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Former-commit-id:a02aeb236c[formerly9f19e3f712] [formerly06a8b51d6d[formerly 64fa9254b946eae7e61bbc3f513b7c3696c4f54f]] Former-commit-id:06a8b51d6dFormer-commit-id:3360eb6c5f
279 lines
11 KiB
HTML
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279 lines
11 KiB
HTML
Executable file
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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"DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
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<title>Scientific.Functions.LeastSquares</title>
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><a class="navbar" target="_top" href="http://dirac.cnrs-orleans.fr/ScientificPython/">Scientific Python</a></th>
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<a href="Scientific-module.html">Package Scientific</a> ::
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<a href="Scientific.Functions-module.html">Package Functions</a> ::
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Module LeastSquares
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</span>
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</td>
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<td>
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<tr><td align="right"><span class="options"
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>[<a href="frames.html" target="_top">frames</a
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target="_top">no frames</a>]</span></td></tr>
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</table>
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<!-- ==================== MODULE DESCRIPTION ==================== -->
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<h1 class="epydoc">Module LeastSquares</h1><p class="nomargin-top"></p>
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<p>Non-linear least squares fitting</p>
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<p>Usage example:</p>
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<pre class="literalblock">
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from Scientific.N import exp
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def f(param, t):
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return param[0]*exp(-param[1]/t)
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data_quantum = [(100, 3.445e+6),(200, 2.744e+7),
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(300, 2.592e+8),(400, 1.600e+9)]
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data_classical = [(100, 4.999e-8),(200, 5.307e+2),
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(300, 1.289e+6),(400, 6.559e+7)]
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print leastSquaresFit(f, (1e13,4700), data_classical)
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def f2(param, t):
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return 1e13*exp(-param[0]/t)
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print leastSquaresFit(f2, (3000.,), data_quantum)
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</pre>
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<!-- ==================== FUNCTIONS ==================== -->
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<a name="section-Functions"></a>
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<table class="summary" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr bgcolor="#70b0f0" class="table-header">
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<td align="left" colspan="2" class="table-header">
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<span class="table-header">Functions</span></td>
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</tr>
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<tr>
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<td width="15%" align="right" valign="top" class="summary">
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<span class="summary-type"><code>(list, float)</code></span>
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</td><td class="summary">
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td><span class="summary-sig"><a href="Scientific.Functions.LeastSquares-module.html#leastSquaresFit" class="summary-sig-name">leastSquaresFit</a>(<span class="summary-sig-arg">model</span>,
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<span class="summary-sig-arg">parameters</span>,
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<span class="summary-sig-arg">data</span>,
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<span class="summary-sig-arg">max_iterations</span>=<span class="summary-sig-default">None</span>,
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<span class="summary-sig-arg">stopping_limit</span>=<span class="summary-sig-default">0.005</span>)</span><br />
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General non-linear least-squares fit using the <a
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name="index-Levenberg_Marquardt"></a><i
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class="indexterm">Levenberg-Marquardt</i> algorithm and <a
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name="index-automatic_differentiation"></a><i
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class="indexterm">automatic differentiation</i>.</td>
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<td align="right" valign="top">
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</td>
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</tr>
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</table>
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</td>
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</tr>
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<tr>
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<td width="15%" align="right" valign="top" class="summary">
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<span class="summary-type"> </span>
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</td><td class="summary">
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
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<tr>
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<td><span class="summary-sig"><a href="Scientific.Functions.LeastSquares-module.html#polynomialLeastSquaresFit" class="summary-sig-name">polynomialLeastSquaresFit</a>(<span class="summary-sig-arg">parameters</span>,
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<span class="summary-sig-arg">data</span>)</span><br />
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Least-squares fit to a polynomial whose order is defined by the
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number of parameter values.</td>
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<td align="right" valign="top">
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</td>
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</tr>
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</table>
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</td>
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</tr>
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</table>
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<!-- ==================== FUNCTION DETAILS ==================== -->
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<a name="section-FunctionDetails"></a>
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<table class="details" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr bgcolor="#70b0f0" class="table-header">
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<td align="left" colspan="2" class="table-header">
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<span class="table-header">Function Details</span></td>
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</tr>
