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1<?xml version="1.0" ?>
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3<html xmlns="http://www.w3.org/1999/xhtml">
4<head>
5<title>lmfit: a self-contained C library for Levenberg-Marquardt least-squares minimization and curve fitting</title>
6<meta http-equiv="content-type" content="text/html; charset=utf-8" />
7<link rev="made" href="mailto:root@localhost" />
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10<body>
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16<link rel="stylesheet" href="podstyle.css" type="text/css" />
17
18<h1 id="NAME">NAME</h1>
19
20<p>lmcurve - Levenberg-Marquardt least-squares fit of a curve (t,y)</p>
21
22<h1 id="SYNOPSIS">SYNOPSIS</h1>
23
24<p><b>#include &lt;lmcurve.h</b>&gt;</p>
25
26<p><b>void lmcurve( const int</b> <i>n_par</i><b>, double *</b><i>par</i><b>, const int</b> <i>m_dat</i><b>, const<span style="white-space: nowrap;"> </span>double *</b><i>t</i><b>, const<span style="white-space: nowrap;"> </span>double *</b><i>y</i><b>, double (*</b><i>f</i><b>)( const double </b><i>ti</i><b>, const double *</b><i>par</i><b> ), const<span style="white-space: nowrap;"> </span>lm_control_struct *</b><i>control</i><b>, lm_status_struct *</b><i>status</i><b>);</b></p>
27
28<p><b>void lmcurve_tyd( const int</b> <i>n_par</i><b>, double *</b><i>par</i><b>, const int</b> <i>m_dat</i><b>, const<span style="white-space: nowrap;"> </span>double *</b><i>t</i><b>, const<span style="white-space: nowrap;"> </span>double *</b><i>y</i><b>, const<span style="white-space: nowrap;"> </span>double *</b><i>dy</i><b>, double (*</b><i>f</i><b>)( const double </b><i>ti</i><b>, const double *</b><i>par</i><b> ), const<span style="white-space: nowrap;"> </span>lm_control_struct *</b><i>control</i><b>, lm_status_struct *</b><i>status</i><b>);</b></p>
29
30<p><b>extern const lm_control_struct lm_control_double;</b></p>
31
32<p><b>extern const lm_control_struct lm_control_float;</b></p>
33
34<p><b>extern const char *lm_infmsg[];</b></p>
35
36<p><b>extern const char *lm_shortmsg[];</b></p>
37
38<h1 id="DESCRIPTION">DESCRIPTION</h1>
39
40<p><b>lmcurve()</b> and <b>lmcurve_tyd()</b> wrap the more generic minimization function <b>lmmin()</b>, for use in curve fitting.</p>
41
42<p><b>lmcurve()</b> determines a vector <i>par</i> that minimizes the sum of squared elements of a residue vector <i>r</i>[i] := <i>y</i>[i] - <i>f</i>(<i>t</i>[i];<i>par</i>). Typically, <b>lmcurve()</b> is used to approximate a data set <i>t</i>,<i>y</i> by a parametric function <i>f</i>(<i>ti</i>;<i>par</i>). On success, <i>par</i> represents a local minimum, not necessarily a global one; it may depend on its starting value.</p>
43
44<p><b>lmcurve_tyd()</b> does the same for a data set <i>t</i>,<i>y</i>,<i>dy</i>, where <i>dy</i> represents the standard deviation of empirical data <i>y</i>. Residues are computed as <i>r</i>[i] := (<i>y</i>[i] - <i>f</i>(<i>t</i>[i];<i>par</i>))/<i>dy</i>[i]. Users must ensure that all <i>dy</i>[i] are positive.</p>
45
46<p>Function arguments:</p>
47
48<dl>
49
50<dt id="n_par"><i>n_par</i></dt>
51<dd>
52
53<p>Number of free variables. Length of parameter vector <i>par</i>.</p>
54
55</dd>
56<dt id="par"><i>par</i></dt>
57<dd>
58
59<p>Parameter vector. On input, it must contain a reasonable guess. On output, it contains the solution found to minimize ||<i>r</i>||.</p>
60
61</dd>
62<dt id="m_dat"><i>m_dat</i></dt>
63<dd>
64
65<p>Number of data points. Length of vectors <i>t</i> and <i>y</i>. Must statisfy <i>n_par</i> &lt;= <i>m_dat</i>.</p>
