/usr/share/doc/python-scientific/Reference/Scientific.Functions.LeastSquares-module.html is in python-scientific-doc 2.8-2build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 | <?xml version="1.0" encoding="ascii"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en">
<head>
<title>Scientific.Functions.LeastSquares</title>
<link rel="stylesheet" href="epydoc.css" type="text/css" />
<script type="text/javascript" src="epydoc.js"></script>
</head>
<body bgcolor="white" text="black" link="blue" vlink="#204080"
alink="#204080">
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
bgcolor="#a0c0ff" cellspacing="0">
<tr valign="middle">
<!-- Home link -->
<th> <a
href="Scientific-module.html">Home</a> </th>
<!-- Tree link -->
<th> <a
href="module-tree.html">Trees</a> </th>
<!-- Index link -->
<th> <a
href="identifier-index.html">Indices</a> </th>
<!-- Help link -->
<th> <a
href="help.html">Help</a> </th>
<!-- Project homepage -->
<th class="navbar" align="right" width="100%">
<table border="0" cellpadding="0" cellspacing="0">
<tr><th class="navbar" align="center"
><a class="navbar" target="_top" href="http://dirac.cnrs-orleans.fr/ScientificPython/">Scientific Python</a></th>
</tr></table></th>
</tr>
</table>
<table width="100%" cellpadding="0" cellspacing="0">
<tr valign="top">
<td width="100%">
<span class="breadcrumbs">
<a href="Scientific-module.html">Package Scientific</a> ::
<a href="Scientific.Functions-module.html">Package Functions</a> ::
Module LeastSquares
</span>
</td>
<td>
<table cellpadding="0" cellspacing="0">
<!-- hide/show private -->
<tr><td align="right"><span class="options"
>[<a href="frames.html" target="_top">frames</a
>] | <a href="Scientific.Functions.LeastSquares-module.html"
target="_top">no frames</a>]</span></td></tr>
</table>
</td>
</tr>
</table>
<!-- ==================== MODULE DESCRIPTION ==================== -->
<h1 class="epydoc">Module LeastSquares</h1><p class="nomargin-top"></p>
<p>Non-linear least squares fitting</p>
<p>Usage example:</p>
<pre class="literalblock">
from Scientific.N import exp
def f(param, t):
return param[0]*exp(-param[1]/t)
data_quantum = [(100, 3.445e+6),(200, 2.744e+7),
(300, 2.592e+8),(400, 1.600e+9)]
data_classical = [(100, 4.999e-8),(200, 5.307e+2),
(300, 1.289e+6),(400, 6.559e+7)]
print leastSquaresFit(f, (1e13,4700), data_classical)
def f2(param, t):
return 1e13*exp(-param[0]/t)
print leastSquaresFit(f2, (3000.,), data_quantum)
</pre>
<!-- ==================== FUNCTIONS ==================== -->
<a name="section-Functions"></a>
<table class="summary" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Functions</span></td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"><code>(list, float)</code></span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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>,
<span class="summary-sig-arg">parameters</span>,
<span class="summary-sig-arg">data</span>,
<span class="summary-sig-arg">max_iterations</span>=<span class="summary-sig-default">None</span>,
<span class="summary-sig-arg">stopping_limit</span>=<span class="summary-sig-default">0.005</span>)</span><br />
General non-linear least-squares fit using the <a
name="index-Levenberg_Marquardt"></a><i
class="indexterm">Levenberg-Marquardt</i> algorithm and <a
name="index-automatic_differentiation"></a><i
class="indexterm">automatic differentiation</i>.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
<tr>
<td width="15%" align="right" valign="top" class="summary">
<span class="summary-type"> </span>
</td><td class="summary">
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr>
<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>,
<span class="summary-sig-arg">data</span>)</span><br />
Least-squares fit to a polynomial whose order is defined by the
number of parameter values.</td>
<td align="right" valign="top">
</td>
</tr>
</table>
</td>
</tr>
</table>
<!-- ==================== FUNCTION DETAILS ==================== -->
<a name="section-FunctionDetails"></a>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr bgcolor="#70b0f0" class="table-header">
<td align="left" colspan="2" class="table-header">
<span class="table-header">Function Details</span></td>
</tr>
</table>
<a name="leastSquaresFit"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">leastSquaresFit</span>(<span class="sig-arg">model</span>,
<span class="sig-arg">parameters</span>,
<span class="sig-arg">data</span>,
