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<title>numerical.fit — pylib 2019.5.19 documentation</title>
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<h1>Source code for numerical.fit</h1><div class="highlight"><pre>
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<span></span><span class="ch">#!/usr/bin/env python</span>
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<span class="c1"># -*- coding: utf-8 -*-</span>
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<span class="sd">"""Function and approximation.</span>
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<span class="sd">.. module:: fit</span>
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<span class="sd"> :platform: *nix, Windows</span>
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<span class="sd"> :synopsis: Function and approximation.</span>
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<span class="sd">.. moduleauthor:: Daniel Weschke <daniel.weschke@directbox.de></span>
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<span class="sd">"""</span>
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<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
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<span class="kn">from</span> <span class="nn">pylab</span> <span class="k">import</span> <span class="n">array</span><span class="p">,</span> <span class="n">argmax</span><span class="p">,</span> <span class="n">gradient</span><span class="p">,</span> <span class="n">exp</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">,</span> <span class="n">log</span><span class="p">,</span> <span class="n">linspace</span>
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<span class="kn">from</span> <span class="nn">scipy.optimize</span> <span class="k">import</span> <span class="n">curve_fit</span>
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<div class="viewcode-block" id="gauss"><a class="viewcode-back" href="../../numerical.html#numerical.fit.gauss">[docs]</a><span class="k">def</span> <span class="nf">gauss</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="o">*</span><span class="n">p</span><span class="p">):</span>
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<span class="sd">"""Gauss distribution function.</span>
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<span class="sd"> .. math::</span>
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<span class="sd"> f(x)=ae^{-(x-b)^{2}/(2c^{2})}</span>
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<span class="sd"> :param x: positions where the gauss function will be calculated</span>
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<span class="sd"> :type x: int or float or list or numpy.ndarray</span>
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<span class="sd"> :param p: gauss parameters [a, b, c, d]:</span>
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<span class="sd"> * a -- amplitude (:math:`\int y \\,\\mathrm{d}x=1 \Leftrightarrow a=1/(c\\sqrt{2\\pi})` )</span>
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<span class="sd"> * b -- expected value :math:`\\mu` (position of maximum, default = 0)</span>
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<span class="sd"> * c -- standard deviation :math:`\\sigma` (variance :math:`\\sigma^2=c^2`)</span>
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<span class="sd"> * d -- vertical offset (default = 0)</span>
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<span class="sd"> :type p: list</span>
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<span class="sd"> :returns: gauss values at given positions x</span>
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<span class="sd"> :rtype: numpy.ndarray</span>
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<span class="sd"> """</span>
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<span class="n">x</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="c1"># cast e. g. list to numpy array</span>
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<span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">d</span> <span class="o">=</span> <span class="n">p</span>
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<span class="k">return</span> <span class="n">a</span><span class="o">*</span><span class="n">exp</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">b</span><span class="p">)</span><span class="o">**</span><span class="mf">2.</span><span class="o">/</span><span class="p">(</span><span class="mf">2.</span> <span class="o">*</span> <span class="n">c</span><span class="o">**</span><span class="mf">2.</span><span class="p">))</span> <span class="o">+</span> <span class="n">d</span></div>
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<div class="viewcode-block" id="gauss_fit"><a class="viewcode-back" href="../../numerical.html#numerical.fit.gauss_fit">[docs]</a><span class="k">def</span> <span class="nf">gauss_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">e</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">x_fit</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
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<span class="sd">"""Fit Gauss distribution function to data.</span>
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<span class="sd"> :param x: positions</span>
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<span class="sd"> :type x: int or float or list or numpy.ndarray</span>
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<span class="sd"> :param y: values</span>
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<span class="sd"> :type y: int or float or list or numpy.ndarray</span>
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<span class="sd"> :param e: error values (default = None)</span>
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<span class="sd"> :type e: int or float or list or numpy.ndarray</span>
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<span class="sd"> :param x_fit: positions of fitted function (default = None, if None then x</span>
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<span class="sd"> is used)</span>
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<span class="sd"> :type x_fit: int or float or list or numpy.ndarray</span>
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<span class="sd"> :param verbose: verbose information (default = False)</span>
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<span class="sd"> :type verbose: bool</span>
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<span class="sd"> :returns:</span>
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<span class="sd"> * numpy.ndarray -- fitted values (y_fit)</span>
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<span class="sd"> * numpy.ndarray -- parameters of gauss distribution function (popt:</span>
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<span class="sd"> amplitude a, expected value :math:`\\mu`, standard deviation</span>
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<span class="sd"> :math:`\\sigma`, vertical offset d)</span>
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<span class="sd"> * numpy.float64 -- full width at half maximum (FWHM)</span>
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<span class="sd"> :rtype: tuple</span>
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<span class="sd"> .. seealso::</span>
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<span class="sd"> :meth:`gauss`</span>
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<span class="sd"> """</span>
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<span class="n">x</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="c1"># cast e. g. list to numpy array</span>
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<span class="n">y</span> <span class="o">=</span> <span class="n">array</span><span class="p">(</span><span class="n">y</span><span class="p">)</span> <span class="c1"># cast e. g. list to numpy array</span>
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<span class="n">y_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
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<span class="n">y_max_pos</span> <span class="o">=</span> <span class="n">argmax</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
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<span class="n">x_y_max</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">y_max_pos</span><span class="p">]</span>
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<span class="c1"># starting parameter</span>
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<span class="n">p0</span> <span class="o">=</span> <span class="p">[</span><span class="n">y_max</span><span class="p">,</span> <span class="n">x_y_max</span><span class="p">,</span> <span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="n">y</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'p0:'</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">p0</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">e</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
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<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="n">gauss</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">p0</span><span class="o">=</span><span class="n">p0</span><span class="p">,</span> <span class="n">sigma</span><span class="o">=</span><span class="n">e</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">popt</span><span class="p">,</span> <span class="n">pcov</span> <span class="o">=</span> <span class="n">curve_fit</span><span class="p">(</span><span class="n">gauss</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">p0</span><span class="o">=</span><span class="n">p0</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'popt:'</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">popt</span><span class="p">)</span>
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<span class="c1">#print(pcov)</span>
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<span class="n">FWHM</span> <span class="o">=</span> <span class="mi">2</span><span class="o">*</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">log</span><span class="p">(</span><span class="mi">2</span><span class="p">))</span><span class="o">*</span><span class="n">popt</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
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<span class="k">if</span> <span class="n">verbose</span><span class="p">:</span>
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<span class="nb">print</span><span class="p">(</span><span class="s1">'FWHM'</span><span class="p">,</span> <span class="n">FWHM</span><span class="p">)</span>
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<span class="k">if</span> <span class="n">x_fit</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
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<span class="n">x_fit</span> <span class="o">=</span> <span class="n">x</span>
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<span class="n">y_fit</span> <span class="o">=</span> <span class="n">gauss</span><span class="p">(</span><span class="n">x_fit</span><span class="p">,</span> <span class="o">*</span><span class="n">popt</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">y_fit</span><span class="p">,</span> <span class="n">popt</span><span class="p">,</span> <span class="n">FWHM</span></div>
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<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s2">"__main__"</span><span class="p">:</span>
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<span class="kc">True</span>
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</pre></div>
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