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</table>
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<a name="leastSquaresFit"></a>
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<div>
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<table class="details" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr><td>
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
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<tr valign="top"><td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">leastSquaresFit</span>(<span class="sig-arg">model</span>,
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<span class="sig-arg">parameters</span>,
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<span class="sig-arg">data</span>,
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<span class="sig-arg">max_iterations</span>=<span class="sig-default">None</span>,
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<span class="sig-arg">stopping_limit</span>=<span class="sig-default">0.005</span>)</span>
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</h3>
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</td><td align="right" valign="top"
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>
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</td>
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</tr></table>
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<p>General non-linear least-squares fit using the <a
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name="index-Levenberg_Marquardt"></a><i
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class="indexterm">Levenberg-Marquardt</i> algorithm and <a
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name="index-automatic_differentiation"></a><i class="indexterm">automatic
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differentiation</i>.</p>
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<dl class="fields">
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<dt>Parameters:</dt>
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<dd><ul class="nomargin-top">
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<li><strong class="pname"><code>model</code></strong> (callable) - the function to be fitted. It will be called with two parameters:
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the first is a tuple containing all fit parameters, and the
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second is the first element of a data point (see below). The
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return value must be a number. Since automatic differentiation
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is used to obtain the derivatives with respect to the parameters,
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the function may only use the mathematical functions known to the
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module FirstDerivatives.</li>
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<li><strong class="pname"><code>parameters</code></strong> (<code>tuple</code> of numbers) - a tuple of initial values for the fit parameters</li>
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<li><strong class="pname"><code>data</code></strong> (<code>list</code>) - a list of data points to which the model is to be fitted. Each
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data point is a tuple of length two or three. Its first element
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specifies the independent variables of the model. It is passed to
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the model function as its first parameter, but not used in any
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other way. The second element of each data point tuple is the
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number that the return value of the model function is supposed to
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match as well as possible. The third element (which defaults to
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1.) is the statistical variance of the data point, i.e. the
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inverse of its statistical weight in the fitting procedure.</li>
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</ul></dd>
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<dt>Returns: <code>(list, float)</code></dt>
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<dd>a list containing the optimal parameter values and the
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chi-squared value describing the quality of the fit</dd>
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</dl>
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</td></tr></table>
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</div>
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<a name="polynomialLeastSquaresFit"></a>
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<div>
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<table class="details" border="1" cellpadding="3"
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cellspacing="0" width="100%" bgcolor="white">
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<tr><td>
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<table width="100%" cellpadding="0" cellspacing="0" border="0">
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<tr valign="top"><td>
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<h3 class="epydoc"><span class="sig"><span class="sig-name">polynomialLeastSquaresFit</span>(<span class="sig-arg">parameters</span>,
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<span class="sig-arg">data</span>)</span>
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</h3>
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</td><td align="right" valign="top"
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>
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</td>
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</tr></table>
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<p>Least-squares fit to a polynomial whose order is defined by the number
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of parameter values.</p>
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<dl class="fields">
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<dt>Parameters:</dt>
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<dd><ul class="nomargin-top">
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<li><strong class="pname"><code>parameters</code></strong> (<code>tuple</code>) - a tuple of initial values for the polynomial coefficients</li>
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<li><strong class="pname"><code>data</code></strong> (<code>list</code>) - the data points, as for <a
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href="Scientific.Functions.LeastSquares-module.html#leastSquaresFit"
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class="link">leastSquaresFit</a></li>
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</ul></dd>
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</dl>
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<div class="fields"> <p><strong>Note:</strong>
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This could also be done with a linear least squares fit from <code
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class="link">Scientific.LA</code>
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</p>
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</div></td></tr></table>
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</div>
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<br />
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Generated by Epydoc 3.0 on Tue Oct 28 14:15:59 2008
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