<span class="sig-arg">max_iterations</span>=<span class="sig-default">None</span>,
<span class="sig-arg">stopping_limit</span>=<span class="sig-default">0.005</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>General non-linear least-squares fit using the <a
name="index-Levenberg_Marquardt"></a><i
class="indexterm">Levenberg-Marquardt</i> algorithm and <a
name="index-automatic_differentiation"></a><i class="indexterm">automatic
differentiation</i>.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>model</code></strong> (callable) - the function to be fitted. It will be called with two parameters:
the first is a tuple containing all fit parameters, and the
second is the first element of a data point (see below). The
return value must be a number. Since automatic differentiation
is used to obtain the derivatives with respect to the parameters,
the function may only use the mathematical functions known to the
module FirstDerivatives.</li>
<li><strong class="pname"><code>parameters</code></strong> (<code>tuple</code> of numbers) - a tuple of initial values for the fit parameters</li>
<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
data point is a tuple of length two or three. Its first element
specifies the independent variables of the model. It is passed to
the model function as its first parameter, but not used in any
other way. The second element of each data point tuple is the
number that the return value of the model function is supposed to
match as well as possible. The third element (which defaults to
1.) is the statistical variance of the data point, i.e. the
inverse of its statistical weight in the fitting procedure.</li>
</ul></dd>
<dt>Returns: <code>(list, float)</code></dt>
<dd>a list containing the optimal parameter values and the
chi-squared value describing the quality of the fit</dd>
</dl>
</td></tr></table>
</div>
<a name="polynomialLeastSquaresFit"></a>
<div>
<table class="details" border="1" cellpadding="3"
cellspacing="0" width="100%" bgcolor="white">
<tr><td>
<table width="100%" cellpadding="0" cellspacing="0" border="0">
<tr valign="top"><td>
<h3 class="epydoc"><span class="sig"><span class="sig-name">polynomialLeastSquaresFit</span>(<span class="sig-arg">parameters</span>,
<span class="sig-arg">data</span>)</span>
</h3>
</td><td align="right" valign="top"
>
</td>
</tr></table>
<p>Least-squares fit to a polynomial whose order is defined by the number
of parameter values.</p>
<dl class="fields">
<dt>Parameters:</dt>
<dd><ul class="nomargin-top">
<li><strong class="pname"><code>parameters</code></strong> (<code>tuple</code>) - a tuple of initial values for the polynomial coefficients</li>
<li><strong class="pname"><code>data</code></strong> (<code>list</code>) - the data points, as for <a
href="Scientific.Functions.LeastSquares-module.html#leastSquaresFit"
class="link">leastSquaresFit</a></li>
</ul></dd>
</dl>
<div class="fields"> <p><strong>Note:</strong>
This could also be done with a linear least squares fit from <code
class="link">Scientific.LA</code>
</p>
</div></td></tr></table>
</div>
<br />
<!-- ==================== NAVIGATION BAR ==================== -->
<table class="navbar" border="0" width="100%" cellpadding="0"
bgcolor="#a0c0ff" cellspacing="0">
<tr valign="middle">
<!-- Home link -->
<th> <a
href="Scientific-module.html">Home</a> </th>
<!-- Tree link -->
<th> <a
href="module-tree.html">Trees</a> </th>
<!-- Index link -->
<th> <a
href="identifier-index.html">Indices</a> </th>
<!-- Help link -->
<th> <a
href="help.html">Help</a> </th>
<!-- Project homepage -->
<th class="navbar" align="right" width="100%">
<table border="0" cellpadding="0" cellspacing="0">
<tr><th class="navbar" align="center"
><a class="navbar" target="_top" href="http://dirac.cnrs-orleans.fr/ScientificPython/">Scientific Python</a></th>
</tr></table></th>
</tr>
</table>
<table border="0" cellpadding="0" cellspacing="0" width="100%%">
<tr>
<td align="left" class="footer">
Generated by Epydoc 3.0 on Tue Oct 28 14:15:59 2008
</td>
<td align="right" class="footer">
<a target="mainFrame" href="http://epydoc.sourceforge.net"
>http://epydoc.sourceforge.net</a>
</td>
</tr>
</table>
<script type="text/javascript">
<!--
// Private objects are initially displayed (because if
// javascript is turned off then we want them to be
// visible); but by default, we want to hide them. So hide
// them unless we have a cookie that says to show them.
checkCookie();
// -->
</script>
</body>
</html>
|