66
67</dd>
68<dt id="t"><i>t</i></dt>
69<dd>
70
71<p>Array of length <i>m_dat</i>. Contains the abcissae (time, or &quot;x&quot;) for which function <i>f</i> will be evaluated.</p>
72
73</dd>
74<dt id="y"><i>y</i></dt>
75<dd>
76
77<p>Array of length <i>m_dat</i>. Contains the ordinate values that shall be fitted.</p>
78
79</dd>
80<dt id="dy"><i>dy</i></dt>
81<dd>
82
83<p>Only in <b>lmcurve_tyd()</b>. Array of length <i>m_dat</i>. Contains the standard deviations of the values <i>y</i>.</p>
84
85</dd>
86<dt id="f"><i>f</i></dt>
87<dd>
88
89<p>A user-supplied parametric function <i>f</i>(ti;<i>par</i>).</p>
90
91</dd>
92<dt id="control"><i>control</i></dt>
93<dd>
94
95<p>Parameter collection for tuning the fit procedure. In most cases, the default &amp;<i>lm_control_double</i> is adequate. If <i>f</i> is only computed with single-precision accuracy, <i>&amp;lm_control_float</i> should be used. Parameters are explained in <b>lmmin(3)</b>.</p>
96
97</dd>
98<dt id="status"><i>status</i></dt>
99<dd>
100
101<p>A record used to return information about the minimization process: For details, see <b>lmmin(3)</b>.</p>
102
103</dd>
104</dl>
105
106<h1 id="EXAMPLE">EXAMPLE</h1>
107
108<p>Fit a data set y(x) by a curve f(x;p):</p>
109
110<pre><code>    #include &quot;lmcurve.h&quot;
111    #include &lt;stdio.h&gt;
112
113    /* model function: a parabola */
114
115    double f( double t, const double *p )
116    {
117        return p[0] + p[1]*t + p[2]*t*t;
118    }
119
120    int main()
121    {
122        int n = 3; /* number of parameters in model function f */
123        double par[3] = { 100, 0, -10 }; /* really bad starting value */
124
125        /* data points: a slightly distorted standard parabola */
126        int m = 9;
127        int i;
128        double t[9] = { -4., -3., -2., -1.,  0., 1.,  2.,  3.,  4. };
129        double y[9] = { 16.6, 9.9, 4.4, 1.1, 0., 1.1, 4.2, 9.3, 16.4 };
130
131        lm_control_struct control = lm_control_double;
132        lm_status_struct status;
133        control.verbosity = 7;
134
135        printf( &quot;Fitting ...\n&quot; );
136        lmcurve( n, par, m, t, y, f, &amp;control, &amp;status );
137
138        printf( &quot;Results:\n&quot; );
139        printf( &quot;status after %d function evaluations:\n  %s\n&quot;,
140                status.nfev, lm_infmsg[status.outcome] );
141
142        printf(&quot;obtained parameters:\n&quot;);
143        for ( i = 0; i &lt; n; ++i)
144            printf(&quot;  par[%i] = %12g\n&quot;, i, par[i]);
145        printf(&quot;obtained norm:\n  %12g\n&quot;, status.fnorm );
146
147        printf(&quot;fitting data as follows:\n&quot;);
148        for ( i = 0; i &lt; m; ++i)
149            printf( &quot;  t[%2d]=%4g y=%6g fit=%10g residue=%12g\n&quot;,
150                    i, t[i], y[i], f(t[i],par), y[i] - f(t[i],par) );
151
152        return 0;
153    }</code></pre>
154
155<h1 id="COPYING">COPYING</h1>
156
157<p>Copyright (C) 2009-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH</p>
158
159<p>Software: FreeBSD License</p>
160
161<p>Documentation: Creative Commons Attribution Share Alike</p>
162
163<h1 id="SEE-ALSO">SEE ALSO</h1>
164
165
166
167<a href="http://apps.jcns.fz-juelich.de/man/lmmin.html"><b>lmmin</b>(3)</a>
168
169<p>Homepage: http://apps.jcns.fz-juelich.de/lmfit</p>
170
171<h1 id="BUGS">BUGS</h1>
172
173<p>Please send bug reports and suggestions to the author &lt;j.wuttke@fz-juelich.de&gt;.</p>
174
175
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