
|
|
|
<div class="docstring"><p>Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>
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